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432 pages, Hardcover
First published September 28, 2021
Suppose that the prevalence of breast cancer in the population of women is 1 percent. Suppose that the sensitivity of a breast cancer test (its true-positive rate) is 90 percent. Suppose that its false-positive rate is 9 percent. A woman tests positive. What is the chance that she has the disease?If this same question is worded differently it becomes easier to intuitively arrive at the correct answer.
The most popular answer from a sample of doctors given these numbers ranged from 80 to 90 percent. Bayes's rule allows you to calculate the correct answer: 9 percent. That's right, the professionals whom we entrust with our live flub the basic task of interpreting a medical test, and not by a little bit. They think there's almost a 90 percent chance she has cancer, whereas in reality there's a 90 percent chance she doesn't. (p150)
Forget the generic "a woman"; think about a sample of a thousand women. Out of every 1,000 women, 10 have breast cancer (that's the prevalence, or base rate). Of these 10 women who have breast cancer, 9 will test positive (that's the test's sensitivity). Of the 990 women without breast cancer, about 89 will nevertheless test positive (that's the false-positive rate). A woman tests positive. What is the chance that she actually has breast cancer?" It's not that hard: 98 of the women test positive in all, 9 of them have cancer; 9 divided by 98 is around 9 percent—there's our answer. When the problem is framed in this way, 87 percent of doctors get it right (compared with about 15 percent for the original wording), as do a majority of 10-year-olds. (p169)So what's the lesson here? Is it important that people be able to answer questions like this correctly?
By tapping preexisting intuitions and translating information into mind-friendly formats, it's possible to hone people's statistical reasoning. Hone we must. Risk literacy is essential for doctors, judges, policymakers, and others who hold our lives in their hands. And since we all live in a world in which God plays dice, fluency in Bayesian reasoning and other forms of statistical competence is a public good that should be a priority in education. The principles of cognitive psychology suggest that it's better to work with the rationality people have and enhance it further than to write off the majority of our species as chronically crippled by fallacies and biases. (p171)Here's a quote that verifies my own observation of today's political divide.
We are not...living in a "post truth" society. The problem is that we are living in a myside society. The sides are the left and the right, and both sides believe in the truth but have incommen-surable ideas of what the truth is. The bias has invaded more and more of our deliberations. The spectacle of face masks during a respiratory pandemic turning into political symbols is just the most recent symptom of the polarization. (p295-p296)
Epistemic rationality: to systematically improve the probabilities of your beliefs about reality.
Instrumental rationality: to systematically improve at achieving your goals.
"Truth, as Karl Popper said, is a regulative principle. Like north, it is a direction, an orientation, not a destination. When we join the reality-based community—when we sign up for the years of training, the exacting research, the criticism and lost arguments—we resolve to conduct ourselves as if reality were out there and objectivity were possible, even while acknowledging that reality is elusive and perfect objectivity is impossible."
"It is noteworthy that modern Platonists, almost without exception, are ignorant of mathematics, despite the immense importance that Plato attached to arithmetic and geometry, and the immense influence that they had on his philosophy... a man must not write on Plato unless he has spent so much of his youth on Greek as to have had no time for the things that Plato thought important."
"Whereas reason is commonly viewed as a superior means to think better on one’s own, we argue that it is mainly used in our interactions with others. We produce reasons in order to justify our thoughts and actions to others and to produce arguments to convince others to think and act as we suggest."
"My dear Kepler, I wish we could laugh at the extraordinary stupidity of the mob. What say you about the foremost philosophers of this University, who with the obstinacy of a stuffed snake, and despite my attempts and invitations a thousand times they have refused to look at the planets, or the moon, or my telescope?"
One of the bad effects of an anti-intellectual philosophy, such as that of Bergson [and Hegel], is that it thrives upon the errors and confusions of the intellect. Hence it is led to prefer bad thinking to good, to declare every momentary difficulty insoluble, and to regard every foolish mistake as revealing the bankruptcy of intellect and the triumph of intuitions.
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