Andrey Nikolaevich Kolmogorov was one of the giants of 20th-century mathematics. I’ve always found it amazing that the same man was responsible both for establishing the foundations of classical probability theory in the 1930s, and also for co-inventing the theory of algorithmic randomness (a.k.a. Kolmogorov complexity) in the 1960s, which challenged the classical foundations, by holding that it is possible after all to talk about the entropy of an individual object, without reference to any ensemble from which the object was drawn. Incredibly, going strong into his eighties, Kolmogorov then pioneered the study of “sophistication,” which amends Kolmogorov complexity to assign low values both to “simple” objects and “random” ones, and high values only to a third category of objects, which are “neither simple nor random.” So, Kolmogorov was at the vanguard of the revolution, counter-revolution, and counter-counter-revolution.
But that doesn’t even scratch the surface of his accomplishments: he made fundamental contributions to topology and dynamical systems, and together with Vladimir Arnold, solved Hilbert’s thirteenth problem, showing that any multivariate continuous function can be written as a composition of continuous functions of two variables. He mentored an awe-inspiring list of young mathematicians, whose names (besides Arnold) include Dobrushin, Dynkin, Gelfand, Martin-Löf, Sinai, and in theoretical computer science, our own Leonid Levin. If that wasn’t enough, during World War II Kolmogorov applied his mathematical gifts to artillery problems, helping to protect Moscow from German bombardment.
Kolmogorov was private in his personal and political life, which might have had something to do with being gay, at a time and place when that was in no way widely accepted. From what I’ve read—for example, in Gessen’s biography of Perelman—Kolmogorov seems to have been generally a model of integrity and decency. He established schools for mathematically gifted children, which became jewels of the Soviet Union; one still reads about them with awe. And at a time when Soviet mathematics was convulsed by antisemitism—with students of Jewish descent excluded from the top math programs for made-up reasons, sent instead to remote trade schools—Kolmogorov quietly protected Jewish researchers.
OK, but all this leaves a question. Kolmogorov was a leading and admired Soviet scientist all through the era of Stalin’s purges, the Gulag, the KGB, the murders and disappearances and forced confessions, the show trials, the rewritings of history, the allies suddenly denounced as traitors, the tragicomedy of Lysenkoism. Anyone as intelligent, individualistic, and morally sensitive as Kolmogorov would obviously have seen through the lies of his government, and been horrified by its brutality. So then why did he utter nary a word in public against what was happening?
As far as I can tell, the answer is simply: because Kolmogorov knew better than to pick fights he couldn’t win. He judged that he could best serve the cause of truth by building up an enclosed little bubble of truth, and protecting that bubble from interference by the Soviet system, and even making the bubble useful to the system wherever he could—rather than futilely struggling to reform the system, and simply making martyrs of himself and all his students for his trouble.
There’s a saying of Kolmogorov, which associates wisdom with keeping your mouth shut:
“Every mathematician believes that he is ahead of the others. The reason none state this belief in public is because they are intelligent people.”
There’s also a story that Kolmogorov loved to tell about himself, which presents math as a sort of refuge from the arbitrariness of the world: he said that he once studied to become a historian, but was put off by the fact that historians demanded ten different proofs for the same proposition, whereas in math, a single proof suffices.
There was also a dark side to political quietism. In 1936, Kolmogorov joined other mathematicians in testifying against his former mentor in the so-called Luzin affair. By many accounts, he did this because the police blackmailed him, by threatening to reveal his homosexual relationship with Pavel Aleksandrov. On the other hand, while he was never foolish enough to take on Lysenko directly, Kolmogorov did publish a paper in 1940 courageously supporting Mendelian genetics.
It seems likely that in every culture, there have been truths, which moreover everyone knows to be true on some level, but which are so corrosive to the culture’s moral self-conception that one can’t assert them, or even entertain them seriously, without (in the best case) being ostracized for the rest of one’s life. In the USSR, those truths were the ones that undermined the entire communist project: for example, that humans are not blank slates; that Mendelian genetics is right; that Soviet collectivized agriculture was a humanitarian disaster. In our own culture, those truths are—well, you didn’t expect me to say, did you?
