BUMPS

For my last entry into this section before I hand over management of the website to John Meyer, I thought I’d share a favourite puzzle of mine with you. The below text is adapted from the blog of Terry Tao.

On a remote island in the Pacific, there is a tribe of 1000 people, 100 of whom have blue eyes and 900 of whom have brown eyes. The tribe is highly religious and one strict law of their religion is that they are forbidden from knowing their own eye colour or even discussing the topic with one another, though each tribesman can see the eyes of every other tribesman. The island is even devoid of reflective surfaces to prevent tribesmen from accidentally discovering their own eye colour, since if any member of the tribe does discover the colour of his eyes, the religion requires him to commit ritual suicide at noon the following day in the village square for all to witness. Prior to joining the tribe, all prospective members are required to undergo intense training in logic. In the village square, where daily prayers are carried out, it is inscribed on the tablet of holy laws, together with the rule about eye colour, that no person may be a member of the tribe without having first demonstrated that he is flawlessly logical and entirely committed to the laws of the religion.

What effect, if anything, does this faux pas have on the tribe?

Think about this yourself for a bit, then click here to unmask some further comment.

Despite the very convincing-sounding argument, “he hasn’t told them anything they didn’t already know”, the answer is not that the foreigner’s words have no effect. Think a little more, and if you want to see the answer, click here.

The correct answer is that 100 days after the foreigner’s address, all the blue-eyed people will commit suicide. Prove that your logic skills are good enough to join the tribe and work out why this is true and the previous answer is false!

If you want to read any more about this problem, there’s plenty to be found using Google.

Top effort by Phil Keen, recorded here for all time… Click for full size images.

Purely by chance, I just stumbled across a website claiming to sort MathSciNet reviews “by amusement factor”. I thought I’d share some of my findings…

• MR1427830: “He … adds an acknowledgement to the referee but fails to add an acknowledgement to Whittle for writing the original paper.”
• MR0746748: “This paper was incompetently refereed and should not have been published. In fact, the paper under review and the other papers by the author referenced in this paper constitute an embarrassment to the mathematical community.”
• MR0429922: “It is hard to imagine in a single paper such an accumulation of garbled English, unfinished sentences, undefined notions and notations, and mathematical nonsense. The author has apparently read a large number of books and papers on the subject, if one looks at his bibliography; but it is doubtful that he has understood any of them.”
• MR1786212: “This paper contains barely a single correct statement.”
• MR1884582: “Not every text containing mathematical formulae or terminology may be considered as a scientific work. Sometimes it is a mere imitation.”
• MR1418826: “Herein the author states ‘her genuine concern’ about Wiles’s purported proof of Fermat’s last theorem … which, after all, appeared in an ‘in-house publication in the Annals of Mathematics at Princeton’. … Of course, she has no such worries about the validity of her own, Euclidean-algorithm-inspired, proof of Fermat’s last theorem.”
• MR1656069: “The new proof is ‘quick’ only in the sense that a careful derivation is replaced by a few short and rather cryptic statements.”
• MR1428296: “This paper seems to the reviewer to contain no mathematics.”
• MR0785999: “They take the depraved view that this is the model of an optimal seducing policy for a dynamic continuous lover who at time t will have been done in by rivals or scorned women with probability 1-x(t). … No evidence is presented for the success of these policies in practice so we must conclude that the authors have had none.”
• MR1459261:“A famous Polish mathematician and one-time editor of Fundamenta Mathematicae is sometimes quoted as saying that he had never accepted an article more than eight pages in length, because a longer proof could not possibly be correct. The reviewer has never written an article which was less than nine pages, so needless to say, he doesn’t agree. But as many a provocative overstatement, this one has some truth to it, particularly if eight is replaced with eighty. … If one believes in miracles, such a paper may still be right. But will it ever find a devoted enough reader to be read, not just skimmed or quoted?”
  
  Many many more at Exceptional MathReviews.

This entry from PHD Comics seems like it’ll be relevant in the coming days:

“Piled Higher and Deeper” by Jorge Cham – www.phdcomics.com. Reproduced with permission.

Those of you who missed the Christmas party (how could you?!) missed out on a fantastic quiz this year, complete with a fiendish Dingbat-style (and mathematically influenced) picture round. Fortunately, all is not lost as you can now download the picture round in PowerPoint format here.

All the answers are Christmas themed and the second page is exclusively Christmas carols/songs. Enjoy!

A couple of optical illusions I stumbled across this evening that I thought I’d share with you all:

Believe it or not, both the orange circles and the squares containing them are exactly the same colours. Check it with your computer if you don’t believe me (or try squinting…?)

I promise you that this is an entirely stationary image. Click here for a larger and even scarier version.

Both files sourced from Wikimedia Commons.

It seems that we might be teaching our undergraduates a little too enthusiastically. The following photo of the low wall outside the Watson Building was taken last week (click on it for a larger version):

(sorry for the poor quality)

According to the caption on the right, “Chris and Olivia” are to blame…

OK, my first contribution to this section. An old one, but a good one, particularly for those who haven’t seen it before:

First introduced in 1948, the Curta mechanical calculator was concieved by Curt Herzstark in the 1930s. Capable of performing addition, subtraction, multiplication, division and even square roots, they sell for around £500 on ebay.

If you’re bored and looking for something of a (mathematical) challenge, the Harvard-MIT Mathematics Tournament has over ten years’ worth of problems at their web page. The tournament is aimed at A-Level students, so the questions generally do not use high level mathematics but they can be very tricky nonetheless.