Some years ago I was trying to decide whether or not to move to Harvard from Stanford. I had bored my friends silly with endless discussion. Finally, one of them said, “You’re one of our leading decision theorists. Maybe you should make a list of the costs and benefits and try to roughly calculate your expected utility.” Without thinking, I blurted out, “Come on, Sandy, this is serious.”
There is not very much variability in coin flips, and practiced magicians (including myself ) can control them pretty precisely. My colleagues at the Harvard Physics Department built me a perfect coin flipper that comes up heads every time. Most human flippers do not have this kind of control and are in the range of 51⁄2 mph and 35 to 40 rps. Where is this on Figure 1? In the units of Figure 1, the velocity is about 1⁄5—very close to the zero. However, the spin coordinate is about 40—way off the graph. Thus, the picture says nothing about real flips. However, the math behind the picture determines how close the regions are in the appropriate zone. Using this and the observed spread of the measured data allows us to conclude that coin tossing is fair to two decimals but not to three. That is, typical flips show biases such as .495 or .503.
Or:
One of the most useful things to come out of my study is a collection of the rules of thumb my friends use in their decision making. For example, one of my Ph.D. advisers, Fred Mosteller, told me, “Other things being equal, finish the job that is nearest done.” A famous physicist offered this advice: “Don’t waste time on obscure fine points that rarely occur.” I’ve been told that Albert Einstein displayed the following aphorism in his office: “Things that are difficult to do are being done from the wrong centers and are not worth doing.” Decision theorist I. J. Good writes, “The older we become, the more important it is to use what we know rather than learn more.” Galen offered this: “If a lot of smart people have thought about a problem [e.g., God’s existence, life on other planets] and disagree, then it can’t be decided.”
-Persi Diaconis
By the way, Diaconis stayed at Stanford. He’s giving a public lecture on Nov. 30.
That’s a pretty cool paper; eg.
Or:
I’m glad Vaniver brought it to my attention.