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Feed title: Random Ramblings on Math, Juggling, Programming, Business, and stuff ...
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Feed has 169 items.
First item published on 2021-03-18T12:00:00.000Z
Last item published on 2011-04-02T19:30:30.000Z
Home page URL: https://www.solipsys.co.uk/new/ColinsBlog.html
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<title>Random Ramblings on Math, Juggling, Programming, Business, and stuff ...</title>
<link>https://www.solipsys.co.uk/new/ColinsBlog.html</link>
<description>Although titled "blog", this is more just random rants and streams
of consciousness, touching on math, juggling, programming, user interaction,
business, and anything that comes to mind. Read at your peril!</description>
<item>
<title>Tesseract Teaser</title>
<link>http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS</link>
<guid>http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS</guid>
<pubDate>Thu, 18 Mar 2021 12:00:00 +0000</pubDate>
<description>Not the four-dimensional cube sort of Tesseract, this is the
Optical Character Recognition (OCR) "Tesseract", software that
takes an image of some lettering and produces a plain text
file containing the text. Or not. It's well-known that this
is "Actually Quite Hard(tm)" and Tesseract does a pretty good
job "Out of the Box" with very little messing about. But the
other day I ran across something that has me utterly baffled.
Let me share my bebafflement with you.</description>
</item>
<item>
<title>More Mental Model Missteps</title>
<link>http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS</link>
<guid>http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS</guid>
<pubDate>Sun, 31 Jan 2021 12:00:00 +0000</pubDate>
<description>I mentioned when talking about an oddity in vim that the behaviour
of the command "<n>J" didn't match my mental model. Sometimes
software does that, it had behaviour that's totally reasonable when
you think about it one way, but there's another way of thinking that
causes you to be surprised. Here's another, as reported to me by a
friend.</description>
</item>
<item>
<title>An Oddity In VIM</title>
<link>http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS</link>
<guid>http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS</guid>
<pubDate>Sun, 24 Jan 2021 12:00:00 +0000</pubDate>
<description>I'm going to tell you a story, so this is quite a long post. If
you'd like to skip the story get directly to the main point then
feel free to do so. But if you're interested in the story, make
sure you're sitting comfortably, and I'll tell you how I found an
oddity in /vim./</description>
</item>
<item>
<title>Double Double Division Algorithm</title>
<link>https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS</link>
<guid>https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS</guid>
<pubDate>Mon, 18 Jan 2021 12:00:00 +0000</pubDate>
<description>For some of my readers, this will all be completely mysterious.
But for others, part way through they will go "I recognise this!"
So I'd really like to hear from you ... if you recognise this,
at which point did the penny drop? I'd also really like to know
if you think this is obvious, and possibly even if you've seen
it before.
Consider the following algorithm. I'll work through an example.
I'll divide 450 by 23.</description>
</item>
<item>
<title>Continuity Concerns</title>
<link>https://www.solipsys.co.uk/new/ContinuityConcerns.html?RSS</link>
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<pubDate>Fri, 01 Jan 2021 12:00:00 +0000</pubDate>
<description>Recently, Rachel and I have been watching the episodes of
"The Adventures of Paddington Bear" that have been transmitted on
broadcast TV here in the UK. It's not exactly gentle viewing, but
Paddington is kind, helpful (or tries to be), and it always turns
out well. Not very realistic, but if you watch with the right
attitude, it is uplifting. Judge us if you will - we don't care.</description>
</item>
<item>
<title>Counting Carbon Calories</title>
<link>https://www.solipsys.co.uk/new/CountingCarbonCalories.html?RSS</link>
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<pubDate>Wed, 30 Dec 2020 12:00:00 +0000</pubDate>
<description>"When you lose weight, where does it go?"
An interesting question, and one where most people haven't thought
about it, don't know, and really don't care. But when I was asked,
it set in motion a train of thought. Follow along, and see if it
makes sense.</description>
</item>
<item>
<title>The Parity Of Zero</title>
<link>https://www.solipsys.co.uk/new/TheParityOfZero.html?RSS</link>
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<pubDate>Mon, 21 Dec 2020 12:00:00 +0000</pubDate>
<description>Before you react to the title, and before you guess where this
is going and form a reaction, pause. I might not be about to
say what you expect. Of course, I might, but I might not, and
I'd ask you to wait a bit.</description>
</item>
<item>
<title>When The Text And HTML Disagree</title>
<link>https://www.solipsys.co.uk/new/WhenTheTextAndHtmlDisagree.html?RSS</link>
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<pubDate>Sat, 12 Dec 2020 12:00:00 +0000</pubDate>
<description>Second Saturday of the month, and that means the Farmers' Market is
on. Even in this second lockdown it will be running, with a one-way
system and limited numbers permitted inside at any one time.
But is it at the usual time? Let's check the email.
Oh, I seem to have deleted it. Never mind, there will be a backup ...</description>
</item>
<item>
<title>Recursion Revisited</title>
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<pubDate>Wed, 14 Oct 2020 12:00:00 +0100</pubDate>
<description>Some time ago I wrote a post on Thinking About Recursion, and
more recently I wrote about a problem concerning the problem
of the number of Vertices Required For Cycles. As it happens,
the code for that problem is heavily recursive, and provides
a great example of using recursion to solve a real problem.</description>
</item>
<item>
<title>Vertices Required For Cycles</title>
<link>https://www.solipsys.co.uk/new/VerticesRequiredForCycles.html?RSS</link>
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<pubDate>Fri, 02 Oct 2020 12:00:00 +0100</pubDate>
<description>A few weeks ago Chris Purcell (@[email protected]) said:
Let a_n be the size of the smallest graph with exactly n cycles.
(The first few terms are: 3, 5, 4, 6, ...) The first few values
are easy enough to compute, but it gets quite tricky quite quickly.
How can one construct a (simple undirected) graph with exactly
5 cycles?</description>
</item>
<item>
<title>Reflex Actions</title>
<link>https://www.solipsys.co.uk/new/ReflexActions.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ReflexActions.html?RSS</guid>
<pubDate>Mon, 24 Aug 2020 12:00:00 +0100</pubDate>
<description>The machine wouldn't read my credit card.
That's not uncommon ... sometimes the contacts on my card
are dirty, sometimes the contacts on the machine are dirty
... no big deal. Just lick your thumb, rub the contacts,
and try again.</description>
</item>
<item>
<title>The Ballad Of Bunter</title>
<link>https://www.solipsys.co.uk/new/TheBalladOfBunter.html?RSS</link>
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<pubDate>Sun, 26 Jul 2020 12:00:00 +0100</pubDate>
<description>In late May it was becoming increasingly clear that Rachel's laptop
was increasingly eccentric. A replacement would be needed, and while
it wasn't yet urgent, we felt we should do something before it became
so. And so the hunt began.</description>
</item>
<item>
<title>Infinite Ramsey Theorem</title>
<link>https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?RSS</link>
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<pubDate>Sun, 12 Jul 2020 12:00:00 +0100</pubDate>
<description>With the passing of Ron Graham a few people have been in touch
with me to ask what "Ramsey Theory" is. So I've given a brief
outline, and pointers in case people want to follow up. In
truth, just stick "Ramsey Theory" into your favourite search
engine and you'll get lots to follow up and chase down (as
opposed, of course, to "follow down" or "chase up").</description>
</item>
<item>
<title>Signal Reflection</title>
<link>https://www.solipsys.co.uk/new/SignalReflection.html?RSS</link>
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<pubDate>Mon, 06 Jul 2020 12:00:00 +0100</pubDate>
<description>Way back in the 70s when I was building logic circuits, I was
warned repeatedly that I'd have to get a few things right, or
risk "locking up" or "burning out" the CMOS chips I was using.
The bogeyman was "Signal Reflection", but no one could tell me
what it was, or why it was so bad.</description>
</item>
<item>
<title>Analogies Not Considered Harmful</title>
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<pubDate>Sun, 05 Jul 2020 12:00:00 +0100</pubDate>
<description>While I was writing my post on SignalReflection, I was given cause
to reflect (pun intended ... sorry) on exactly the role and value
of analogies in science, maths, and life in general. I've come to
the conclusion that, like so many thing, analogies are neither good
nor bad. They have their purpose, and each lies somewhere on a
spectrum.</description>
</item>
<item>
<title>Twitter Reply vs Quote Tweet</title>
<link>https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS</guid>
<pubDate>Wed, 17 Jun 2020 12:00:00 +0100</pubDate>
<description>More than once now I've seen someone on social media using an
option which has, for their purposes, been sub-optimal. In one
case it led to a very unpleasant exchange, purely because one
person assumed an implication that simply wasn't intended.</description>
</item>
<item>
<title>Proofs To Make You Go WOW</title>
<link>https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS</guid>
<pubDate>Tue, 16 Jun 2020 12:00:00 +0100</pubDate>
<description>For those of us who love maths, it's sad to see how many people
hate it, or have a phobia of it, or proudly announce "I was never
very good at maths at school." The question we often counter with
is "Would you be so proud of being unable to read?"</description>
</item>
<item>
<title>Laptop Purchase Advice Received</title>
<link>https://www.solipsys.co.uk/new/LaptopPurchaseAdviceReceived.html?RSS</link>
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<pubDate>Mon, 08 Jun 2020 12:00:00 +0100</pubDate>
<description>Rachel's laptop has become ... eccentric. Like a toddler, or an aging
relative, who won't get up in the morning, won't go to bed at night,
and won't play nicely with others, I'm afraid The Admirable Crichton
has taken to not starting up properly, not shutting down properly, and
occasionally just refusing to connect either over ethernet, or Wi-Fi.</description>
</item>
<item>
<title>Blow Up Your Ability Balloon</title>
<link>https://www.solipsys.co.uk/new/BlowUpYourAbilityBalloon.html?RSS</link>
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<pubDate>Fri, 29 May 2020 12:00:00 +0100</pubDate>
<description>It's pretty clear to most of us that skills unpractised are
eventually lost. Anything at the limits of our abilities
need to be exercised regularly to avoid having them waste
away.</description>
</item>
<item>
<title>A Factlet For All</title>
<link>https://www.solipsys.co.uk/new/AFactletForAll.html?RSS</link>
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<pubDate>Wed, 27 May 2020 12:00:00 +0100</pubDate>
<description>More and more often I hear people saying and see people writing
"factoid", by which they mean "A Small Fact". But is that right?</description>
</item>
<item>
<title>Anatomy of a Hit</title>
<link>https://www.solipsys.co.uk/new/AnatomyOfAHit.html?RSS</link>
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<pubDate>Fri, 22 May 2020 12:00:00 +0100</pubDate>
<description>Recently I was *very* surprised when a post got significant traction
on a forum I visit, and I set up some tracking to see what happened
... this is the report.</description>
</item>
<item>
<title>Sell Yourself, Sell Your Work</title>
<link>https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS</guid>
<pubDate>Wed, 20 May 2020 12:00:00 +0100</pubDate>
<description>Doing technically brilliant work may be enough for your
personal gratification, but you should never think it's
enough. If you lock yourself in a room and do the most
marvellous work but don't tell anyone, then no one will
know, no one will benefit, and the work will be lost. You
may as well not have bothered. For the world to benefit
from your work, and therefore for you to benefit fully
from your work, you have to make it known.</description>
</item>
<item>
<title>All The Letters</title>
<link>https://www.solipsys.co.uk/new/AllTheLetters.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AllTheLetters.html?RSS</guid>
<pubDate>Mon, 18 May 2020 12:00:00 +0100</pubDate>
<description>Most people are aware of the phrase: "The quick brown fox
jumped over the lazy dog." But many, perhaps most, don't
realise (a) Why it's interesting, and (b) It's wrong.</description>
</item>
<item>
<title>Being Slow To Criticise</title>
<link>https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS</guid>
<pubDate>Sat, 09 May 2020 12:00:00 +0100</pubDate>
<description>Software that deliberately kills the servers it is monitoring is
an interesting idea. A story I read recently told of a situation
where the programmer and/or engineer involved wasn't able to fix
the real, underlying problem, so an overlay solution was devised
that (a) worked, and (b) was feasible. This post is not about
that story. This post is about a comment made by one of the readers
in the forum where I saw it.</description>
</item>
<item>
<title>State Machine In Real Life</title>
<link>https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS</guid>
<pubDate>Fri, 01 May 2020 12:00:00 +0100</pubDate>
<description>In April 2016 my wife and I were travelling. We stayed in a
reasonably comfortable but very inexpensive hotel, and meals
weren't provided. As it happened, across the way was a large
retail park with a large well-known supermarket chain, and
they had a restaurant. We ate there four or five times, and
I noticed that they were using a finite state machine.</description>
</item>
<item>
<title>Coxeter Once Nerd-Sniped Conway</title>
<link>https://www.solipsys.co.uk/new/CoxeterOnceNerdSnipedConway.html?RSS</link>
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<pubDate>Tue, 28 Apr 2020 12:00:00 +0100</pubDate>
<description>I wrote earlier about John Conway's passing and some of my memories
of him. I also mentioned there how he was once nerd-sniped by Coxeter.
John didn't call it "nerd sniping" - he didn't know the term - but when
I explained it, he was delighted, as it exactly matched his experience.
So here is the story, as told to me by Conway at MathFest, 2015 ...</description>
</item>
<item>
<title>Not Always Your Fault</title>
<link>https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS</guid>
<pubDate>Tue, 21 Apr 2020 12:00:00 +0100</pubDate>
<description>"I must have done something wrong." I hear this a lot when people
are using computer interfaces. These days that's often websites,
often for large corporations, and often trying to accomplish
something one feels should be simple. And yet in all honesty,
it's not always your fault.</description>
</item>
<item>
<title>Remembering Conway</title>
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<guid isPermaLink="true">https://www.solipsys.co.uk/new/RememberingConway.html?RSS</guid>
<pubDate>Sun, 12 Apr 2020 12:00:00 +0100</pubDate>
<description>John Conway has left us.</description>
</item>
<item>
<title>Perception of Space</title>
<link>https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS</guid>
<pubDate>Fri, 03 Apr 2020 08:30:00 +0100</pubDate>
<description>During this time of lockdown and/or self-isolation, it's
tempting for those of us content with our own company to
sit tight indoors and wait it out. But I'm reminding of
some stories told to me by my friend Laurie Brokenshire.</description>
</item>
<item>
<title>Parallelogram Puzzle</title>
<link>https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS</guid>
<pubDate>Sat, 21 Mar 2020 12:00:00 +0100</pubDate>
<description>A while ago Ed Southall asked a great question on Twitter about
joining dots to make a parallelogram. Several people chimed in
quite quickly, others took a little longer. Some were happy to
have found any solution at all, others were happy to have found
two solutions, and then quite a few people started to claim that
there were, in fact, exactly two solutions. That made me wonder
...</description>
</item>
<item>
<title>Back Of The Envelope COVID19</title>
<link>https://www.solipsys.co.uk/new/BackOfTheEnvelopeCOVID19.html?RSS</link>
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<pubDate>Thu, 12 Mar 2020 12:00:00 +0100</pubDate>
<description>I did a rough "Back of the Envelope" calculation about
COVID-19. Here are my rough-and-ready results.</description>
</item>
<item>
<title>A Point Against The Axiom Of Choice</title>
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<pubDate>Mon, 09 Mar 2020 12:00:00 +0100</pubDate>
<description>Last time we saw that the Axiom Of Choice seems so reasonable.
It's basically saying that that the product of non-empty sets
is always non-empty, and that seems obvious. But in this post
we look at one of the implications of accepting the Axiom Of
Choice, and wonder if perhaps it's not so obvious after all.</description>
</item>
<item>
<title>In Defense Of The Axiom Of Choice</title>
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<pubDate>Wed, 26 Feb 2020 12:00:00 +0100</pubDate>
<description>The first of a two-parter, here we provide a reason to accept
that the Axiom of Choice is reasonable, and should be used.</description>
</item>
<item>
<title>Journeying Home Through Storm Dennis</title>
<link>https://www.solipsys.co.uk/new/JourneyingHomeThroughStormDennis.html?RSS</link>
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<pubDate>Fri, 21 Feb 2020 12:00:00 +0100</pubDate>
<description>Saturday, Feb 15th, 2020, and I'd delivered a Maths Masterclass
just north of Cardiff in South Wales. I'd packed my things and
was offered a lift to the station, which was gratefully accepted.
It was raining, although not torrentially, but Storm Dennis was
due to hit, and we were feeling the initial effects. This is
the story of what happened next ...</description>
</item>
<item>
<title>Earth Radius - Refined</title>
<link>https://www.solipsys.co.uk/new/EarthRadiusRefined.html?RSS</link>
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<pubDate>Sun, 09 Feb 2020 12:00:00 +0100</pubDate>
<description>Previously we looked at computing the radius of the Earth
by watching the Sun coming down a building at sunrise, but
there's been some question about the answer, so now let's
do it "properly".</description>
</item>
<item>
<title>Volume Of A Sphere</title>
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<pubDate>Sun, 05 Jan 2020 12:00:00 +0100</pubDate>
<description>Fermat's Library on Twitter tweeted "Euler presented in his textbooks
the exact formula for the volume of a sphere" and there followed an
image with the actual formula. Over 12 thousand people "Liked" the
tweet, but someone said: "How would you go about proving this one?"
So here is how we can prove it.</description>
</item>
<item>
<title>Big-Oh and Relations</title>
<link>https://www.solipsys.co.uk/new/BigOhAndRelations.html?RSS</link>
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<pubDate>Wed, 04 Dec 2019 12:00:00 GMT</pubDate>
<description>In an earlier post we saw that the function f(n)=n dominates
g(n)=n-ln(n), but that's no surprise. What does come as a
surprise is that g dominates f. So even though for any value
of n greater than 2 we already have f(n)>g(n), still we say
that g dominates f. That feels *very* unexpected, and as
a result you might question the value of the concept of
"dominates", so we'll pause and take a moment to see if we
can get a handle on what's going on.</description>
</item>
<item>
<title>Mathematical Relations</title>
<link>https://www.solipsys.co.uk/new/MathematicalRelations.html?RSS</link>
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<pubDate>Fri, 22 Nov 2019 12:00:00 +0000</pubDate>
<description>Ubiquitous in mathematics is the concept of comparing things,
and examining the relationships between them. Since we do that
all the time and everywhere, it's worth having a look at the
concept of a "Relation" in an abstract sense to try to tease
out the common themes.</description>
</item>
<item>
<title>Introducing Big-Oh</title>
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<guid isPermaLink="true">https://www.solipsys.co.uk/new/IntroducingBigOh.html?RSS</guid>
<pubDate>Mon, 28 Oct 2019 12:00:00 +0000</pubDate>
<description>Last time I said: "If you do this for two different algorithms and
the results are, apart from a scaling factor, pretty much the same,
then the algorithms are said to have the same 'Time Complexity'."
Now we'll look at that more carefully.</description>
</item>
<item>
<title>Constant Differences</title>
<link>https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS</guid>
<pubDate>Sat, 12 Oct 2019 12:00:00 +0100</pubDate>
<description>It's time to get our hands dirty. In this post we look carefully at
a particular algorithm, and think hard about how long it takes for a
given instance. From that we find an important concept emerging.</description>
</item>
<item>
<title>Algorithms and Sizes of Instances</title>
<link>https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS</guid>
<pubDate>Mon, 07 Oct 2019 12:00:00 +0100</pubDate>
<description>We've looked at what we mean by a "Problem", and by an "Instance" of
a problem. For each challenge, we need a way of working out what the
response should be. Such a method is called an "Algorithm" for that
problem, so let's think carefully about algorithms.</description>
</item>
<item>
<title>Introducing Time Complexity</title>
<link>https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS</guid>
<pubDate>Mon, 30 Sep 2019 12:00:00 +0100</pubDate>
<description>Recently I discovered that a friend of mine, an outstandingly
good mathematician, didn't know anything about how the whole
"Time Complexity" thing worked, and didn't understand about
$P$ versus $NP$ and similar concepts. So here is an outline
of the ideas in what I hope will be bite-sized, accessible
chunks.</description>
</item>
<item>
<title>The Linear Frog</title>
<link>https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS</guid>
<pubDate>Sat, 14 Sep 2019 12:00:00 +0100</pubDate>
<description>I was given a problem recently, and I was really pleased to get
the solution. I wonder if you can (a) solve it, and (b) tell me
where it comes from. I've not been able to track it down at all.
It's the problem of the Linear Baby Frog.</description>
</item>
<item>
<title>Seventy Versus One Hundred Revisited</title>
<link>https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS</guid>
<pubDate>Sat, 24 Aug 2019 12:00:00 +0100</pubDate>
<description>Earlier we looked at the situation of two identical cars,
one doing 70, the other doing 100, slamming on their brakes
at exactly the same location to avoid an obstruction. The
model we used was that the two cars shed energy at a rate
proportional to distance. But what if the rate energy is
shed is proportional not to distance, but to time?</description>
</item>
<item>
<title>How The Farrago Works</title>
<link>https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS</guid>
<pubDate>Sat, 17 Aug 2019 12:00:00 +0100</pubDate>
<description>Some time ago I was asked about the way this website works,
and as I started to explain, I realised just how much there
was going on and how complicated it seemed. But they seemed
to think it was neat and elegant, so I thought I'd write it
up.</description>
</item>
<item>
<title>Seventy Versus One Hundred</title>
<link>https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS</guid>
<pubDate>Mon, 05 Aug 2019 12:00:00 +0100</pubDate>
<description>Supposed two identical cars are traveling along the same
straight road, with one traveling at 70 kilometres an hour,
the other at 100 kilometres an hour. Just as the faster
car draws roughly level with the slower, they both see an
obstruction in the road ahead, and (as luck would have it)
at the exact same moment, exactly when they are level with
each other, they both slam on the brakes.</description>
</item>
<item>
<title>Powers Of Two In Lex Order</title>
<link>https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS</guid>
<pubDate>Mon, 22 Jul 2019 12:00:00 +0100</pubDate>
<description>Recently I was sent a lovely little twitchet, so I thought
I'd share it for people to think about. No answers provided.
Firstly, let's do something odd with the powers of two ...</description>
</item>
<item>
<title>Emerging e Expanded</title>
<link>https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS</guid>
<pubDate>Tue, 16 Jul 2019 12:00:00 +0100</pubDate>
<description>Expanding on the post from earlier, and with more detail ...
put "10" into a calculator and take the square root. Then
again, then again, then again, and so on. Fairly quickly we
get a number that's marginally larger than 1, so we can think
of it as 1 plus small rubbish. But thinking carefully about
the rubbish leads to some interesting results.</description>
</item>
<item>
<title>Rage Inducing System Implementation</title>
<link>https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS</guid>
<pubDate>Sat, 13 Jul 2019 12:00:00 +0100</pubDate>
<description>I'm about to go on an extended business trip, so I'm making note
of broadcast TV programs that I want to record, and making sure
there is enough space on the recorder. I have a large external
HDD attached, so I've been transferring programs to that to make
space on the internal HDD. All was going well. There's still 240
hours of space on the external HDD, so no problems anticipated.
What could possibly go wrong?</description>
</item>
<item>
<title>The Book Is Not Always Right</title>
<link>https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS</guid>
<pubDate>Sat, 06 Jul 2019 12:00:00 +0100</pubDate>
<description>Recently someone tweeted a picture of a page from a book. It
seems to be some sort a book about maths aimed at students,
but in one simple paragraph there was just so much wrong, it
attracted many comments from many of my friends and colleagues.</description>
</item>
<item>
<title>Emerging e ...</title>
<link>https://www.solipsys.co.uk/new/EmergingE.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/EmergingE.html?RSS</guid>
<pubDate>Sun, 09 Jun 2019 12:00:00 +0100</pubDate>
<description>Start with 10, and square root many times over. After a while you
get 1+(rubbish). Taking the square root of that halves the rubbish,
so we can deduce that when epsilon is small, 10 to the power of
epsilon is 1 plus some constant times epsilon. Starting with 5
instead of 10 you get a different constant, so we have a function
where you start with a value, successively take the square root,
compute the constant, and that's the value of the function. Looking
at this function, I have questions ...</description>
</item>
<item>
<title>Impossible To Translate</title>
<link>https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS</guid>
<pubDate>Tue, 04 Jun 2019 12:00:00 +0100</pubDate>
<description>Some time ago, while on a business trip to Spain, I was
asked a question that turns out to be impossible to
translate into English.</description>
</item>
<item>
<title>Waiting In Vain</title>
<link>https://www.solipsys.co.uk/new/WaitingInVain.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WaitingInVain.html?RSS</guid>
<pubDate>Wed, 29 May 2019 12:00:00 +0100</pubDate>
<description>Over the past few years I've occasionally been contacted by my
ISP to say that one of my scripts had gone rogue and was using
100% CPU, and would it be OK to kill it. This has always been
a surprise to me because I'm usually pretty careful about my
code, especially when it's running "out there" on someone
else's hardware.</description>
</item>
<item>
<title>Non-Repeating Decimals</title>
<link>https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS</guid>
<pubDate>Fri, 24 May 2019 12:00:00 +0100</pubDate>
<description>In the previous post we talked about repeating decimals, and showed
that every (eventually) repeating decimal is a rational number, and
that every rational number has a (possibly trivial) (eventually)
repeating decimal representation. Now we'll look at some cases of
decimals that don't repeat, and hence are irrational, and vice versa.</description>
</item>
<item>
<title>Rational Repeats</title>
<link>https://www.solipsys.co.uk/new/RationalRepeats.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RationalRepeats.html?RSS</guid>
<pubDate>Thu, 09 May 2019 12:00:00 +0100</pubDate>
<description>Recently on-line I saw someone talking about the decimal expansion
of pi, and they said: "I'm told pi goes on forever and never repeats,
I can't see how that can be proved." I didn't try to explain how pi
never repeats, but I did have a go at explaining some of the ideas.</description>
</item>
<item>
<title>Why is it Lovely</title>
<link>https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS</guid>
<pubDate>Sun, 05 May 2019 12:00:00 +0100</pubDate>
<description>Recently on one of my "social network feeds" I saw a post saying:
"X% of Y equals Y% of X." I commented that this was lovely, and
someone asked "Why?"</description>
</item>
<item>
<title>Compiling Crypto-Connections</title>
<link>https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS</guid>
<pubDate>Sat, 27 Apr 2019 12:00:00 +0100</pubDate>
<description>Having given the maths club talk last Saturday (which went very well)
I was left with the preparative work that I'd done. That consists of
lists of concepts, people, algorithms, cryptosystems, and some of the
connections between them. What to do with it ...</description>
</item>
<item>
<title>Exploring Connections Between Crypto Systems</title>
<link>https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS</guid>
<pubDate>Sat, 20 Apr 2019 12:00:00 +0100</pubDate>
<description>I'm giving a talk for the Liverpool Maths Club this Saturday, April
23rd, 2019. I do this roughly twice a year, and it's always a real
challenge - the ages range between 13 and 18, and while some of the
students have been coming for years, for others it might be their
first time. So whatever the topic might be, it needs to be engaging,
accessible, and challenging, all at the same time.</description>
</item>
<item>
<title>Meeting Elwyn Berlekamp</title>
<link>https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS</guid>
<pubDate>Sat, 13 Apr 2019 12:00:00 +0100</pubDate>
<description>I remember meeting Elwyn Berlekamp.</description>
</item>
<item>
<title>Root Cause Analysis and the Photocopier Question</title>
<link>https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS</guid>
<pubDate>Thu, 11 Apr 2019 12:00:00 +0100</pubDate>
<description>"Root Cause Analysis" is complex, involved, and requires both
tenacity and creativity. When there's a problem, often the cause
isn't a simple, single thing, it's often a collection of things,
and each of those might not be easily characterised. Even so,
it's a crucial exercise in many technology based industries and
activities. So in this post I want to talk about my most recent
brush with the challenges of performing RCA, and even of getting
other people to see that it's there to be done.</description>
</item>
<item>
<title>The Up/Down Tides</title>
<link>https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS</guid>
<pubDate>Tue, 26 Mar 2019 12:00:00 GMT</pubDate>
<description>So while in orbit at about the altitude of the ISS we've looked at
throwing a ball sideways, and we've looked at throwing a ball forwards
or backwards. What happens if we throw the ball up? Or down? Is that
different? Do we finally have the ball travel away in a straight line
at a constant speed? What new horrors lie in store?</description>
</item>
<item>
<title>The Fore/Aft Tide</title>
<link>https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS</guid>
<pubDate>Tue, 19 Mar 2019 12:00:00 GMT</pubDate>
<description>You're in orbit around the Earth with the International Space Station,
and you have a juggling ball. (Don't ask). You hold it next to your
helmet and release it, and it just stays there, apparently floating.
