Vladimir Arnold and Our Decline Into Innumerate Savagery

If there’s one thing you should read by Vladimir Arnold-who died last week at the age of 72, and who is memorialized by the Times today as “a founder of singularity theory, or, as it is sometimes more ominously called, catastrophe theory”-it’s his January, 1998 article “Innumeracy and the Fires of the Inquisition.” While Arnold’s work was what we laypeople would regard as a completely incomprehensible math, he was cognizant of the problems of the gulf between the state of written and taught mathematics and the ability of common people to understand it-and also extremely observant regarding politics, particularly sensitive to the presence and history of antisemitism, and greatly interested in the drift of Russia as a state concerned with an intellectual populace.

Here are some bits of that piece (available as a cached pdf here), which was, really, quite vicious (and came at a fascinating time):

We live in an insane world, in which most governments behave like the pigs under an oak tree in the fable by Krylov, both eating the acorns and digging up its roots, thus destroying the source of their very sustenance.

With the (temporary?) cessation of military confrontation between east and West, the funding of science in Russia has been virtually discontinued. Experts say that during the last 10 years it has decreased seventeen-fold and stands now at one-fourth of the level required for its mere survival. The spending on education decreased from 7% of the GDP in 1970 to 0.6% in 1997 (with further reductions planned for 1998).

[…]

It is somehow ridiculous to have to prove that every civilized person needs to be numerate: only savages think that bread comes down from the sky, that cars have always existed, and that there are no benefits from having airplanes.

Even more important than the ability to add fractions is the fact that a basic acquaintance with mathematics allows one to distinguish a correct argument from a faulty one. Without this ability, a society turns into a herd, easily manipulated by demagogues. According to Western experts, in the current situation in Russia, the assumption of power by a Hitler is even more likely than it was in Germany in the 1920s.

[…]

Whether our next ruler will be the Mafia or a charismatic nationalistic extremist (as is predicted by the head of the Department of Political Science of the MSU, who also calls for a struggle against the US, a struggle which “will require great courage and the ability to take risks”, and which will most
likely be of a “military-strategic” nature (Vestnik RAN, 1997, p. 1017)), the basics of fractions and percentages are absolutely essential in modern society. The future of a Russia in which the study of fractions is replaced by macrame appears bleak.

MACRAME, PEOPLE.

Let us leave you with a bit in which he took a look at the applications of real-world mathematics. That a complex mathematical thinker was also such a concrete thinker on politics and the applications of science is highly unusual.

All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA.).