Un million de singes...

The Infinite Monkey Theorem is a favorite of many. It was selected by as one of the Top Eight Best Thought Experiments ever, and it was attempted in real life once by six monkeys and a £2,000 grant.

The concept is as simple as often repeated: half a dozen, dozens, an army, a million, or infinite monkeys, in front of as many typewriters, given enough time, would type in all the works of Shakespeare, or the books in the British Museum, or the books in all languages in all the finest libraries in the world.

But who came up with the idea in the first place?

Many will assign it to Arthur Eddington, the British astrophysicist mainly famous for his work with relativity. In 1927 he wrote:

… If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules returning to one half of the vessel.
(A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927. New York: Macmillan, 1929, page 72.)

Yet it was Félix Émile Borel, the French mathematician with works in set theory, that, in 1913, first conceived the probabilistic consequence of having a million idle monkeys with typewriters available:

… Concevons qu’on ait dressé un million de singes à frapper au hasard sur les touches d’une machine à écrire et que, sous la surveillance de contremaîtres illettrés, ces singes dactylographes travaillent avec ardeur dix heures par jour avec un million de machines à écrire de types variés. Les contremaîtres illettrés rassembleraient les feuilles noircies et les relieraient en volumes. Et au bout d’un an, ces volumes se trouveraient renfermer la copie exacte des livres de toute nature et de toutes langues conservés dans les plus riches bibliothèques du monde. Telle est la probabilité pour qu’il se produise pendant un instant très court, dans un espace de quelque étendue, un écart notable de ce que la mécanique statistique considère comme la phénomène le plus probable…
(Émile Borel, “Mécanique Statistique et Irréversibilité,” J. Phys. 5e série, vol. 3, 1913, pp.189-196.)

Allez singes!


I came across a bizarre post from a self-proclaimed “high-school teacher”. [UPDATE: Mark claimed he “has taught high school students”, not to be a teacher ]

A high schooler’s knowledge of math won’t get you all that far, anyway. It only comes from higher study, and America still has the world’s best system of institutes of higher learning. […] If our goal is to be a scientifically and technologically vital society, the masses are not the place to look.

That argument is stunning given current news. When so many admit “they didn’t fully understand the mortgage papers they were signing”, to say that high-school math won’t get you that far is disconcerting.

At this point, it should be obvious that the educational system works as Babushka matryoshka dolls, where each level requires knowledge and skills acquired in the previous level. So how can we expect poorly skilled high-schoolers to do well in the undergrad and graduate schools?

Anedoctal evidence points out the inability of American students to follow through in American Universities. American students do not have the math skills necessary for a science-and-engineering graduate degree. Not because they are dumb, but because they simply never learned these skills: at UWM, for example,

about 65% of incoming freshman test into courses that cover material they should have mastered at or before their junior year of high school. Only 5% test as ready for calculus.

Foreign students in America

Foreign students in America

Hard evidence comes from the National Science Foundation: in 2005, foreign students on temporary visas earned half or more of doctoral degrees awarded in engineering, mathematics, computer sciences, physics, and economics. Perhaps American universities “prefer” foreign students… but maybe they are just better students regardless of their origin.

Most of postdoc students in US are foreigners

Most of postdoc students in US are foreigners

Noncitizens account for much of the increase in the number of science and engineering postdocs, especially in biological sciences and medical and other life sciences.

The number of science and engineering postdocs with temporary visas at U.S. universities increased from approximately 8,900 in 1985 to 27,000 in 2005. The number of U.S. citizen and permanent resident science and engineering postdocs at these institutions increased more modestly from approximately 13,500 in 1985 to 21,700 in 2005.

So much for a “scientifically and technologically vital society”.

But nothing summarizes better the utter state of denial as this sentence:

Anything that requires a minimal amount of the sort of mathematical, logical, and/or algorithmic thinking employed by a math, science, or computer-type person can now be automated to the point where an intelligent chimpanzee can do it.

Hopefully that doesn’t include teaching in high-school.

Science and Math Defeated” is the name of a very interesting blog I stumbled upon. According to itself, its noble purpose is truth-telling, and the author admits (emphasis is mine):

“while the views expressed here are not always representative of academia at large, the views are nevertheless correct.”

Dark Matter, nature of light and time, infinite numbers and logical induction are at peril, as the blogger sides with the “smartest man in the world” (that would be Noam Chomsky) when appropriate or follows the… let’s be generous here, somewhat outdated Rene Descartes philosophy.

This blog will challenge your definitions, senses and sanity.

UPDATE: Now it’s about Probabilities! :-)