Now gently push the ball ahead of you in orbit. In effect you are
throwing the ball away from you, and the expectation is that it will
drift away from you in a straight line at a constant speed. But it
doesn't.</description>
</item>
<item>
<title>The Sideways Tide</title>
<link>https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS</guid>
<pubDate>Tue, 12 Mar 2019 12:00:00 GMT</pubDate>
<description>Stand outside the International Space Station and hold a juggling ball
right by your helmet. Let it go, and it will stay there. Now give it
a gentle push "sideways". As you will probably know, it then travels
away from you in a straight line at a constant speed, because that's
what happens in zero gravity. But it doesn't ...</description>
</item>
<item>
<title>Wrapping Up Wrapping Up The Earth</title>
<link>https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS</guid>
<pubDate>Tue, 05 Mar 2019 12:00:00 GMT</pubDate>
<description>We're coming to the end of this series. Our friend has purchased
too much rope, too little rope, too much miraculous wrapping sheet,
and now, finally, we come to the question of too little. But first,
let's look at the different "rope" scenarios, and see what happens
in each of the analogous "sheet" cases. Then we'll see how it all
comes together.</description>
</item>
<item>
<title>The *Other* Wrapping The Earth Problem</title>
<link>https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS</guid>
<pubDate>Tue, 26 Feb 2019 12:00:00 GMT</pubDate>
<description>Having gone around the world to wrap it, in truth our friend is too
tired (or too lazy) to prop up the wrapping everywhere. So just as in
the Other Rope Around the Earth problem, instead we look at propping
it up in just one place. We need to take up one million square
metres of excess. How high will that tent pole have to be?</description>
</item>
<item>
<title>The "Wrapping The Earth" Problem</title>
<link>https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS</guid>
<pubDate>Tue, 19 Feb 2019 12:00:00 GMT</pubDate>
<description>Our friend once again has too much to drink, and once again indulges
in a little late night internet shopping. This time, however, it's
fueled by curiousity, having discovered that there is a material that
is infinitely stretchy, but which always retains its area. So while
you can stretch it one direction, it will keep its area by shrinking
in another direction. What if we try to wrap the Earth ...</description>
</item>
<item>
<title>The Ring Of Steel</title>
<link>https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS</guid>
<pubDate>Wed, 13 Feb 2019 12:00:00 GMT</pubDate>
<description>Our friend has encircled the Earth with Rope, discovered that
it's 6 metres longer than needed, so expanded the circle by
0.95 metres to take up the slack. Thus we have a ring of rope
around the Earth at height just about 1 metre. But overnight,
somehow, magically, the rope gets converted to steel! Then,
over breakfast, a slight Earth tremor gently rattles the props,
and they all fall down, leaving the ring of steel completely
unsupported.
What happens next?</description>
</item>
<item>
<title>Rounding Up The Ropes</title>
<link>https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS</guid>
<pubDate>Sun, 10 Feb 2019 12:00:00 GMT</pubDate>
<description>We've seen the $(Other)^k$ rope around the Earth for
$k=0, 1, 2,$ and $3$. In this post we'll look at $k=4$,
but we'll start with a "heads up" for where we'll be going next.</description>
</item>
<item>
<title>The Other Other Other Rope Around The Earth</title>
<link>https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS</guid>
<pubDate>Tue, 05 Feb 2019 12:00:00 GMT</pubDate>
<description>So we have the Rope Around the Earth problem,
the Other Rope Around the Earth problem,
and the Other Other Rope Around the Earth.
You might think that was the end of it, but no, there is more!</description>
</item>
<item>
<title>Rope Around The Earth - Refined</title>
<link>https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS</guid>
<pubDate>Tue, 22 Jan 2019 12:00:00 GMT</pubDate>
<description>As previously mentioned, the Rope Around the Earth problem is
a lovely one, and everyone should know it. But even if you do,
there's still a nice added extra. In this post we'll have a
look at that.</description>
</item>
<item>
<title>The Other Rope Around The Earth</title>
<link>https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS</guid>
<pubDate>Thu, 17 Jan 2019 12:00:00 GMT</pubDate>
<description>The well-known "Rope Around the Earth" problem is lovely, and, as
I say, well known. But some time ago David Bedford mentioned
*another* rope around the Earth problem. A *different* rope
around the Earth problem. And it goes like this.</description>
</item>
<item>
<title>Elementary Estimates</title>
<link>https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS</guid>
<pubDate>Tue, 08 Jan 2019 20:00:00 GMT</pubDate>
<description>Every now and again as I'm doing various estimates or calculations
I use an approximation, and a few days ago it was brought home to me
how much I rely on these, and how few people know them. So I thought
I'd gather some of them together in one place to be a reference.</description>
</item>
<item>
<title>Latitude Correction</title>
<link>https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS</guid>
<pubDate>Tue, 01 Jan 2019 20:00:00 GMT</pubDate>
<description>Recently I've been discussing the details of measuring the
size of the Earth by watching a shadow descending a wall at
sunrise, or ascending at sunset. The sums are easy enough if
you do it at either Equinox, and at the Equator.
But what if you're not at the Equator? What then?</description>
</item>
<item>
<title>Just Give Me The Answer</title>
<link>https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS</guid>
<pubDate>Sun, 07 Oct 2018 20:00:00 GMT</pubDate>
<description>A while ago I saw an exchange on a programming forum I visit on occasion.
A poster had asked a question that at first sight (and in all honesty,
subsequent examination) appeared pretty simple. The poster claimed to
have tried everything they could think of, that nothing worked, and
they'd appreciate any help.</description>
</item>
<item>
<title>More Musing On Pollard Rho</title>
<link>https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS</guid>
<pubDate>Wed, 19 Sep 2018 20:00:00 GMT</pubDate>
<description>After my previous post I started to explore a little more about
how the function in Pollard Rho affects what's going on. As yet
I've not come to any conclusions, and I'm currently deep in the
"I'm confused" stage of the exploration. I'm sure there are other
people know all this, but I don't know who they are, and haven't
been able to find any write-ups, so I'll just carry on.</description>
</item>
<item>
<title>Idle Thoughts About Pollard Rho</title>
<link>https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS</guid>
<pubDate>Mon, 10 Sep 2018 20:00:00 GMT</pubDate>
<description>I've had an idle thought about the Pollard Rho method of
integer factoring. To start with, let's sketch how it works.</description>
</item>
<item>
<title>When Optimising Code, Measure</title>
<link>https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS</guid>
<pubDate>Tue, 04 Sep 2018 20:00:00 GMT</pubDate>
<description>This is a truism that lots of people quote, but it can be hard to
remember, especially in the heat of battle (as it were). Rather
fortunately it came to mind just when needed, as I found something
completely unexpected.</description>
</item>
<item>
<title>A Dog Called Mixture</title>
<link>https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS</guid>
<pubDate>Mon, 27 Aug 2018 12:00:00 GMT</pubDate>
<description>Some considerable time ago I was giving some talks at a school, and
my wife and I were kindly hosted at the home of the Headmaster and
his family. And his menagerie, as it turned out.</description>
</item>
<item>
<title>Another PayPal Scam</title>
<link>https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS</guid>
<pubDate>Fri, 03 Aug 2018 12:00:00 GMT</pubDate>
<description>Received as part of the newsletter of a publishing company :
We've been living in interesting times at Wildside Press since our
last newsletter. Our PayPal account was VERY creatively hacked, and
we briefly lost about $15,000 of the money we'd been saving up for
royalty payments to authors.</description>
</item>
<item>
<title>Why Top Posting Has Won</title>
<link>https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS</guid>
<pubDate>Wed, 13 Jun 2018 14:20:00 GMT</pubDate>
<description>I've recently realised that, in my head, there's a connection
between top-posting in email and washing the dishes. Stay
with me, I'll see if I can make the connection for you.</description>
</item>
<item>
<title>Archimedes' "Hat Box" Theorem</title>
<link>https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS</guid>
<pubDate>Wed, 06 Jun 2018 11:50:00 GMT</pubDate>
<description>Take a sphere, and encase it in a cylinder. Take a horizontal slice
between two planes. You end up with a narrow cylinder, and a smaller,
"slopey" cylinder.
The Archimedes Hat-Box Theorem says these two cylinders have the same
surface area. In fact the theorem says that the surface areas are the
same no matter how thick the slice is, so as a consequence we can take
a "slice" that captures the entire cylinder and sphere, and that means
that the surface area of the curved surface of the cylinder is exactly
the same as the surface area of the sphere.</description>
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<item>
<title>Considering a Sphere</title>
<link>https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS</guid>
<pubDate>Tue, 05 Jun 2018 14:56:00 GMT</pubDate>
<description>Recently someone posted an animation of a way to visualise the area of
a circle. Someone else then asked if there was a similar visualisation
of the volume of a sphere, or the surface area of a sphere, and that
started me thinking.</description>
</item>
<item>
<title>To Link Or Not To Link</title>
<link>https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS</guid>
<pubDate>Thu, 17 May 2018 14:04:00 GMT</pubDate>
<description>Over the past few years I've noticed a rise in a particular type of
spam that I'm receiving. It takes the form of an email like this ...</description>
</item>
<item>
<title>Generic Advice For Writing A Thesis</title>
<link>https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS</guid>
<pubDate>Mon, 07 May 2018 20:30:00 GMT</pubDate>
<description>I have some generic thesis-writing advice to supplement
that given by your supervisor, but only if it's welcome.</description>
</item>
<item>
<title>Just Teach My Child The Maths</title>
<link>https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS</guid>
<pubDate>Sun, 18 Feb 2018 09:15:01 GMT</pubDate>
<description>It is astounding to me that mathematics - of all school
subjects - elicits such potent emotional reaction when
"reform" is in the air.</description>
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<item>
<title>Not A Spectator Sport</title>
<link>https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS</guid>
<pubDate>Wed, 13 Dec 2017 13:00:00 GMT</pubDate>
<description>One of my university lecturers gave what we all thought were dreadful
lectures. Muddled, unclear, chaotic, with no discernible thread. It
took ages to reconstruct and rework the material to a point where we
could attack the problems and old exam questions.</description>
</item>
<item>
<title>Left Truncatable Prime</title>
<link>https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS</guid>
<pubDate>Sat, 21 Oct 2017 15:00:00 GMT</pubDate>
<description>Recently Maths Inspiration produced some pencils with a fantastic idea.
Yes, their name is on it, yes, it has a slightly cheesy catch-phrase,
But then there is something really clever.</description>
</item>
<item>
<title>The Doctor and the Lawyer</title>
<link>https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS</guid>
<pubDate>Sun, 15 Oct 2017 14:00:00 GMT</pubDate>
<description>A doctor and a lawyer were chatting at a party when someone approached
the doctor. They wanted advice, and started to describe their symptoms
when the doctor interrupted and said "It might be better to make an
appointment so we can talk in private."</description>
</item>
<item>
<title>Four Points Two Distances Proof</title>
<link>https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS</guid>
<pubDate>Tue, 03 Oct 2017 11:25:00 GMT</pubDate>
<description>The Four Points Puzzle challenge that Peter Winkler set me was this:
"Find all configurations of four (distinct) points in the plane that
determine exactly two distances." He then added: "Nearly everyone
misses at least one, and every solution has been missed by at least
one person." So the challenge isn't to find all the configurations
so much as to be able to prove that you have them all. It's the proof
that matters. Here's mine.</description>
</item>
<item>
<title>Meeting Ron Graham</title>
<link>https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS</guid>
<pubDate>Sun, 01 Oct 2017 18:14:00 GMT</pubDate>
<description>I was a lowly PhD student when I first met Ron Graham. It was at a
conference, and there was something I wanted to show him. In my mind
it was pretty much guaranteed that he would be interested, but he was
(and still is!) extremely well known, extremely eminent, and extremely
popular. As a result he is extremely busy, and somewhat besieged with
people, all wanting a piece of his time. How could I possibly attract
and hold his attention long enough to get him interested?
So I hatched a plan.</description>
</item>
<item>
<title>Napkin Ring Vs Spherical Cap</title>
<link>https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS</guid>
<pubDate>Thu, 28 Sep 2017 08:26:00 GMT</pubDate>
<description>Many years ago I was at a semi-social gathering and a somewhat odd
incident occurred. Over the course of conversation it emerged that
I was studying maths, and one chap, at one point, turned to me and
said: "So, do you like puzzles, then?" Not especially on my guard
I said yes, and he went on to say something like this: "OK, I'll
give you a puzzle ..."</description>
</item>
<item>
<title>The Four Points Puzzle</title>
<link>https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS</guid>
<pubDate>Tue, 26 Sep 2017 16:43:00 GMT</pubDate>
<description>At the MOVES conference in New York in August I was lucky enough to
spend some time with Peter Winkler, mathematician, puzzle master
extraordinaire, and author of "Mathematical Puzzles: A Connoisseur's
Collection". As we talked about many things he set me this puzzle:
"Find all configurations of four (distinct) points in the plane that
determine exactly two distances."</description>
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<item>
<title>Radius of the Earth - Part Two</title>
<link>https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS</guid>
<pubDate>Sat, 16 Sep 2017 08:30:00 GMT</pubDate>
<description>Some nine and a bit weeks ago I posted about a method of calculating
(or estimating) The Radius Of The Earth using a stopwatch and watching
the Sun at sunrise (or sunset). When "Mike the Sundial" told me the
idea I was quite simply stunned at the simplicity and elegance. Colin
Beveridge took up the challenge. But when I read his calculation I was
interested to see just how different his take was from mine.</description>
</item>
<item>
<title>Grep Timing Anomaly</title>
<link>https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS</guid>
<pubDate>Fri, 28 Jul 2017 08:30:00 GMT</pubDate>
<description>Some considerable time ago - long enough that probably the details
are no longer relevant, or accurate - I got seriously fed up with
the spam filtering on my email service. There were so many false
positives that I had to wade through the spam bin every day, pulling
out obviously good emails that needed attention. It got so that it
cost me more time to have it running.</description>
</item>
<item>
<title>The Radius of the Earth</title>
<link>https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS</guid>
<pubDate>Wed, 12 Jul 2017 08:30:00 GMT</pubDate>
<description>The talk/workshop I give about computing the distance to the Moon uses,
it claims, nothing more than a pendulum and a stopwatch. And while it's
sort of true that it uses nothing else, it's not really true, because it
also uses the period of the Moon, and the size of the Earth. Now it might
be possible to persuade you that it's OK to use the period of the Moon,
since you can simply look out the window and measure that for yourself,
but to use the size of the Earth seems a bit of a stretch. Surely there
is no way to compute that from your back garden. But there is.</description>
</item>
<item>
<title>This Works to Cure My Hiccoughs</title>
<link>https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS</guid>
<pubDate>Sun, 09 Jul 2017 18:30:00 GMT</pubDate>
<description>It's many years ago that I was told about this trick. People rarely
believe me, but it honestly works for me, and it has worked for others.
So I thought I'd write it up.</description>
</item>
<item>
<title>Perhaps We Saved One</title>
<link>https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS</guid>
<pubDate>Sun, 02 Jul 2017 19:50:00 GMT</pubDate>
<description>Many years ago a good friend of mine, Bill Mullarkey, organised a
"Science and Technology Extravaganza" in Wigan. It was a fabulous
two-day event with hundreds of teenagers and adults in attendance.
The buzz of excitement was huge, and it was an honour to be part
of the whole thing.</description>
</item>
<item>
<title>Thinking About Mastodon</title>
<link>https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS</guid>
<pubDate>Sun, 18 Jun 2017 17:50:00 GMT</pubDate>
<description>Some people are describing Mastodon as a decentralised Twitter, but that's
rather misleading. It's better not to try to understand it like that.
Instead, here's my way of thinking.</description>
</item>
<item>
<title>Disappearing Trains On Virgin</title>
<link>https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS</guid>
<pubDate>Sat, 17 Jun 2017 18:58:00 GMT</pubDate>
<description>I'm planning a significant set of travels, so as always, I started by
sketching an idea of what might be possible, then confirmed the various
parts on the usual National Rail web site. Having picked my trains,
I then went to the Virgin Trains web site to actually buy the tickets.
This time there was a surprise awating me.</description>
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<item>
<title>The Independence Game</title>
<link>https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS</guid>
<pubDate>Tue, 18 Apr 2017 11:00:00 GMT</pubDate>
<description>A few weeks ago I was honoured to be able to attend the gathering at the
Royal Society where Rob Eastaway was given his Christopher Zeeman medal.
He gave an excellent talk, full of interest and humour, the only downside
being that he made us play a game. Although at the time Rob called it
"Avoid the Neighbours", I now think of it simply as "Rob's Dots". He
said he didn't know how to play it optimally beyond 11 points, so
I thought I'd have a go.</description>
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<item>
<title>One Of My Favourite Puzzles</title>
<link>https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS</guid>
<pubDate>Thu, 06 Apr 2017 20:00:00 GMT</pubDate>
<description>It is impossible to choose a single problem as my favourite. There
are so many, each with their own attractions, each with their own
charms. But there is one that I solved quickly, and then found that
I had only just started to scratch the surface.</description>
</item>
<item>
<title>Thinking About Recursion</title>
<link>https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS</guid>
<pubDate>Wed, 08 Mar 2017 12:00:00 GMT</pubDate>
<description>It has been said that there are two hard problems in computing:
Cache Invalidation, Naming Things, and Off-By-One Errors.
Well, that's certainly true when you get into the practice of
programming. But on the way to becoming a programmer we find
that there are multiple levels of enlightenment.</description>
</item>
<item>
<title>Memorising The Tube</title>
<link>https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS</guid>
<pubDate>Sat, 03 Dec 2016 19:40:00 GMT</pubDate>
<description>Recently I memorised the period table of elements. When I tell
people that, the response has generally been a moderate pause,
followed by a rather puzzled - "Why?" So I thought I'd explain.</description>
</item>
<item>
<title>Spikey Spheres</title>
<link>https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS</guid>
<pubDate>Sun, 20 Nov 2016 20:00:00 GMT</pubDate>
<description>I've recently been working on an optimisation problem, and I've
come to realise that I can consider it as wandering around on a
smooth landscape in 1800 dimensions. The problem is that while
the error function may be "smooth," your intuition of what this
means is wrong.</description>
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<item>
<title>Surprisingly Quick</title>
<link>https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS</guid>
<pubDate>Thu, 06 Oct 2016 20:00:00 GMT</pubDate>
<description>In the 1990s I had a job at Liverpool University doing research into
how we might make it possible for non-computing specialists to use
paraallel computers. Even today, over 20 years later, this is still
an unsolved problem, and the machines now are designed to be easier
to use. The machine I was using was a Parsys SuperNode with 96 T800
transputers, hooked together with a reconfigurable switch, cunningly
designed so that any 4-regular network could be realised.</description>
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<item>
<title>An Unexpected Fraction</title>
<link>https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS</guid>
<pubDate>Sun, 18 Sep 2016 19:30:00 GMT</pubDate>
<description>On 2016-09-09, @MEIMaths tweeted an image and said: "Start with any
convex quadrilateral. Mark the midpoint of each side, join these
midpoints to the vertex two places clockwise around the quadrilateral.
What fraction of the original quadrilateral is the new quadrilateral?"
From the way it's phrased you'd expect the answer to be the same
regardless of the quadrilateral chosen ...</description>
</item>
<item>
<title>You Have To Admire Their Optimism</title>
<link>https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS</guid>
<pubDate>28 Aug 2016 19:30:00 GMT</pubDate>
<description>Coming back from Australia, Rachel and I landed at Heathrow
(which we usually avoid) and caught trains back home. Our
final leg was from Chester to home, and I had a look at the
live departures board to see how things were looking. There
I found something puzzling ...</description>
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<item>
<title>Representatives Matter</title>
<link>https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS</guid>
<pubDate>10 Jul 2016 19:30:00 GMT</pubDate>
<description>My uncle has a Ferrari, and it has led him to make an interesting observation.</description>
</item>
<item>
<title>Pythagoras By Incircle</title>
<link>https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS</guid>
<pubDate>08 Jun 2016 19:30:00 GMT</pubDate>
<description>Some time ago I was working on a puzzle about incircles, and
unexpectedly a proof of Pythagoras' Theorem dropped out! I'm
sure it's well known to people who know lots about Pythagoras'
Theorem, but I thought I'd share it.</description>
</item>
<item>
<title>A Puzzle About Puzzles</title>
<link>https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS</guid>
<pubDate>31 May 2016 19:30:00 GMT</pubDate>
<description>Some time ago a friend of mine, Adam Atkinson, mentioned to me what he
referred to as "Semi-Chestnuts" - puzzles that should be classics, but
are for some reason effectively unknown. Recently one of these caught
the attention of the Twitter-verse.</description>
</item>
<item>
<title>How not to do Twitter</title>
<link>https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS</guid>
<pubDate>24 May 2016 19:30:00 GMT</pubDate>
<description>Recently I had an exchange on Twitter that beautifully exemplifies
how companies get it so totally, totally wrong. Usually I don't
name names, but on this occasion it's just spectacularly bad, and
then they asked me to point them at a write-up, that I've decided
to go ahead and do so.</description>
</item>
<item>
<title>Calculating 52 Factorial By Hand</title>
<link>https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS</guid>
<pubDate>04 Jan 2016 19:30:00 GMT</pubDate>
<description>Some time ago I gave a talk where I showed that something unexpected
happening with a deck of playing cards. I had some volunteers try it,
and while they did so I talked about just how many orderings there are
for 52 cards. To do this I computed (an approximation to) 52!
(52 factorial) by hand. It's not so hard - you just calculate 54!
and then divide by 3000.</description>
</item>
<item>
<title>Sometimes small things aren't</title>
<link>https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS</guid>
<pubDate>02 Jan 2016 19:30:00 GMT</pubDate>
<description>Twenty years ago (or thereabouts) there was a Christmas road safety
campaign in which they said: "Wearing a seatbelt doubles your chance
of surviving an accident." But that's obviously nonsense.</description>
</item>
<item>
<title>Not If You Hurry</title>
<link>https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS</guid>
<pubDate>20 Dec 2015 19:30:30 GMT</pubDate>
<description>On one occasion, when I was a teenager, I was in the car with my
parents going somewhere. We had to turn right (equivalent to
turning left in the States) and hence had to cross a lane of
traffic and merge into the far lane. My father was looking to
the right to see if there was anything approaching in the lane
we had to cross, and asked my mother - "Is there anything coming?"</description>
</item>
<item>
<title>Factoring Via Graph Three Colouring</title>
<link>https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS</guid>
<pubDate>17 Dec 2015 19:30:30 GMT</pubDate>
<description>Occasionally someone comes to me and says that they have a polynomial
time algorithm for solving an NP-Complete problem. More specifically,
someone came to me and said they could Graph Vertex Three Colour (G3C)
in polynomial time. They'd tried lots of example, and it always
worked. So I produced a graph ... They didn't come back.</description>
</item>
<item>
<title>Another Proof Of The Doodle Theorem</title>
<link>https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS</guid>
<pubDate>16 Dec 2015 19:30:30 GMT</pubDate>
<description>So on the "Doodle Theorem" page we have a proof of, yes, you guessed it, the
Doodle Theorem. Here, on a page entitled "Another Proof of the Doodle Theorem"
we have, yes, you guessed it, another proof of the Doodle Theorem. However,
here we take a rather unusual approach ...</description>
</item>
<item>
<title>When Obvious Is Not Obvious</title>
<link>https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS</guid>
<pubDate>15 Dec 2015 19:30:30 GMT</pubDate>
<description>There's an old story that goes something like this:
A math professor is teaching a class, and in the middle of a proof
he says "Clearly we have the following." A student puts up his
hand and says: "That's not clear to me."</description>
</item>
<item>
<title>Graph Three (Vertex) Colouring</title>
<link>https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS</guid>
<pubDate>13 Dec 2015 19:30:30 GMT</pubDate>
<description>Here is something you may have seen before. Take a map, any map, and
colour the regions so that if two regions share a border, they must
get different colours. In this post we start with the usual game,
but take off in an unusual direction and quickly find ourselves in
deeper waters.</description>
</item>
<item>
<title>The Doodle Theorem</title>
<link>https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS</guid>
<pubDate>12 Dec 2015 19:30:30 GMT</pubDate>
<description>The Doodle Theorem says that any map drawn with a single pen
stroke that returns to its starting point can be two-coloured.
Here's one proof.</description>
</item>
<item>
<title>Be Careful What You Say</title>
<link>https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS</guid>
<pubDate>25 Oct 2015 19:30:30 GMT</pubDate>
<description>Here's an amazing story. A young child writing to a popular
television programme with wild claims and, quite frankly,
ridiculous aspirations. The output is a lesson to us all.</description>
</item>
<item>
<title>The Mutilated Chessboard Revisited</title>
<link>https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS</guid>
<pubDate>10 Oct 2015 19:30:30 GMT</pubDate>
<description>Puzzle enthusiasts know that a really good puzzle is more than just
a problem to solve. The very best problems and puzzles can provide
insights that go beyond the original setting. Sometimes even classic
puzzles can turn up something new and interesting. Here we re-visit
the classic question of when we can tile a chessboard with dominoes.</description>
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<item>
<title>A Mirror Copied</title>
<link>https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS</guid>
<pubDate>16 Aug 2015 19:30:30 GMT</pubDate>
<description>So earlier I asked: What do you get when you photocopy a mirror? But the real question, as I then expanded, is not "What do you get?" but: "Why *must* you get that?" Can we deduce from first principles, based only on what a good photocopier must do, what the result will be? I claim the answer is "Yes," although there are some who disagree.</description>
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<title>The Other, Other Rope Around The Earth</title>
<link>https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS</guid>
<pubDate>01 Aug 2015 19:30:30 GMT</pubDate>
<description>There's a classic problem: Upon stretching a rope around the Earth, you find that you have 6 metres excess. So you join the ends, and then go around the Earth propping up the rope equally everywhere. How high will it be? An alternative that's been suggested is that instead of propping it up equally everywhere, just prop it up as high as possible in one place. But now Bill Mullins has asked me yet another variant.</description>
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<item>
<title>Photocopy A Mirror</title>
<link>https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS</guid>
<pubDate>29 Jul 2015 19:30:30 GMT</pubDate>
<description>Recently on Twitter I asked the question: What do you get when you photocopy a mirror? But really the question isn't "What do you get?" - the real question is "Why is that the right thing to get?"</description>
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<item>
<title>The Point Of The Banach Tarski Theorem</title>
<link>https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS</guid>
<pubDate>06 Jun 2015 19:30:30 GMT</pubDate>
<description>There's a classic "Limited Audience" joke/riddle that goes:
Q: What's an anagram of "Banach-Tarski"?
A: "Banach-Tarski Banach-Tarski."
