Hello. It’s been a while since the last Aperiodical. That’s exactly how long it takes me to prepare and write each issue, so here we are.
“Here” is not where it used to be, so I should explain — The Aperiodical is now the name of a big maths conblogerate, of which these untimely collections of miscellanea occupy a small corner. The first four editions of the Internet Maths Aperiodical are still available on ACMEScience.com, and will be for as long as Samuel wants them there.
So, on with the interesting maths links and so on!
Everybody in every nation likes to wring their hands and complain that their children are falling behind everybody else’s children in maths, because everybody else teaches maths better. I came across a couple of news stories recently in this vein: “Follow Brits and do the maths, says top advisor” in the Sydney Morning Herald, and “Teaching students the British way” in the Deccan Herald. The latter story contains a rather enticing implication that all British children are taught maths using chocolate. Yum.
Bode’s Law is either the most useless mathematical law or the most interesting mathematical mistake in the solar system, according to io9, who changed the title of their article from the former to the latter some time in between the day I bookmarked it and now. Personally, I think Bode’s Law is further evidence for my strongly-held anti-platonist views.
Humanity’s eternal quest to classify its every activity into the sets P, NP-complete and NP-hard continues, with the surely world-changing news that Pacman is NP-hard, and so are some other computer games, and Masyu is NP-complete. Masyu puzzles don’t always have unique solutions, which rules them out of Simon Tatham’s portable puzzle collection and out of the category of real puzzles, in my mind.
I’m now quite sick of NP-completeness proofs. I know they’ve become a sort of tradition in the Aperiodical, but I now find them entirely uninteresting. Will some marvellous new NP result regenerate my enthusiasm before the next instance of this organ? Maybe that question is NP-hard. Goddammit all.
Here are some real real puzzles, though: the Jerry Slocum Mechanical Puzzle Collection is being photographed and archived online. The collection contains over 34,000 puzzles. You’ll have to go to Indiana University to play with them though, which isn’t a constraint Gurmeet’s Delightful Puzzles suffer under. Working your way through Gurmeet’s list, from the easy to the difficult puzzles, might be a satisfying way to spend a portion of your life.
Arts and crafts now, with a proof in the style of Dr Seuss that the halting problem is undecidable by Geoffrey K. Pullum, titled “Scooping the loop snooper.” I didn’t mean to imply that there is a Dr Seuss style of mathematical proof in the previous sentence, by the way: I meant that the poem is funny and rhymes a lot while teaching you things. Hope that clears things up.
I found a post on Google+ about Tchokwé people’s tradition of using algorithmic sand drawings to serve as both mnemonics and illustration for stories. João Figueiredo has provided lots of explanation and links, and a really nice slideshow of pictures.
Do you like maths? Do you like “art”? Are you not entirely sick of seeing the same few popular maths concepts and MC Escher cartoons reproduced in “maths art” pieces? Then watch this short film:
Outside the wider cultural context of every individual item in it having been done to death before Elizabeth ascended to the throne, it’s a pleasant, watchable tour through just about every famous maths thing. Half-heartily recommended!
My final arts item is a gallery of S Harris’s cartoons. S Harris drew the famous “and then a miracle occurs…” cartoon, which is never more than five column inches away from a popular maths article. Don’t associate the cartoons in your mind with the humourless people who keep reprinting that exemplar though, because they’re really good. I can’t link to any of my favourite cartoons individually because, I assume, the cartoonist is worried about copyright infringement. But that’s fine: you won’t regret browsing through the whole lot.
That was a nice arts section. Let’s segue away from it slowly, with some Modern Nomograms. Nomograms are charts which embody particular mathematical formulas, so calculating values just involves plotting a line between the numbers you already know. Anyway, these Modern Nomogram chaps have made up a rather appealing poster to calculate posterior probabilities using Bayes’ Theorem, which I might just buy as a present for the Bayesians in my department.
On her blog, Tanya Khovanova tells us how a theorem becomes a magic trick: just like that!
Interactive proofs form sort of a superset of zero-knowledge proofs because it isn’t necessarily secret knowledge which allows one party to do something the other can’t: superpowers will suffice. A superpower I can appreciate is the ability to distinguish colours. A pleasing, child-accessible (what is it about interactive proofs?) article on Images des mathématiques titled “Je suis daltonien, mais je m’en sors” (“I’m colourblind, but I get by”) recounts a possibly-made-up story of how the author helped his children prove that they can distinguish the colours of his socks better than he could. The article’s in French. Désolé, lecteurs monolingues.
This edition’s interesting esotericum is a breezy paper giving decimal calculations of the continued fractions formed from the sets of primes, double primes, Mersenne primes, etc. The continued fraction whose denominators are the prime numbers is quite coincidentally close to one of Rényi’s parking constants.
Let’s end with a showing of Rubik The Amazing Cube (via metafilter)