Overconfidence from Mathematical Thinking

EUGENICS, ORIGINAL SIN, AND THIS BOOK’S MISLEADING TITLE

In a book called How Not to Be Wrong it’s a bit strange to write about Galton without saying much about his greatest fame among non-mathematicians: the theory of eugenics, of which he’s usually called the father. If, as I claim, an attention to the mathematical side of life is helpful in avoiding mistakes, how could a scientist like Galton, so clear-eyed with regard to mathematical questions, be so wrong about the merits of breeding human beings for desirable properties? Galton saw his own opinions on this subject as modest and sensible, but they shock the contemporary ear:

As in most other cases of novel views, the wrong-headedness of objectors to Eugenics has been curious. The most common misrepresentations now are that its methods must be altogether those of compulsory unions, as in breeding animals. It is not so. I think that stern compulsion ought to be exerted to prevent the free propagation of the stock of those who are seriously afflicted by lunacy, feeble-mindedness, habitual criminality, and pauperism, but that is quite different from compulsory marriage. How to restrain ill-omened marriages is a question by itself, whether it should be effected by seclusion, or in other ways yet to be devised that are consistent with a humane and well-informed public opinion. I cannot doubt that our democracy will ultimately refuse consent to that liberty of propagating children which is now allowed to the undesirable classes, but the populace has yet to be taught the true state of these things. A democracy cannot endure unless it be composed of able citizens; therefore it must in self-defence withstand the free introduction of degenerate stock.

What can I say? Mathematics is a way not to be wrong, but it isn’t a way not to be wrong about everything. (Sorry, no refunds!) Wrongness is like original sin; we are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions. There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we’re still wrong about. We become like those pious people who, over time, accumulate a sense of their own virtuousness so powerful as to make them believe the bad things they do are virtuous too.

I’ll do my best to resist that temptation. But watch me carefully.