Book Review: 'Innumeracy: Mathematical Illiteracy and Its Consequences' by John Allen Paulos

'Innumeracy: Mathematical Illiteracy and Its Consequences' by John Allen Paulos

"Why do even well-educated people understand so little about mathematics?", exclaimed the author in the book's introduction. But after some pounding on the question, one could realize that such claim can hardly be valid by definition. After all, how can someone be regarded as "well-educated" if he has not be learned some of the fundamental mathematical principles presented in the book? Thus the question could be reiterated as:

"Why do even well-educated people who understand mathematics, demonstrate so little such skill when making decision?"

One can approach the question from the angel of the non-mathematical nature of human brain. The design of our brain was largely shaped during the long "hunting and gathering" era, when immediate interest always trumps long-term interest, and a slow decision always tends to be a bad decision. Though we can try to rewire our brain through education and discipline, we cannot change its basic architecture. So, innumeracy is an innate flaw. The author also gently hinted the answer could lie with the manipulative practices of the media and marketing industry and misconceptions of our culture.

Apart from calling for more attention on mathematical literacy, the author also gave a good number examples to illustrate the mathematical principles behind. I tried to summarize some of the principles into shortcuts, as I find it is most effective way incorporate these mathematical principles into daily decision making:

Shortcut 1: The possibility of the virtually impossible:
If the possibility for some event to happen is 1%, it will has 50% chance to happen at least once after 69 iterations. Handy number at fingertip: 0.99^69 = 0.499; 0.9^7 = 0.48; 0.8^4 = 0.41;

Shortcut 2: The possibility of almost certain:
This is the twin-brother of the first shortcut. If something work 99% of the time,there will 50% chance it fails at least once after after 69 tries. (Think about it when you beat the red light next time.)

Shortcut 3: Not that coincidental coincident:
Putting balls into 100 empty drawers randomly, it takes 101 balls to make sure at least 2 balls end up in the same drawer. but it takes only 12 balls (not 50 balls) to have 50% chance. Similarly, If you have a party of 23, expect 50% chance 2 of them share the same date of birth. (and it only takes a party of 4, for almost 50% chance that at least 2 of them are born in the same month.)

Shortcut 4: Decision under uncertainty:
If someone makes offers to give you a random among from $0 to $100, every time you get to choose whether you will take it or pass it. If you pass it, the guy will make you another offer between $0 and $100, and he is going to make that offer a total 100 times. When should you call for a deal? You should always forgo the the first 37% of the chances and take first offer that is better than the best offer in the first 37%. (The deduction of the result is kind of complicated, just remember the magic number of 37%.)