via MetaFilter

Via teacher Tim Dolan on Twitter.

Here’s a collection of clips we recorded while people were digesting both their dinners and the first day’s talks.

And here are Pat Ashforth and Steve Plummer of Woolly Thoughts, showing me their fantastic illusion knit.

Thanks to Katie for drawing the short straw and editing these clips together.

The Hangout was just under an hour and a half long, and we managed to get through five of the seven sequences. Some of them are really hard to understand!

In future seminars, Kannappan Sampath has offered to lead us through something to do with the “kissing number” problem discussed in Sloane’s paper, and John McKenna has suggested “Recounting the rationals” by Calkin and Wilf.

More information

Follow The Aperiodical on Google+ to join in with the recreational maths seminar next time.

See the list of papers we’ve discussed in the Mendeley group.

Spend a day browsing the Online Encyclopedia of Integer Sequences.

I had a lot of fun, and it turned out I picked a particularly good paper to look at. I’m definitely going to try one of the more complicated puzzles this weekend at the big MathsJam.

I’m now going to waffle for a bit about the technicalities of the seminar, because I think a few people are interested and so I can gather my thoughts about it.

The format seemed to work OK. I started a Google+ hangout, invited everyone who had joined the event I set up on The Aperiodical Google+ account, and it all worked remarkably smoothly. I made sure everyone muted their microphones when not talking, to avoid distracting background noise, and encouraged people to use the text chat to ask questions or say when they’d like to speak.

I used the built-in Google+ screenshare feature to display the PDF of the paper, though I asked everyone to have their own copy visible so they could read ahead or linger on a section if they needed to. I think the image was fairly clear in the hangout, and it’s just about legible in the YouTube recording. I could’ve zoomed in another level or two to be sure it would look OK.

The attendees consisted of a couple of university lecturers, a couple of undergrads, and I think a couple of postgrads. I think everyone followed along fairly well, though we had to revise a few definitions from group theory. I think everyone joined in with a question or an explanation at least once, which was very encouraging. I was a bit worried at the start that everyone would sit in silence, waiting for me to tell them all about the paper.

There was a question at the end about how long it had taken me to read through the paper before the seminar. I deliberately didn’t read through it in advance. Either I would’ve got bored re-reading something I already understood, or I would’ve gone too quickly for everyone else to follow. Being unfamiliar with the paper meant there were several opportunities for other people to take over and explain bits, or answer questions asked by the others.

The whole thing took just over an hour. Unlike a physical seminar, people could join and leave without causing too much offence, so I was quite relaxed about not hurrying things along.

Thanks to everyone who took part. If you’re one of those people, I’d love it if you put a comment below with your thoughts on how it went, and any ideas you’ve got for how we could do things better next time.

I think fortnightly is a manageable period for the seminar, so there’ll probably be another one the weekend after next. Any suggestions for papers to discuss are welcome at christian@aperiodical.com.

Way back when, before we even launched this site, Katie and I made a video about a paper I’d found called Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles. The paper described a scheme for proving you can solve a sudoku puzzle without revealing your solution, using only paper and scissors. We tried it out, and it worked!

I’ve been wanting to do more videos like that, but papers describing new mathematical things to do with household objects are quite rare. I also have the problem that most of my Interesting Esoterica collection goes unread, even though there are quite a few things I’d really like to look at in more detail. So I’ve connected those two thoughts and come up with the ‘recreational maths seminar’.

The idea is this: I pick a paper from my collection that looks interesting, and post it along with a date to get together and discuss it. We all pile in to a Google+ On Air hangout and work through it for an hour or two, and leave as better-educated people, with a YouTube recording of the session for people who couldn’t make it.

I had a small test-run a couple of days ago with Colin Beveridge, where we looked at a very interesting paper titled Twin Towers of Hanoi. Here’s Google+’s recording of the session (I wasn’t particularly paying attention to the fact it was being recorded, so it starts and ends quite abruptly):

I need to pick a time that will suit the most people, and that I can make, so if you like the sound of my idea please put a comment below saying which of the following are convenient for you. I expect each seminar will last between one and two hours.

• Weekdays between 1800 and 2300 GMT
  (1300-1800 EST, 1900-0000 CET, 0300-0800 EDT)
• Weekdays between 0700 and 0900 GMT
  (0200-0400 EST, 0800-1000 CET, 1800-2000 EDT)
• Weekends between 0700 and 1100 GMT
  (0200-0600 EST, 0800-1200 CET, 1800-2200 EDT)
• Weekends between 1600 and 2300 GMT
  (1100-1800 EST, 1700-0000 CET, 0100-0800 EDT)

The Calculus of Love is a short film by writer/director Dan Clifton and starring Keith Allen. The film’s distributor got in touch with us last week to direct our attention toward the film, with the following synopsis:

Mathematics Professor AG Bowers is obsessed with solving the fabled 250 year old Goldbach Conjecture. When a series of mystery letters arrive hinting at a solution, Bowers believes his lifelong dream may at last be within reach.

After being shown at various film festivals, the film is now available to view online. I’ve embedded it below the fold, along with an interview with the film’s director, Dan Clifton.

