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%.)

System and Human Nature

Now, I'm so convinced that: the good / the bad of a system will bring out the best / the worst of human nature.

I'm not trying to say that people in a good system behave well, and people in a bad system behave badly. That would be too obvious. What I'm trying to say is that the trait of a system would have this amplifying effect on the people in it. An inch worth of difference of a system will result as a mile worth of difference in the nature of its people. Why is it so?

I hope you have read about Richard Dawkins's theory on Meme and Evolutionarily Stable Strategy (and you should if you haven't. Here are some links: http://en.wikipedia.org/wiki/Richard_Dawkins#Meme http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy). Let's look at human natures as memes, and the system as the environment these memes compete in. When there is a tiny change in the system environment. Some meme would gain some tiny advantage over its rival meme. (It doesn't really matter which meme is good and which is bad. The memes themselves won't care. They just replicate.) What matters is the meme in advantage will result in a slightly higher percentage in the people of the system than its rival meme. But it doesn't just stop there. Same as genes, most of memes are self-reinforcing, which means the more they present inside the memes pool, the more help they will get from one another, and the more advantage they will have over their rival memes. (If you can’t visualize this, just imagine when was the last time you heard of a widely spread religion advocating “we should all believe in some other religion”? As a meme, it just can’t survive. ) This will become a self-propelling upward spiral, which will eventually snuff out the rival meme, or reduce it to an insignificant proportion.
A change of a few centigrades could kill dinosaurs! A slight tilt of a system’s environment will result in a land-slide in the kind of characters the people in it display. So it is not about educating people to think or behave a certain way; it’s all about making small system changes that would nudge people to the right direction, (or the direction you want them to be in).

From Tony Robins

6 Basic Human Needs (in sequence):
Need of personality:
1. Certainty
2. Uncertainty / Variety
3. Being critical / Significance
4. Connection & Love
Spiritual Needs:
5. Growth
6. Contribute beyond oneself

http://www.ted.com/index.php/talks/tony_robbins_asks_why_we_do_what_we_do.html