# Maths Jam Conference 2013 Session 1

The MathsJam ‘conference’ is split into sessions with multiple 5 minute talks. Here’s my summary of the first set of talks.

**Sam and Robbie**

Talked about their love of the game of Set. In short, they got to a point in the game where they couldn’t find a set to be made and tweeted a picture. Twitter found a solution very quickly but they wanted to write a program to find solutions and Sam was wanting to learn to code anyway. They found a way to code it in python but, not satisfied with that, are working on getting a computer to recognise an image of a Set layout to find solutions. It’s a work in progress but I think it brilliantly set the expectations for the rest of the conference. This is wonderful geekiness for its own sake!

I must get a set of Set.

In passing, Sam enthused about a programming website www.projecteuler.net . It doesn’t teach you to code but it provides a place for you to practise.

**Andrew Taylor**

The internet is full of nonsense. This annoys Andrew. Specifically, claims that certain date formations ‘Won’t occur for another 823 years’ particularly get on his nerves. Things like 8:09:10 on 11/12/13 – wow when will another date like that happen!?!

Naturally, he built a twitter account and used python in conjunction with the On-line Encyclopedia of Integer Sequences (OEIS) to tweet other ‘astonishing’ occurrences of integer sequences in the date/time of various days.

The account is @823years and it’s entertaining to follow.

**Phil Ramsden**

Phil’s talk surprised me slightly. He started off talking about how it used to be quite common to rhyme whole words with themselves. He also was talking about sestinas which are a form of poem containing 6 stanzas of 6 lines. I was just starting to think “It’s not #poetryjam” when he started to explain the specific way the rhyming words are reordered for each stanza. Suffice to say it’s a mathematical process that led him into thinking which *n-tinas* would work. This was some interesting maths and showed up issues with the numbers 7 and 8 for example. Phil has taken this really far into thinking about the links with mathematical conjectures and it was nice to see maths coming from an unexpected (to me, at least) place.

**Tony Mann**

This talk was about a gentleman called John Buridan. John wrote a book on self referential statements, leading Tony to make the claim:

*I say that I am the best looking man at mathsjam.*

Which turns out to be true, because he did indeed say it.

Buridan is known for something called Buridan’s ass which doesn’t appear to be actually something he wrote. However, Tony thinks he deserves more credit as he was the first person to see that trading was not a zero-sum game. It’s possible for two people to be trading where the gain to one person is greater than the loss to the other.

Again, an interesting talk about someone I’d not heard of from someone I’d enjoyed hearing from through Math/Maths podcasts.

**Adam Atkinson**

Gave an example of mathematical modelling in action from when he worked for a phone company. One of their clients thought they were being ripped off and Adam’s bosses weren’t sure whether they were ripping them off or not. The contract was of the form:

7p for the first 12 minutes and then 1p per minute after that.

Considering the data from a large number of phone calls led to the discovery that the length of the calls follows an exponential distribution. Rob Eastaway and I had predicted a Poisson curve and were surprised to find that very short phone calls (ie ones that can be considered to be 0 seconds) are the most common.

**Phil Harvey**

Phil gave a delightful talk on triangular numbers including things like:

(Triangle number) x 8 + 1 = Square number

Given the sum of two triangular numbers, he was able to work out (mentally) which two ones had been picked. He also went on to do a similar trick with the addition of two square numbers.

This was an enjoyable talk and it was good to be reminded of a simple mathematical thing (triangular numbers) that seem to impress non-mathematicians so much. It also touched on mental arithmetic tricks, which is something I’m interested in.

**Colin Beveridge**

Colin started by reminding us of the Monty Hall problem. It’s something of a classic in maths.

What came next was the Chris Tarrant problem.

Suppose you’re on *Who wants to be a Millionaire* and it’s the £64,000 question. You don’t know the answer so, in your head, you’ve picked A. You use your 50:50 lifeline and the computer takes away B and C. Should you switch? How is this similar/different to the Monty Hall problem?

Colin wouldn’t tell us the answer. I think I have it sorted in my head now but won’t spoil it for you here. It’s a really nice question!

