Blockbusters of Interesting Maths

As part of the 24 Hour Maths Game Show which took place at the end of October 2022, our own Christian Lawson-Perfect designed a maths/games crossover gameshow format to end them all – a mashup of hexagon-fighting TV quiz Blockbusters, and his own personal obsession: interesting mathematical factoids. Welcome to Blockbusters of Interesting Maths!

The premise of Blockbusters of Interesting Maths is simple. Start by collecting three maths communicators – in this case, me (Katie Steckles), Sheffield Hallam Uni maths lecturer and recreational maths fan Alex Corner, and mathematician and juggler Colin Wright. Colin is a self-described “torturer of adults and confuser of children”, but to clarify, he mostly does that using interesting maths. Alex teaches on the SHU Game Theory and Recreational Maths module with our own Peter Rowlett, and was prepared to have a good go at coming up with some interesting facts. I, on the other hand, have come across far too many interesting maths facts in my time, and can definitely half-remember most of them.

Between us, we’re pitted against Christian’s board of randomly chosen words – from Ogden’s Basic English, a collection of 850 common English words, from which he’s deliberately removed a chunk of the mathematical and scientific terminology. To make our way across the board, we pick a letter and find the word hiding behind, and are then charged with coming up with some kind of interesting maths fact relating to that word.

Christian’s judgement on whether our maths fact was interesting enough is final, and we’ve got to make an unbroken line from one edge of the board to another. If we fail to come up with a sufficiently interesting fact, or our fact is deemed too tangential to the word in question, that tile is blocked off.

Since we could never do anything the easy/conventional way, instead of a tessellation of hexagons, CLP’s gone for the Cairo pentagonal tiling, so each cell is only adjacent to five others instead of six. His web gadget, a version of which can still be found online for anyone to use (BYO interesting mathematicians), was deployed live on the Game Show to challenge the three of us, and the below is a blow-by-blow of what went down, with links to some of the things we talked about.

We’ve also included some additional facts from Christian, who is also a font of interesting maths facts and is making up for the fact that he didn’t get to play himself. Next time!

Word 1: Moon

My initial instinct was to pass over to Colin, as he’s got a whole bit about calculating the distance to the moon using a pendulum, but instead he gave some interesting facts: the distance to the moon is pretty much exactly about 10 earth circumferences (~40 megametres), and it creates tides on opposite sides of the earth at the same time.

Christian: I can’t remember if anyone talked about all the different ways of counting a lunar month… I like the word sidereal and have no idea how many syllables it has.

Word 2: Undermined

We failed to come up with sufficient interesting maths for this – a bit of discussion about publishing results before someone else who’s working on them was deemed to be too depressing.

Word 3: Zebra

Alex talked about the work of Alan Turing on abiogenesis – mathematical models that can be used to describe patterns found on animal fur, including leopard spots and zebra stripes. Christian confirmed this was to do with reaction-diffusion models.

Christian: Back in 2008, a Simon Scarle published a paper connecting Turing’s work on reaction-diffusion to his other work on computability, through simulations of cardiac arrhythmia on the Xbox 360. I’ve never known what to do with this information. If you want to play with reaction-diffusion models yourself, there’s a good simulator called Ready, which we wrote about it in 2012.

Word 4: Quantity

I waffled briefly about the history of counting and the Ishango bone, which is an interesting historical artefact linked to early mathematical activity, and which it turns out I’d got mixed up with the Lebombo bone, which is an even older one.

Word 5: Stalk

Colin took this as a verb, and talked about predator-prey dynamics, particularly related to pursuit predation, including ambush and persistence behaviour in hunting. For each type of hunting, the animal has to weigh the probability of a successful catch against the amount of energy expended on the chase.

Word 6: Engineer

After a brief digression about which direction the real line points in (since we’d missed the opportunity to connect the board top-to-bottom, which most of us hadn’t realised was a thing), Alex couldn’t think of anything to say, so we lost this one.

Word 7: Intercept

After mentioning the mathematical use of the word, I managed to just about describe a particular maths problem this reminded me of that involved chasing something that’s swimming in a river (Christian mentioned this was covered in Dara Ó Briain’s School of Hard Sums, and it turns out there’s a writeup on Marcus Du Sautoy’s blog), and we then went on to another puzzle about a cat in a pond, which Ben Sparks has done a great video about.

Christian: Talking of interception reminded me of this fun paper describing a strategy for avoiding being intercepted while mapping an unfriendly subway system.

Word 8: Control

Colin covered a couple of topics – starting with control theory, which Colin compared to riding a unicycle. The trick is to keep the wheel under you, by (e.g) pedalling faster if you’re falling forwards, which can be understood by solving fairly straightforward differential equations – as unicycling robots often do.

He also talked about controlling a dog’s behaviour, and how rewarding good behaviour every time means the effect of training wears off more quickly, whereas rewarding it randomly some of the time means the effect lasts longer – this is related to spaced repetition as a learning technique.

Word 9: Charge

Back over to Alex, who took electrical inspiration and used it as a chance to talk about capacitor laws. There were lots of nice relationships between different physical laws and it all got a bit physics, and as a result was rejected by Christian, so we lost this one.

Word 10: Salt

I took the opportunity to talk about mathematical crystal structures, bond angles and 3D lattices (and got in a Kathleen Ollerenshaw mention). Christian also connected it to the structures of viruses, and mentioned Hamish Todd’s lovely videos.

Word 11: Mixture

Colin riffed on ratios in mixtures, from concrete to cake recipes, and then moved on to mixed techniques. Combinatorics, for example, uses a variety of different techniques you have to try in different combinations in order to solve a problem, and Colin explained how maths research, particularly in applied contexts, a mixture of techniques can be most powerful. Von Neumann showed that mixed strategies are always more effective in game theory!

Word 12: Client

After a brief digression about profit-loss models in economics, I jumped in with a mention of the version of internet protocols used in communication with objects in space, which Colin then ran with – talking about comms in trading (which relies on the speed of light to make sure transactions are instantaneous). A client-server model can be used, and in some contexts, equations from fluid mechanics are even used to describe how packets of information are moved around.

With that, we finally managed to satisfy Christian’s mathematical interestingness quotient and successfully connected the opposite sides of the board.

If you’d like to rewatch this or any other part of the 24 Hour Maths Game Show, you can find links to each segment on the website, and you can still donate to our charities by visiting 24hourmaths.com/donate.