7 Mathematical Principles That Shape Our Lives Hardcover – Kit Yates

Capture / recapture – estimate the number or snails in garden, fish in the lake or raffle tickets sold. capture all snails in one am, mark them all and let them go. next day capture all an see how many marked ones you have. rough portion of all. if one sixth or second day, multiple first day by six.

Japanese police get 99% conviction rate. able to conduct tough interviews, not record the, no lawyers present and hold you for 3 days. Confession huge part of systems. Investigators told to get confession before gathering evidence. Shame of trial leads many people to confess.

Good reads: He shows that something as unmathematical as algae needs an understanding of math. An algal bloom doubles in size every day, until it covers a lake – in 30 days. If you see the lake is half covered, how long do you think it will take for it to be covered completely? Most would calculate numerous days, based on when the algae first appeared and had reached the halfway point, but the correct answer is one more day. Mistakes like this lead planes to crash, which Yates also shows in painful detail.

Doctors are forever misinterpreting test results, giving patients false death sentences or false reassurances. Yates gives the example of breast cancer tests, by which doctors seem to predict nine out of every two cases of breast cancer in women. The numbers are pretty stark. With false positives from tests, 981 women out of a random 10,000 will be told that they have breast cancer. But of those, only 90 will actually have it. Ninety out of ten thousand (ie. nine per thousand) is not the pandemic plague that should cause panicked fear in women, but that’s how doctors present it when they are surveyed. Given multiple choice questions, doctors fare far worse than if they had chosen random answers. They are prejudiced in the false direction. They have the facts and the numbers wrong. The result is needless surgery, needless chemotherapy, and much pointless suffering.

There is a horrifying chapter on legal ignorance as well. So-called expert witnesses bamboozle judges, juries and opposing lawyers with mumbo-jumbo that no one challenges, because they don’t understand what was said. They just pick out a major conclusion from what they heard, and accept it as true and significant. The result is wrongful convictions. In the major case cited, a young mother went to prison for murdering her first two children, because an expert incorrectly claimed the chances of two children from the same family dying from Sudden Infant Death Syndrome (SIDS) was one in 73 million. (He made up the number himself.) That’s all the jury needed to know. It didn’t matter that the expert was wrong about the odds, or even that the children didn’t really die of SIDS. The number was so overwhelming, the decision was easy to make: she had to be guilty as charged. In upholding the conviction, the appeals court said no one would be fooled by such a wild claim.