**Tiago and Rita**

This pair talked/showed us about a game that I really want to start playing. The basic game is called Hex and was invented by Piet Hein and John Nash and is similar to the TV program *Blockbusters* without the tedious questions and letters. Tiago told us about some variants:

- Product. You take turns placing a counter on the board. You can play your own or your opponent’s pieces. At the end, you multiply the sizes of your two largest areas together. Highest score wins.
- Yavalath. Simply, make 4 in a row to win but, if you make 3 in a row, you lose.
- Hexagain. A 3-player hex variant. The hexagon playing board has sides A,B,C,D,E,F. One player is trying to connect A to C, another B to D and the third E to F.

A great end to the first session and I suspect many games of this were played in the evening.

**End of session 1**

*After all this maths fun, it was time for coffee and a chance to talk to the speakers. I would probably have talked to everyone but only had chance to talk to Colin and Phil really.*

That’s the end of my summary for now. I’d love to include further links to these topics and I’m happy to include the speaker’s links to twitter or blogs etc. If you have additional links I should add or if you spot something I should correct, please let me know.

Yavalav is Yavalath.

Do you really think in hashtags?

Peter.

I think I actually did on this occasion!

My experience of Mathsjam had only been through twitter up until the conference.

Yavalath.

Thanks.

The “discovery” that call lengths are exponential was fake in the sense that I knew they were assumed to be that in modelling (because it’s convenient as I said) and I was a little concerned that everyone at MJ would already know this and throw things. However, until the incident described in the call I hadn’t tried making a histogram of the lengths of a few hundred thousand actual calls and I _was_ surprised that exponential turned out to be as good as it did.

I’m one of the people that didn’t know they were already modelled as exponential.

Even so, it’s interesting that the fit was so good.

The real reason I looked up “exponential distribution” in some A2 books in shops just before mathsjam wasn’t so much to see if it was on the syllabus at all (which I thought it was but I could be wrong) but really to see what examples were given. “telephone call lengths” would have made me go “ah, right, better re-jig that then”. I am pretty sure I did the distribrution itself at A-level but am not sure when I first learned about the telephone calls. Asking a few people at lunch on Saturday suggested that enough people would be surprised that I should carry on regardless.

I’d have guessed an approximate power law distribution rather than exponential.

The plot you drew does look kinda-exponential, but so do lots of other things with different decay rates. I guess there’s better evidence that it’s exponential than the fact that the plot looks kinda exponential?

Yes, I believe Adam did some extensive investigating.

I suspect it’s no worse than e.g. some of the things you get told are approximately normally distributed, and the convenience of “average excess length beyond this point” being the same as the average of the entire distribution is so great that I suspect the usual drunks and car keys story comes in here, and uniform spherical cows. Exponential length distribution is the standard used in telecoms modelling as far as I know. (Note: I don’t actually do this for a living but have some stuff about it.) However… remember modems? They utterly RUINED the exponential call length model while they were common, I gather.

In the original data set (which is not the one I used on Saturday) I did check how good a fit the exponential distribution really was and I also checked to see whether using raw call data vs using the exponential model made a difference when choosing between the 6 prices quoted. (All 6 were of the form “initial so many minutes for this much, then so much per minute after that). It didn’t. Neither did using call logs from some other calendar months if I remember correctly. I’m not saying the exponential model was awesomely perfect but it did seem to be close enough for the sort of thing I was up to, and the convenience factor was a big push obviously.

My graph on Saturday had way too many 0 and 1 second calls and I hope that eliminating incoming and internal calls would deal with this – diverts and voicemail and things showing up as apparent very short calls pollutes the data and as these aren’t outgoing calls they wouldn’t cost anything (from the point of view of the customer in the story) so shouldn’t be in the graph. More generally, the length distributions of non-fake incoming and internal calls might be different from those of outgoing calls so they should be eliminated as well.

If I did a more-than-5-min version of this clearly I’d want to talk about checking it a bit better. Am I kidding myself that the “How do you compare a bunch of offers of this form?” scenario could be used with an A-level (possibly Further) class somehow?

It’s been a long time since I was in an A-level class, but I think it could be done.

It’s certainly nice to know that people really do look into how best to model situations ‘in real life’.

I don’t teach core maths to A level students but I’m sure there’s some way of using this in a class.

On the Chris Tarrant problem … the big difference between this and Monty Hall is that the elimination is independent of your choice. The same answers would have been eliminated whatever you had come up with in your head. If the answer you thought was correct is not eliminated then you should stick with it, because the fact that it remains as an option increases the corroborative evidence for it being correct.