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14 Feb

The Butterfly Effect

The day before yesterday there was a discussion on the tweeter that started by @mathematicsprof - one of the leaders of the tweeter math community.

Difference between a mathematician and a politician, a mathematician tries to say the most with min # of words, the politician the opposite.

While I knew what @mathematicsprof had in mind, I could not agree wholeheartedly. The manner in which mathematicians interact very much depends on the audience, subject, style, temperament, and, probably, other parameters.

For example, Benoit Mandelbrot - the father of fractals - was interested in approaching and communicating mathematics visually while his uncle - Szolem Mandelbrojt - preferred working in a formal manner. He's been quoted to the effect that he was quite satisfied that his works were being of interest to, and read by, at most two dozen of colleagues. For a time, Szolem Mandelbrojt was very active in the Bourbaki group, dropping out later on in part because of their adherence to stringent formalism.

The tweeter discussion was joined by monsoon0 who appeared to concur with @mathematicsprof:

@mathematicsprof I know a mathematician whose after-dinner speech to nonmathematical people started "Let F be a field "

Many a mathematician served a butt of mathematical jokes. There are even published collections of anecdotes concerning mathematical people. I especially love Howard Eves' In Mathematical Circles and Steven Krantz's Mathematical Apocrypha.

My entry into the discussion was

How does this jibe with the idea that mathematicians are always looking for shorter proofs?

With this question I wanted to kill two birds at once. Firstly, if mathematicians are indeed looking for shorter proofs, those that have been already published need not be quite short. Secondly, if mathematicians are indeed looking for shorter proofs, shorter proofs is what they would prefer if they had a choice. That is to say, @mathematicsprof was right, but there are caveats.

There are also extreme cases of mathematical work where the goals defeat brevity in a fundamental way. It took Bertrand Russell and his coauthor Alfred North Whitehead 362 pages in their Principia Mathematica to prove that $1+1=2$.

Of course there may be a chance that they were as cryptic as humanly possible.

The very next day I received a book for review: Invisible in the Storm by Ian Roulstone and John Norbury, with the corroborating subtitle The Role of Mathematics in Understanding Weather.

The little I know about meteorology is that forecasting is an extremely difficult and computationally intensive task that involves enormous amounts of data and nonlinear multidimensional differential equations. The difficulty of forecasting is epitomized by the Butterfly Effect discovered by an American mathematician and meteorologist Edward Lorenz in 1963. (Roughly speaking, hurricane formation somewhere close to, say, Japan, may be contingent on a lone butterfly flapping wings somewhere in Brasil.)

I am writing this after a very short period of browsing. The authors have an admirably lucid style; I'll be spending more time with the book over the weekend and my feeling is that it's going to be an enjoyable experience.

I realize that the book was shipped some time before the tweeter discussion has started; still, the thought that there might be a relation to the butterfly effect crossed my mind. On opening the book I almost immediately noticed a cartoon that did not directly invoke any connection to weather prediction:

The previous page and a special insert provided details on work and life of the American meteorologist Jule Gregory Charney (1917-1981), while the caption read:

Charney's fellow UCLA students enjoyed a cartoon in the student newspaper at his expense. The caption of the original shows what the intense doctoral student is saying to the lady in the evening gown: "... and since these are hypergeometric differential equations with logaritmic singularities ..." Fortunately, Elinor was sympathetic, and they were married in 1946.

It was a kind of a note to go along with @monsoon0's tweet. Mathematicians are very different, even in their idiosyncrasies. Politicians, on the other hand, seem to more universally fall into the pattern of speech alluded to by @mathematicsprof. I yet to find an example that could even remotely compare to Julius Caesar's, "Veni, vidi, vici" or match the terseness of another popular Latin,

dixi.

eight × = 56