Tuesday, August 1, 2017

Mathematics & Totalitarianism in Sohlzenitzyn's First Circle

"Topology! The stratosphere of human thought! Maybe it will be useful in the 24th century, but nowadays...?"
-Nierżyn, In The First Circle, 10

It is not surprising that the officer in charge of the шарашка claims in jest that mathematicians are akin to a sect of knights. Mathematics is that very odd area of academic inquiry which runs the border between the humanities and the natural sciences. Its' conclusions are objective, but its' methodology is primarily deductive. As such it demands a rigor more akin to moral piety than experimental habit.

Math is the closest remnant of a Socratic disposition that remains in the modern world, but unlike much of Socratic philosophy, math offers verifiable answers which cannot be arrived at during wine symposiums but only through stoic work habits. With this in mind, it would do well to consider Solhzenitzyn's reminder that, contrary to Marx, all of the greatest men of science were likewise men of faith. This is not hard for a mathematician to understand. Yet in considering the relation of mathematics to totalitarianism, Sohlzenitzyn introduces a moral dilemma worth pondering.

Let us return again to consider the marked difference between the pseudo-intellectual and the mathematician in the debate between the Jewish Communist Rubin and Solhzenitzyn's fictional ego, Nierżyn. Rubin has quite obviously (as was the case with many Jewish Communists) transplanted his religious fervor from the Talmud to Marxism. Just as Job refused to condemn God even when suffering extreme hardships, so Rubin argues that his imprisonment and suffering cannot in and of themselves invalidate the moral absolute of the dialectical progress of History.

Nierżyn, as a mathematician, does not make the errors which haunt poor theologians with nothing but the religious instinct as their guide. He recognizes that in geometry if we have a right triangle ABC, with angle ACB=90 then the tangent angle BAC= BC/AC and BAC is less than 90 degrees. If we make angle BAC larger, moving towards 90 degrees by increasing the length of BC assuming AC is constant then the ratio BC/AC can be infinitely large yet the resulting angle BAC must remain below 90 degrees (there are an infinity of real numbers below 90 degrees so this is theoretically possible).

A tangent of 90 degrees would have no geometric meaning. This geometric claim is also visible in algebra because tan(x)=sin(x)/cos(x) and if sin(90)=1 and cos(90)=0 division by 0 is impossible and therefore tan(x) is undefined. The Bolshevik revolution sought this undefined tangent and defined it as a heretofore unknown freedom.

If, however, we accepted that this theoretical impossibility were executed in practice, then any further growth in the angle BAC beyond 90 degrees would make the tangent negative (here it helps to think of the lines forming this triangle on an (x,y) axis with AC=(0,1). This practical impossibility was what the Bolshevik revolution aimed for and, having unexpectedly achieved something thought impossible (the communist concept of freedom), it immediately collapsed into its negative (communist tyranny) - something likewise heretofore beyond practical experience.

This knowledge that Nierżyn possesses is simple and elegant, unlike the very complex reality of dialectical materialism. It is an elegance that Nierżyn recalls in conversation with his professor from his days as a student. The contrast between his recollections from before the  шарашка and his current imprisonment is striking:

"This pale gentleman in his bright tinted glasses seemed to Nierżyn, experienced as he was in prison life, a ghost who had illegitimately returned from a world long forgotten. A world divided from the present by the forests by lake Ilman...the sands and mud of Belarus, prosperous Polish farms, the shattered roofs of German towns. In this nine year interval he had experienced the raw 'boxes' and cells of the great Lubyanka, the grey stench of the prisons there...the biting winds of the steppes beating down on crowds of starving and freezing zeks. All of this made it very difficult to revive that old sensation one had in the past when writing down the units in real value functions on a blackboard."

This sentiment is not merely the nostalgia of youth, nor even of academic life. It is a very special type of sentiment proper to the mathematician or philosopher: an earnest love of revealed reality. For education disabuses us of the shadows which dance on the walls of our caves and sets us in motion towards the beauty of the sun and a world made beautiful and brought to life by sunlight.

The sense of belonging and happiness that an educated man feels on Earth, the specific sense of truths invisible to the eye, but clear to the mind which the mathematician spies in his studies - all of this sanctifies and elevates human life to a blissful state. A state no doubt shattered by the reality of war, tyranny, and the unthinking predatory rapaciousness of the human masses in the form of nationalist, communist or democratic ideology which is the norm surrounding Nierżyn.

The brutal reality of this evil norm blunts even the mathematician's sense of order in the universe. This juxtaposition of idyllic intellectual pursuits and the monstrosity of anti-intellectualism is the perfect foil in the progression of the plot for the introduction of Sohlzenitzyn's very complex concept of moral virtue in contradistinction to human happiness.

We have already discussed Sohlzenitzyn's concept of happiness, discovered under conditions of privation as the relinquishment of material desires in favor of spiritual wealth. However, in his introduction of the prospect for a return to humble mathematical application, Sohlzenitzyn touches upon the truly corrupt nature of modern totalitarianism: its reliance upon the beautiful arts in order to maintain the ugly sciences.

Nierżyn' s skills as a mathematician are necessary now - and it suddenly seems as though a brightness has appeared in the tunnel of Soviet oppression: at least he will now sleep on a white sheet, eat meat and immerse himself in mathematics - is this not the fulfillment of the aforementioned ideal of spiritual happiness? Material privation cannot be taken to ridiculous extremes, otherwise it will become sheer masochism. The relinquishment of material goods cannot be the embrace of the Taiga as human ideal. On the other hand, life for its own sake is empty. But to survive for the sake of an intellectual venture, to recover that lost feeling of mathematical wonder: doesn't this appear to be the path of moral virtue? Sohlzenitzyn, already at the beginning of his novel, hints that it might not be so:
"All of the arguments of reason were for, yes sir Mr. Director! But all of the fibres of my soul called out: get behind me Satan!"

Picture: Lake Ilmen

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