Professor Scott Corry from upstairs in the math department will give a Science Hall Colloquium, “Symmetry: An Example from Graph Theory,” on Tuesday, November 1 at 11:10. The Colloquium is intended for a general audience, and according to usually reliable sources, Professor Corry will be speaking at a level the general public like me can understand. Here are the particulars:
Abstract: Professor Corry will provide a glimpse of how mathematicians ask and investigate questions in pure mathematics. Rather than speaking in broad generalities, he will describe one of his recent theorems about symmetries of finite graphs. No specific mathematical knowledge will be presumed, so all interested parties are heartily encouraged to attend.
Regular readers of this blog might remember Professor Corry as the winner of the 2011 Young Teacher Award right here at LU, so you can expect a clear, engaging talk.
You can find out by giving these problems a try. For comparison, here is an 8th grade contest from Math League, which I am not familiar with at all.It definitely wins in the cool pictures category. I suppose you wouldn’t want 8th graders to get bored while solving math problems in a competition. (There is a nontrivial risk of boredom, actually.) To be fair, one can find much better math competition problems in the US, like this one, called Abacus. By a remarkable coincidence, “[t]he program is based on a printed journal for gifted students, originating in Hungary over 100 years ago.”
First, let n be odd. We start with n=3: “Buffalo buffalo buffalo”; that is, some buffalo do buffalo buffalo, i.e., some buffalo are buffaloed by buffalo. But of course the buffalo who are buffaloing may themselves be buffaloed by buffalo, so just as some cats that watch mice are chased by dogs, or as we say, cats dogs chase watch mice, buffalo that buffalo buffalo themselves buffalo buffalo, and we can say that buffalo buffalo buffalo buffalo buffalo. Anytime we have the noun buffalo, we can add the relative clause “who are buffaloed by buffalo”, or better, instead of the noun phrase “buffalo who are buffaloed by buffalo”, we may say simply “buffalo that buffalo buffalo”, then add the rest of the sentence, yielding “Buffalo that buffalo buffalo buffalo buffalo”, or even better, “Buffalo buffalo buffalo buffalo buffalo”. To a sentence consisting of n (odd) occurrences of the word, we can produce a sentence of n+2 occurrences.
Thus for any odd n, a sequence of n occurrences is a sentence.
But just as a dog that chases cats is a dog that chases, buffalo that buffalo some buffalo are buffalo that buffalo, so from one of our sequences of an odd number of occurrences, we can lop off the final direct object, producing a sequence of an even number of occurrences that is a grammatical sentence. For any n>1, odd or even, a sequence of n occurrences of “buffalo” is a grammatical English sentence!
The layperson might take a quick look and say “Hey, that’s a Möbius strip shaped bagel!” Of course, it obviously isn’t, as it has a cream cheese side and a non-cream cheese side. But Mr. Hart does pose the Möbius bagel problem as a possible extension. My guess is that poor young George’s mathematical growth was seriously impeded by remarks such as “How many times have I told you not to play with your food?!” I definitely see an entrepreneurial opportunity here: just imagine how many math conferences would pay big bucks for catering that features Möbius bagels, dodecahedron-noodle soup, a spaghetti-knot challenge, and many Klein bottles of wine. I am soooo tagging this entry “Food for thought…”