Higher goals

LISTEN. "A paradigm case of Bayesian reasoning is medical diagnosis."

I wish my elementary and middle-school teachers had explained that. I always valued verbal literacy over statistical numeracy. Many of us used to sneer, in math class, that we'd never need to know what they were trying to teach us. They didn't seem to try very hard to justify the curriculum themselves. "Someday when you're older," they might have said, "you'll need to decide whether to opt for the drug, the therapy, the surgery... and you'll wish you'd learned a formula or two." 

It's pretty shocking that doctors misestimated a woman's chance of having breast cancer as 90% when in fact a simple formula (below*) revealed it to be 9%, and pretty embarrassing that an 18th-century cleric could have told them so. Our credence should be conditional on the evidence, said Revered Thomas Bayes (1701-1761). 

Bayes' contemporary David Hume famously said "a wise man proportions his belief to the evidence" and "rejects the greater miracle." He and Blaise Pascal, I'll wager, would have had an interesting meeting of minds. Or parting of them.

The plain consequence is (and it is a general maxim worthy of our attention), “That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish: And even in that case, there is a mutual destruction of arguments, and the superior only gives us an assurance suitable to that degree of force, which remains, after deducting the inferior.”

When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion.

Pinker: "Which is more likely--that the laws of the universe as we understand them are false, or that some guy got something wrong?"

It's not uncommon to hear that someone's medical recovery was a miracle, when in fact the laws of the universe are perfectly compatible with the patient's good fortune. The odds are more often in our favor than not, when the diagnosis has been duly proportioned to the evidence and the appropriate "base rate" for the relevant class of comparison, and when adjusted "by the person's particulars." 

The base rate of breast cancer, for instance, is 10 in 1,000. 9 of the 10, and 98 of the 1,000, will test positive. 9 divided by 98 is 9%. That's where the evidence and right reasoning lead. "When the problem is framed in this way, 87% of doctors get it right... as do a majority of ten-year olds."

That's where the evidence and right reasoning lead us, if we're methodical and patient. When we're not, we leap to wrong conclusions. That doesn't make us irrational, just sloppy and impatient.

Nor does it invalidate the sentiment of rationality, it just shows that we must learn to feel more at home, more at ease and peace, in the world of probability and statistics. 

Another crucial point Pinker makes in this chapter, not with respect to medical diagnosis as such but more broadly: we also have to learn when and how to balance the goal of statistical and actuarial accuracy with our other higher goals. "A higher goal is fairness. It's wicked to treat an individual according to that person's race, sex, or ethnicity--to judge them by the color of their skin or the composition of their chromosomes rather than the content of their character." 

If we ever learn to do that consistently, it won't be a miracle. But it will be an improbable overcoming of deep ancestral and institutional malefaction. It will be a triumph of rationality. It will feel right.