Now, if you already know what the Banach-Tarski
theorem says, that riddle is really funny. If
you don't then you're simply not in the audience,
and you'll just go: "Huh?" In this article we
have a look at why the Banach-Tarski theorem is
more than just a curiosity.</description>
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<item>
<title>Sieve Of Eratosthenes In Python</title>
<link>https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS</guid>
<pubDate>24 May 2015 19:30:30 GMT</pubDate>
<description>One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be done quickly and efficiently by using the Sieve of Eratosthenes. Here we use a dynamically generated collection of filters, one for each prime, and run down the list of all numbers, filtering as we go.</description>
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<item>
<title>Fast Perrin Test</title>
<link>https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS</guid>
<pubDate>19 May 2015 19:30:30 GMT</pubDate>
<description>So we've got scaffolding to look for Perrin Pseudo-Primes (PPPs), assuming any exist (which they do) but as we run the existing code we find that it's spending pretty much all its time in the test as to whether n divides k(n). Now we look to speed that up ...</description>
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<item>
<title>Russian Peasant Multiplication</title>
<link>https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS</guid>
<pubDate>18 May 2015 19:30:30 GMT</pubDate>
<description>Sometimes simply called "Peasant Multiplication," sometimes called "Ancient Egyptian multiplication," sometimes called "Ethiopian multiplication," sometimes called "Multiplication by Doubling and Halving," this algorithm is well-known to some, a mystery to others, and more useful than you might think, being applicable not just to multiplication of numbers, but also useful for exponentiation, and for matrices.</description>
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<item>
<title>Finding Perrin Pseudo Primes, Part 2</title>
<link>https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS</guid>
<pubDate>17 May 2015 19:30:30 GMT</pubDate>
<description>So now we've got the scaffolding of a program to find these Perrin Pseudo-Primes. The timing shows that it overwhelmingly spends all of its time in the routine to test whether or not a number passes the "Perrin Test." So there are a few things we need to do.</description>
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<item>
<title>Finding Perrin Pseudo Primes, Part 1</title>
<link>https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS</guid>
<pubDate>15 May 2015 19:30:30 GMT</pubDate>
<description>A while ago I was asked: Consider the sequence k(n) with k(1)=0, k(2)=2, k(3)=3, and k(n)=k(n-2)+k(n-3). Why is it true that n divides k(n) if and only if n is prime?" My immediate response was "Well, it's not true." So I was challenged to find a counter-example.</description>
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<item>
<title>The Unwise Update</title>
<link>https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS</guid>
<pubDate>13 May 2015 19:30:30 GMT</pubDate>
<description>This story passed on to me first-hand from the engineer involved.
It's a true story about how insufficient knowledge among operating
personnel about the operational consequences of new technology may
have accidental effects.</description>
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<item>
<title>Miles Per Gallon</title>
<link>https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS</guid>
<pubDate>03 May 2015 19:30:30 GMT</pubDate>
<description>I remember a while ago attending a talk that did something utterly
bizarre with units of "miles per gallon." I don't remember much
about it, but I thought I'd attempt to reconstruct the process in
a post, just to see how far I get, what conclusion I reach, and
whether people think it's as bonkers as I do. Here we go ...</description>
</item>
<item>
<title>Tracking An Item On Hacker News</title>
<link>https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS</guid>
<pubDate>02 May 2015 19:30:30 GMT</pubDate>
<description>A couple of weeks ago I had an exchange with a user on
Hacker News about user "ages." I wrote that up in my
previous post, and then submitted it. I was surprised
that the item garnered enough attention to make it to
the front page, but that was when a little foresight
paid off. I don't usually bother with analytics on my
site, but on this occasion I put a tracker on the page
to count the number and times of page hits.</description>
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<item>
<title>Hacker News User Ages</title>
<link>https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS</guid>
<pubDate>19 Apr 2015 19:30:30 GMT</pubDate>
<description>A few days ago I was reading Hacker News and someone had
posted a poll with the following question:
How old is your HN account?</description>
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<item>
<title>Poking The Dusty Corners</title>
<link>https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS</guid>
<pubDate>14 Apr 2015 19:30:30 GMT</pubDate>
<description>In chatting with people about what a maths degree is, and what it
does for you, I've often been intrigued by a particular response.
I've shown them something that they expect to be true (or false)
and then shown that their expectations can be confounded. When
I do that, a common response is "Well, you're just being stupid."</description>
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<item>
<title>There Is No Time For This</title>
<link>https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS</guid>
<pubDate>03 Apr 2015 19:30:30 GMT</pubDate>
<description>I'm finding these days that I just don't have
the time to do everything myself. I don't have
time to evaluate everything on its merit ...</description>
</item>
<item>
<title>Publically Sharing Links</title>
<link>https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS</guid>
<pubDate>05 Jan 2015 19:30:30 GMT</pubDate>
<description>For years I've been visiting, reading, and contributing to a site
called "Hacker News." About 3.5 years ago I basically withdrew,
finding it increasingly frustrating, but I never really went away.
Slowly I've returned and contributed again, although not at the same
level, and generally just by contributing links and not often getting
involved in the discussions. But once again I'm getting frustrated
and want to leave, but where else can I share things I find, and then
enter into discussions?</description>
</item>
<item>
<title>Learning Times Tables</title>
<link>https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS</guid>
<pubDate>14 Dec 2014 19:30:30 GMT</pubDate>
<description>Should primary school students be drilled on their times tables?</description>
</item>
<item>
<title>Graceful Degradation</title>
<link>https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS</guid>
<pubDate>12 Dec 2014 19:30:30 GMT</pubDate>
<description>I first learned about graceful degradation from a colleague. He prefaced
his story by saying that good people learn from their mistakes, but the
best people learn from other people's mistakes. This is a bit like the
saying in aviation circles that a good landing is one you can walk away
from, an excellent landing is when they can use the 'plane again ...</description>
</item>
<item>
<title>Diagramming Maths Topics</title>
<link>https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS</guid>
<pubDate>22 Nov 2014 19:30:30 GMT</pubDate>
<description>An impossible task, but wouldn't it be useful to have some sort
of diagram of topics in maths, connected somehow to show the links
between topics? How could such a diagram been created? How could
it be explored? How could it be dynamic? Maintainable? Usable?</description>
</item>
<item>
<title>On the Rack</title>
<link>https://www.solipsys.co.uk/new/OnTheRack.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/OnTheRack.html?RSS</guid>
<pubDate>26 Aug 2014 19:30:30 GMT</pubDate>
<description>When travelling, I usually go as light as possible. Certainly when
travelling by plane I try to go "hand luggage only", and when doing
various mini-tours of talks, and so on, I try to travel with just a
single, small backpack. Sometimes it's not possible, but I usually
manage. Here's a story of one time when this had unexpected
consequences ...</description>
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<item>
<title>Square Root By Long Division</title>
<link>https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS</guid>
<pubDate>11 Aug 2014 19:30:30 GMT</pubDate>
<description>The other day someone asked:
"Is the product of 4 consecutive positive integers always one less than a square?"
Good question. The answer is yes, and I solved it using a technique the interlocutor
didn't know.</description>
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<item>
<title>Beyond the Boundary</title>
<link>https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS</guid>
<pubDate>23 May 2014 19:30:30 GMT</pubDate>
<description>In which we show that 1+2+4+8+16+... is not equal to -1, and how that
might both surprise us, and not surprise us.</description>
</item>
<item>
<title>Fill In The Gaps</title>
<link>https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS</guid>
<pubDate>03 May 2014 19:30:30 GMT</pubDate>
<description>Recently I had an interesting conversation on twitter, insofar as one can
have a conversation at all in that medium. It started with the following
perfectly reasonable question ... "Sorry for what may be a stupid question,
but sin(x)/x has a limit of 1 as x -> 0, so does it not cross x=0 at 1?"</description>
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<item>
<title>Software Checklist</title>
<link>https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS</guid>
<pubDate>24 Apr 2014 19:30:30 GMT</pubDate>
<description>During the second World War, fighter pilots would scramble to take off.
Their heart would stop when the engine mis-fired. Was the fuel mix too
rich, or too lean? Turn the control wrong way and they could die ...</description>
</item>
<item>
<title>NASA Space Crews</title>
<link>https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS</guid>
<pubDate>10 Feb 2013 19:30:30 GMT</pubDate>
<description>In the Apollo missions many of the crew were experienced, but some were
not. So I drew a diagram - see what patterns you see.</description>
</item>
<item>
<title>The Birthday Paradox</title>
<link>https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS</guid>
<pubDate>06 Nov 2012 19:30:30 GMT</pubDate>
<description>A classic puzzle/paradox is to ask: How many people do you need to have
in a room before two of them share a birthday. In this post we see what
happens when 365 is not equal to 365, and how this affects computing the
sizes of hash spaces.</description>
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<item>
<title>The Trapezium Conundrum</title>
<link>https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS</guid>
<pubDate>17 Apr 2012 19:30:30 GMT</pubDate>
<description>Clear, precise, unambiguous and useful definitions are hard to come by
in the real world. In maths we have the luxury of creating definitions
that we want, and then chasing down the consequences. If the definition
doesn't produce what we want, we can change it. But even things, things
aren't always as easy as we might hope.</description>
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<item>
<title>Revisting the Ant</title>
<link>https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS</guid>
<pubDate>20 Feb 2012 19:30:30 GMT</pubDate>
<description>So last time in TheAntAndTheRubberBand we were talking about an infinitely
patient ant walking on an infinitely stretchy rubber band. If you haven't
already, you'll need to read that.
So here's what's happening.</description>
</item>
<item>
<title>The Ant and the Rubber Band</title>
<link>https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS</guid>
<pubDate>09 Feb 2012 19:30:30 GMT</pubDate>
<description>There's a 1 metre long rubber band, and an ant, standing on it at one end.
The ant starts walking along it at a speed of 1 cm/min. Every minute the
rubber band is stretched (uniformly and instantaneously) to be one metre
longer. The question is this: Will the ant ever get to the far end?</description>
</item>
<item>
<title>Irrationals Exist</title>
<link>https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS</guid>
<pubDate>20 Dec 2011 19:30:30 GMT</pubDate>
<description>For this post I thought I'd have a quick diversion into talking about
the so-called "Real Numbers." Upon reflection, however, I found that
there was so much I wanted to say that there was no way to fit it sensibly
into a single post. So instead I'll put some preliminary comments here,
and then expand on them later.
In particular, I'll give an explicit proof that for every interval you
choose of non-zero length, there is an irrational in it.</description>
</item>
<item>
<title>Multiple Choice Probability Puzzle</title>
<link>https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS</guid>
<pubDate>15 Nov 2011 19:30:30 GMT</pubDate>
<description>Recently the following puzzle was running around the 'net:
If you choose an answer at random, what is your probability
of being correct: A: 25%; B: 50%; C: 60%; D: 25% ?
The immediate thought is - there are four options, so if I pick
one at random then each has a one in four chance of being chosen.
That means the answer is 1/4, or 25%. But that doesn't work ...</description>
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<item>
<title>Random Eratosthenes</title>
<link>https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS</guid>
<pubDate>28 Oct 2011 19:30:30 GMT</pubDate>
<description>Why do people think of the primes as somehow being "random"?
What does that mean? How can we investigate? In this post
I'll talk about a way of generating primes, and then see what
happens when we toss in some randomness, just for fun.</description>
</item>
<item>
<title>Wrapping Up Square Dissection</title>
<link>https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS</guid>
<pubDate>13 Sep 2011 19:30:30 GMT</pubDate>
<description>We now have five valid dissections, and one "dissection" that might
be regarded as invalid. So what do we mean by "a piece" and just how
many dissections are there?</description>
</item>
<item>
<title>Dissecting a Square (Part 2)</title>
<link>https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS</guid>
<pubDate>08 Aug 2011 19:30:30 GMT</pubDate>
<description>So we return to the square. It's simple enough to cut it up into
identical pieces so that all the pieces touch the centre. But in
how many ways? I rapidly got 5 (or 6, depending on a technicality),
and I started to wonder about a proof that 5 (or 6) was all of them.
I posted a badly worded question on an internet forum, and rightly
got flamed for it, but in the answers was a shock. There was an
infinite family of solutions. And not just one ...</description>
</item>
<item>
<title>Dissecting a Circle</title>
<link>https://www.solipsys.co.uk/new/DissectingACircle.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingACircle.html?RSS</guid>
<pubDate>26 Jul 2011 19:30:30 GMT</pubDate>
<description>There are three possibilities when we dissect any shape:
One piece touches the centre point;
There's more than one piece and they all touch the centre point;
Two or more pieces touch the centre point, but some don't.
But what about the circle? If we just cut it like a pizza then we
get all the pieces touching the centre. No problem there.
What about the other possibilities?</description>
</item>
<item>
<title>Dissecting a square (Part 1)</title>
<link>https://www.solipsys.co.uk/new/DissectingASquare.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingASquare.html?RSS</guid>
<pubDate>01 Jun 2011 19:30:30 GMT</pubDate>
<description>Some time ago I was given a challenge that turned out to be
surprisingly rich in surprises. It all starts by trying to
dissect a square.</description>
</item>
<item>
<title>An Oddity in Tennis (Part 3 of Decision Trees in Games)</title>
<link>https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS</guid>
<pubDate>24 May 2011 19:30:30 GMT</pubDate>
<description>In this final part we see how a proper analysis can throw
up some surprising results in the detail, defying our
expectations.</description>
</item>
<item>
<title>Decision Tree For Tennis (Part 2 of Decision Trees in Games)</title>
<link>https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS</guid>
<pubDate>18 May 2011 19:30:30 GMT</pubDate>
<description>Having seen the basic ideas in decision trees for games,
we now put it to real use in analysing tennis. This is
the prelude for a surprise ...</description>
</item>
<item>
<title>Decision Trees In Games (Part 1)</title>
<link>https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS</guid>
<pubDate>15 May 2011 19:30:30 GMT</pubDate>
<description>A fairly standard exercise in probability is to ask who,
under a given scoring system, will win a game given the
probability of each move. In this first in a series,
we look at how to analyse simple games as a prelude to
finding a surprise in a well-known example.</description>
</item>
<item>
<title>A Matter of Convention</title>
<link>https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS</guid>
<pubDate>09 May 2011 19:30:30 GMT</pubDate>
<description>There are some things in life where people argue about how they
should be, and in fact there is no single "right" answer, we just
need to agree on one of them. So what is 6/2(2+1)?</description>
</item>
<item>
<title>Do You Nourish Or Tarnish?</title>
<link>https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS</guid>
<pubDate>21 Apr 2011 19:30:30 GMT</pubDate>
<description>Interactions with others can nourish your soul, or can tarnish it.
Seek out those who nourish your soul, but ask yourself: which do
you do?</description>
</item>
<item>
<title>Binary Search Reconsidered ...</title>
<link>https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS</guid>
<pubDate>18 Apr 2011 19:30:30 GMT</pubDate>
<description>"Binary Search" was made popular as an interesting test problem
by Jon Bentley ... I was stupid - I claimed: "There is a simpler
invariant and simpler code that together have a few advantages."</description>
</item>
<item>
<title>Two Equals Four</title>
<link>https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS</guid>
<pubDate>14 Apr 2011 19:30:30 GMT</pubDate>
<description>A cool puzzle. Solve one equation and discover that the
answer is two. Solve another equation and discover that
the answer is four. Realise that they are the same, and
confusion results.</description>
</item>
<item>
<title>The Lost Property Office</title>
<link>https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS</guid>
<pubDate>11 Apr 2011 19:30:30 GMT</pubDate>
<description>A story of love lost, and how administrative processes
can cost your customers time, money and good will.</description>
</item>
<item>
<title>The Forgiving User Interface</title>
<link>https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS</guid>
<pubDate>05 Apr 2011 19:30:30 GMT</pubDate>
<description>A user interface may seem obvious to the designer, but here are
some musings and examples that are not necessarily obvious. Or right.</description>
</item>
<item>
<title>Setting up RSS</title>
<link>https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS</guid>
<pubDate>03 Apr 2011 19:30:30 GMT</pubDate>
<description>After my post about withdrawing from Hacker News
someone asked if I could set up an RSS feed for my "blog."
Here are the first steps.</description>
</item>
<item>
<title>Withdrawing from Hacker News</title>
<link>https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS</guid>
<pubDate>03 Apr 2011 19:30:30 GMT</pubDate>
<description>For over 2 years I've been participating in a community
of programmers, entrepreneurs and people interested in similar idea,
but the time has come to move on. Here's a post explaining why.</description>
</item>
<item>
<title>Colin's Blog</title>
<link>https://www.solipsys.co.uk/new/ColinsBlog.html?RSS</link>
<guid isPermaLink="true">https://www.solipsys.co.uk/new/ColinsBlog.html?RSS</guid>
<pubDate>02 Apr 2011 19:30:30 GMT</pubDate>
<description>Re-starting my "blog" and trying to get the structure
to be more, well, "structured."</description>
</item>
</channel>
</rss>
Raw text
<?xml version="1.0" encoding="UTF-8" ?> <?xml-stylesheet type="text/css" href="https://www.solipsys.co.uk/rss.css" ?> <rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"> <channel> <atom:link href="https://www.solipsys.co.uk/rss.xml" rel="self" type="application/rss+xml" /> <title>Random Ramblings on Math, Juggling, Programming, Business, and stuff ...</title> <link>https://www.solipsys.co.uk/new/ColinsBlog.html</link> <description>Although titled "blog", this is more just random rants and streams of consciousness, touching on math, juggling, programming, user interaction, business, and anything that comes to mind. Read at your peril!</description> <item> <title>Tesseract Teaser</title> <link>http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS</link> <guid>http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS</guid> <pubDate>Thu, 18 Mar 2021 12:00:00 +0000</pubDate> <description> Not the four-dimensional cube sort of Tesseract, this is the Optical Character Recognition (OCR) "Tesseract", software that takes an image of some lettering and produces a plain text file containing the text. Or not. It's well-known that this is "Actually Quite Hard(tm)" and Tesseract does a pretty good job "Out of the Box" with very little messing about. But the other day I ran across something that has me utterly baffled. Let me share my bebafflement with you. </description> </item> <item> <title>More Mental Model Missteps</title> <link>http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS</link> <guid>http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS</guid> <pubDate>Sun, 31 Jan 2021 12:00:00 +0000</pubDate> <description> I mentioned when talking about an oddity in vim that the behaviour of the command "<n>J" didn't match my mental model. Sometimes software does that, it had behaviour that's totally reasonable when you think about it one way, but there's another way of thinking that causes you to be surprised. Here's another, as reported to me by a friend. </description> </item> <item> <title>An Oddity In VIM</title> <link>http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS</link> <guid>http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS</guid> <pubDate>Sun, 24 Jan 2021 12:00:00 +0000</pubDate> <description> I'm going to tell you a story, so this is quite a long post. If you'd like to skip the story get directly to the main point then feel free to do so. But if you're interested in the story, make sure you're sitting comfortably, and I'll tell you how I found an oddity in /vim./ </description> </item> <item> <title>Double Double Division Algorithm</title> <link>https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS</link> <guid>https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS</guid> <pubDate>Mon, 18 Jan 2021 12:00:00 +0000</pubDate> <description> For some of my readers, this will all be completely mysterious. But for others, part way through they will go "I recognise this!" So I'd really like to hear from you ... if you recognise this, at which point did the penny drop? I'd also really like to know if you think this is obvious, and possibly even if you've seen it before. Consider the following algorithm. I'll work through an example. I'll divide 450 by 23. </description> </item> <item> <title>Continuity Concerns</title> <link>https://www.solipsys.co.uk/new/ContinuityConcerns.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ContinuityConcerns.html?RSS</guid> <pubDate>Fri, 01 Jan 2021 12:00:00 +0000</pubDate> <description> Recently, Rachel and I have been watching the episodes of "The Adventures of Paddington Bear" that have been transmitted on broadcast TV here in the UK. It's not exactly gentle viewing, but Paddington is kind, helpful (or tries to be), and it always turns out well. Not very realistic, but if you watch with the right attitude, it is uplifting. Judge us if you will - we don't care. </description> </item> <item> <title>Counting Carbon Calories</title> <link>https://www.solipsys.co.uk/new/CountingCarbonCalories.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/CountingCarbonCalories.html?RSS</guid> <pubDate>Wed, 30 Dec 2020 12:00:00 +0000</pubDate> <description> "When you lose weight, where does it go?" An interesting question, and one where most people haven't thought about it, don't know, and really don't care. But when I was asked, it set in motion a train of thought. Follow along, and see if it makes sense. </description> </item> <item> <title>The Parity Of Zero</title> <link>https://www.solipsys.co.uk/new/TheParityOfZero.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheParityOfZero.html?RSS</guid> <pubDate>Mon, 21 Dec 2020 12:00:00 +0000</pubDate> <description> Before you react to the title, and before you guess where this is going and form a reaction, pause. I might not be about to say what you expect. Of course, I might, but I might not, and I'd ask you to wait a bit. </description> </item> <item> <title>When The Text And HTML Disagree</title> <link>https://www.solipsys.co.uk/new/WhenTheTextAndHtmlDisagree.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WhenTheTextAndHtmlDisagree.html?RSS</guid> <pubDate>Sat, 12 Dec 2020 12:00:00 +0000</pubDate> <description> Second Saturday of the month, and that means the Farmers' Market is on. Even in this second lockdown it will be running, with a one-way system and limited numbers permitted inside at any one time. But is it at the usual time? Let's check the email. Oh, I seem to have deleted it. Never mind, there will be a backup ... </description> </item> <item> <title>Recursion Revisited</title> <link>https://www.solipsys.co.uk/new/RecursionRevisited.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RecursionRevisited.html?RSS</guid> <pubDate>Wed, 14 Oct 2020 12:00:00 +0100</pubDate> <description> Some time ago I wrote a post on Thinking About Recursion, and more recently I wrote about a problem concerning the problem of the number of Vertices Required For Cycles. As it happens, the code for that problem is heavily recursive, and provides a great example of using recursion to solve a real problem. </description> </item> <item> <title>Vertices Required For Cycles</title> <link>https://www.solipsys.co.uk/new/VerticesRequiredForCycles.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/VerticesRequiredForCycles.html?RSS</guid> <pubDate>Fri, 02 Oct 2020 12:00:00 +0100</pubDate> <description> A few weeks ago Chris Purcell (@[email protected]) said: Let a_n be the size of the smallest graph with exactly n cycles. (The first few terms are: 3, 5, 4, 6, ...) The first few values are easy enough to compute, but it gets quite tricky quite quickly. How can one construct a (simple undirected) graph with exactly 5 cycles? </description> </item> <item> <title>Reflex Actions</title> <link>https://www.solipsys.co.uk/new/ReflexActions.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ReflexActions.html?RSS</guid> <pubDate>Mon, 24 Aug 2020 12:00:00 +0100</pubDate> <description> The machine wouldn't read my credit card. That's not uncommon ... sometimes the contacts on my card are dirty, sometimes the contacts on the machine are dirty ... no big deal. Just lick your thumb, rub the contacts, and try again. </description> </item> <item> <title>The Ballad Of Bunter</title> <link>https://www.solipsys.co.uk/new/TheBalladOfBunter.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheBalladOfBunter.html?RSS</guid> <pubDate>Sun, 26 Jul 2020 12:00:00 +0100</pubDate> <description> In late May it was becoming increasingly clear that Rachel's laptop was increasingly eccentric. A replacement would be needed, and while it wasn't yet urgent, we felt we should do something before it became so. And so the hunt began. </description> </item> <item> <title>Infinite Ramsey Theorem</title> <link>https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?RSS</guid> <pubDate>Sun, 12 Jul 2020 12:00:00 +0100</pubDate> <description> With the passing of Ron Graham a few people have been in touch with me to ask what "Ramsey Theory" is. So I've given a brief outline, and pointers in case people want to follow up. In truth, just stick "Ramsey Theory" into your favourite search engine and you'll get lots to follow up and chase down (as opposed, of course, to "follow down" or "chase up"). </description> </item> <item> <title>Signal Reflection</title> <link>https://www.solipsys.co.uk/new/SignalReflection.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SignalReflection.html?RSS</guid> <pubDate>Mon, 06 Jul 2020 12:00:00 +0100</pubDate> <description> Way back in the 70s when I was building logic circuits, I was warned repeatedly that I'd have to get a few things right, or risk "locking up" or "burning out" the CMOS chips I was using. The bogeyman was "Signal Reflection", but no one could tell me what it was, or why it was so bad. </description> </item> <item> <title>Analogies Not Considered Harmful</title> <link>https://www.solipsys.co.uk/new/AnalogiesNotConsideredHarmful.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnalogiesNotConsideredHarmful.html?RSS</guid> <pubDate>Sun, 05 Jul 2020 12:00:00 +0100</pubDate> <description> While I was writing my post on SignalReflection, I was given cause to reflect (pun intended ... sorry) on exactly the role and value of analogies in science, maths, and life in general. I've come to the conclusion that, like so many thing, analogies are neither good nor bad. They have their purpose, and each lies somewhere on a spectrum. </description> </item> <item> <title>Twitter Reply vs Quote Tweet</title> <link>https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS</guid> <pubDate>Wed, 17 Jun 2020 12:00:00 +0100</pubDate> <description> More than once now I've seen someone on social media using an option which has, for their purposes, been sub-optimal. In one case it led to a very unpleasant exchange, purely because one person assumed an implication that simply wasn't intended. </description> </item> <item> <title>Proofs To Make You Go WOW</title> <link>https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS</guid> <pubDate>Tue, 16 Jun 2020 12:00:00 +0100</pubDate> <description> For those of us who love maths, it's sad to see how many people hate it, or have a phobia of it, or proudly announce "I was never very good at maths at school." The question we often counter with is "Would you be so proud of being unable to read?" </description> </item> <item> <title>Laptop Purchase Advice Received</title> <link>https://www.solipsys.co.uk/new/LaptopPurchaseAdviceReceived.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/LaptopPurchaseAdviceReceived.html?RSS</guid> <pubDate>Mon, 08 Jun 2020 12:00:00 +0100</pubDate> <description> Rachel's laptop has become ... eccentric. Like a toddler, or an aging relative, who won't get up in the morning, won't go to bed at night, and won't play nicely with others, I'm afraid The Admirable Crichton has taken to not starting up properly, not shutting down properly, and occasionally just refusing to connect either over ethernet, or Wi-Fi. </description> </item> <item> <title>Blow Up Your Ability Balloon</title> <link>https://www.solipsys.co.uk/new/BlowUpYourAbilityBalloon.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BlowUpYourAbilityBalloon.html?RSS</guid> <pubDate>Fri, 29 May 2020 12:00:00 +0100</pubDate> <description> It's pretty clear to most of us that skills unpractised are eventually lost. Anything at the limits of our abilities need to be exercised regularly to avoid having them waste away. </description> </item> <item> <title>A Factlet For All</title> <link>https://www.solipsys.co.uk/new/AFactletForAll.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AFactletForAll.html?RSS</guid> <pubDate>Wed, 27 May 2020 12:00:00 +0100</pubDate> <description> More and more often I hear people saying and see people writing "factoid", by which they mean "A Small Fact". But is that right? </description> </item> <item> <title>Anatomy of a Hit</title> <link>https://www.solipsys.co.uk/new/AnatomyOfAHit.