I’ve long been fascinated by the psychology of unspeakable truths. Like, for any halfway perceptive person in the USSR, there must have been an incredible temptation to make a name for yourself as a daring truth-teller: so much low-hanging fruit! So much to say that’s correct and important, and that best of all, hardly anyone else is saying!
But then one would think better of it. It’s not as if, when you speak a forbidden truth, your colleagues and superiors will thank you for correcting their misconceptions. Indeed, it’s not as if they didn’t already know, on some level, whatever you imagined yourself telling them. In fact it’s often because they fear you might be right that the authorities see no choice but to make an example of you, lest the heresy spread more widely. One corollary is that the more reasonably and cogently you make your case, the more you force the authorities’ hand.
But what’s the inner psychology of the authorities? For some, it probably really is as cynical as the preceding paragraph makes it sound. But for most, I doubt that. I think that most authorities simply internalize the ruling ideology so deeply that they equate dissent with sin. So in particular, the better you can ground your case in empirical facts, the craftier and more conniving a deceiver you become in their eyes, and hence the more virtuous they are for punishing you. Someone who’s arrived at that point is completely insulated from argument: absent some crisis that makes them reevaluate their entire life, there’s no sense in even trying. The question of whether or not your arguments have merit won’t even get entered upon, nor will the authority ever be able to repeat back your arguments in a form you’d recognize—for even repeating the arguments correctly could invite accusations of secretly agreeing with them. Instead, the sole subject of interest will be you: who you think you are, what your motivations were to utter something so divisive and hateful. And you have as good a chance of convincing authorities of your benign motivations as you’d have of convincing the Inquisition that, sure, you’re a heretic, but the good kind of heretic, the kind who rejects the divinity of Jesus but believes in niceness and tolerance and helping people. To an Inquisitor, “good heretic” doesn’t parse any better than “round square,” and the very utterance of such a phrase is an invitation to mockery. If the Inquisition had had Twitter, its favorite sentence would be “I can’t even.”
If it means anything to be a lover of truth, it means that anytime society finds itself stuck in one of these naked-emperor equilibriums—i.e., an equilibrium with certain facts known to nearly everyone, but severe punishments for anyone who tries to make those facts common knowledge—you hope that eventually society climbs its way out. But crucially, you can hope this while also realizing that, if you tried singlehandedly to change the equilibrium, it wouldn’t achieve anything good for the cause of truth. If iconoclasts simply throw themselves against a ruling ideology one by one, they can be picked off as easily as tribesmen charging a tank with spears, and each kill will only embolden the tank-gunners still further. The charging tribesmen don’t even have the assurance that, if truth ultimately does prevail, then they’ll be honored as martyrs: they might instead end up like Ted Nelson babbling about hypertext in 1960, or H.C. Pocklington yammering about polynomial-time algorithms in 1917, nearly forgotten by history for being too far ahead of their time.
Does this mean that, like Winston Smith, the iconoclast simply must accept that 2+2=5, and that a boot will stamp on a human face forever? No, not at all. Instead the iconoclast can choose what I think of as the Kolmogorov option. This is where you build up fortresses of truth in places the ideological authorities don’t particularly understand or care about, like pure math, or butterfly taxonomy, or irregular verbs. You avoid a direct assault on any beliefs your culture considers necessary for it to operate. You even seek out common ground with the local enforcers of orthodoxy. Best of all is a shared enemy, and a way your knowledge and skills might be useful against that enemy. For Kolmogorov, the shared enemy was the Nazis; for someone today, an excellent choice might be Trump, who’s rightly despised by many intellectual factions that spend most of their time despising each other. Meanwhile, you wait for a moment when, because of social tectonic shifts beyond your control, the ruling ideology has become fragile enough that truth-tellers acting in concert really can bring it down. You accept that this moment of reckoning might never arrive, or not in your lifetime. But even if so, you could still be honored by future generations for building your local pocket of truth, and for not giving falsehood any more aid or comfort than was necessary for your survival.
