Hexaflexagons are great.
If you haven’t seen one before, you’re about to have a lovely time.
If you have seen them before, the reason I’m writing about them is that I’ve made a webpage that helps you create a template for a hexaflexagon with your choice of picture on each of the three faces.
A couple of days ago, a question occurred to me:
What’s the furthest I’ve ever been from anyone else?
Maths news didn’t stop coming this month, and if you missed it, here was our coverage of the new Spectre aperiodic monotile, an improvement on the previous monotile discovery. Here’s some other news that happened in May and June which we didn’t otherwise cover here.
Vladimir Drinfeld and Shing-Tung Yau have been awarded the 2023 Shaw Prize for their contributions related to mathematical physics, to arithmetic geometry, differential geometry and Kähler geometry. (via the European Mathematical Society)
According to provisional 2023 entry data, mathematics remains the most popular choice at A level in England and Wales this year.
Ticket sales continue apace for this year’s TMiP maths communication conference, and in the meantime it’s inspired a nascent equivalent network for math communicators in the US – sign up if you’re an American math communicator who WLTM others.
There’s been a moderation strike at Stack Overflow, which includes Math Overflow, in response to AI-generated content policy changes. “Striking community members will refrain from moderating and curating content, including casting flags, and critical community-driven anti-spam and quality control infrastructure will be shut down.” (via theHigherGeometer)
There’s a free online IMA event, including a talk called ‘How Maths Helped Me to Annoy My Insurance Company’ by Victoria Sánchez Muñoz taking place at 5pm on Thursday 13 July.
Obviously the most important news this month is the new Rubik’s cube world record – it’s now possible for a human to solve the cube in as little as 3.13 seconds (furious they’ve skipped π seconds) and the GIF included in the article shows just how impressive the feat was.
And finally, this Nature article outlines how deep reinforcement learning has discovered faster sorting algorithms. Algorithms such as sorting or hashing are everywhere – used trillions of times a day, according to the article. This means even small efficiency improvements can be huge because of the scale, but these algorithms are so well-studied that further efficiency was difficult to imagine. DeepMind trained a deep reinforcement agent, AlphaDev, to work from scratch using assembly code to attempt to find a better sorting routine. The researchers reverse engineered the algorithms found by AlphaDev to C++ and found these led to performance improvements of “up to 70% for sequences of a length of five and roughly 1.7% for sequences exceeding 250,000 elements”. The Nature paper has details of the algorithmic improvements. The improved algorithms have already been implemented into the LLVM libc++ standard sorting library.
A conversation about mathematics and literature inspired by a book. Presented by Katie Steckles and Peter Rowlett with special guest Sarah Hart, author of Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature.
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The UK Government have announced the first set of King’s Birthday Honours for King Charles III. Here’s our selection of particularly mathematical entries for this year. If you spot any more, let us know in the comments and we’ll add to the list.
Get the full list of honours on gov.uk.
Disclosure: I know Kit slightly, off the back of conferences and WhatsApp groups. I try to remain impartial in reviews, but you know, human biases. From here on, in the interests of neutrality, Kit will be known only as Yates.
At some point during the pandemic, Kit Yates‘s bushy beard (and the rest of his face) popped onto our TV screen and I said to the kids “oh! I know him!”
It seemed like every news broadcast for the next month was interrupted by shouts of “hey! That’s dad’s maths friend!” Someone they’d never noticed before was suddenly in their consciousness; they had become victims of the Baader-Meinhof phenomenon. Meanwhile, I suffered from linearity bias, fearing that this was going to be the case forever — lockdown would never end, and he would be eternally prevented from writing his book by having to go on telly and explain that COVID is a big deal, actually, to people suffering from normalcy bias.
If you’re not happy with the occasional, justified bit of sweariness, then this probably isn’t the book for you
Cards on the table, I’m a Yates fan. His style is all-clarity-no-bullshit, and apparently happy to argue his corner against all-comers. His first book, The Maths of Life and Death, I reviewed here previously; I expected his second to build from there. Which, given that it’s called How to Expect the Unexpected, gave me a slight worry that I’d fallen into a paradox.
Don’t worry. It’s good.
Of course I wasn’t going to miss a chance to mention the Baader-Meinhof phenomenon again, who do you take me for?
The premise is that humans are, by nature, not very good at prediction, but can be better (at least sometimes). We have evolved an ad-hoc collection of heuristics that have served us perfectly well up to now, thank-you-very-much — like the linearity bias of thinking things will continue much as they are, the normalcy bias of thinking it’s not worth moving camp just because Ug saw what might have been a tiger in the undergrowth, and the Baader-Meinhof tendency of paying attention to new things.
These are admirable starting points — but they’re nowhere near the whole story. A linearity bias lulls us into a false sense of security when a process is exponential; everything is absolutely fine until suddenly it goes very very wrong very very quickly. A normalcy bias means that we’re loath to evacuate a building that really is under attack by tigers.
The book gives us tools to overcome these biases, backed up with plentiful examples and supporting evidence. If I say “Bayes’ rule and basic game theory,” you’ll roll your eyes; practically every pop-maths book of the last few decades has covered both in depth. However, Yates doesn’t tackle them from the usual direction; his examples are fresh and shed a new light on them — for example, he doesn’t lead with the birthday paradox when he’s talking about a combinatorial explosion, he uses several different applications first.
He also looks at the limitations of prediction, for example in the face of feedback loops: if the chief of a bank publicly admits they’re in difficulty, it only makes the difficulty worse (a snowball); if an epidemiologist says “we need to lock down or we risk 500,000 deaths” and we follow their advice, we lose rather fewer people to the disease, making the forecast wrong (a boomerang).
Prediction (especially weather forecasting) is also cursed by people not understanding probability and by chaos; Yates gives a brief history of meteorology, from sailors’ tales to modern supercomputing, that puts these curses in context.
My main gripe with How to Expect the Unexpected is that it starts off a bit dense — it’s really hard to keep track of all of the biases, fallacies and effects introduced, rat-a-tat-a-tat, in the early stages. I was a bit uncomfortable with the first chapter, in which he visits (and gently misleads) a spiritualist; for all that I agree that spiritualism runs a gamut from self-delusion to outright fraud, it still felt a tiny bit mean-spirited.
Despite that, I enjoyed How to Expect the Unexpected as much as I expected to. Yates has good science, good jokes and good explanations, and I hope for all our sakes that his next book isn’t held up by bird flu or something.
A conversation about mathematics inspired by a Battenberg cake. Presented by Katie Steckles and Peter Rowlett.
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Subscribe: RSS | List of episodes