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnatomyOfAHit.html?RSS</guid> <pubDate>Fri, 22 May 2020 12:00:00 +0100</pubDate> <description> Recently I was *very* surprised when a post got significant traction on a forum I visit, and I set up some tracking to see what happened ... this is the report. </description> </item> <item> <title>Sell Yourself, Sell Your Work</title> <link>https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS</guid> <pubDate>Wed, 20 May 2020 12:00:00 +0100</pubDate> <description> Doing technically brilliant work may be enough for your personal gratification, but you should never think it's enough. If you lock yourself in a room and do the most marvellous work but don't tell anyone, then no one will know, no one will benefit, and the work will be lost. You may as well not have bothered. For the world to benefit from your work, and therefore for you to benefit fully from your work, you have to make it known. </description> </item> <item> <title>All The Letters</title> <link>https://www.solipsys.co.uk/new/AllTheLetters.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AllTheLetters.html?RSS</guid> <pubDate>Mon, 18 May 2020 12:00:00 +0100</pubDate> <description> Most people are aware of the phrase: "The quick brown fox jumped over the lazy dog." But many, perhaps most, don't realise (a) Why it's interesting, and (b) It's wrong. </description> </item> <item> <title>Being Slow To Criticise</title> <link>https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS</guid> <pubDate>Sat, 09 May 2020 12:00:00 +0100</pubDate> <description> Software that deliberately kills the servers it is monitoring is an interesting idea. A story I read recently told of a situation where the programmer and/or engineer involved wasn't able to fix the real, underlying problem, so an overlay solution was devised that (a) worked, and (b) was feasible. This post is not about that story. This post is about a comment made by one of the readers in the forum where I saw it. </description> </item> <item> <title>State Machine In Real Life</title> <link>https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS</guid> <pubDate>Fri, 01 May 2020 12:00:00 +0100</pubDate> <description> In April 2016 my wife and I were travelling. We stayed in a reasonably comfortable but very inexpensive hotel, and meals weren't provided. As it happened, across the way was a large retail park with a large well-known supermarket chain, and they had a restaurant. We ate there four or five times, and I noticed that they were using a finite state machine. </description> </item> <item> <title>Coxeter Once Nerd-Sniped Conway</title> <link>https://www.solipsys.co.uk/new/CoxeterOnceNerdSnipedConway.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/CoxeterOnceNerdSnipedConway.html?RSS</guid> <pubDate>Tue, 28 Apr 2020 12:00:00 +0100</pubDate> <description> I wrote earlier about John Conway's passing and some of my memories of him. I also mentioned there how he was once nerd-sniped by Coxeter. John didn't call it "nerd sniping" - he didn't know the term - but when I explained it, he was delighted, as it exactly matched his experience. So here is the story, as told to me by Conway at MathFest, 2015 ... </description> </item> <item> <title>Not Always Your Fault</title> <link>https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS</guid> <pubDate>Tue, 21 Apr 2020 12:00:00 +0100</pubDate> <description> "I must have done something wrong." I hear this a lot when people are using computer interfaces. These days that's often websites, often for large corporations, and often trying to accomplish something one feels should be simple. And yet in all honesty, it's not always your fault. </description> </item> <item> <title>Remembering Conway</title> <link>https://www.solipsys.co.uk/new/RememberingConway.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RememberingConway.html?RSS</guid> <pubDate>Sun, 12 Apr 2020 12:00:00 +0100</pubDate> <description> John Conway has left us. </description> </item> <item> <title>Perception of Space</title> <link>https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS</guid> <pubDate>Fri, 03 Apr 2020 08:30:00 +0100</pubDate> <description> During this time of lockdown and/or self-isolation, it's tempting for those of us content with our own company to sit tight indoors and wait it out. But I'm reminding of some stories told to me by my friend Laurie Brokenshire. </description> </item> <item> <title>Parallelogram Puzzle</title> <link>https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS</guid> <pubDate>Sat, 21 Mar 2020 12:00:00 +0100</pubDate> <description> A while ago Ed Southall asked a great question on Twitter about joining dots to make a parallelogram. Several people chimed in quite quickly, others took a little longer. Some were happy to have found any solution at all, others were happy to have found two solutions, and then quite a few people started to claim that there were, in fact, exactly two solutions. That made me wonder ... </description> </item> <item> <title>Back Of The Envelope COVID19</title> <link>https://www.solipsys.co.uk/new/BackOfTheEnvelopeCOVID19.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BackOfTheEnvelopeCOVID19.html?RSS</guid> <pubDate>Thu, 12 Mar 2020 12:00:00 +0100</pubDate> <description> I did a rough "Back of the Envelope" calculation about COVID-19. Here are my rough-and-ready results. </description> </item> <item> <title>A Point Against The Axiom Of Choice</title> <link>https://www.solipsys.co.uk/new/APointAgainstTheAxiomOfChoice.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/APointAgainstTheAxiomOfChoice.html?RSS</guid> <pubDate>Mon, 09 Mar 2020 12:00:00 +0100</pubDate> <description> Last time we saw that the Axiom Of Choice seems so reasonable. It's basically saying that that the product of non-empty sets is always non-empty, and that seems obvious. But in this post we look at one of the implications of accepting the Axiom Of Choice, and wonder if perhaps it's not so obvious after all. </description> </item> <item> <title>In Defense Of The Axiom Of Choice</title> <link>https://www.solipsys.co.uk/new/InDefenseOfTheAxiomOfChoice.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/InDefenseOfTheAxiomOfChoice.html?RSS</guid> <pubDate>Wed, 26 Feb 2020 12:00:00 +0100</pubDate> <description> The first of a two-parter, here we provide a reason to accept that the Axiom of Choice is reasonable, and should be used. </description> </item> <item> <title>Journeying Home Through Storm Dennis</title> <link>https://www.solipsys.co.uk/new/JourneyingHomeThroughStormDennis.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/JourneyingHomeThroughStormDennis.html?RSS</guid> <pubDate>Fri, 21 Feb 2020 12:00:00 +0100</pubDate> <description> Saturday, Feb 15th, 2020, and I'd delivered a Maths Masterclass just north of Cardiff in South Wales. I'd packed my things and was offered a lift to the station, which was gratefully accepted. It was raining, although not torrentially, but Storm Dennis was due to hit, and we were feeling the initial effects. This is the story of what happened next ... </description> </item> <item> <title>Earth Radius - Refined</title> <link>https://www.solipsys.co.uk/new/EarthRadiusRefined.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/EarthRadiusRefined.html?RSS</guid> <pubDate>Sun, 09 Feb 2020 12:00:00 +0100</pubDate> <description> Previously we looked at computing the radius of the Earth by watching the Sun coming down a building at sunrise, but there's been some question about the answer, so now let's do it "properly". </description> </item> <item> <title>Volume Of A Sphere</title> <link>https://www.solipsys.co.uk/new/VolumeOfASphere.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/VolumeOfASphere.html?RSS</guid> <pubDate>Sun, 05 Jan 2020 12:00:00 +0100</pubDate> <description> Fermat's Library on Twitter tweeted "Euler presented in his textbooks the exact formula for the volume of a sphere" and there followed an image with the actual formula. Over 12 thousand people "Liked" the tweet, but someone said: "How would you go about proving this one?" So here is how we can prove it. </description> </item> <item> <title>Big-Oh and Relations</title> <link>https://www.solipsys.co.uk/new/BigOhAndRelations.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BigOhAndRelations.html?RSS</guid> <pubDate>Wed, 04 Dec 2019 12:00:00 GMT</pubDate> <description> In an earlier post we saw that the function f(n)=n dominates g(n)=n-ln(n), but that's no surprise. What does come as a surprise is that g dominates f. So even though for any value of n greater than 2 we already have f(n)>g(n), still we say that g dominates f. That feels *very* unexpected, and as a result you might question the value of the concept of "dominates", so we'll pause and take a moment to see if we can get a handle on what's going on. </description> </item> <item> <title>Mathematical Relations</title> <link>https://www.solipsys.co.uk/new/MathematicalRelations.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MathematicalRelations.html?RSS</guid> <pubDate>Fri, 22 Nov 2019 12:00:00 +0000</pubDate> <description> Ubiquitous in mathematics is the concept of comparing things, and examining the relationships between them. Since we do that all the time and everywhere, it's worth having a look at the concept of a "Relation" in an abstract sense to try to tease out the common themes. </description> </item> <item> <title>Introducing Big-Oh</title> <link>https://www.solipsys.co.uk/new/IntroducingBigOh.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/IntroducingBigOh.html?RSS</guid> <pubDate>Mon, 28 Oct 2019 12:00:00 +0000</pubDate> <description> Last time I said: "If you do this for two different algorithms and the results are, apart from a scaling factor, pretty much the same, then the algorithms are said to have the same 'Time Complexity'." Now we'll look at that more carefully. </description> </item> <item> <title>Constant Differences</title> <link>https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS</guid> <pubDate>Sat, 12 Oct 2019 12:00:00 +0100</pubDate> <description> It's time to get our hands dirty. In this post we look carefully at a particular algorithm, and think hard about how long it takes for a given instance. From that we find an important concept emerging. </description> </item> <item> <title>Algorithms and Sizes of Instances</title> <link>https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS</guid> <pubDate>Mon, 07 Oct 2019 12:00:00 +0100</pubDate> <description> We've looked at what we mean by a "Problem", and by an "Instance" of a problem. For each challenge, we need a way of working out what the response should be. Such a method is called an "Algorithm" for that problem, so let's think carefully about algorithms. </description> </item> <item> <title>Introducing Time Complexity</title> <link>https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS</guid> <pubDate>Mon, 30 Sep 2019 12:00:00 +0100</pubDate> <description> Recently I discovered that a friend of mine, an outstandingly good mathematician, didn't know anything about how the whole "Time Complexity" thing worked, and didn't understand about $P$ versus $NP$ and similar concepts. So here is an outline of the ideas in what I hope will be bite-sized, accessible chunks. </description> </item> <item> <title>The Linear Frog</title> <link>https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS</guid> <pubDate>Sat, 14 Sep 2019 12:00:00 +0100</pubDate> <description> I was given a problem recently, and I was really pleased to get the solution. I wonder if you can (a) solve it, and (b) tell me where it comes from. I've not been able to track it down at all. It's the problem of the Linear Baby Frog. </description> </item> <item> <title>Seventy Versus One Hundred Revisited</title> <link>https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS</guid> <pubDate>Sat, 24 Aug 2019 12:00:00 +0100</pubDate> <description> Earlier we looked at the situation of two identical cars, one doing 70, the other doing 100, slamming on their brakes at exactly the same location to avoid an obstruction. The model we used was that the two cars shed energy at a rate proportional to distance. But what if the rate energy is shed is proportional not to distance, but to time? </description> </item> <item> <title>How The Farrago Works</title> <link>https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS</guid> <pubDate>Sat, 17 Aug 2019 12:00:00 +0100</pubDate> <description> Some time ago I was asked about the way this website works, and as I started to explain, I realised just how much there was going on and how complicated it seemed. But they seemed to think it was neat and elegant, so I thought I'd write it up. </description> </item> <item> <title>Seventy Versus One Hundred</title> <link>https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS</guid> <pubDate>Mon, 05 Aug 2019 12:00:00 +0100</pubDate> <description> Supposed two identical cars are traveling along the same straight road, with one traveling at 70 kilometres an hour, the other at 100 kilometres an hour. Just as the faster car draws roughly level with the slower, they both see an obstruction in the road ahead, and (as luck would have it) at the exact same moment, exactly when they are level with each other, they both slam on the brakes. </description> </item> <item> <title>Powers Of Two In Lex Order</title> <link>https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS</guid> <pubDate>Mon, 22 Jul 2019 12:00:00 +0100</pubDate> <description> Recently I was sent a lovely little twitchet, so I thought I'd share it for people to think about. No answers provided. Firstly, let's do something odd with the powers of two ... </description> </item> <item> <title>Emerging e Expanded</title> <link>https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS</guid> <pubDate>Tue, 16 Jul 2019 12:00:00 +0100</pubDate> <description> Expanding on the post from earlier, and with more detail ... put "10" into a calculator and take the square root. Then again, then again, then again, and so on. Fairly quickly we get a number that's marginally larger than 1, so we can think of it as 1 plus small rubbish. But thinking carefully about the rubbish leads to some interesting results. </description> </item> <item> <title>Rage Inducing System Implementation</title> <link>https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS</guid> <pubDate>Sat, 13 Jul 2019 12:00:00 +0100</pubDate> <description> I'm about to go on an extended business trip, so I'm making note of broadcast TV programs that I want to record, and making sure there is enough space on the recorder. I have a large external HDD attached, so I've been transferring programs to that to make space on the internal HDD. All was going well. There's still 240 hours of space on the external HDD, so no problems anticipated. What could possibly go wrong? </description> </item> <item> <title>The Book Is Not Always Right</title> <link>https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS</guid> <pubDate>Sat, 06 Jul 2019 12:00:00 +0100</pubDate> <description> Recently someone tweeted a picture of a page from a book. It seems to be some sort a book about maths aimed at students, but in one simple paragraph there was just so much wrong, it attracted many comments from many of my friends and colleagues. </description> </item> <item> <title>Emerging e ...</title> <link>https://www.solipsys.co.uk/new/EmergingE.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/EmergingE.html?RSS</guid> <pubDate>Sun, 09 Jun 2019 12:00:00 +0100</pubDate> <description> Start with 10, and square root many times over. After a while you get 1+(rubbish). Taking the square root of that halves the rubbish, so we can deduce that when epsilon is small, 10 to the power of epsilon is 1 plus some constant times epsilon. Starting with 5 instead of 10 you get a different constant, so we have a function where you start with a value, successively take the square root, compute the constant, and that's the value of the function. Looking at this function, I have questions ... </description> </item> <item> <title>Impossible To Translate</title> <link>https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS</guid> <pubDate>Tue, 04 Jun 2019 12:00:00 +0100</pubDate> <description> Some time ago, while on a business trip to Spain, I was asked a question that turns out to be impossible to translate into English. </description> </item> <item> <title>Waiting In Vain</title> <link>https://www.solipsys.co.uk/new/WaitingInVain.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WaitingInVain.html?RSS</guid> <pubDate>Wed, 29 May 2019 12:00:00 +0100</pubDate> <description> Over the past few years I've occasionally been contacted by my ISP to say that one of my scripts had gone rogue and was using 100% CPU, and would it be OK to kill it. This has always been a surprise to me because I'm usually pretty careful about my code, especially when it's running "out there" on someone else's hardware. </description> </item> <item> <title>Non-Repeating Decimals</title> <link>https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS</guid> <pubDate>Fri, 24 May 2019 12:00:00 +0100</pubDate> <description> In the previous post we talked about repeating decimals, and showed that every (eventually) repeating decimal is a rational number, and that every rational number has a (possibly trivial) (eventually) repeating decimal representation. Now we'll look at some cases of decimals that don't repeat, and hence are irrational, and vice versa. </description> </item> <item> <title>Rational Repeats</title> <link>https://www.solipsys.co.uk/new/RationalRepeats.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RationalRepeats.html?RSS</guid> <pubDate>Thu, 09 May 2019 12:00:00 +0100</pubDate> <description> Recently on-line I saw someone talking about the decimal expansion of pi, and they said: "I'm told pi goes on forever and never repeats, I can't see how that can be proved." I didn't try to explain how pi never repeats, but I did have a go at explaining some of the ideas. </description> </item> <item> <title>Why is it Lovely</title> <link>https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS</guid> <pubDate>Sun, 05 May 2019 12:00:00 +0100</pubDate> <description> Recently on one of my "social network feeds" I saw a post saying: "X% of Y equals Y% of X." I commented that this was lovely, and someone asked "Why?" </description> </item> <item> <title>Compiling Crypto-Connections</title> <link>https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS</guid> <pubDate>Sat, 27 Apr 2019 12:00:00 +0100</pubDate> <description> Having given the maths club talk last Saturday (which went very well) I was left with the preparative work that I'd done. That consists of lists of concepts, people, algorithms, cryptosystems, and some of the connections between them. What to do with it ... </description> </item> <item> <title>Exploring Connections Between Crypto Systems</title> <link>https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS</guid> <pubDate>Sat, 20 Apr 2019 12:00:00 +0100</pubDate> <description> I'm giving a talk for the Liverpool Maths Club this Saturday, April 23rd, 2019. I do this roughly twice a year, and it's always a real challenge - the ages range between 13 and 18, and while some of the students have been coming for years, for others it might be their first time. So whatever the topic might be, it needs to be engaging, accessible, and challenging, all at the same time. </description> </item> <item> <title>Meeting Elwyn Berlekamp</title> <link>https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS</guid> <pubDate>Sat, 13 Apr 2019 12:00:00 +0100</pubDate> <description> I remember meeting Elwyn Berlekamp. </description> </item> <item> <title>Root Cause Analysis and the Photocopier Question</title> <link>https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS</guid> <pubDate>Thu, 11 Apr 2019 12:00:00 +0100</pubDate> <description> "Root Cause Analysis" is complex, involved, and requires both tenacity and creativity. When there's a problem, often the cause isn't a simple, single thing, it's often a collection of things, and each of those might not be easily characterised. Even so, it's a crucial exercise in many technology based industries and activities. So in this post I want to talk about my most recent brush with the challenges of performing RCA, and even of getting other people to see that it's there to be done. </description> </item> <item> <title>The Up/Down Tides</title> <link>https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS</guid> <pubDate>Tue, 26 Mar 2019 12:00:00 GMT</pubDate> <description> So while in orbit at about the altitude of the ISS we've looked at throwing a ball sideways, and we've looked at throwing a ball forwards or backwards. What happens if we throw the ball up? Or down? Is that different? Do we finally have the ball travel away in a straight line at a constant speed? What new horrors lie in store? </description> </item> <item> <title>The Fore/Aft Tide</title> <link>https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS</guid> <pubDate>Tue, 19 Mar 2019 12:00:00 GMT</pubDate> <description> You're in orbit around the Earth with the International Space Station, and you have a juggling ball. (Don't ask). You hold it next to your helmet and release it, and it just stays there, apparently floating. Now gently push the ball ahead of you in orbit. In effect you are throwing the ball away from you, and the expectation is that it will drift away from you in a straight line at a constant speed. But it doesn't. </description> </item> <item> <title>The Sideways Tide</title> <link>https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS</guid> <pubDate>Tue, 12 Mar 2019 12:00:00 GMT</pubDate> <description> Stand outside the International Space Station and hold a juggling ball right by your helmet. Let it go, and it will stay there. Now give it a gentle push "sideways". As you will probably know, it then travels away from you in a straight line at a constant speed, because that's what happens in zero gravity. But it doesn't ... </description> </item> <item> <title>Wrapping Up Wrapping Up The Earth</title> <link>https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS</guid> <pubDate>Tue, 05 Mar 2019 12:00:00 GMT</pubDate> <description> We're coming to the end of this series. Our friend has purchased too much rope, too little rope, too much miraculous wrapping sheet, and now, finally, we come to the question of too little. But first, let's look at the different "rope" scenarios, and see what happens in each of the analogous "sheet" cases. Then we'll see how it all comes together. </description> </item> <item> <title>The *Other* Wrapping The Earth Problem</title> <link>https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS</guid> <pubDate>Tue, 26 Feb 2019 12:00:00 GMT</pubDate> <description> Having gone around the world to wrap it, in truth our friend is too tired (or too lazy) to prop up the wrapping everywhere. So just as in the Other Rope Around the Earth problem, instead we look at propping it up in just one place. We need to take up one million square metres of excess. How high will that tent pole have to be? </description> </item> <item> <title>The "Wrapping The Earth" Problem</title> <link>https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS</guid> <pubDate>Tue, 19 Feb 2019 12:00:00 GMT</pubDate> <description> Our friend once again has too much to drink, and once again indulges in a little late night internet shopping. This time, however, it's fueled by curiousity, having discovered that there is a material that is infinitely stretchy, but which always retains its area. So while you can stretch it one direction, it will keep its area by shrinking in another direction. What if we try to wrap the Earth ... </description> </item> <item> <title>The Ring Of Steel</title> <link>https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS</guid> <pubDate>Wed, 13 Feb 2019 12:00:00 GMT</pubDate> <description> Our friend has encircled the Earth with Rope, discovered that it's 6 metres longer than needed, so expanded the circle by 0.95 metres to take up the slack. Thus we have a ring of rope around the Earth at height just about 1 metre. But overnight, somehow, magically, the rope gets converted to steel! Then, over breakfast, a slight Earth tremor gently rattles the props, and they all fall down, leaving the ring of steel completely unsupported. What happens next? </description> </item> <item> <title>Rounding Up The Ropes</title> <link>https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS</guid> <pubDate>Sun, 10 Feb 2019 12:00:00 GMT</pubDate> <description> We've seen the $(Other)^k$ rope around the Earth for $k=0, 1, 2,$ and $3$. In this post we'll look at $k=4$, but we'll start with a "heads up" for where we'll be going next. </description> </item> <item> <title>The Other Other Other Rope Around The Earth</title> <link>https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS</guid> <pubDate>Tue, 05 Feb 2019 12:00:00 GMT</pubDate> <description> So we have the Rope Around the Earth problem, the Other Rope Around the Earth problem, and the Other Other Rope Around the Earth. You might think that was the end of it, but no, there is more! </description> </item> <item> <title>Rope Around The Earth - Refined</title> <link>https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS</guid> <pubDate>Tue, 22 Jan 2019 12:00:00 GMT</pubDate> <description> As previously mentioned, the Rope Around the Earth problem is a lovely one, and everyone should know it. But even if you do, there's still a nice added extra. In this post we'll have a look at that. </description> </item> <item> <title>The Other Rope Around The Earth</title> <link>https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS</guid> <pubDate>Thu, 17 Jan 2019 12:00:00 GMT</pubDate> <description> The well-known "Rope Around the Earth" problem is lovely, and, as I say, well known. But some time ago David Bedford mentioned *another* rope around the Earth problem. A *different* rope around the Earth problem. And it goes like this. </description> </item> <item> <title>Elementary Estimates</title> <link>https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS</guid> <pubDate>Tue, 08 Jan 2019 20:00:00 GMT</pubDate> <description> Every now and again as I'm doing various estimates or calculations I use an approximation, and a few days ago it was brought home to me how much I rely on these, and how few people know them. So I thought I'd gather some of them together in one place to be a reference. </description> </item> <item> <title>Latitude Correction</title> <link>https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS</guid> <pubDate>Tue, 01 Jan 2019 20:00:00 GMT</pubDate> <description> Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator. But what if you're not at the Equator? What then? </description> </item> <item> <title>Just Give Me The Answer</title> <link>https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS</guid> <pubDate>Sun, 07 Oct 2018 20:00:00 GMT</pubDate> <description> A while ago I saw an exchange on a programming forum I visit on occasion. A poster had asked a question that at first sight (and in all honesty, subsequent examination) appeared pretty simple. The poster claimed to have tried everything they could think of, that nothing worked, and they'd appreciate any help. </description> </item> <item> <title>More Musing On Pollard Rho</title> <link>https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS</guid> <pubDate>Wed, 19 Sep 2018 20:00:00 GMT</pubDate> <description> After my previous post I started to explore a little more about how the function in Pollard Rho affects what's going on. As yet I've not come to any conclusions, and I'm currently deep in the "I'm confused" stage of the exploration. I'm sure there are other people know all this, but I don't know who they are, and haven't been able to find any write-ups, so I'll just carry on. </description> </item> <item> <title>Idle Thoughts About Pollard Rho</title> <link>https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS</guid> <pubDate>Mon, 10 Sep 2018 20:00:00 GMT</pubDate> <description> I've had an idle thought about the Pollard Rho method of integer factoring. To start with, let's sketch how it works. </description> </item> <item> <title>When Optimising Code, Measure</title> <link>https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS</guid> <pubDate>Tue, 04 Sep 2018 20:00:00 GMT</pubDate> <description> This is a truism that lots of people quote, but it can be hard to remember, especially in the heat of battle (as it were). Rather fortunately it came to mind just when needed, as I found something completely unexpected. </description> </item> <item> <title>A Dog Called Mixture</title> <link>https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS</guid> <pubDate>Mon, 27 Aug 2018 12:00:00 GMT</pubDate> <description> Some considerable time ago I was giving some talks at a school, and my wife and I were kindly hosted at the home of the Headmaster and his family. And his menagerie, as it turned out. </description> </item> <item> <title>Another PayPal Scam</title> <link>https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS</guid> <pubDate>Fri, 03 Aug 2018 12:00:00 GMT</pubDate> <description> Received as part of the newsletter of a publishing company : We've been living in interesting times at Wildside Press since our last newsletter. Our PayPal account was VERY creatively hacked, and we briefly lost about $15,000 of the money we'd been saving up for royalty payments to authors. </description> </item> <item> <title>Why Top Posting Has Won</title> <link>https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS</guid> <pubDate>Wed, 13 Jun 2018 14:20:00 GMT</pubDate> <description> I've recently realised that, in my head, there's a connection between top-posting in email and washing the dishes. Stay with me, I'll see if I can make the connection for you. </description> </item> <item> <title>Archimedes' "Hat Box" Theorem</title> <link>https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS</guid> <pubDate>Wed, 06 Jun 2018 11:50:00 GMT</pubDate> <description> Take a sphere, and encase it in a cylinder. Take a horizontal slice between two planes. You end up with a narrow cylinder, and a smaller, "slopey" cylinder. The Archimedes Hat-Box Theorem says these two cylinders have the same surface area. In fact the theorem says that the surface areas are the same no matter how thick the slice is, so as a consequence we can take a "slice" that captures the entire cylinder and sphere, and that means that the surface area of the curved surface of the cylinder is exactly the same as the surface area of the sphere. </description> </item> <item> <title>Considering a Sphere</title> <link>https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS</guid> <pubDate>Tue, 05 Jun 2018 14:56:00 GMT</pubDate> <description> Recently someone posted an animation of a way to visualise the area of a circle. Someone else then asked if there was a similar visualisation of the volume of a sphere, or the surface area of a sphere, and that started me thinking. </description> </item> <item> <title>To Link Or Not To Link</title> <link>https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS</guid> <pubDate>Thu, 17 May 2018 14:04:00 GMT</pubDate> <description> Over the past few years I've noticed a rise in a particular type of spam that I'm receiving. It takes the form of an email like this ... </description> </item> <item> <title>Generic Advice For Writing A Thesis</title> <link>https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS</guid> <pubDate>Mon, 07 May 2018 20:30:00 GMT</pubDate> <description> I have some generic thesis-writing advice to supplement that given by your supervisor, but only if it's welcome. </description> </item> <item> <title>Just Teach My Child The Maths</title> <link>https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS</guid> <pubDate>Sun, 18 Feb 2018 09:15:01 GMT</pubDate> <description> It is astounding to me that mathematics - of all school subjects - elicits such potent emotional reaction when "reform" is in the air. </description> </item> <item> <title>Not A Spectator Sport</title> <link>https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS</guid> <pubDate>Wed, 13 Dec 2017 13:00:00 GMT</pubDate> <description> One of my university lecturers gave what we all thought were dreadful