Turtles all the way down

From Logicomix: an epic search for truth by Apostolos Doxiadis and Christos H. Papadimitriou, art by Alecos Papadatos and Annie Di Donna. More about this when I find time to read it!

The three jars problem

Here is a relatively well known puzzle (it appears, for example, in the film Fermat's Room.

"You are given three closed tins of sweets that are labelled "Lemon Sherbet", "Toffees" and "Mixture". One contains lemon sherbets, one contains toffees and the third contains a mixture of the two, and they are all wrongly labelled. What is the minimum number of sweets that you have to remove in order to ascertain which jar contains which variety?"

If you don't know the problem, work out the answer now before reading any more. So that you can't immediately see the answer I give below, I'm interposing a totally irrelevant image:

(Bottles of sherbet powder in Goodies Sweet Shop, Steep Hill, Lincoln: photograph by Andy Dingley from Wikipedia Commons.)

The book answer is one. If you take one from the tin labelled "mixture" it tells you what is in that tin, since it isn't the mixture. You can then easily identify the other two, knowing that neither is correctly labelled.

I think this answer is wrong. The true answer is zero. (And this is not because of any issue with the wording, that you might be able to feel or smell what is in the mixture tin without actually removing anything.)

You don't actually have to remove a whole sweet. You could open the mixture tin and break one of the sweets into two, remove half a sweet and work out the answer. You could take a smaller piece than a half - it could be a third, or a quarter, or a fifth, or even smaller.

In fact, for any epsilon greater than zero, you could remove a piece smaller than that size and it would give you the solution. So the number of pieces you have to examine is smaller than any positive number. The only such number is zero, so zero pieces suffice.

Maths puzzle competition result

The entries for the freshers' maths puzzle competition on Friday have been marked and we can now announce the winner. It was very close, with all teams scoring well, but Adam's group scored 78/100 to beat Andrew and Daniel's group by a single point.

Congratulations to the winners. And, while some of the expositions could have been clearer, remarkably, every script submitted was easily legible. Keep that up, please!

Greenwich Scavenger Hunt Result

Winners: Jodie, Chris, Kieron, Corin etc.
(Note: I'll act as middleman and get you all a discounted membership of the OR Society for only £150 a month each)
Highly commended: Roxy
Finding out the hard way that rebels don't win anything: Nic and his group

Games in Greenwich Park with new students

A very successful afternoon of mathematical games in Greenwich Park with new first year students and their mentors. Naturally the staff team, with superior knowledge of the mathematics of statics and dynamics, scored a decisive victory at Jenga.

iSquared special issue

The latest issue of the excellent maths magazine iSquared is a special issue about "Women in maths". It contains a number of thought-provoking articles, interviews, reviews and quotes, from Emilie du Chatelet on the prejudice which excluded women from the sciences in the eighteenth century to Julia Robinson wishing to be remembered as a mathematician regardless of her sex.

iSquared has been nominated for the Maggies awards for the best magazine covers of the past year. A tip - if you are thinking of subscribing to iSquared (which I recommend), if you vote for the awards you get a voucher which gives you a discount on a subscription.

Science Museum

A visit to the Science Museum is always fun. Highlights today were seeing the original book with Kepler's view of the planets fitting into the Platonic solids, Henry Perigal's geometric pen, ome Indian weights and measures (the same object being both), a model of Kelvin's tide-predicting machine, Alan Bennett's blown glass Klein Bottles, and the wonderful range of polyhedra models.

Any visit to the Science Museum reminds me of previous visits, from my first visit to London when I was 11, a later visit with my father when I finished my sixth form, visits during my undergraduate days and ever since. And of course my favourite object of all, Bill Phillips's water-powered economic computer Moniac, which I remember admiring with my father on that first visit forty years ago. It's a false memory - the Museum didn't have the object then - but it's still part of my personal story of how I became interested in mathematics, mathematical modelling and computing: the areas in which I have spent my entire working life.

Coincidence?

One of the freakest random events ever seems to have occurred in the Bulgarian national lottery, when the same six winning numbers were selected on two consecutive draws on 6 and 10 September. An investigation has apparently found no evidence of wrong-doing: it was just a remarkable coincidence. I find that hard to believe. What do you think?

http://news.bbc.co.uk/1/hi/8259801.stm

Ian Stewart coming to Greenwich!

I'm thrilled to hear that Ian Stewart has accepted an invitation to give the keynote speech at the Undergraduate Mathematics Conference which the maths department at Greenwich is organising, with support from the IMA, next February. (For more details of the conference contact the organiser Noel-Ann Bradshaw.)

Ian Stewart is the author of many wonderful books including Why beauty is truth: a history of symmetry, Letters to a young mathematician, Professor Stewart's Cabinet of Mathematical Curiosities and Taming the Infinite: The Story of Mathematics. This summer he was awarded the Christopher Zeeman Medal, awarded jointly by the LMS and the IMA for his work on promoting mathematics. He is a brilliant speaker, and it will be wonderful to hear him at Greenwich again.

(Photo by Avril Stewart from Wikipedia Commons.)

A fascinating novel

I've only just got around to reading this fascinating novel, published last year. It fictionalises the relationship between the mathematicians Hardy, Littlewood and Ramanujan almost a hundred years ago. Historians may object to some of the liberties taken by the novelist, but it is a loving examination of a mathematical world, not ar removed in time, but now almost unthinkable. It deals with the characters' dilemmas sympathetically. As one who was brought up on the story of Hardy and Ramanujan as it has become part of mathematical folklore, I was particularly interested to see a non-mathematician's take. A thought-provoking novel which I strongly recommend.

Simon Singh at the British Science Festival

A wonderfully entertaining and thought-provoking lecture by Simon Singh at the British Science Festival on "Why journalists love stupid equations and other problems in the media". The issue of how to promote maths is not straightforward and Simon brought out the complexities through a range of examples ranging from the blatant commercial creation of an equation designed solely to gather press coverage for a PR company's client. to serious research which appealed to the press: Simon showed that it's not always easy to distinguish these. In my opinion (for what it's worth) we have to live with the media we have and it's not worth getting worried about the appeal of stupid equations. Much more serious is the second issue Simon raised: that of the way the libel laws are constraining scientific debate and suppressing the expression of serious scientific comment. For more about this see the Sense about Science campaign.