When it comes to the amount of flak one takes for defending controversial views in public under one’s own name, I defer to almost no one. For anyone tempted, based on this post, to call me a conformist or coward: how many times have you been denounced online, and from how many different corners of the ideological spectrum? How many people have demanded your firing? How many death threats have you received? How many threatened lawsuits? How many comments that simply say “kill yourself kike” or similar? Answer and we can talk about cowardice.
But, yes, there are places even I won’t go, hills I won’t die on. Broadly speaking:
- My Law is that, as a scientist, I’ll hold discovering and disseminating the truth to be a central duty of my life, one that overrides almost every other value. I’ll constantly urge myself to share what I see as the truth, even if it’s wildly unpopular, or makes me look weird, or is otherwise damaging to me.
- The Amendment to the Law is that I’ll go to great lengths not to hurt anyone else’s feelings: for example, by propagating negative stereotypes, or by saying anything that might discourage any enthusiastic person from entering science. And if I don’t understand what is or isn’t hurtful, then I’ll defer to the leading intellectuals in my culture to tell me. This Amendment often overrides the Law, causing me to bite my tongue.
- The Amendment to the Amendment is that, when pushed, I’ll stand by what I care about—such as free scientific inquiry, liberal Enlightenment norms, humor, clarity, and the survival of the planet and of family and friends and colleagues and nerdy misfits wherever they might be found. So if someone puts me in a situation where there’s no way to protect what I care about without speaking a truth that hurts someone’s feelings, then I might speak the truth, feelings be damned. (Even then, though, I’ll try to minimize collateral damage.)
When I see social media ablaze with this or that popular falsehood, I sometimes feel the “Galileo urge” washing over me. I think: I’m a tenured professor with a semi-popular blog. How can I look myself in the mirror, if I won’t use my platform and relative job safety to declare to the world, “and yet it moves”?
But then I remember that even Galileo weighed his options and tried hard to be prudent. In his mind, the Dialogue Concerning the Two Chief World Systems actually represented a compromise (!). Galileo never declared outright that the earth orbits the sun. Instead, he put the Copernican doctrine, as a “possible view,” into the mouth of his character Salviati—only to have Simplicio “refute” Salviati, by the final dialogue, with the argument that faith always trumps reason, and that human beings are pathetically unequipped to deduce the plan of God from mere surface appearances. Then, when that fig-leaf turned out not to be wide enough to fool the Church, Galileo quickly capitulated. He repented of his error, and agreed never to defend the Copernican heresy again. And he didn’t, at least not publicly.
Some have called Galileo a coward for that. But the great David Hilbert held a different view. Hilbert said that science, unlike religion, has no need for martyrs, because it’s based on facts that can’t be denied indefinitely. Given that, Hilbert considered Galileo’s response to be precisely correct: in effect Galileo told the Inquisitors, hey, you’re the ones with the torture rack. Just tell me which way you want it. I can have the earth orbiting Mars and Venus in figure-eights by tomorrow if you decree it so.
Three hundred years later, Andrey Kolmogorov would say to the Soviet authorities, in so many words: hey, you’re the ones with the Gulag and secret police. Consider me at your service. I’ll even help you stop Hitler’s ideology from taking over the world—you’re 100% right about that one, I’ll give you that. Now as for your own wondrous ideology: just tell me the dogma of the week, and I’ll try to make sure Soviet mathematics presents no threat to it.
There’s a quiet dignity to Kolmogorov’s (and Galileo’s) approach: a dignity that I suspect will be alien to many, but recognizable to those in the business of science.
Comment Policy: I welcome discussion about the responses of Galileo, Kolmogorov, and other historical figures to official ideologies that they didn’t believe in; and about the meta-question of how a truth-valuing person ought to behave when living under such ideologies. In the hopes of maintaining a civil discussion, any comments that mention current hot-button ideological disputes will be ruthlessly deleted.