lectures. Muddled, unclear, chaotic, with no discernible thread. It took ages to reconstruct and rework the material to a point where we could attack the problems and old exam questions. </description> </item> <item> <title>Left Truncatable Prime</title> <link>https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS</guid> <pubDate>Sat, 21 Oct 2017 15:00:00 GMT</pubDate> <description> Recently Maths Inspiration produced some pencils with a fantastic idea. Yes, their name is on it, yes, it has a slightly cheesy catch-phrase, But then there is something really clever. </description> </item> <item> <title>The Doctor and the Lawyer</title> <link>https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS</guid> <pubDate>Sun, 15 Oct 2017 14:00:00 GMT</pubDate> <description> A doctor and a lawyer were chatting at a party when someone approached the doctor. They wanted advice, and started to describe their symptoms when the doctor interrupted and said "It might be better to make an appointment so we can talk in private." </description> </item> <item> <title>Four Points Two Distances Proof</title> <link>https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS</guid> <pubDate>Tue, 03 Oct 2017 11:25:00 GMT</pubDate> <description> The Four Points Puzzle challenge that Peter Winkler set me was this: "Find all configurations of four (distinct) points in the plane that determine exactly two distances." He then added: "Nearly everyone misses at least one, and every solution has been missed by at least one person." So the challenge isn't to find all the configurations so much as to be able to prove that you have them all. It's the proof that matters. Here's mine. </description> </item> <item> <title>Meeting Ron Graham</title> <link>https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS</guid> <pubDate>Sun, 01 Oct 2017 18:14:00 GMT</pubDate> <description> I was a lowly PhD student when I first met Ron Graham. It was at a conference, and there was something I wanted to show him. In my mind it was pretty much guaranteed that he would be interested, but he was (and still is!) extremely well known, extremely eminent, and extremely popular. As a result he is extremely busy, and somewhat besieged with people, all wanting a piece of his time. How could I possibly attract and hold his attention long enough to get him interested? So I hatched a plan. </description> </item> <item> <title>Napkin Ring Vs Spherical Cap</title> <link>https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS</guid> <pubDate>Thu, 28 Sep 2017 08:26:00 GMT</pubDate> <description> Many years ago I was at a semi-social gathering and a somewhat odd incident occurred. Over the course of conversation it emerged that I was studying maths, and one chap, at one point, turned to me and said: "So, do you like puzzles, then?" Not especially on my guard I said yes, and he went on to say something like this: "OK, I'll give you a puzzle ..." </description> </item> <item> <title>The Four Points Puzzle</title> <link>https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS</guid> <pubDate>Tue, 26 Sep 2017 16:43:00 GMT</pubDate> <description> At the MOVES conference in New York in August I was lucky enough to spend some time with Peter Winkler, mathematician, puzzle master extraordinaire, and author of "Mathematical Puzzles: A Connoisseur's Collection". As we talked about many things he set me this puzzle: "Find all configurations of four (distinct) points in the plane that determine exactly two distances." </description> </item> <item> <title>Radius of the Earth - Part Two</title> <link>https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS</guid> <pubDate>Sat, 16 Sep 2017 08:30:00 GMT</pubDate> <description> Some nine and a bit weeks ago I posted about a method of calculating (or estimating) The Radius Of The Earth using a stopwatch and watching the Sun at sunrise (or sunset). When "Mike the Sundial" told me the idea I was quite simply stunned at the simplicity and elegance. Colin Beveridge took up the challenge. But when I read his calculation I was interested to see just how different his take was from mine. </description> </item> <item> <title>Grep Timing Anomaly</title> <link>https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS</guid> <pubDate>Fri, 28 Jul 2017 08:30:00 GMT</pubDate> <description> Some considerable time ago - long enough that probably the details are no longer relevant, or accurate - I got seriously fed up with the spam filtering on my email service. There were so many false positives that I had to wade through the spam bin every day, pulling out obviously good emails that needed attention. It got so that it cost me more time to have it running. </description> </item> <item> <title>The Radius of the Earth</title> <link>https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS</guid> <pubDate>Wed, 12 Jul 2017 08:30:00 GMT</pubDate> <description> The talk/workshop I give about computing the distance to the Moon uses, it claims, nothing more than a pendulum and a stopwatch. And while it's sort of true that it uses nothing else, it's not really true, because it also uses the period of the Moon, and the size of the Earth. Now it might be possible to persuade you that it's OK to use the period of the Moon, since you can simply look out the window and measure that for yourself, but to use the size of the Earth seems a bit of a stretch. Surely there is no way to compute that from your back garden. But there is. </description> </item> <item> <title>This Works to Cure My Hiccoughs</title> <link>https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS</guid> <pubDate>Sun, 09 Jul 2017 18:30:00 GMT</pubDate> <description> It's many years ago that I was told about this trick. People rarely believe me, but it honestly works for me, and it has worked for others. So I thought I'd write it up. </description> </item> <item> <title>Perhaps We Saved One</title> <link>https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS</guid> <pubDate>Sun, 02 Jul 2017 19:50:00 GMT</pubDate> <description> Many years ago a good friend of mine, Bill Mullarkey, organised a "Science and Technology Extravaganza" in Wigan. It was a fabulous two-day event with hundreds of teenagers and adults in attendance. The buzz of excitement was huge, and it was an honour to be part of the whole thing. </description> </item> <item> <title>Thinking About Mastodon</title> <link>https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS</guid> <pubDate>Sun, 18 Jun 2017 17:50:00 GMT</pubDate> <description> Some people are describing Mastodon as a decentralised Twitter, but that's rather misleading. It's better not to try to understand it like that. Instead, here's my way of thinking. </description> </item> <item> <title>Disappearing Trains On Virgin</title> <link>https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS</guid> <pubDate>Sat, 17 Jun 2017 18:58:00 GMT</pubDate> <description> I'm planning a significant set of travels, so as always, I started by sketching an idea of what might be possible, then confirmed the various parts on the usual National Rail web site. Having picked my trains, I then went to the Virgin Trains web site to actually buy the tickets. This time there was a surprise awating me. </description> </item> <item> <title>The Independence Game</title> <link>https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS</guid> <pubDate>Tue, 18 Apr 2017 11:00:00 GMT</pubDate> <description> A few weeks ago I was honoured to be able to attend the gathering at the Royal Society where Rob Eastaway was given his Christopher Zeeman medal. He gave an excellent talk, full of interest and humour, the only downside being that he made us play a game. Although at the time Rob called it "Avoid the Neighbours", I now think of it simply as "Rob's Dots". He said he didn't know how to play it optimally beyond 11 points, so I thought I'd have a go. </description> </item> <item> <title>One Of My Favourite Puzzles</title> <link>https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS</guid> <pubDate>Thu, 06 Apr 2017 20:00:00 GMT</pubDate> <description> It is impossible to choose a single problem as my favourite. There are so many, each with their own attractions, each with their own charms. But there is one that I solved quickly, and then found that I had only just started to scratch the surface. </description> </item> <item> <title>Thinking About Recursion</title> <link>https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS</guid> <pubDate>Wed, 08 Mar 2017 12:00:00 GMT</pubDate> <description> It has been said that there are two hard problems in computing: Cache Invalidation, Naming Things, and Off-By-One Errors. Well, that's certainly true when you get into the practice of programming. But on the way to becoming a programmer we find that there are multiple levels of enlightenment. </description> </item> <item> <title>Memorising The Tube</title> <link>https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS</guid> <pubDate>Sat, 03 Dec 2016 19:40:00 GMT</pubDate> <description> Recently I memorised the period table of elements. When I tell people that, the response has generally been a moderate pause, followed by a rather puzzled - "Why?" So I thought I'd explain. </description> </item> <item> <title>Spikey Spheres</title> <link>https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS</guid> <pubDate>Sun, 20 Nov 2016 20:00:00 GMT</pubDate> <description> I've recently been working on an optimisation problem, and I've come to realise that I can consider it as wandering around on a smooth landscape in 1800 dimensions. The problem is that while the error function may be "smooth," your intuition of what this means is wrong. </description> </item> <item> <title>Surprisingly Quick</title> <link>https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS</guid> <pubDate>Thu, 06 Oct 2016 20:00:00 GMT</pubDate> <description> In the 1990s I had a job at Liverpool University doing research into how we might make it possible for non-computing specialists to use paraallel computers. Even today, over 20 years later, this is still an unsolved problem, and the machines now are designed to be easier to use. The machine I was using was a Parsys SuperNode with 96 T800 transputers, hooked together with a reconfigurable switch, cunningly designed so that any 4-regular network could be realised. </description> </item> <item> <title>An Unexpected Fraction</title> <link>https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS</guid> <pubDate>Sun, 18 Sep 2016 19:30:00 GMT</pubDate> <description> On 2016-09-09, @MEIMaths tweeted an image and said: "Start with any convex quadrilateral. Mark the midpoint of each side, join these midpoints to the vertex two places clockwise around the quadrilateral. What fraction of the original quadrilateral is the new quadrilateral?" From the way it's phrased you'd expect the answer to be the same regardless of the quadrilateral chosen ... </description> </item> <item> <title>You Have To Admire Their Optimism</title> <link>https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS</guid> <pubDate>28 Aug 2016 19:30:00 GMT</pubDate> <description> Coming back from Australia, Rachel and I landed at Heathrow (which we usually avoid) and caught trains back home. Our final leg was from Chester to home, and I had a look at the live departures board to see how things were looking. There I found something puzzling ... </description> </item> <item> <title>Representatives Matter</title> <link>https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS</guid> <pubDate>10 Jul 2016 19:30:00 GMT</pubDate> <description> My uncle has a Ferrari, and it has led him to make an interesting observation. </description> </item> <item> <title>Pythagoras By Incircle</title> <link>https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS</guid> <pubDate>08 Jun 2016 19:30:00 GMT</pubDate> <description> Some time ago I was working on a puzzle about incircles, and unexpectedly a proof of Pythagoras' Theorem dropped out! I'm sure it's well known to people who know lots about Pythagoras' Theorem, but I thought I'd share it. </description> </item> <item> <title>A Puzzle About Puzzles</title> <link>https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS</guid> <pubDate>31 May 2016 19:30:00 GMT</pubDate> <description> Some time ago a friend of mine, Adam Atkinson, mentioned to me what he referred to as "Semi-Chestnuts" - puzzles that should be classics, but are for some reason effectively unknown. Recently one of these caught the attention of the Twitter-verse. </description> </item> <item> <title>How not to do Twitter</title> <link>https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS</guid> <pubDate>24 May 2016 19:30:00 GMT</pubDate> <description> Recently I had an exchange on Twitter that beautifully exemplifies how companies get it so totally, totally wrong. Usually I don't name names, but on this occasion it's just spectacularly bad, and then they asked me to point them at a write-up, that I've decided to go ahead and do so. </description> </item> <item> <title>Calculating 52 Factorial By Hand</title> <link>https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS</guid> <pubDate>04 Jan 2016 19:30:00 GMT</pubDate> <description> Some time ago I gave a talk where I showed that something unexpected happening with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. To do this I computed (an approximation to) 52! (52 factorial) by hand. It's not so hard - you just calculate 54! and then divide by 3000. </description> </item> <item> <title>Sometimes small things aren't</title> <link>https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS</guid> <pubDate>02 Jan 2016 19:30:00 GMT</pubDate> <description> Twenty years ago (or thereabouts) there was a Christmas road safety campaign in which they said: "Wearing a seatbelt doubles your chance of surviving an accident." But that's obviously nonsense. </description> </item> <item> <title>Not If You Hurry</title> <link>https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS</guid> <pubDate>20 Dec 2015 19:30:30 GMT</pubDate> <description> On one occasion, when I was a teenager, I was in the car with my parents going somewhere. We had to turn right (equivalent to turning left in the States) and hence had to cross a lane of traffic and merge into the far lane. My father was looking to the right to see if there was anything approaching in the lane we had to cross, and asked my mother - "Is there anything coming?" </description> </item> <item> <title>Factoring Via Graph Three Colouring</title> <link>https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS</guid> <pubDate>17 Dec 2015 19:30:30 GMT</pubDate> <description> Occasionally someone comes to me and says that they have a polynomial time algorithm for solving an NP-Complete problem. More specifically, someone came to me and said they could Graph Vertex Three Colour (G3C) in polynomial time. They'd tried lots of example, and it always worked. So I produced a graph ... They didn't come back. </description> </item> <item> <title>Another Proof Of The Doodle Theorem</title> <link>https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS</guid> <pubDate>16 Dec 2015 19:30:30 GMT</pubDate> <description> So on the "Doodle Theorem" page we have a proof of, yes, you guessed it, the Doodle Theorem. Here, on a page entitled "Another Proof of the Doodle Theorem" we have, yes, you guessed it, another proof of the Doodle Theorem. However, here we take a rather unusual approach ... </description> </item> <item> <title>When Obvious Is Not Obvious</title> <link>https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS</guid> <pubDate>15 Dec 2015 19:30:30 GMT</pubDate> <description>There's an old story that goes something like this: A math professor is teaching a class, and in the middle of a proof he says "Clearly we have the following." A student puts up his hand and says: "That's not clear to me." </description> </item> <item> <title>Graph Three (Vertex) Colouring</title> <link>https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS</guid> <pubDate>13 Dec 2015 19:30:30 GMT</pubDate> <description> Here is something you may have seen before. Take a map, any map, and colour the regions so that if two regions share a border, they must get different colours. In this post we start with the usual game, but take off in an unusual direction and quickly find ourselves in deeper waters. </description> </item> <item> <title>The Doodle Theorem</title> <link>https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS</guid> <pubDate>12 Dec 2015 19:30:30 GMT</pubDate> <description> The Doodle Theorem says that any map drawn with a single pen stroke that returns to its starting point can be two-coloured. Here's one proof. </description> </item> <item> <title>Be Careful What You Say</title> <link>https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS</guid> <pubDate>25 Oct 2015 19:30:30 GMT</pubDate> <description> Here's an amazing story. A young child writing to a popular television programme with wild claims and, quite frankly, ridiculous aspirations. The output is a lesson to us all. </description> </item> <item> <title>The Mutilated Chessboard Revisited</title> <link>https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS</guid> <pubDate>10 Oct 2015 19:30:30 GMT</pubDate> <description> Puzzle enthusiasts know that a really good puzzle is more than just a problem to solve. The very best problems and puzzles can provide insights that go beyond the original setting. Sometimes even classic puzzles can turn up something new and interesting. Here we re-visit the classic question of when we can tile a chessboard with dominoes. </description> </item> <item> <title>A Mirror Copied</title> <link>https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS</guid> <pubDate>16 Aug 2015 19:30:30 GMT</pubDate> <description> So earlier I asked: What do you get when you photocopy a mirror? But the real question, as I then expanded, is not "What do you get?" but: "Why *must* you get that?" Can we deduce from first principles, based only on what a good photocopier must do, what the result will be? I claim the answer is "Yes," although there are some who disagree. </description> </item> <item> <title>The Other, Other Rope Around The Earth</title> <link>https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS</guid> <pubDate>01 Aug 2015 19:30:30 GMT</pubDate> <description>There's a classic problem: Upon stretching a rope around the Earth, you find that you have 6 metres excess. So you join the ends, and then go around the Earth propping up the rope equally everywhere. How high will it be? An alternative that's been suggested is that instead of propping it up equally everywhere, just prop it up as high as possible in one place. But now Bill Mullins has asked me yet another variant. </description> </item> <item> <title>Photocopy A Mirror</title> <link>https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS</guid> <pubDate>29 Jul 2015 19:30:30 GMT</pubDate> <description> Recently on Twitter I asked the question: What do you get when you photocopy a mirror? But really the question isn't "What do you get?" - the real question is "Why is that the right thing to get?" </description> </item> <item> <title>The Point Of The Banach Tarski Theorem</title> <link>https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS</guid> <pubDate>06 Jun 2015 19:30:30 GMT</pubDate> <description> There's a classic "Limited Audience" joke/riddle that goes: Q: What's an anagram of "Banach-Tarski"? A: "Banach-Tarski Banach-Tarski." Now, if you already know what the Banach-Tarski theorem says, that riddle is really funny. If you don't then you're simply not in the audience, and you'll just go: "Huh?" In this article we have a look at why the Banach-Tarski theorem is more than just a curiosity. </description> </item> <item> <title>Sieve Of Eratosthenes In Python</title> <link>https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS</guid> <pubDate>24 May 2015 19:30:30 GMT</pubDate> <description> One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be done quickly and efficiently by using the Sieve of Eratosthenes. Here we use a dynamically generated collection of filters, one for each prime, and run down the list of all numbers, filtering as we go. </description> </item> <item> <title>Fast Perrin Test</title> <link>https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS</guid> <pubDate>19 May 2015 19:30:30 GMT</pubDate> <description> So we've got scaffolding to look for Perrin Pseudo-Primes (PPPs), assuming any exist (which they do) but as we run the existing code we find that it's spending pretty much all its time in the test as to whether n divides k(n). Now we look to speed that up ... </description> </item> <item> <title>Russian Peasant Multiplication</title> <link>https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS</guid> <pubDate>18 May 2015 19:30:30 GMT</pubDate> <description> Sometimes simply called "Peasant Multiplication," sometimes called "Ancient Egyptian multiplication," sometimes called "Ethiopian multiplication," sometimes called "Multiplication by Doubling and Halving," this algorithm is well-known to some, a mystery to others, and more useful than you might think, being applicable not just to multiplication of numbers, but also useful for exponentiation, and for matrices. </description> </item> <item> <title>Finding Perrin Pseudo Primes, Part 2</title> <link>https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS</guid> <pubDate>17 May 2015 19:30:30 GMT</pubDate> <description> So now we've got the scaffolding of a program to find these Perrin Pseudo-Primes. The timing shows that it overwhelmingly spends all of its time in the routine to test whether or not a number passes the "Perrin Test." So there are a few things we need to do. </description> </item> <item> <title>Finding Perrin Pseudo Primes, Part 1</title> <link>https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS</guid> <pubDate>15 May 2015 19:30:30 GMT</pubDate> <description> A while ago I was asked: Consider the sequence k(n) with k(1)=0, k(2)=2, k(3)=3, and k(n)=k(n-2)+k(n-3). Why is it true that n divides k(n) if and only if n is prime?" My immediate response was "Well, it's not true." So I was challenged to find a counter-example. </description> </item> <item> <title>The Unwise Update</title> <link>https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS</guid> <pubDate>13 May 2015 19:30:30 GMT</pubDate> <description> This story passed on to me first-hand from the engineer involved. It's a true story about how insufficient knowledge among operating personnel about the operational consequences of new technology may have accidental effects. </description> </item> <item> <title>Miles Per Gallon</title> <link>https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS</guid> <pubDate>03 May 2015 19:30:30 GMT</pubDate> <description> I remember a while ago attending a talk that did something utterly bizarre with units of "miles per gallon." I don't remember much about it, but I thought I'd attempt to reconstruct the process in a post, just to see how far I get, what conclusion I reach, and whether people think it's as bonkers as I do. Here we go ... </description> </item> <item> <title>Tracking An Item On Hacker News</title> <link>https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS</guid> <pubDate>02 May 2015 19:30:30 GMT</pubDate> <description> A couple of weeks ago I had an exchange with a user on Hacker News about user "ages." I wrote that up in my previous post, and then submitted it. I was surprised that the item garnered enough attention to make it to the front page, but that was when a little foresight paid off. I don't usually bother with analytics on my site, but on this occasion I put a tracker on the page to count the number and times of page hits. </description> </item> <item> <title>Hacker News User Ages</title> <link>https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS</guid> <pubDate>19 Apr 2015 19:30:30 GMT</pubDate> <description> A few days ago I was reading Hacker News and someone had posted a poll with the following question: How old is your HN account? </description> </item> <item> <title>Poking The Dusty Corners</title> <link>https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS</guid> <pubDate>14 Apr 2015 19:30:30 GMT</pubDate> <description> In chatting with people about what a maths degree is, and what it does for you, I've often been intrigued by a particular response. I've shown them something that they expect to be true (or false) and then shown that their expectations can be confounded. When I do that, a common response is "Well, you're just being stupid." </description> </item> <item> <title>There Is No Time For This</title> <link>https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS</guid> <pubDate>03 Apr 2015 19:30:30 GMT</pubDate> <description> I'm finding these days that I just don't have the time to do everything myself. I don't have time to evaluate everything on its merit ... </description> </item> <item> <title>Publically Sharing Links</title> <link>https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS</guid> <pubDate>05 Jan 2015 19:30:30 GMT</pubDate> <description> For years I've been visiting, reading, and contributing to a site called "Hacker News." About 3.5 years ago I basically withdrew, finding it increasingly frustrating, but I never really went away. Slowly I've returned and contributed again, although not at the same level, and generally just by contributing links and not often getting involved in the discussions. But once again I'm getting frustrated and want to leave, but where else can I share things I find, and then enter into discussions? </description> </item> <item> <title>Learning Times Tables</title> <link>https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS</guid> <pubDate>14 Dec 2014 19:30:30 GMT</pubDate> <description> Should primary school students be drilled on their times tables? </description> </item> <item> <title>Graceful Degradation</title> <link>https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS</guid> <pubDate>12 Dec 2014 19:30:30 GMT</pubDate> <description> I first learned about graceful degradation from a colleague. He prefaced his story by saying that good people learn from their mistakes, but the best people learn from other people's mistakes. This is a bit like the saying in aviation circles that a good landing is one you can walk away from, an excellent landing is when they can use the 'plane again ... </description> </item> <item> <title>Diagramming Maths Topics</title> <link>https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS</guid> <pubDate>22 Nov 2014 19:30:30 GMT</pubDate> <description> An impossible task, but wouldn't it be useful to have some sort of diagram of topics in maths, connected somehow to show the links between topics? How could such a diagram been created? How could it be explored? How could it be dynamic? Maintainable? Usable? </description> </item> <item> <title>On the Rack</title> <link>https://www.solipsys.co.uk/new/OnTheRack.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/OnTheRack.html?RSS</guid> <pubDate>26 Aug 2014 19:30:30 GMT</pubDate> <description> When travelling, I usually go as light as possible. Certainly when travelling by plane I try to go "hand luggage only", and when doing various mini-tours of talks, and so on, I try to travel with just a single, small backpack. Sometimes it's not possible, but I usually manage. Here's a story of one time when this had unexpected consequences ... </description> </item> <item> <title>Square Root By Long Division</title> <link>https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS</guid> <pubDate>11 Aug 2014 19:30:30 GMT</pubDate> <description> The other day someone asked: "Is the product of 4 consecutive positive integers always one less than a square?" Good question. The answer is yes, and I solved it using a technique the interlocutor didn't know. </description> </item> <item> <title>Beyond the Boundary</title> <link>https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS</guid> <pubDate>23 May 2014 19:30:30 GMT</pubDate> <description> In which we show that 1+2+4+8+16+... is not equal to -1, and how that might both surprise us, and not surprise us. </description> </item> <item> <title>Fill In The Gaps</title> <link>https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS</guid> <pubDate>03 May 2014 19:30:30 GMT</pubDate> <description> Recently I had an interesting conversation on twitter, insofar as one can have a conversation at all in that medium. It started with the following perfectly reasonable question ... "Sorry for what may be a stupid question, but sin(x)/x has a limit of 1 as x -> 0, so does it not cross x=0 at 1?" </description> </item> <item> <title>Software Checklist</title> <link>https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS</guid> <pubDate>24 Apr 2014 19:30:30 GMT</pubDate> <description> During the second World War, fighter pilots would scramble to take off. Their heart would stop when the engine mis-fired. Was the fuel mix too rich, or too lean? Turn the control wrong way and they could die ... </description> </item> <item> <title>NASA Space Crews</title> <link>https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS</guid> <pubDate>10 Feb 2013 19:30:30 GMT</pubDate> <description> In the Apollo missions many of the crew were experienced, but some were not. So I drew a diagram - see what patterns you see. </description> </item> <item> <title>The Birthday Paradox</title> <link>https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS</guid> <pubDate>06 Nov 2012 19:30:30 GMT</pubDate> <description> A classic puzzle/paradox is to ask: How many people do you need to have in a room before two of them share a birthday. In this post we see what happens when 365 is not equal to 365, and how this affects computing the sizes of hash spaces. </description> </item> <item> <title>The Trapezium Conundrum</title> <link>https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS</guid> <pubDate>17 Apr 2012 19:30:30 GMT</pubDate> <description> Clear, precise, unambiguous and useful definitions are hard to come by in the real world. In maths we have the luxury of creating definitions that we want, and then chasing down the consequences. If the definition doesn't produce what we want, we can change it. But even things, things aren't always as easy as we might hope. </description> </item> <item> <title>Revisting the Ant</title> <link>https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS</guid> <pubDate>20 Feb 2012 19:30:30 GMT</pubDate> <description> So last time in TheAntAndTheRubberBand we were talking about an infinitely patient ant walking on an infinitely stretchy rubber band. If you haven't already, you'll need to read that. So here's what's happening. </description> </item> <item> <title>The Ant and the Rubber Band</title> <link>https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS</guid> <pubDate>09 Feb 2012 19:30:30 GMT</pubDate> <description> There's a 1 metre long rubber band, and an ant, standing on it at one end. The ant starts walking along it at a speed of 1 cm/min. Every minute the rubber band is stretched (uniformly and instantaneously) to be one metre longer. The question is this: Will the ant ever get to the far end? </description> </item> <item> <title>Irrationals Exist</title> <link>https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS</guid> <pubDate>20 Dec 2011 19:30:30 GMT</pubDate> <description> For this post I thought I'd have a quick diversion into talking about the so-called "Real Numbers." Upon reflection, however, I found that there was so much I wanted to say that there was no way to fit it sensibly into a single post. So instead I'll put some preliminary comments here, and then expand on them later. In particular, I'll give an explicit proof that for every interval you choose of non-zero length, there is an irrational in it. </description> </item> <item> <title>Multiple Choice Probability Puzzle</title> <link>https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS</guid> <pubDate>15 Nov 2011 19:30:30 GMT</pubDate> <description> Recently the following puzzle was running around the 'net: If you choose an answer at random, what is your probability of being correct: A: 25%; B: 50%; C: 60%; D: 25% ? The immediate thought is - there are four options, so if I pick one at random then each has a one in four chance of being chosen. That means the answer is 1/4, or 25%. But that doesn't work ... </description> </item> <item> <title>Random Eratosthenes</title> <link>https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS</guid> <pubDate>28 Oct 2011 19:30:30 GMT</pubDate> <description> Why do people think of the primes as somehow being "random"? What does that mean? How can we investigate? In this post I'll talk about a way of generating primes, and then see what happens when we toss in some randomness, just for fun. </description> </item> <item> <title>Wrapping Up Square Dissection</title> <link>https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS</guid> <pubDate>13 Sep 2011 19:30:30 GMT</pubDate> <description> We now have five valid dissections, and one "dissection" that might be regarded as invalid. So what do we mean by "a piece" and just how many dissections are there? </description> </item> <item> <title>Dissecting a Square (Part 2)</title> <link>https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS</guid> <pubDate>08 Aug 2011 19:30:30 GMT</pubDate> <description> So we return to the square. It's simple enough to cut it up into identical pieces so that all the pieces touch the centre. But in how many ways? I rapidly got 5 (or 6, depending on a technicality), and I started to wonder about a proof that 5 (or 6) was all of them. I posted a badly worded question on an internet forum, and rightly got flamed for it, but in the answers was a shock. There was an infinite family of solutions. And not just one ... </description> </item> <item> <title>Dissecting a Circle</title> <link>https://www.solipsys.co.uk/new/DissectingACircle.