CP: Why make a film about maths?

DC: I’ve made a lot of films about science and with scientists. I’ve always been interested in the idea that science is a noble pursuit for the truth, but that the pursuers – scientists themselves – suffer from all the usual human flaws. A character’s obsession with proving an unsolved mathematical conjecture felt like a good way to dramatise this conflict<

CP: Do you have a mathematical background, or did you consult with any mathematicians on the development of the film? If so, how was it working with them?

DC: I did Maths and Applied Maths to A Level standard here in the UK, so I’m not completely unversed in it. I did get a bit of help from the Institute of Mathematics though to be honest I pretty much formed the story alone.

CP: There have been quite a few mathematical thrillers (Fermat’s Room, A Beautiful Mind, Proof, Pi, Cube, to name a few). Why do you think that is? Is it something to do with the popular stereotype of a mathematician as a highly intense personality?

DC: I think it goes back to the nature of the quest – the quest for mathematical truth. It’s like beauty in art. Mathematical truth has an intrinsic rather than utilitarian value, and yet people can be completely captivated by it – and I think we all admire that trait. We’re fascinated by people who devote themselves to that pursuit, even though the character of Professor Bowers in my film is ultimately destroyed by it.

CP: The specific maths problem in the film didn’t seem too important – it could have been Goldbach, or Riemann, or P=NP, or any of the big unsolved problems. Instead the film seems to revolve around Bowers’ opinion of women mathematicians. Did you set out to make a statement about the treatment of women in maths?

DC: That’s an interesting note, and something a couple of other people have commented on! But the answer is no, that wasn’t what I set out to do particularly. And you’re right that the problem is quite general. As I say I wanted to find something unsolved, but that people are still interested in and committed to solving. But I also wanted to use that as a means of exploring the flaws in our motivation – how the quest for something beautiful and pure can be corrupted by baser motives.

CP: Do you plan on making any more films with a mathematical setting?

DC: My next project is hopefully going to be an adaptation of a William Boyd short story. It’s called PATIENT 39 and it’s about the relationship between a soldier with a serious head injury who’s lost his memory, and the doctor who cares for him, so it’s staying with a scientific theme. I certainly wouldn’t rule out returning to maths in the future, whether in my fiction or documentary work.

∎

So I hope you enjoyed that. The film has a website at thecalculusoflove.com where you can find a bit more information.

Ingredients:

• this sheet of combinator tiles
• some cardboard (I used an old pizza box, which was a terrible, smelly idea)
• glue
• blu-tack
• a quick read of the Wikipedia page on the SKI calculus

You’ve almost definitely heard of Turing machines and Turing completeness. You might have heard of the λ-calculus, which was invented by Alonzo Church around the same time as Turing was thinking about machines, and has exactly the same computing power (the Church-Turing thesis!) but looks very different. λ-calculus deals purely with functions and function application, in a very abstract algebraic way, so unlike with Turing machines it’s very hard to fix in your head a physical model of how computations happen.

The SKI calculus boils λ-calculus down to just three operations, or combinators. Those three¹ are enough to recreate every expression you can create with λ-calculus. I’ve been meaning to get my head round it for a while, but implementing it on a computer wasn’t very enlightening.

So I had a brainwave recently, which was that I could make tiles representing the combinators, and the way they fit together would dictate how they act. I just about worked out something reasonable yesterday, which is why I decided to record a video. I hope you found it interesting!

Further reading:

A nice page by Mike O’Donnell introducing the SKI calculus and explaining why it’s so great.

A browser-based SKI expression evaluator (it uses a different notation to the one I used in the video)

Lazy K, an SKI-based programming language you can use to write actual useful² programs in!

1. in fact you only need S and K or, if you’re really Zen, you can create a single combinator which does everything 
2. subject to your definition of the word ‘useful’

Numberphile filmmaker and general internet legend Brady Haran has been busy putting together a series of YouTube videos about the Rubik’s cube, with contributions from Aperiodical friends Matt Parker and James Grime. The videos also feature lots of solving clips sent in by viewers, and Aperiodical Editor triumvir and sometime maths-talker-abouter Katie Steckles (that’s me) occasionally pops in to make comments and state facts which are no longer true (a world record was broken 4 days after filming).

The series includes a video about the number 43,252,003,274,489,856,000, which is the order of the Rubik’s cube group (with excellent group theory from group theorist James); the number 20, which is sometimes called ‘God’s Number‘ and is the maximum minimum number of moves needed to solve a cube (aka the diameter of the Cayley graph of the Rubik’s cube group with the natural generating set); and also one about Superflip, the most hardest & difficultest scramble of a cube to solve, and one which does actually take at least the full 20 moves.

The whole collection of videos was released on 7th September, and can be found in this playlist.

This one is with Robert MacPherson, who invented instersection homology with Mark Goresky. I’d never heard of him and topology gives me the heebie-jeebs, but I’ve spent a very happy morning reading the fascinating biography and listening to the interview. The interviewer is Robert L. Bryant, also a research mathematician, so the questions don’t stray away from difficult topics. MacPherson comes across as an all-round excellent guy; I really recommend playing through all the clips when you have some time.