The Mathematics of Freedom

While reading about the recent protests in China against the government’s Zero Covid policy (and, more generally, the totalitarian surveillance state established by the Chinese Communist Party), I was reminded of a fascinating quote from logician Kurt Gödel extending the results of his Incompleteness Theorem to matters of society and governance:

A completely unfree society (i.e., one proceeding in everything by strict rules of “conformity”) will, in its behavior, be either inconsistent or incomplete, i.e., unable to solve certain problems, perhaps of vital importance. Both, of course, may jeopardize its survival in a difficult situation. A similar remark would also apply to individual human beings.

It strikes me that the CCP is running up against some of these problems of vital importance. They are certain that they have discovered all the truths of human society, that human experience is finite and exhaustible, that they can solve all problems through the pseudo-scientific formalisms of dialectical materialism and Marxist-Leninist-Maoist theory.

Yet the Russian novelist Yevgeny Zamyatin identified the fallacies of such thinking as far back as the 1920s:

Fortunately, all truths are erroneous. This is the very essence of the dialectical process: today’s truths become errors tomorrow; there is no final number. This truth (the only one) is for the strong alone. Weak-nerved minds insist on a finite universe, a last number; they need, in Nietzsche’s words, “the crutches of certainty.” The weak-nerved lack the strength to include themselves in the dialectical syllogism.

Although we might think of mathematics as cold and forbidding, Gödel and Zamyatin perceived a connection between mathematics and humanity: both are incompletable and inexhaustible; they cannot be utterly formalized under a fully consistent and complete set of rigid rules; there is no final truth, no final certainty, no final number; freedom is an inherent condition of every human activity, even mathematics.

Is there a certain cosmic justice in the fact that some Chinese students held up printouts of the Friedmann (“freed-man”) equation while speaking out against totalitarian tyranny? Perhaps more than they know…

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