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingACircle.html?RSS</guid> <pubDate>26 Jul 2011 19:30:30 GMT</pubDate> <description> There are three possibilities when we dissect any shape: One piece touches the centre point; There's more than one piece and they all touch the centre point; Two or more pieces touch the centre point, but some don't. But what about the circle? If we just cut it like a pizza then we get all the pieces touching the centre. No problem there. What about the other possibilities? </description> </item> <item> <title>Dissecting a square (Part 1)</title> <link>https://www.solipsys.co.uk/new/DissectingASquare.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DissectingASquare.html?RSS</guid> <pubDate>01 Jun 2011 19:30:30 GMT</pubDate> <description> Some time ago I was given a challenge that turned out to be surprisingly rich in surprises. It all starts by trying to dissect a square. </description> </item> <item> <title>An Oddity in Tennis (Part 3 of Decision Trees in Games)</title> <link>https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS</guid> <pubDate>24 May 2011 19:30:30 GMT</pubDate> <description> In this final part we see how a proper analysis can throw up some surprising results in the detail, defying our expectations. </description> </item> <item> <title>Decision Tree For Tennis (Part 2 of Decision Trees in Games)</title> <link>https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS</guid> <pubDate>18 May 2011 19:30:30 GMT</pubDate> <description> Having seen the basic ideas in decision trees for games, we now put it to real use in analysing tennis. This is the prelude for a surprise ... </description> </item> <item> <title>Decision Trees In Games (Part 1)</title> <link>https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS</guid> <pubDate>15 May 2011 19:30:30 GMT</pubDate> <description> A fairly standard exercise in probability is to ask who, under a given scoring system, will win a game given the probability of each move. In this first in a series, we look at how to analyse simple games as a prelude to finding a surprise in a well-known example. </description> </item> <item> <title>A Matter of Convention</title> <link>https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS</guid> <pubDate>09 May 2011 19:30:30 GMT</pubDate> <description> There are some things in life where people argue about how they should be, and in fact there is no single "right" answer, we just need to agree on one of them. So what is 6/2(2+1)? </description> </item> <item> <title>Do You Nourish Or Tarnish?</title> <link>https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS</guid> <pubDate>21 Apr 2011 19:30:30 GMT</pubDate> <description> Interactions with others can nourish your soul, or can tarnish it. Seek out those who nourish your soul, but ask yourself: which do you do? </description> </item> <item> <title>Binary Search Reconsidered ...</title> <link>https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS</guid> <pubDate>18 Apr 2011 19:30:30 GMT</pubDate> <description> "Binary Search" was made popular as an interesting test problem by Jon Bentley ... I was stupid - I claimed: "There is a simpler invariant and simpler code that together have a few advantages." </description> </item> <item> <title>Two Equals Four</title> <link>https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS</guid> <pubDate>14 Apr 2011 19:30:30 GMT</pubDate> <description> A cool puzzle. Solve one equation and discover that the answer is two. Solve another equation and discover that the answer is four. Realise that they are the same, and confusion results. </description> </item> <item> <title>The Lost Property Office</title> <link>https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS</guid> <pubDate>11 Apr 2011 19:30:30 GMT</pubDate> <description> A story of love lost, and how administrative processes can cost your customers time, money and good will. </description> </item> <item> <title>The Forgiving User Interface</title> <link>https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS</guid> <pubDate>05 Apr 2011 19:30:30 GMT</pubDate> <description> A user interface may seem obvious to the designer, but here are some musings and examples that are not necessarily obvious. Or right. </description> </item> <item> <title>Setting up RSS</title> <link>https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS</guid> <pubDate>03 Apr 2011 19:30:30 GMT</pubDate> <description>After my post about withdrawing from Hacker News someone asked if I could set up an RSS feed for my "blog." Here are the first steps.</description> </item> <item> <title>Withdrawing from Hacker News</title> <link>https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS</guid> <pubDate>03 Apr 2011 19:30:30 GMT</pubDate> <description>For over 2 years I've been participating in a community of programmers, entrepreneurs and people interested in similar idea, but the time has come to move on. Here's a post explaining why.</description> </item> <item> <title>Colin's Blog</title> <link>https://www.solipsys.co.uk/new/ColinsBlog.html?RSS</link> <guid isPermaLink="true">https://www.solipsys.co.uk/new/ColinsBlog.html?RSS</guid> <pubDate>02 Apr 2011 19:30:30 GMT</pubDate> <description>Re-starting my "blog" and trying to get the structure to be more, well, "structured."</description> </item> </channel> </rss>
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"description": "Although titled \"blog\", this is more just random rants and streams\nof consciousness, touching on math, juggling, programming, user interaction,\nbusiness, and anything that comes to mind. Read at your peril!",
"copyright": null,
"url": "https://www.solipsys.co.uk/new/ColinsBlog.html",
"self": "https://www.solipsys.co.uk/rss.xml",
"published": null,
"updated": null,
"generator": null,
"image": null,
"authors": [],
"categories": [],
"items": [
{
"id": "http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS",
"title": "Tesseract Teaser",
"description": "Not the four-dimensional cube sort of Tesseract, this is the\nOptical Character Recognition (OCR) \"Tesseract\", software that\ntakes an image of some lettering and produces a plain text\nfile containing the text. Or not. It's well-known that this\nis \"Actually Quite Hard(tm)\" and Tesseract does a pretty good\njob \"Out of the Box\" with very little messing about. But the\nother day I ran across something that has me utterly baffled.\nLet me share my bebafflement with you.",
"url": "http://www.solipsys.co.uk/new/TesseractTeaser.html?RSS",
"published": "2021-03-18T12:00:00.000Z",
"updated": "2021-03-18T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS",
"title": "More Mental Model Missteps",
"description": "I mentioned when talking about an oddity in vim that the behaviour\nof the command \"<n>J\" didn't match my mental model. Sometimes\nsoftware does that, it had behaviour that's totally reasonable when\nyou think about it one way, but there's another way of thinking that\ncauses you to be surprised. Here's another, as reported to me by a\nfriend.",
"url": "http://www.solipsys.co.uk/new/MoreMentalModelMissteps.html?RSS",
"published": "2021-01-31T12:00:00.000Z",
"updated": "2021-01-31T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS",
"title": "An Oddity In VIM",
"description": "I'm going to tell you a story, so this is quite a long post. If\nyou'd like to skip the story get directly to the main point then\nfeel free to do so. But if you're interested in the story, make\nsure you're sitting comfortably, and I'll tell you how I found an\noddity in /vim./",
"url": "http://www.solipsys.co.uk/new/AnOddityInVIM.html?RSS",
"published": "2021-01-24T12:00:00.000Z",
"updated": "2021-01-24T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS",
"title": "Double Double Division Algorithm",
"description": "For some of my readers, this will all be completely mysterious.\nBut for others, part way through they will go \"I recognise this!\"\nSo I'd really like to hear from you ... if you recognise this,\nat which point did the penny drop? I'd also really like to know\nif you think this is obvious, and possibly even if you've seen\nit before.\n\nConsider the following algorithm. I'll work through an example.\nI'll divide 450 by 23.",
"url": "https://www.solipsys.co.uk/new/DoubleDoubleDivisionAlgorithm.html?RSS",
"published": "2021-01-18T12:00:00.000Z",
"updated": "2021-01-18T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ContinuityConcerns.html?RSS",
"title": "Continuity Concerns",
"description": "Recently, Rachel and I have been watching the episodes of\n\"The Adventures of Paddington Bear\" that have been transmitted on\nbroadcast TV here in the UK. It's not exactly gentle viewing, but\nPaddington is kind, helpful (or tries to be), and it always turns\nout well. Not very realistic, but if you watch with the right\nattitude, it is uplifting. Judge us if you will - we don't care.",
"url": "https://www.solipsys.co.uk/new/ContinuityConcerns.html?RSS",
"published": "2021-01-01T12:00:00.000Z",
"updated": "2021-01-01T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/CountingCarbonCalories.html?RSS",
"title": "Counting Carbon Calories",
"description": "\"When you lose weight, where does it go?\"\nAn interesting question, and one where most people haven't thought\nabout it, don't know, and really don't care. But when I was asked,\nit set in motion a train of thought. Follow along, and see if it\nmakes sense.",
"url": "https://www.solipsys.co.uk/new/CountingCarbonCalories.html?RSS",
"published": "2020-12-30T12:00:00.000Z",
"updated": "2020-12-30T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheParityOfZero.html?RSS",
"title": "The Parity Of Zero",
"description": "Before you react to the title, and before you guess where this\nis going and form a reaction, pause. I might not be about to\nsay what you expect. Of course, I might, but I might not, and\nI'd ask you to wait a bit.",
"url": "https://www.solipsys.co.uk/new/TheParityOfZero.html?RSS",
"published": "2020-12-21T12:00:00.000Z",
"updated": "2020-12-21T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WhenTheTextAndHtmlDisagree.html?RSS",
"title": "When The Text And HTML Disagree",
"description": "Second Saturday of the month, and that means the Farmers' Market is\non. Even in this second lockdown it will be running, with a one-way\nsystem and limited numbers permitted inside at any one time. \nBut is it at the usual time? Let's check the email.\nOh, I seem to have deleted it. Never mind, there will be a backup ...",
"url": "https://www.solipsys.co.uk/new/WhenTheTextAndHtmlDisagree.html?RSS",
"published": "2020-12-12T12:00:00.000Z",
"updated": "2020-12-12T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RecursionRevisited.html?RSS",
"title": "Recursion Revisited",
"description": "Some time ago I wrote a post on Thinking About Recursion, and\nmore recently I wrote about a problem concerning the problem\nof the number of Vertices Required For Cycles. As it happens,\nthe code for that problem is heavily recursive, and provides\na great example of using recursion to solve a real problem.",
"url": "https://www.solipsys.co.uk/new/RecursionRevisited.html?RSS",
"published": "2020-10-14T11:00:00.000Z",
"updated": "2020-10-14T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/VerticesRequiredForCycles.html?RSS",
"title": "Vertices Required For Cycles",
"description": "A few weeks ago Chris Purcell (@[email protected]) said:\nLet a_n be the size of the smallest graph with exactly n cycles.\n(The first few terms are: 3, 5, 4, 6, ...) The first few values\nare easy enough to compute, but it gets quite tricky quite quickly.\nHow can one construct a (simple undirected) graph with exactly\n5 cycles?",
"url": "https://www.solipsys.co.uk/new/VerticesRequiredForCycles.html?RSS",
"published": "2020-10-02T11:00:00.000Z",
"updated": "2020-10-02T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ReflexActions.html?RSS",
"title": "Reflex Actions",
"description": "The machine wouldn't read my credit card.\nThat's not uncommon ... sometimes the contacts on my card\nare dirty, sometimes the contacts on the machine are dirty\n... no big deal. Just lick your thumb, rub the contacts,\nand try again.",
"url": "https://www.solipsys.co.uk/new/ReflexActions.html?RSS",
"published": "2020-08-24T11:00:00.000Z",
"updated": "2020-08-24T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheBalladOfBunter.html?RSS",
"title": "The Ballad Of Bunter",
"description": "In late May it was becoming increasingly clear that Rachel's laptop\nwas increasingly eccentric. A replacement would be needed, and while\nit wasn't yet urgent, we felt we should do something before it became\nso. And so the hunt began.",
"url": "https://www.solipsys.co.uk/new/TheBalladOfBunter.html?RSS",
"published": "2020-07-26T11:00:00.000Z",
"updated": "2020-07-26T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?RSS",
"title": "Infinite Ramsey Theorem",
"description": "With the passing of Ron Graham a few people have been in touch\nwith me to ask what \"Ramsey Theory\" is. So I've given a brief\noutline, and pointers in case people want to follow up. In\ntruth, just stick \"Ramsey Theory\" into your favourite search\nengine and you'll get lots to follow up and chase down (as\nopposed, of course, to \"follow down\" or \"chase up\").",
"url": "https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?RSS",
"published": "2020-07-12T11:00:00.000Z",
"updated": "2020-07-12T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SignalReflection.html?RSS",
"title": "Signal Reflection",
"description": "Way back in the 70s when I was building logic circuits, I was\nwarned repeatedly that I'd have to get a few things right, or\nrisk \"locking up\" or \"burning out\" the CMOS chips I was using.\nThe bogeyman was \"Signal Reflection\", but no one could tell me\nwhat it was, or why it was so bad.",
"url": "https://www.solipsys.co.uk/new/SignalReflection.html?RSS",
"published": "2020-07-06T11:00:00.000Z",
"updated": "2020-07-06T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnalogiesNotConsideredHarmful.html?RSS",
"title": "Analogies Not Considered Harmful",
"description": "While I was writing my post on SignalReflection, I was given cause\nto reflect (pun intended ... sorry) on exactly the role and value\nof analogies in science, maths, and life in general. I've come to\nthe conclusion that, like so many thing, analogies are neither good\nnor bad. They have their purpose, and each lies somewhere on a\nspectrum.",
"url": "https://www.solipsys.co.uk/new/AnalogiesNotConsideredHarmful.html?RSS",
"published": "2020-07-05T11:00:00.000Z",
"updated": "2020-07-05T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS",
"title": "Twitter Reply vs Quote Tweet",
"description": "More than once now I've seen someone on social media using an\noption which has, for their purposes, been sub-optimal. In one\ncase it led to a very unpleasant exchange, purely because one\nperson assumed an implication that simply wasn't intended.",
"url": "https://www.solipsys.co.uk/new/TwitterReplyVsQuoteTweet.html?RSS",
"published": "2020-06-17T11:00:00.000Z",
"updated": "2020-06-17T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS",
"title": "Proofs To Make You Go WOW",
"description": "For those of us who love maths, it's sad to see how many people\nhate it, or have a phobia of it, or proudly announce \"I was never\nvery good at maths at school.\" The question we often counter with\nis \"Would you be so proud of being unable to read?\"",
"url": "https://www.solipsys.co.uk/new/ProofsToMakeYouGoWOW.html?RSS",
"published": "2020-06-16T11:00:00.000Z",
"updated": "2020-06-16T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/LaptopPurchaseAdviceReceived.html?RSS",
"title": "Laptop Purchase Advice Received",
"description": "Rachel's laptop has become ... eccentric. Like a toddler, or an aging\nrelative, who won't get up in the morning, won't go to bed at night,\nand won't play nicely with others, I'm afraid The Admirable Crichton\nhas taken to not starting up properly, not shutting down properly, and\noccasionally just refusing to connect either over ethernet, or Wi-Fi.",
"url": "https://www.solipsys.co.uk/new/LaptopPurchaseAdviceReceived.html?RSS",
"published": "2020-06-08T11:00:00.000Z",
"updated": "2020-06-08T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BlowUpYourAbilityBalloon.html?RSS",
"title": "Blow Up Your Ability Balloon",
"description": "It's pretty clear to most of us that skills unpractised are\neventually lost. Anything at the limits of our abilities\nneed to be exercised regularly to avoid having them waste\naway.",
"url": "https://www.solipsys.co.uk/new/BlowUpYourAbilityBalloon.html?RSS",
"published": "2020-05-29T11:00:00.000Z",
"updated": "2020-05-29T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AFactletForAll.html?RSS",
"title": "A Factlet For All",
"description": "More and more often I hear people saying and see people writing\n\"factoid\", by which they mean \"A Small Fact\". But is that right?",
"url": "https://www.solipsys.co.uk/new/AFactletForAll.html?RSS",
"published": "2020-05-27T11:00:00.000Z",
"updated": "2020-05-27T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnatomyOfAHit.html?RSS",
"title": "Anatomy of a Hit",
"description": "Recently I was *very* surprised when a post got significant traction\non a forum I visit, and I set up some tracking to see what happened\n... this is the report.",
"url": "https://www.solipsys.co.uk/new/AnatomyOfAHit.html?RSS",
"published": "2020-05-22T11:00:00.000Z",
"updated": "2020-05-22T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS",
"title": "Sell Yourself, Sell Your Work",
"description": "Doing technically brilliant work may be enough for your\npersonal gratification, but you should never think it's\nenough. If you lock yourself in a room and do the most\nmarvellous work but don't tell anyone, then no one will\nknow, no one will benefit, and the work will be lost. You\nmay as well not have bothered. For the world to benefit\nfrom your work, and therefore for you to benefit fully\nfrom your work, you have to make it known.",
"url": "https://www.solipsys.co.uk/new/SellYourselfSellYourWork.html?RSS",
"published": "2020-05-20T11:00:00.000Z",
"updated": "2020-05-20T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AllTheLetters.html?RSS",
"title": "All The Letters",
"description": "Most people are aware of the phrase: \"The quick brown fox\njumped over the lazy dog.\" But many, perhaps most, don't\nrealise (a) Why it's interesting, and (b) It's wrong.",
"url": "https://www.solipsys.co.uk/new/AllTheLetters.html?RSS",
"published": "2020-05-18T11:00:00.000Z",
"updated": "2020-05-18T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS",
"title": "Being Slow To Criticise",
"description": "Software that deliberately kills the servers it is monitoring is\nan interesting idea. A story I read recently told of a situation\nwhere the programmer and/or engineer involved wasn't able to fix\nthe real, underlying problem, so an overlay solution was devised\nthat (a) worked, and (b) was feasible. This post is not about\nthat story. This post is about a comment made by one of the readers\nin the forum where I saw it.",
"url": "https://www.solipsys.co.uk/new/BeingSlowToCriticise.html?RSS",
"published": "2020-05-09T11:00:00.000Z",
"updated": "2020-05-09T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS",
"title": "State Machine In Real Life",
"description": "In April 2016 my wife and I were travelling. We stayed in a\nreasonably comfortable but very inexpensive hotel, and meals\nweren't provided. As it happened, across the way was a large\nretail park with a large well-known supermarket chain, and\nthey had a restaurant. We ate there four or five times, and\nI noticed that they were using a finite state machine.",
"url": "https://www.solipsys.co.uk/new/StateMachineInRealLife.html?RSS",
"published": "2020-05-01T11:00:00.000Z",
"updated": "2020-05-01T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/CoxeterOnceNerdSnipedConway.html?RSS",
"title": "Coxeter Once Nerd-Sniped Conway",
"description": "I wrote earlier about John Conway's passing and some of my memories\nof him. I also mentioned there how he was once nerd-sniped by Coxeter.\nJohn didn't call it \"nerd sniping\" - he didn't know the term - but when\nI explained it, he was delighted, as it exactly matched his experience.\nSo here is the story, as told to me by Conway at MathFest, 2015 ...",
"url": "https://www.solipsys.co.uk/new/CoxeterOnceNerdSnipedConway.html?RSS",
"published": "2020-04-28T11:00:00.000Z",
"updated": "2020-04-28T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS",
"title": "Not Always Your Fault",
"description": "\"I must have done something wrong.\" I hear this a lot when people\nare using computer interfaces. These days that's often websites,\noften for large corporations, and often trying to accomplish\nsomething one feels should be simple. And yet in all honesty,\nit's not always your fault.",
"url": "https://www.solipsys.co.uk/new/NotAlwaysYourFault.html?RSS",
"published": "2020-04-21T11:00:00.000Z",
"updated": "2020-04-21T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RememberingConway.html?RSS",
"title": "Remembering Conway",
"description": "John Conway has left us.",
"url": "https://www.solipsys.co.uk/new/RememberingConway.html?RSS",
"published": "2020-04-12T11:00:00.000Z",
"updated": "2020-04-12T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS",
"title": "Perception of Space",
"description": "During this time of lockdown and/or self-isolation, it's\ntempting for those of us content with our own company to\nsit tight indoors and wait it out. But I'm reminding of\nsome stories told to me by my friend Laurie Brokenshire.",
"url": "https://www.solipsys.co.uk/new/PerceptionOfSpace.html?RSS",
"published": "2020-04-03T07:30:00.000Z",
"updated": "2020-04-03T07:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS",
"title": "Parallelogram Puzzle",
"description": "A while ago Ed Southall asked a great question on Twitter about\njoining dots to make a parallelogram. Several people chimed in\nquite quickly, others took a little longer. Some were happy to\nhave found any solution at all, others were happy to have found\ntwo solutions, and then quite a few people started to claim that\nthere were, in fact, exactly two solutions. That made me wonder\n...",
"url": "https://www.solipsys.co.uk/new/ParallelogramPuzzle.html?RSS",
"published": "2020-03-21T11:00:00.000Z",
"updated": "2020-03-21T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BackOfTheEnvelopeCOVID19.html?RSS",
"title": "Back Of The Envelope COVID19",
"description": "I did a rough \"Back of the Envelope\" calculation about\nCOVID-19. Here are my rough-and-ready results.",
"url": "https://www.solipsys.co.uk/new/BackOfTheEnvelopeCOVID19.html?RSS",
"published": "2020-03-12T11:00:00.000Z",
"updated": "2020-03-12T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/APointAgainstTheAxiomOfChoice.html?RSS",
"title": "A Point Against The Axiom Of Choice",
"description": "Last time we saw that the Axiom Of Choice seems so reasonable.\nIt's basically saying that that the product of non-empty sets\nis always non-empty, and that seems obvious. But in this post\nwe look at one of the implications of accepting the Axiom Of\nChoice, and wonder if perhaps it's not so obvious after all.",
"url": "https://www.solipsys.co.uk/new/APointAgainstTheAxiomOfChoice.html?RSS",
"published": "2020-03-09T11:00:00.000Z",
"updated": "2020-03-09T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/InDefenseOfTheAxiomOfChoice.html?RSS",
"title": "In Defense Of The Axiom Of Choice",
"description": "The first of a two-parter, here we provide a reason to accept\nthat the Axiom of Choice is reasonable, and should be used.",
"url": "https://www.solipsys.co.uk/new/InDefenseOfTheAxiomOfChoice.html?RSS",
"published": "2020-02-26T11:00:00.000Z",
"updated": "2020-02-26T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/JourneyingHomeThroughStormDennis.html?RSS",
"title": "Journeying Home Through Storm Dennis",
"description": "Saturday, Feb 15th, 2020, and I'd delivered a Maths Masterclass\njust north of Cardiff in South Wales. I'd packed my things and\nwas offered a lift to the station, which was gratefully accepted.\nIt was raining, although not torrentially, but Storm Dennis was\ndue to hit, and we were feeling the initial effects. This is\nthe story of what happened next ...",
"url": "https://www.solipsys.co.uk/new/JourneyingHomeThroughStormDennis.html?RSS",
"published": "2020-02-21T11:00:00.000Z",
"updated": "2020-02-21T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/EarthRadiusRefined.html?RSS",
"title": "Earth Radius - Refined",
"description": "Previously we looked at computing the radius of the Earth\nby watching the Sun coming down a building at sunrise, but\nthere's been some question about the answer, so now let's\ndo it \"properly\".",
"url": "https://www.solipsys.co.uk/new/EarthRadiusRefined.html?RSS",
"published": "2020-02-09T11:00:00.000Z",
"updated": "2020-02-09T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/VolumeOfASphere.html?RSS",
"title": "Volume Of A Sphere",
"description": "Fermat's Library on Twitter tweeted \"Euler presented in his textbooks\nthe exact formula for the volume of a sphere\" and there followed an\nimage with the actual formula. Over 12 thousand people \"Liked\" the\ntweet, but someone said: \"How would you go about proving this one?\"\nSo here is how we can prove it.",
"url": "https://www.solipsys.co.uk/new/VolumeOfASphere.html?RSS",
"published": "2020-01-05T11:00:00.000Z",
"updated": "2020-01-05T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BigOhAndRelations.html?RSS",
"title": "Big-Oh and Relations",
"description": "In an earlier post we saw that the function f(n)=n dominates\ng(n)=n-ln(n), but that's no surprise. What does come as a\nsurprise is that g dominates f. So even though for any value\nof n greater than 2 we already have f(n)>g(n), still we say\nthat g dominates f. That feels *very* unexpected, and as\na result you might question the value of the concept of\n\"dominates\", so we'll pause and take a moment to see if we\ncan get a handle on what's going on.",
"url": "https://www.solipsys.co.uk/new/BigOhAndRelations.html?RSS",
"published": "2019-12-04T12:00:00.000Z",
"updated": "2019-12-04T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MathematicalRelations.html?RSS",
"title": "Mathematical Relations",
"description": "Ubiquitous in mathematics is the concept of comparing things,\nand examining the relationships between them. Since we do that\nall the time and everywhere, it's worth having a look at the\nconcept of a \"Relation\" in an abstract sense to try to tease\nout the common themes.",
"url": "https://www.solipsys.co.uk/new/MathematicalRelations.html?RSS",
"published": "2019-11-22T12:00:00.000Z",
"updated": "2019-11-22T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/IntroducingBigOh.html?RSS",
"title": "Introducing Big-Oh",
"description": "Last time I said: \"If you do this for two different algorithms and\nthe results are, apart from a scaling factor, pretty much the same,\nthen the algorithms are said to have the same 'Time Complexity'.\"\nNow we'll look at that more carefully.",
"url": "https://www.solipsys.co.uk/new/IntroducingBigOh.html?RSS",
"published": "2019-10-28T12:00:00.000Z",
"updated": "2019-10-28T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS",
"title": "Constant Differences",
"description": "It's time to get our hands dirty. In this post we look carefully at\na particular algorithm, and think hard about how long it takes for a\ngiven instance. From that we find an important concept emerging.",
"url": "https://www.solipsys.co.uk/new/ConstantDifferences.html?RSS",
"published": "2019-10-12T11:00:00.000Z",
"updated": "2019-10-12T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS",
"title": "Algorithms and Sizes of Instances",
"description": "We've looked at what we mean by a \"Problem\", and by an \"Instance\" of\na problem. For each challenge, we need a way of working out what the\nresponse should be. Such a method is called an \"Algorithm\" for that\nproblem, so let's think carefully about algorithms.",
"url": "https://www.solipsys.co.uk/new/AlgorithmsAndSizesOfInstances.html?RSS",
"published": "2019-10-07T11:00:00.000Z",
"updated": "2019-10-07T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS",
"title": "Introducing Time Complexity",
"description": "Recently I discovered that a friend of mine, an outstandingly\ngood mathematician, didn't know anything about how the whole\n\"Time Complexity\" thing worked, and didn't understand about\n$P$ versus $NP$ and similar concepts. So here is an outline\nof the ideas in what I hope will be bite-sized, accessible\nchunks.",
"url": "https://www.solipsys.co.uk/new/IntroducingTimeComplexity.html?RSS",
"published": "2019-09-30T11:00:00.000Z",
"updated": "2019-09-30T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS",
"title": "The Linear Frog",
"description": "I was given a problem recently, and I was really pleased to get\nthe solution. I wonder if you can (a) solve it, and (b) tell me\nwhere it comes from. I've not been able to track it down at all.\nIt's the problem of the Linear Baby Frog.",
"url": "https://www.solipsys.co.uk/new/TheLinearFrog.html?RSS",
"published": "2019-09-14T11:00:00.000Z",
"updated": "2019-09-14T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS",
"title": "Seventy Versus One Hundred Revisited",
"description": "Earlier we looked at the situation of two identical cars,\none doing 70, the other doing 100, slamming on their brakes\nat exactly the same location to avoid an obstruction. The\nmodel we used was that the two cars shed energy at a rate\nproportional to distance. But what if the rate energy is\nshed is proportional not to distance, but to time?",
"url": "https://www.solipsys.co.uk/new/SeventyVersusOneHundredRevisited.html?RSS",
"published": "2019-08-24T11:00:00.000Z",
"updated": "2019-08-24T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS",
"title": "How The Farrago Works",
"description": "Some time ago I was asked about the way this website works,\nand as I started to explain, I realised just how much there\nwas going on and how complicated it seemed. But they seemed\nto think it was neat and elegant, so I thought I'd write it\nup.",
"url": "https://www.solipsys.co.uk/new/HowTheFarragoWorks.html?RSS",
"published": "2019-08-17T11:00:00.000Z",
"updated": "2019-08-17T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS",
"title": "Seventy Versus One Hundred",
"description": "Supposed two identical cars are traveling along the same\nstraight road, with one traveling at 70 kilometres an hour,\nthe other at 100 kilometres an hour. Just as the faster\ncar draws roughly level with the slower, they both see an\nobstruction in the road ahead, and (as luck would have it)\nat the exact same moment, exactly when they are level with\neach other, they both slam on the brakes.",
"url": "https://www.solipsys.co.uk/new/SeventyVersusOneHundred.html?RSS",
"published": "2019-08-05T11:00:00.000Z",
"updated": "2019-08-05T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS",
"title": "Powers Of Two In Lex Order",
"description": "Recently I was sent a lovely little twitchet, so I thought\nI'd share it for people to think about. No answers provided.\nFirstly, let's do something odd with the powers of two ...",
"url": "https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html?RSS",
"published": "2019-07-22T11:00:00.000Z",
"updated": "2019-07-22T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS",
"title": "Emerging e Expanded",
"description": "Expanding on the post from earlier, and with more detail ...\nput \"10\" into a calculator and take the square root. Then\nagain, then again, then again, and so on. Fairly quickly we\nget a number that's marginally larger than 1, so we can think\nof it as 1 plus small rubbish. But thinking carefully about\nthe rubbish leads to some interesting results.",
"url": "https://www.solipsys.co.uk/new/EmergingEExpanded.html?RSS",
"published": "2019-07-16T11:00:00.000Z",
"updated": "2019-07-16T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS",
"title": "Rage Inducing System Implementation",
"description": "I'm about to go on an extended business trip, so I'm making note\nof broadcast TV programs that I want to record, and making sure\nthere is enough space on the recorder. I have a large external\nHDD attached, so I've been transferring programs to that to make\nspace on the internal HDD. All was going well. There's still 240\nhours of space on the external HDD, so no problems anticipated.\nWhat could possibly go wrong?",
"url": "https://www.solipsys.co.uk/new/RageInducingSystemImplementation.html?RSS",
"published": "2019-07-13T11:00:00.000Z",
"updated": "2019-07-13T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS",
"title": "The Book Is Not Always Right",
"description": "Recently someone tweeted a picture of a page from a book. It\nseems to be some sort a book about maths aimed at students,\nbut in one simple paragraph there was just so much wrong, it\nattracted many comments from many of my friends and colleagues.",
"url": "https://www.solipsys.co.uk/new/TheBookIsNotAlwaysRight.html?RSS",
"published": "2019-07-06T11:00:00.000Z",
"updated": "2019-07-06T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/EmergingE.html?RSS",
"title": "Emerging e ...",
"description": "Start with 10, and square root many times over. After a while you\nget 1+(rubbish). Taking the square root of that halves the rubbish,\nso we can deduce that when epsilon is small, 10 to the power of\nepsilon is 1 plus some constant times epsilon. Starting with 5\ninstead of 10 you get a different constant, so we have a function\nwhere you start with a value, successively take the square root,\ncompute the constant, and that's the value of the function. Looking\nat this function, I have questions ...",
"url": "https://www.solipsys.co.uk/new/EmergingE.html?RSS",
"published": "2019-06-09T11:00:00.000Z",
"updated": "2019-06-09T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS",
"title": "Impossible To Translate",
"description": "Some time ago, while on a business trip to Spain, I was\nasked a question that turns out to be impossible to\ntranslate into English.",
"url": "https://www.solipsys.co.uk/new/ImpossibleToTranslate.html?RSS",
"published": "2019-06-04T11:00:00.000Z",
"updated": "2019-06-04T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WaitingInVain.html?RSS",
"title": "Waiting In Vain",
"description": "Over the past few years I've occasionally been contacted by my\nISP to say that one of my scripts had gone rogue and was using\n100% CPU, and would it be OK to kill it. This has always been\na surprise to me because I'm usually pretty careful about my\ncode, especially when it's running \"out there\" on someone\nelse's hardware.",
"url": "https://www.solipsys.co.uk/new/WaitingInVain.html?RSS",
"published": "2019-05-29T11:00:00.000Z",
"updated": "2019-05-29T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS",
"title": "Non-Repeating Decimals",
"description": "In the previous post we talked about repeating decimals, and showed\nthat every (eventually) repeating decimal is a rational number, and\nthat every rational number has a (possibly trivial) (eventually)\nrepeating decimal representation. Now we'll look at some cases of\ndecimals that don't repeat, and hence are irrational, and vice versa.",
"url": "https://www.solipsys.co.uk/new/NonRepeatingDecimals.html?RSS",
"published": "2019-05-24T11:00:00.000Z",
"updated": "2019-05-24T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RationalRepeats.html?RSS",
"title": "Rational Repeats",
"description": "Recently on-line I saw someone talking about the decimal expansion\nof pi, and they said: \"I'm told pi goes on forever and never repeats,\nI can't see how that can be proved.\" I didn't try to explain how pi\nnever repeats, but I did have a go at explaining some of the ideas.",
"url": "https://www.solipsys.co.uk/new/RationalRepeats.html?RSS",
"published": "2019-05-09T11:00:00.000Z",
"updated": "2019-05-09T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS",
"title": "Why is it Lovely",
"description": "Recently on one of my \"social network feeds\" I saw a post saying:\n\"X% of Y equals Y% of X.\" I commented that this was lovely, and\nsomeone asked \"Why?\"",
"url": "https://www.solipsys.co.uk/new/WhyIsItLovely.html?RSS",
"published": "2019-05-05T11:00:00.000Z",
"updated": "2019-05-05T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS",
"title": "Compiling Crypto-Connections",
"description": "Having given the maths club talk last Saturday (which went very well)\nI was left with the preparative work that I'd done. That consists of\nlists of concepts, people, algorithms, cryptosystems, and some of the\nconnections between them. What to do with it ...",
"url": "https://www.solipsys.co.uk/new/CompilingCryptoConnections.html?RSS",
"published": "2019-04-27T11:00:00.000Z",
"updated": "2019-04-27T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS",
"title": "Exploring Connections Between Crypto Systems",
"description": "I'm giving a talk for the Liverpool Maths Club this Saturday, April\n23rd, 2019. I do this roughly twice a year, and it's always a real\nchallenge - the ages range between 13 and 18, and while some of the\nstudents have been coming for years, for others it might be their\nfirst time. So whatever the topic might be, it needs to be engaging,\naccessible, and challenging, all at the same time.",
"url": "https://www.solipsys.co.uk/new/ExploringConnectionsBetweenCryptoSystems.html?RSS",
"published": "2019-04-20T11:00:00.000Z",
"updated": "2019-04-20T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS",
"title": "Meeting Elwyn Berlekamp",
"description": "I remember meeting Elwyn Berlekamp.",
"url": "https://www.solipsys.co.uk/new/ElwynBerlekampHasLeftUs.html?RSS",
"published": "2019-04-13T11:00:00.000Z",
"updated": "2019-04-13T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS",
"title": "Root Cause Analysis and the Photocopier Question",
"description": "\"Root Cause Analysis\" is complex, involved, and requires both\ntenacity and creativity. When there's a problem, often the cause\nisn't a simple, single thing, it's often a collection of things,\nand each of those might not be easily characterised. Even so,\nit's a crucial exercise in many technology based industries and\nactivities. So in this post I want to talk about my most recent\nbrush with the challenges of performing RCA, and even of getting\nother people to see that it's there to be done.",
"url": "https://www.solipsys.co.uk/new/RootCauseAnalysisAndThePhotocopierQuestion.html?RSS",
"published": "2019-04-11T11:00:00.000Z",
"updated": "2019-04-11T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS",
"title": "The Up/Down Tides",
"description": "So while in orbit at about the altitude of the ISS we've looked at\nthrowing a ball sideways, and we've looked at throwing a ball forwards\nor backwards. What happens if we throw the ball up? Or down? Is that\ndifferent? Do we finally have the ball travel away in a straight line\nat a constant speed? What new horrors lie in store?",
"url": "https://www.solipsys.co.uk/new/TheUpDownTides.html?RSS",
"published": "2019-03-26T12:00:00.000Z",
"updated": "2019-03-26T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS",
"title": "The Fore/Aft Tide",
"description": "You're in orbit around the Earth with the International Space Station,\nand you have a juggling ball. (Don't ask). You hold it next to your\nhelmet and release it, and it just stays there, apparently floating.\nNow gently push the ball ahead of you in orbit. In effect you are\nthrowing the ball away from you, and the expectation is that it will\ndrift away from you in a straight line at a constant speed. But it\ndoesn't.",
"url": "https://www.solipsys.co.uk/new/TheForeAftTide.html?RSS",
"published": "2019-03-19T12:00:00.000Z",
"updated": "2019-03-19T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS",
"title": "The Sideways Tide",
"description": "Stand outside the International Space Station and hold a juggling ball\nright by your helmet. Let it go, and it will stay there. Now give it\na gentle push \"sideways\". As you will probably know, it then travels\naway from you in a straight line at a constant speed, because that's\nwhat happens in zero gravity. But it doesn't ...",
"url": "https://www.solipsys.co.uk/new/TheSidewaysTide.html?RSS",
"published": "2019-03-12T12:00:00.000Z",
"updated": "2019-03-12T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS",
"title": "Wrapping Up Wrapping Up The Earth",
"description": "We're coming to the end of this series. Our friend has purchased\ntoo much rope, too little rope, too much miraculous wrapping sheet,\nand now, finally, we come to the question of too little. But first,\nlet's look at the different \"rope\" scenarios, and see what happens\nin each of the analogous \"sheet\" cases. Then we'll see how it all\ncomes together.",
"url": "https://www.solipsys.co.uk/new/WrappingUpWrappingUpTheEarth.html?RSS",
"published": "2019-03-05T12:00:00.000Z",
"updated": "2019-03-05T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS",
"title": "The *Other* Wrapping The Earth Problem",
"description": "Having gone around the world to wrap it, in truth our friend is too\ntired (or too lazy) to prop up the wrapping everywhere. So just as in\nthe Other Rope Around the Earth problem, instead we look at propping\nit up in just one place. We need to take up one million square\nmetres of excess. How high will that tent pole have to be?",
"url": "https://www.solipsys.co.uk/new/TheOtherWrappingTheEarthProblem.html?RSS",
"published": "2019-02-26T12:00:00.000Z",
"updated": "2019-02-26T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS",
"title": "The \"Wrapping The Earth\" Problem",
"description": "Our friend once again has too much to drink, and once again indulges\nin a little late night internet shopping. This time, however, it's\nfueled by curiousity, having discovered that there is a material that\nis infinitely stretchy, but which always retains its area. So while\nyou can stretch it one direction, it will keep its area by shrinking\nin another direction. What if we try to wrap the Earth ...",
"url": "https://www.solipsys.co.uk/new/WrappingTheEarth.html?RSS",
"published": "2019-02-19T12:00:00.000Z",
"updated": "2019-02-19T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS",
"title": "The Ring Of Steel",
"description": "Our friend has encircled the Earth with Rope, discovered that\nit's 6 metres longer than needed, so expanded the circle by\n0.95 metres to take up the slack. Thus we have a ring of rope\naround the Earth at height just about 1 metre. But overnight,\nsomehow, magically, the rope gets converted to steel! Then,\nover breakfast, a slight Earth tremor gently rattles the props,\nand they all fall down, leaving the ring of steel completely\nunsupported.\n\nWhat happens next?",
"url": "https://www.solipsys.co.uk/new/TheRingOfSteel.html?RSS",
"published": "2019-02-13T12:00:00.000Z",
"updated": "2019-02-13T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS",
"title": "Rounding Up The Ropes",
"description": "We've seen the $(Other)^k$ rope around the Earth for\n$k=0, 1, 2,$ and $3$. In this post we'll look at $k=4$,\nbut we'll start with a \"heads up\" for where we'll be going next.",
"url": "https://www.solipsys.co.uk/new/RoundingUpTheRopes.html?RSS",
"published": "2019-02-10T12:00:00.000Z",
"updated": "2019-02-10T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS",
"title": "The Other Other Other Rope Around The Earth",
"description": "So we have the Rope Around the Earth problem,\nthe Other Rope Around the Earth problem,\nand the Other Other Rope Around the Earth. \nYou might think that was the end of it, but no, there is more!",
"url": "https://www.solipsys.co.uk/new/OtherOtherOtherRopeAroundTheEarth.html?RSS",
"published": "2019-02-05T12:00:00.000Z",
"updated": "2019-02-05T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS",
"title": "Rope Around The Earth - Refined",
"description": "As previously mentioned, the Rope Around the Earth problem is\na lovely one, and everyone should know it. But even if you do,\nthere's still a nice added extra. In this post we'll have a\nlook at that.",
"url": "https://www.solipsys.co.uk/new/RopeAroundTheEarthRefined.html?RSS",
"published": "2019-01-22T12:00:00.000Z",
"updated": "2019-01-22T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS",
"title": "The Other Rope Around The Earth",
"description": "The well-known \"Rope Around the Earth\" problem is lovely, and, as\nI say, well known. But some time ago David Bedford mentioned\n*another* rope around the Earth problem. A *different* rope\naround the Earth problem. And it goes like this.",
"url": "https://www.solipsys.co.uk/new/TheOtherRopeAroundTheEarth.html?RSS",
"published": "2019-01-17T12:00:00.000Z",
"updated": "2019-01-17T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS",
"title": "Elementary Estimates",
"description": "Every now and again as I'm doing various estimates or calculations\nI use an approximation, and a few days ago it was brought home to me\nhow much I rely on these, and how few people know them. So I thought\nI'd gather some of them together in one place to be a reference.",
"url": "https://www.solipsys.co.uk/new/ElementaryEstimates.html?RSS",
"published": "2019-01-08T20:00:00.000Z",
"updated": "2019-01-08T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS",
"title": "Latitude Correction",
"description": "Recently I've been discussing the details of measuring the\nsize of the Earth by watching a shadow descending a wall at\nsunrise, or ascending at sunset. The sums are easy enough if\nyou do it at either Equinox, and at the Equator. \nBut what if you're not at the Equator? What then?",
"url": "https://www.solipsys.co.uk/new/LatitudeCorrection.html?RSS",
"published": "2019-01-01T20:00:00.000Z",
"updated": "2019-01-01T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS",
"title": "Just Give Me The Answer",
"description": "A while ago I saw an exchange on a programming forum I visit on occasion.\nA poster had asked a question that at first sight (and in all honesty,\nsubsequent examination) appeared pretty simple. The poster claimed to\nhave tried everything they could think of, that nothing worked, and\nthey'd appreciate any help.",
"url": "https://www.solipsys.co.uk/new/JustGiveMeTheAnswer.html?RSS",
"published": "2018-10-07T20:00:00.000Z",
"updated": "2018-10-07T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS",
"title": "More Musing On Pollard Rho",
"description": "After my previous post I started to explore a little more about\nhow the function in Pollard Rho affects what's going on. As yet\nI've not come to any conclusions, and I'm currently deep in the\n\"I'm confused\" stage of the exploration. I'm sure there are other\npeople know all this, but I don't know who they are, and haven't\nbeen able to find any write-ups, so I'll just carry on.",
"url": "https://www.solipsys.co.uk/new/MoreMusingOnPollardRho.html?RSS",
"published": "2018-09-19T20:00:00.000Z",
"updated": "2018-09-19T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS",
"title": "Idle Thoughts About Pollard Rho",
"description": "I've had an idle thought about the Pollard Rho method of\ninteger factoring. To start with, let's sketch how it works.",
"url": "https://www.solipsys.co.uk/new/IdleThoughtsAboutPollardRho.html?RSS",
"published": "2018-09-10T20:00:00.000Z",
"updated": "2018-09-10T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS",
"title": "When Optimising Code, Measure",
"description": "This is a truism that lots of people quote, but it can be hard to\nremember, especially in the heat of battle (as it were). Rather\nfortunately it came to mind just when needed, as I found something\ncompletely unexpected.",
"url": "https://www.solipsys.co.uk/new/WhenOptimisingCodeMeasure.html?RSS",
"published": "2018-09-04T20:00:00.000Z",
"updated": "2018-09-04T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS",
"title": "A Dog Called Mixture",
"description": "Some considerable time ago I was giving some talks at a school, and\nmy wife and I were kindly hosted at the home of the Headmaster and\nhis family. And his menagerie, as it turned out.",
"url": "https://www.solipsys.co.uk/new/ADogCalledMixture.html?RSS",
"published": "2018-08-27T12:00:00.000Z",
"updated": "2018-08-27T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS",
"title": "Another PayPal Scam",
"description": "Received as part of the newsletter of a publishing company :\nWe've been living in interesting times at Wildside Press since our\nlast newsletter. Our PayPal account was VERY creatively hacked, and\nwe briefly lost about $15,000 of the money we'd been saving up for\nroyalty payments to authors.",
"url": "https://www.solipsys.co.uk/new/AnotherPayPalScam.html?RSS",
"published": "2018-08-03T12:00:00.000Z",
"updated": "2018-08-03T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS",
"title": "Why Top Posting Has Won",
"description": "I've recently realised that, in my head, there's a connection\nbetween top-posting in email and washing the dishes. Stay\nwith me, I'll see if I can make the connection for you.",
"url": "https://www.solipsys.co.uk/new/WhyTopPostingHasWon.html?RSS",
"published": "2018-06-13T14:20:00.000Z",
"updated": "2018-06-13T14:20:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS",
"title": "Archimedes' \"Hat Box\" Theorem",
"description": "Take a sphere, and encase it in a cylinder. Take a horizontal slice\nbetween two planes. You end up with a narrow cylinder, and a smaller,\n\"slopey\" cylinder.\n\nThe Archimedes Hat-Box Theorem says these two cylinders have the same\nsurface area. In fact the theorem says that the surface areas are the\nsame no matter how thick the slice is, so as a consequence we can take\na \"slice\" that captures the entire cylinder and sphere, and that means\nthat the surface area of the curved surface of the cylinder is exactly\nthe same as the surface area of the sphere.",
"url": "https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RSS",
"published": "2018-06-06T11:50:00.000Z",
"updated": "2018-06-06T11:50:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS",
"title": "Considering a Sphere",
"description": "Recently someone posted an animation of a way to visualise the area of\na circle. Someone else then asked if there was a similar visualisation\nof the volume of a sphere, or the surface area of a sphere, and that\nstarted me thinking.",
"url": "https://www.solipsys.co.uk/new/ConsideringASphere.html?RSS",
"published": "2018-06-05T14:56:00.000Z",
"updated": "2018-06-05T14:56:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS",
"title": "To Link Or Not To Link",
"description": "Over the past few years I've noticed a rise in a particular type of\nspam that I'm receiving. It takes the form of an email like this ...",
"url": "https://www.solipsys.co.uk/new/ToLinkOrNotToLink.html?RSS",
"published": "2018-05-17T14:04:00.000Z",
"updated": "2018-05-17T14:04:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS",
"title": "Generic Advice For Writing A Thesis",
"description": "I have some generic thesis-writing advice to supplement\nthat given by your supervisor, but only if it's welcome.",
"url": "https://www.solipsys.co.uk/new/GenericAdviceForWritingAThesis.html?RSS",
"published": "2018-05-07T20:30:00.000Z",
"updated": "2018-05-07T20:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS",
"title": "Just Teach My Child The Maths",
"description": "It is astounding to me that mathematics - of all school\nsubjects - elicits such potent emotional reaction when\n\"reform\" is in the air.",
"url": "https://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html?RSS",
"published": "2018-02-18T09:15:01.000Z",
"updated": "2018-02-18T09:15:01.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS",
"title": "Not A Spectator Sport",
"description": "One of my university lecturers gave what we all thought were dreadful\nlectures. Muddled, unclear, chaotic, with no discernible thread. It\ntook ages to reconstruct and rework the material to a point where we\ncould attack the problems and old exam questions.",
"url": "https://www.solipsys.co.uk/new/NotASpectatorSport.html?RSS",
"published": "2017-12-13T13:00:00.000Z",
"updated": "2017-12-13T13:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS",
"title": "Left Truncatable Prime",
"description": "Recently Maths Inspiration produced some pencils with a fantastic idea.\nYes, their name is on it, yes, it has a slightly cheesy catch-phrase,\nBut then there is something really clever.",
"url": "https://www.solipsys.co.uk/new/LeftTruncatablePrime.html?RSS",
"published": "2017-10-21T15:00:00.000Z",
"updated": "2017-10-21T15:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS",
"title": "The Doctor and the Lawyer",
"description": "A doctor and a lawyer were chatting at a party when someone approached\nthe doctor. They wanted advice, and started to describe their symptoms\nwhen the doctor interrupted and said \"It might be better to make an\nappointment so we can talk in private.\"",
"url": "https://www.solipsys.co.uk/new/TheDoctorAndTheLawyer.html?RSS",
"published": "2017-10-15T14:00:00.000Z",
"updated": "2017-10-15T14:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS",
"title": "Four Points Two Distances Proof",
"description": "The Four Points Puzzle challenge that Peter Winkler set me was this:\n\"Find all configurations of four (distinct) points in the plane that\ndetermine exactly two distances.\" He then added: \"Nearly everyone\nmisses at least one, and every solution has been missed by at least\none person.\" So the challenge isn't to find all the configurations\nso much as to be able to prove that you have them all. It's the proof\nthat matters. Here's mine.",
"url": "https://www.solipsys.co.uk/new/FourPointsTwoDistancesProof.html?RSS",
"published": "2017-10-03T11:25:00.000Z",
"updated": "2017-10-03T11:25:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS",
"title": "Meeting Ron Graham",
"description": "I was a lowly PhD student when I first met Ron Graham. It was at a\nconference, and there was something I wanted to show him. In my mind\nit was pretty much guaranteed that he would be interested, but he was\n(and still is!) extremely well known, extremely eminent, and extremely\npopular. As a result he is extremely busy, and somewhat besieged with\npeople, all wanting a piece of his time. How could I possibly attract\nand hold his attention long enough to get him interested?\n\nSo I hatched a plan.",
"url": "https://www.solipsys.co.uk/new/MeetingRonGraham.html?RSS",
"published": "2017-10-01T18:14:00.000Z",
"updated": "2017-10-01T18:14:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS",
"title": "Napkin Ring Vs Spherical Cap",
"description": "Many years ago I was at a semi-social gathering and a somewhat odd\nincident occurred. Over the course of conversation it emerged that\nI was studying maths, and one chap, at one point, turned to me and\nsaid: \"So, do you like puzzles, then?\" Not especially on my guard\nI said yes, and he went on to say something like this: \"OK, I'll\ngive you a puzzle ...\"",
"url": "https://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.html?RSS",
"published": "2017-09-28T08:26:00.000Z",
"updated": "2017-09-28T08:26:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS",
"title": "The Four Points Puzzle",
"description": "At the MOVES conference in New York in August I was lucky enough to\nspend some time with Peter Winkler, mathematician, puzzle master\nextraordinaire, and author of \"Mathematical Puzzles: A Connoisseur's\nCollection\". As we talked about many things he set me this puzzle:\n\"Find all configurations of four (distinct) points in the plane that\ndetermine exactly two distances.\"",
"url": "https://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?RSS",
"published": "2017-09-26T16:43:00.000Z",
"updated": "2017-09-26T16:43:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS",
"title": "Radius of the Earth - Part Two",
"description": "Some nine and a bit weeks ago I posted about a method of calculating\n(or estimating) The Radius Of The Earth using a stopwatch and watching\nthe Sun at sunrise (or sunset). When \"Mike the Sundial\" told me the\nidea I was quite simply stunned at the simplicity and elegance. Colin\nBeveridge took up the challenge. But when I read his calculation I was\ninterested to see just how different his take was from mine.",
"url": "https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?RSS",
"published": "2017-09-16T08:30:00.000Z",
"updated": "2017-09-16T08:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS",
"title": "Grep Timing Anomaly",
"description": "Some considerable time ago - long enough that probably the details\nare no longer relevant, or accurate - I got seriously fed up with\nthe spam filtering on my email service. There were so many false\npositives that I had to wade through the spam bin every day, pulling\nout obviously good emails that needed attention. It got so that it\ncost me more time to have it running.",
"url": "https://www.solipsys.co.uk/new/GrepTimingAnomaly.html?RSS",
"published": "2017-07-28T08:30:00.000Z",
"updated": "2017-07-28T08:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS",
"title": "The Radius of the Earth",
"description": "The talk/workshop I give about computing the distance to the Moon uses,\nit claims, nothing more than a pendulum and a stopwatch. And while it's\nsort of true that it uses nothing else, it's not really true, because it\nalso uses the period of the Moon, and the size of the Earth. Now it might\nbe possible to persuade you that it's OK to use the period of the Moon,\nsince you can simply look out the window and measure that for yourself,\nbut to use the size of the Earth seems a bit of a stretch. Surely there\nis no way to compute that from your back garden. But there is.",
"url": "https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?RSS",
"published": "2017-07-12T08:30:00.000Z",
"updated": "2017-07-12T08:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS",
"title": "This Works to Cure My Hiccoughs",
"description": "It's many years ago that I was told about this trick. People rarely\nbelieve me, but it honestly works for me, and it has worked for others.\nSo I thought I'd write it up.",
"url": "https://www.solipsys.co.uk/new/ThisWorksToCureMyHiccoughs.html?RSS",
"published": "2017-07-09T18:30:00.000Z",
"updated": "2017-07-09T18:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS",
"title": "Perhaps We Saved One",
"description": "Many years ago a good friend of mine, Bill Mullarkey, organised a\n\"Science and Technology Extravaganza\" in Wigan. It was a fabulous\ntwo-day event with hundreds of teenagers and adults in attendance.\nThe buzz of excitement was huge, and it was an honour to be part\nof the whole thing.",
"url": "https://www.solipsys.co.uk/new/PerhapsWeSavedOne.html?RSS",
"published": "2017-07-02T19:50:00.000Z",
"updated": "2017-07-02T19:50:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS",
"title": "Thinking About Mastodon",
"description": "Some people are describing Mastodon as a decentralised Twitter, but that's\nrather misleading. It's better not to try to understand it like that.\nInstead, here's my way of thinking.",
"url": "https://www.solipsys.co.uk/new/ThinkingAboutMastodon.html?RSS",
"published": "2017-06-18T17:50:00.000Z",
"updated": "2017-06-18T17:50:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS",
"title": "Disappearing Trains On Virgin",
"description": "I'm planning a significant set of travels, so as always, I started by\nsketching an idea of what might be possible, then confirmed the various\nparts on the usual National Rail web site. Having picked my trains,\nI then went to the Virgin Trains web site to actually buy the tickets.\nThis time there was a surprise awating me.",
"url": "https://www.solipsys.co.uk/new/DisappearingTrainsOnVirgin.html?RSS",
"published": "2017-06-17T18:58:00.000Z",
"updated": "2017-06-17T18:58:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS",
"title": "The Independence Game",
"description": "A few weeks ago I was honoured to be able to attend the gathering at the\nRoyal Society where Rob Eastaway was given his Christopher Zeeman medal.\nHe gave an excellent talk, full of interest and humour, the only downside\nbeing that he made us play a game. Although at the time Rob called it\n\"Avoid the Neighbours\", I now think of it simply as \"Rob's Dots\". He\nsaid he didn't know how to play it optimally beyond 11 points, so\nI thought I'd have a go.",
"url": "https://www.solipsys.co.uk/new/TheIndependenceGame.html?RSS",
"published": "2017-04-18T11:00:00.000Z",
"updated": "2017-04-18T11:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS",
"title": "One Of My Favourite Puzzles",
"description": "It is impossible to choose a single problem as my favourite. There\nare so many, each with their own attractions, each with their own\ncharms. But there is one that I solved quickly, and then found that\nI had only just started to scratch the surface.",
"url": "https://www.solipsys.co.uk/new/OneOfMyFavouritePuzzles.html?RSS",
"published": "2017-04-06T20:00:00.000Z",
"updated": "2017-04-06T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS",
"title": "Thinking About Recursion",
"description": "It has been said that there are two hard problems in computing:\nCache Invalidation, Naming Things, and Off-By-One Errors.\nWell, that's certainly true when you get into the practice of\nprogramming. But on the way to becoming a programmer we find\nthat there are multiple levels of enlightenment.",
"url": "https://www.solipsys.co.uk/new/ThinkingAboutRecursion.html?RSS",
"published": "2017-03-08T12:00:00.000Z",
"updated": "2017-03-08T12:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS",
"title": "Memorising The Tube",
"description": "Recently I memorised the period table of elements. When I tell\npeople that, the response has generally been a moderate pause,\nfollowed by a rather puzzled - \"Why?\" So I thought I'd explain.",
"url": "https://www.solipsys.co.uk/new/MemorisingTheTube.html?RSS",
"published": "2016-12-03T19:40:00.000Z",
"updated": "2016-12-03T19:40:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS",
"title": "Spikey Spheres",
"description": "I've recently been working on an optimisation problem, and I've\ncome to realise that I can consider it as wandering around on a\nsmooth landscape in 1800 dimensions. The problem is that while\nthe error function may be \"smooth,\" your intuition of what this\nmeans is wrong.",
"url": "https://www.solipsys.co.uk/new/SpikeySpheres.html?RSS",
"published": "2016-11-20T20:00:00.000Z",
"updated": "2016-11-20T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS",
"title": "Surprisingly Quick",
"description": "In the 1990s I had a job at Liverpool University doing research into\nhow we might make it possible for non-computing specialists to use\nparaallel computers. Even today, over 20 years later, this is still\nan unsolved problem, and the machines now are designed to be easier\nto use. The machine I was using was a Parsys SuperNode with 96 T800\ntransputers, hooked together with a reconfigurable switch, cunningly\ndesigned so that any 4-regular network could be realised.",
"url": "https://www.solipsys.co.uk/new/SurprisinglyQuick.html?RSS",
"published": "2016-10-06T20:00:00.000Z",
"updated": "2016-10-06T20:00:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS",
"title": "An Unexpected Fraction",
"description": "On 2016-09-09, @MEIMaths tweeted an image and said: \"Start with any\nconvex quadrilateral. Mark the midpoint of each side, join these\nmidpoints to the vertex two places clockwise around the quadrilateral.\nWhat fraction of the original quadrilateral is the new quadrilateral?\"\nFrom the way it's phrased you'd expect the answer to be the same\nregardless of the quadrilateral chosen ...",
"url": "https://www.solipsys.co.uk/new/AnUnexpectedFraction.html?RSS",
"published": "2016-09-18T19:30:00.000Z",
"updated": "2016-09-18T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS",
"title": "You Have To Admire Their Optimism",
"description": "Coming back from Australia, Rachel and I landed at Heathrow\n(which we usually avoid) and caught trains back home. Our\nfinal leg was from Chester to home, and I had a look at the\nlive departures board to see how things were looking. There\nI found something puzzling ...",
"url": "https://www.solipsys.co.uk/new/YouHaveToAdmireTheirOptimism.html?RSS",
"published": "2016-08-28T19:30:00.000Z",
"updated": "2016-08-28T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS",
"title": "Representatives Matter",
"description": "My uncle has a Ferrari, and it has led him to make an interesting observation.",
"url": "https://www.solipsys.co.uk/new/RepresentativesMatter.html?RSS",
"published": "2016-07-10T19:30:00.000Z",
"updated": "2016-07-10T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS",
"title": "Pythagoras By Incircle",
"description": "Some time ago I was working on a puzzle about incircles, and\nunexpectedly a proof of Pythagoras' Theorem dropped out! I'm\nsure it's well known to people who know lots about Pythagoras'\nTheorem, but I thought I'd share it.",
"url": "https://www.solipsys.co.uk/new/PythagorasByIncircle.html?RSS",
"published": "2016-06-08T19:30:00.000Z",
"updated": "2016-06-08T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS",
"title": "A Puzzle About Puzzles",
"description": "Some time ago a friend of mine, Adam Atkinson, mentioned to me what he\nreferred to as \"Semi-Chestnuts\" - puzzles that should be classics, but\nare for some reason effectively unknown. Recently one of these caught\nthe attention of the Twitter-verse.",
"url": "https://www.solipsys.co.uk/new/APuzzleAboutPuzzles.html?RSS",
"published": "2016-05-31T19:30:00.000Z",
"updated": "2016-05-31T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS",
"title": "How not to do Twitter",
"description": "Recently I had an exchange on Twitter that beautifully exemplifies\nhow companies get it so totally, totally wrong. Usually I don't\nname names, but on this occasion it's just spectacularly bad, and\nthen they asked me to point them at a write-up, that I've decided\nto go ahead and do so.",
"url": "https://www.solipsys.co.uk/new/HowNotToDoTwitter.html?RSS",
"published": "2016-05-24T19:30:00.000Z",
"updated": "2016-05-24T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS",
"title": "Calculating 52 Factorial By Hand",
"description": "Some time ago I gave a talk where I showed that something unexpected\nhappening with a deck of playing cards. I had some volunteers try it,\nand while they did so I talked about just how many orderings there are\nfor 52 cards. To do this I computed (an approximation to) 52!\n(52 factorial) by hand. It's not so hard - you just calculate 54!\nand then divide by 3000.",
"url": "https://www.solipsys.co.uk/new/Calculating52FactorialByHand.html?RSS",
"published": "2016-01-04T19:30:00.000Z",
"updated": "2016-01-04T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS",
"title": "Sometimes small things aren't",
"description": "Twenty years ago (or thereabouts) there was a Christmas road safety\ncampaign in which they said: \"Wearing a seatbelt doubles your chance\nof surviving an accident.\" But that's obviously nonsense.",
"url": "https://www.solipsys.co.uk/new/SmallThingsMightNotBeSoSmall.html?RSS",
"published": "2016-01-02T19:30:00.000Z",
"updated": "2016-01-02T19:30:00.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS",
"title": "Not If You Hurry",
"description": "On one occasion, when I was a teenager, I was in the car with my\nparents going somewhere. We had to turn right (equivalent to\nturning left in the States) and hence had to cross a lane of\ntraffic and merge into the far lane. My father was looking to\nthe right to see if there was anything approaching in the lane\nwe had to cross, and asked my mother - \"Is there anything coming?\"",
"url": "https://www.solipsys.co.uk/new/NotIfYouHurry.html?RSS",
"published": "2015-12-20T19:30:30.000Z",
"updated": "2015-12-20T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS",
"title": "Factoring Via Graph Three Colouring",
"description": "Occasionally someone comes to me and says that they have a polynomial\ntime algorithm for solving an NP-Complete problem. More specifically,\nsomeone came to me and said they could Graph Vertex Three Colour (G3C)\nin polynomial time. They'd tried lots of example, and it always\nworked. So I produced a graph ... They didn't come back.",
"url": "https://www.solipsys.co.uk/new/FactoringViaGraphThreeColouring.html?RSS",
"published": "2015-12-17T19:30:30.000Z",
"updated": "2015-12-17T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS",
"title": "Another Proof Of The Doodle Theorem",
"description": "So on the \"Doodle Theorem\" page we have a proof of, yes, you guessed it, the\nDoodle Theorem. Here, on a page entitled \"Another Proof of the Doodle Theorem\"\nwe have, yes, you guessed it, another proof of the Doodle Theorem. However,\nhere we take a rather unusual approach ...",
"url": "https://www.solipsys.co.uk/new/AnotherProofOfTheDoodleTheorem.html?RSS",
"published": "2015-12-16T19:30:30.000Z",
"updated": "2015-12-16T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS",
"title": "When Obvious Is Not Obvious",
"description": "There's an old story that goes something like this:\nA math professor is teaching a class, and in the middle of a proof\nhe says \"Clearly we have the following.\" A student puts up his\nhand and says: \"That's not clear to me.\"",
"url": "https://www.solipsys.co.uk/new/WhenObviousIsNotObvious.html?RSS",
"published": "2015-12-15T19:30:30.000Z",
"updated": "2015-12-15T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS",
"title": "Graph Three (Vertex) Colouring",
"description": "Here is something you may have seen before. Take a map, any map, and\ncolour the regions so that if two regions share a border, they must\nget different colours. In this post we start with the usual game,\nbut take off in an unusual direction and quickly find ourselves in\ndeeper waters.",
"url": "https://www.solipsys.co.uk/new/GraphThreeColouring.html?RSS",
"published": "2015-12-13T19:30:30.000Z",
"updated": "2015-12-13T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS",
"title": "The Doodle Theorem",
"description": "The Doodle Theorem says that any map drawn with a single pen\nstroke that returns to its starting point can be two-coloured.\nHere's one proof.",
"url": "https://www.solipsys.co.uk/new/TheDoodleTheorem.html?RSS",
"published": "2015-12-12T19:30:30.000Z",
"updated": "2015-12-12T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS",
"title": "Be Careful What You Say",
"description": "Here's an amazing story. A young child writing to a popular\ntelevision programme with wild claims and, quite frankly,\nridiculous aspirations. The output is a lesson to us all.",
"url": "https://www.solipsys.co.uk/new/BeCarefulWhatYouSay.html?RSS",
"published": "2015-10-25T19:30:30.000Z",
"updated": "2015-10-25T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS",
"title": "The Mutilated Chessboard Revisited",
"description": "Puzzle enthusiasts know that a really good puzzle is more than just\na problem to solve. The very best problems and puzzles can provide\ninsights that go beyond the original setting. Sometimes even classic\npuzzles can turn up something new and interesting. Here we re-visit\nthe classic question of when we can tile a chessboard with dominoes.",
"url": "https://www.solipsys.co.uk/new/TheMutilatedChessboardRevisited.html?RSS",
"published": "2015-10-10T19:30:30.000Z",
"updated": "2015-10-10T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS",
"title": "A Mirror Copied",
"description": "So earlier I asked: What do you get when you photocopy a mirror? But the real question, as I then expanded, is not \"What do you get?\" but: \"Why *must* you get that?\" Can we deduce from first principles, based only on what a good photocopier must do, what the result will be? I claim the answer is \"Yes,\" although there are some who disagree.",
"url": "https://www.solipsys.co.uk/new/AMirrorCopied.html?RSS",
"published": "2015-08-16T19:30:30.000Z",
"updated": "2015-08-16T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS",
"title": "The Other, Other Rope Around The Earth",
"description": "There's a classic problem: Upon stretching a rope around the Earth, you find that you have 6 metres excess. So you join the ends, and then go around the Earth propping up the rope equally everywhere. How high will it be? An alternative that's been suggested is that instead of propping it up equally everywhere, just prop it up as high as possible in one place. But now Bill Mullins has asked me yet another variant.",
"url": "https://www.solipsys.co.uk/new/TheOtherOtherRopeAroundTheEarth.html?RSS",
"published": "2015-08-01T19:30:30.000Z",
"updated": "2015-08-01T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS",
"title": "Photocopy A Mirror",
"description": "Recently on Twitter I asked the question: What do you get when you photocopy a mirror? But really the question isn't \"What do you get?\" - the real question is \"Why is that the right thing to get?\"",
"url": "https://www.solipsys.co.uk/new/PhotocopyAMirror.html?RSS",
"published": "2015-07-29T19:30:30.000Z",
"updated": "2015-07-29T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS",
"title": "The Point Of The Banach Tarski Theorem",
"description": "There's a classic \"Limited Audience\" joke/riddle that goes:\nQ: What's an anagram of \"Banach-Tarski\"?\nA: \"Banach-Tarski Banach-Tarski.\"\nNow, if you already know what the Banach-Tarski\ntheorem says, that riddle is really funny. If\nyou don't then you're simply not in the audience,\nand you'll just go: \"Huh?\" In this article we\nhave a look at why the Banach-Tarski theorem is\nmore than just a curiosity.",
"url": "https://www.solipsys.co.uk/new/ThePointOfTheBanachTarskiTheorem.html?RSS",
"published": "2015-06-06T19:30:30.000Z",
"updated": "2015-06-06T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS",
"title": "Sieve Of Eratosthenes In Python",
"description": "One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of \"small\") this can be done quickly and efficiently by using the Sieve of Eratosthenes. Here we use a dynamically generated collection of filters, one for each prime, and run down the list of all numbers, filtering as we go.",
"url": "https://www.solipsys.co.uk/new/SieveOfEratosthenesInPython.html?RSS",
"published": "2015-05-24T19:30:30.000Z",
"updated": "2015-05-24T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS",
"title": "Fast Perrin Test",
"description": "So we've got scaffolding to look for Perrin Pseudo-Primes (PPPs), assuming any exist (which they do) but as we run the existing code we find that it's spending pretty much all its time in the test as to whether n divides k(n). Now we look to speed that up ...",
"url": "https://www.solipsys.co.uk/new/FastPerrinTest.html?RSS",
"published": "2015-05-19T19:30:30.000Z",
"updated": "2015-05-19T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS",
"title": "Russian Peasant Multiplication",
"description": "Sometimes simply called \"Peasant Multiplication,\" sometimes called \"Ancient Egyptian multiplication,\" sometimes called \"Ethiopian multiplication,\" sometimes called \"Multiplication by Doubling and Halving,\" this algorithm is well-known to some, a mystery to others, and more useful than you might think, being applicable not just to multiplication of numbers, but also useful for exponentiation, and for matrices.",
"url": "https://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?RSS",
"published": "2015-05-18T19:30:30.000Z",
"updated": "2015-05-18T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS",
"title": "Finding Perrin Pseudo Primes, Part 2",
"description": "So now we've got the scaffolding of a program to find these Perrin Pseudo-Primes. The timing shows that it overwhelmingly spends all of its time in the routine to test whether or not a number passes the \"Perrin Test.\" So there are a few things we need to do.",
"url": "https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part2.html?RSS",
"published": "2015-05-17T19:30:30.000Z",
"updated": "2015-05-17T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS",
"title": "Finding Perrin Pseudo Primes, Part 1",
"description": "A while ago I was asked: Consider the sequence k(n) with k(1)=0, k(2)=2, k(3)=3, and k(n)=k(n-2)+k(n-3). Why is it true that n divides k(n) if and only if n is prime?\" My immediate response was \"Well, it's not true.\" So I was challenged to find a counter-example.",
"url": "https://www.solipsys.co.uk/new/FindingPerrinPseudoPrimes_Part1.html?RSS",
"published": "2015-05-15T19:30:30.000Z",
"updated": "2015-05-15T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS",
"title": "The Unwise Update",
"description": "This story passed on to me first-hand from the engineer involved.\nIt's a true story about how insufficient knowledge among operating\npersonnel about the operational consequences of new technology may\nhave accidental effects.",
"url": "https://www.solipsys.co.uk/new/TheUnwiseUpdate.html?RSS",
"published": "2015-05-13T19:30:30.000Z",
"updated": "2015-05-13T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS",
"title": "Miles Per Gallon",
"description": "I remember a while ago attending a talk that did something utterly\nbizarre with units of \"miles per gallon.\" I don't remember much\nabout it, but I thought I'd attempt to reconstruct the process in\na post, just to see how far I get, what conclusion I reach, and\nwhether people think it's as bonkers as I do. Here we go ...",
"url": "https://www.solipsys.co.uk/new/MilesPerGallon.html?RSS",
"published": "2015-05-03T19:30:30.000Z",
"updated": "2015-05-03T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS",
"title": "Tracking An Item On Hacker News",
"description": "A couple of weeks ago I had an exchange with a user on\nHacker News about user \"ages.\" I wrote that up in my\nprevious post, and then submitted it. I was surprised\nthat the item garnered enough attention to make it to\nthe front page, but that was when a little foresight\npaid off. I don't usually bother with analytics on my\nsite, but on this occasion I put a tracker on the page\nto count the number and times of page hits.",
"url": "https://www.solipsys.co.uk/new/TrackingAnItemOnHackerNews.html?RSS",
"published": "2015-05-02T19:30:30.000Z",
"updated": "2015-05-02T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS",
"title": "Hacker News User Ages",
"description": "A few days ago I was reading Hacker News and someone had\nposted a poll with the following question:\nHow old is your HN account?",
"url": "https://www.solipsys.co.uk/new/HackerNewsUserAges.html?RSS",
"published": "2015-04-19T19:30:30.000Z",
"updated": "2015-04-19T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS",
"title": "Poking The Dusty Corners",
"description": "In chatting with people about what a maths degree is, and what it\ndoes for you, I've often been intrigued by a particular response.\nI've shown them something that they expect to be true (or false)\nand then shown that their expectations can be confounded. When\nI do that, a common response is \"Well, you're just being stupid.\"",
"url": "https://www.solipsys.co.uk/new/PokingTheDustyCorners.html?RSS",
"published": "2015-04-14T19:30:30.000Z",
"updated": "2015-04-14T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS",
"title": "There Is No Time For This",
"description": "I'm finding these days that I just don't have\nthe time to do everything myself. I don't have\ntime to evaluate everything on its merit ...",
"url": "https://www.solipsys.co.uk/new/ThereIsNoTimeForThis.html?RSS",
"published": "2015-04-03T19:30:30.000Z",
"updated": "2015-04-03T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS",
"title": "Publically Sharing Links",
"description": "For years I've been visiting, reading, and contributing to a site\ncalled \"Hacker News.\" About 3.5 years ago I basically withdrew,\nfinding it increasingly frustrating, but I never really went away.\nSlowly I've returned and contributed again, although not at the same\nlevel, and generally just by contributing links and not often getting\ninvolved in the discussions. But once again I'm getting frustrated\nand want to leave, but where else can I share things I find, and then\nenter into discussions?",
"url": "https://www.solipsys.co.uk/new/PublicallySharingLinks.html?RSS",
"published": "2015-01-05T19:30:30.000Z",
"updated": "2015-01-05T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS",
"title": "Learning Times Tables",
"description": "Should primary school students be drilled on their times tables?",
"url": "https://www.solipsys.co.uk/new/LearningTimesTables.html?RSS",
"published": "2014-12-14T19:30:30.000Z",
"updated": "2014-12-14T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS",
"title": "Graceful Degradation",
"description": "I first learned about graceful degradation from a colleague. He prefaced\nhis story by saying that good people learn from their mistakes, but the\nbest people learn from other people's mistakes. This is a bit like the\nsaying in aviation circles that a good landing is one you can walk away\nfrom, an excellent landing is when they can use the 'plane again ...",
"url": "https://www.solipsys.co.uk/new/GracefulDegradation.html?RSS",
"published": "2014-12-12T19:30:30.000Z",
"updated": "2014-12-12T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS",
"title": "Diagramming Maths Topics",
"description": "An impossible task, but wouldn't it be useful to have some sort\nof diagram of topics in maths, connected somehow to show the links\nbetween topics? How could such a diagram been created? How could\nit be explored? How could it be dynamic? Maintainable? Usable?",
"url": "https://www.solipsys.co.uk/new/DiagrammingMathsTopics.html?RSS",
"published": "2014-11-22T19:30:30.000Z",
"updated": "2014-11-22T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/OnTheRack.html?RSS",
"title": "On the Rack",
"description": "When travelling, I usually go as light as possible. Certainly when\ntravelling by plane I try to go \"hand luggage only\", and when doing\nvarious mini-tours of talks, and so on, I try to travel with just a\nsingle, small backpack. Sometimes it's not possible, but I usually\nmanage. Here's a story of one time when this had unexpected\nconsequences ...",
"url": "https://www.solipsys.co.uk/new/OnTheRack.html?RSS",
"published": "2014-08-26T19:30:30.000Z",
"updated": "2014-08-26T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS",
"title": "Square Root By Long Division",
"description": "The other day someone asked:\n\"Is the product of 4 consecutive positive integers always one less than a square?\" \nGood question. The answer is yes, and I solved it using a technique the interlocutor\ndidn't know.",
"url": "https://www.solipsys.co.uk/new/SquareRootByLongDivision.html?RSS",
"published": "2014-08-11T19:30:30.000Z",
"updated": "2014-08-11T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS",
"title": "Beyond the Boundary",
"description": "In which we show that 1+2+4+8+16+... is not equal to -1, and how that\nmight both surprise us, and not surprise us.",
"url": "https://www.solipsys.co.uk/new/BeyondTheBoundary.html?RSS",
"published": "2014-05-23T19:30:30.000Z",
"updated": "2014-05-23T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS",
"title": "Fill In The Gaps",
"description": "Recently I had an interesting conversation on twitter, insofar as one can\nhave a conversation at all in that medium. It started with the following\nperfectly reasonable question ... \"Sorry for what may be a stupid question,\nbut sin(x)/x has a limit of 1 as x -> 0, so does it not cross x=0 at 1?\"",
"url": "https://www.solipsys.co.uk/new/FillInTheGaps.html?RSS",
"published": "2014-05-03T19:30:30.000Z",
"updated": "2014-05-03T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS",
"title": "Software Checklist",
"description": "During the second World War, fighter pilots would scramble to take off.\nTheir heart would stop when the engine mis-fired. Was the fuel mix too\nrich, or too lean? Turn the control wrong way and they could die ...",
"url": "https://www.solipsys.co.uk/new/SoftwareChecklist.html?RSS",
"published": "2014-04-24T19:30:30.000Z",
"updated": "2014-04-24T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS",
"title": "NASA Space Crews",
"description": "In the Apollo missions many of the crew were experienced, but some were\nnot. So I drew a diagram - see what patterns you see.",
"url": "https://www.solipsys.co.uk/new/NASASpaceCrews.html?RSS",
"published": "2013-02-10T19:30:30.000Z",
"updated": "2013-02-10T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS",
"title": "The Birthday Paradox",
"description": "A classic puzzle/paradox is to ask: How many people do you need to have\nin a room before two of them share a birthday. In this post we see what\nhappens when 365 is not equal to 365, and how this affects computing the\nsizes of hash spaces.",
"url": "https://www.solipsys.co.uk/new/TheBirthdayParadox.html?RSS",
"published": "2012-11-06T19:30:30.000Z",
"updated": "2012-11-06T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS",
"title": "The Trapezium Conundrum",
"description": "Clear, precise, unambiguous and useful definitions are hard to come by\nin the real world. In maths we have the luxury of creating definitions\nthat we want, and then chasing down the consequences. If the definition\ndoesn't produce what we want, we can change it. But even things, things\naren't always as easy as we might hope.",
"url": "https://www.solipsys.co.uk/new/TheTrapeziumConundrum.html?RSS",
"published": "2012-04-17T19:30:30.000Z",
"updated": "2012-04-17T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS",
"title": "Revisting the Ant",
"description": "So last time in TheAntAndTheRubberBand we were talking about an infinitely\npatient ant walking on an infinitely stretchy rubber band. If you haven't\nalready, you'll need to read that.\n\nSo here's what's happening.",
"url": "https://www.solipsys.co.uk/new/RevisitingTheAnt.html?RSS",
"published": "2012-02-20T19:30:30.000Z",
"updated": "2012-02-20T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS",
"title": "The Ant and the Rubber Band",
"description": "There's a 1 metre long rubber band, and an ant, standing on it at one end.\nThe ant starts walking along it at a speed of 1 cm/min. Every minute the\nrubber band is stretched (uniformly and instantaneously) to be one metre\nlonger. The question is this: Will the ant ever get to the far end?",
"url": "https://www.solipsys.co.uk/new/TheAntAndTheRubberBand.html?RSS",
"published": "2012-02-09T19:30:30.000Z",
"updated": "2012-02-09T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS",
"title": "Irrationals Exist",
"description": "For this post I thought I'd have a quick diversion into talking about\nthe so-called \"Real Numbers.\" Upon reflection, however, I found that\nthere was so much I wanted to say that there was no way to fit it sensibly\ninto a single post. So instead I'll put some preliminary comments here,\nand then expand on them later. \nIn particular, I'll give an explicit proof that for every interval you\nchoose of non-zero length, there is an irrational in it.",
"url": "https://www.solipsys.co.uk/new/IrrationalsExist.html?RSS",
"published": "2011-12-20T19:30:30.000Z",
"updated": "2011-12-20T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS",
"title": "Multiple Choice Probability Puzzle",
"description": "Recently the following puzzle was running around the 'net:\nIf you choose an answer at random, what is your probability\nof being correct: A: 25%; B: 50%; C: 60%; D: 25% ?\n\nThe immediate thought is - there are four options, so if I pick\none at random then each has a one in four chance of being chosen.\nThat means the answer is 1/4, or 25%. But that doesn't work ...",
"url": "https://www.solipsys.co.uk/new/MultipleChoiceProbabilityPuzzle.html?RSS",
"published": "2011-11-15T19:30:30.000Z",
"updated": "2011-11-15T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS",
"title": "Random Eratosthenes",
"description": "Why do people think of the primes as somehow being \"random\"?\nWhat does that mean? How can we investigate? In this post\nI'll talk about a way of generating primes, and then see what\nhappens when we toss in some randomness, just for fun.",
"url": "https://www.solipsys.co.uk/new/RandomEratosthenes.html?RSS",
"published": "2011-10-28T19:30:30.000Z",
"updated": "2011-10-28T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS",
"title": "Wrapping Up Square Dissection",
"description": "We now have five valid dissections, and one \"dissection\" that might\nbe regarded as invalid. So what do we mean by \"a piece\" and just how\nmany dissections are there?",
"url": "https://www.solipsys.co.uk/new/WrappingUpSquareDissection.html?RSS",
"published": "2011-09-13T19:30:30.000Z",
"updated": "2011-09-13T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS",
"title": "Dissecting a Square (Part 2)",
"description": "So we return to the square. It's simple enough to cut it up into\nidentical pieces so that all the pieces touch the centre. But in\nhow many ways? I rapidly got 5 (or 6, depending on a technicality),\nand I started to wonder about a proof that 5 (or 6) was all of them.\nI posted a badly worded question on an internet forum, and rightly\ngot flamed for it, but in the answers was a shock. There was an\ninfinite family of solutions. And not just one ...",
"url": "https://www.solipsys.co.uk/new/DissectingASquarePart2.html?RSS",
"published": "2011-08-08T19:30:30.000Z",
"updated": "2011-08-08T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DissectingACircle.html?RSS",
"title": "Dissecting a Circle",
"description": "There are three possibilities when we dissect any shape:\nOne piece touches the centre point;\nThere's more than one piece and they all touch the centre point;\nTwo or more pieces touch the centre point, but some don't.\nBut what about the circle? If we just cut it like a pizza then we\nget all the pieces touching the centre. No problem there. \nWhat about the other possibilities?",
"url": "https://www.solipsys.co.uk/new/DissectingACircle.html?RSS",
"published": "2011-07-26T19:30:30.000Z",
"updated": "2011-07-26T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DissectingASquare.html?RSS",
"title": "Dissecting a square (Part 1)",
"description": "Some time ago I was given a challenge that turned out to be\nsurprisingly rich in surprises. It all starts by trying to\ndissect a square.",
"url": "https://www.solipsys.co.uk/new/DissectingASquare.html?RSS",
"published": "2011-06-01T19:30:30.000Z",
"updated": "2011-06-01T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS",
"title": "An Oddity in Tennis (Part 3 of Decision Trees in Games)",
"description": "In this final part we see how a proper analysis can throw\nup some surprising results in the detail, defying our\nexpectations.",
"url": "https://www.solipsys.co.uk/new/AnOddityInTennis.html?RSS",
"published": "2011-05-24T19:30:30.000Z",
"updated": "2011-05-24T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS",
"title": "Decision Tree For Tennis (Part 2 of Decision Trees in Games)",
"description": "Having seen the basic ideas in decision trees for games,\nwe now put it to real use in analysing tennis. This is\nthe prelude for a surprise ...",
"url": "https://www.solipsys.co.uk/new/DecisionTreeForTennis.html?RSS",
"published": "2011-05-18T19:30:30.000Z",
"updated": "2011-05-18T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS",
"title": "Decision Trees In Games (Part 1)",
"description": "A fairly standard exercise in probability is to ask who,\nunder a given scoring system, will win a game given the\nprobability of each move. In this first in a series,\nwe look at how to analyse simple games as a prelude to\nfinding a surprise in a well-known example.",
"url": "https://www.solipsys.co.uk/new/DecisionTreesInGames.html?RSS",
"published": "2011-05-15T19:30:30.000Z",
"updated": "2011-05-15T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS",
"title": "A Matter of Convention",
"description": "There are some things in life where people argue about how they\nshould be, and in fact there is no single \"right\" answer, we just\nneed to agree on one of them. So what is 6/2(2+1)?",
"url": "https://www.solipsys.co.uk/new/AMatterOfConvention.html?RSS",
"published": "2011-05-09T19:30:30.000Z",
"updated": "2011-05-09T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS",
"title": "Do You Nourish Or Tarnish?",
"description": "Interactions with others can nourish your soul, or can tarnish it.\nSeek out those who nourish your soul, but ask yourself: which do\nyou do?",
"url": "https://www.solipsys.co.uk/new/DoYouNourishOrTarnish.html?RSS",
"published": "2011-04-21T19:30:30.000Z",
"updated": "2011-04-21T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS",
"title": "Binary Search Reconsidered ...",
"description": "\"Binary Search\" was made popular as an interesting test problem\nby Jon Bentley ... I was stupid - I claimed: \"There is a simpler\ninvariant and simpler code that together have a few advantages.\"",
"url": "https://www.solipsys.co.uk/new/BinarySearchReconsidered.html?RSS",
"published": "2011-04-18T19:30:30.000Z",
"updated": "2011-04-18T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS",
"title": "Two Equals Four",
"description": "A cool puzzle. Solve one equation and discover that the\nanswer is two. Solve another equation and discover that\nthe answer is four. Realise that they are the same, and\nconfusion results.",
"url": "https://www.solipsys.co.uk/new/TwoEqualsFour.html?RSS",
"published": "2011-04-14T19:30:30.000Z",
"updated": "2011-04-14T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS",
"title": "The Lost Property Office",
"description": "A story of love lost, and how administrative processes\ncan cost your customers time, money and good will.",
"url": "https://www.solipsys.co.uk/new/TheLostPropertyOffice.html?RSS",
"published": "2011-04-11T19:30:30.000Z",
"updated": "2011-04-11T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS",
"title": "The Forgiving User Interface",
"description": "A user interface may seem obvious to the designer, but here are\nsome musings and examples that are not necessarily obvious. Or right.",
"url": "https://www.solipsys.co.uk/new/TheForgivingUserInterface.html?RSS",
"published": "2011-04-05T19:30:30.000Z",
"updated": "2011-04-05T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS",
"title": "Setting up RSS",
"description": "After my post about withdrawing from Hacker News\nsomeone asked if I could set up an RSS feed for my \"blog.\"\nHere are the first steps.",
"url": "https://www.solipsys.co.uk/new/SettingUpRSS.html?RSS",
"published": "2011-04-03T19:30:30.000Z",
"updated": "2011-04-03T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS",
"title": "Withdrawing from Hacker News",
"description": "For over 2 years I've been participating in a community\nof programmers, entrepreneurs and people interested in similar idea,\nbut the time has come to move on. Here's a post explaining why.",
"url": "https://www.solipsys.co.uk/new/WithdrawingFromHackerNews.html?RSS",
"published": "2011-04-03T19:30:30.000Z",
"updated": "2011-04-03T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
},
{
"id": "https://www.solipsys.co.uk/new/ColinsBlog.html?RSS",
"title": "Colin's Blog",
"description": "Re-starting my \"blog\" and trying to get the structure\nto be more, well, \"structured.\"",
"url": "https://www.solipsys.co.uk/new/ColinsBlog.html?RSS",
"published": "2011-04-02T19:30:30.000Z",
"updated": "2011-04-02T19:30:30.000Z",
"content": null,
"image": null,
"media": [],
"authors": [],
"categories": []
}
]
}