I recently attended two lectures that reminded me of the importance of analysis. This post will focus on Dr. Persi Diaconis.
Diaconis (see his Wikipedia entry and this YouTube video), currently at Stanford University, began his career as a magician, before earning a Ph.D. in Mathematical Statistics from Harvard University. He was twice awarded the prestigious MacArthur Fellowship. With over 200 papers to his credit, he has made path-breaking contributions to many areas of mathematics and statistics.
The description of his talk was deceptive:
I will take a careful look at some of our most primitive images of random phenomena: flipping a coin, shuffling cards, and rolling a roulette ball. In each case, physics and math show that (usually) things are not very random. Some implications to the use and misuse of "statistical modeling"
He spent a fair amount of time discussing coin flipping. There was a lot to learn, from how to persist in gathering data to the difference between flipping and spinning a coin.
When he first began studying coin flips he naturally wanted to understand the physical processes - for example, how high is a typical flip and how many times does the coin rotate. The first thought was to use a high speed camera to film a series of flips. And there was one on campus, in the obvious place - the football program owned it. After much bargaining he was finally able to use the camera only to find that it did not provide the information he needed regarding the rotational counts. At which point he came up with a low tech solution - he glued one end of a flat piece of dental floss to the coin, flipped it and then counted the number of twists in the floss.
Some of the results: The typical toss is a foot, it takes a half second, and the coin normally rotates 18-20 times. And a toss is random to two decimal places, but not to three - 51% come up on the same side they started.
A coin flip that most of us perform is reasonably random, that is if we catch the coin. If we let it hit the ground - which most of us would think is somehow fairer - the odds change dramatically. Coins that are spun tend to be much less fair, depending on the individual coin.
What do we learn from these stories? Analysis is critical, but doesn't have to be overwhelmingly complex. Sometimes thinking about a problem for a while, based on years of experience, can yield approaches that are at heart relatively simple, but yield powerful insights. This is one reason why engaging experts in modernization and transformation to collaborate with your own subject matter experts can yield amazing results.
Finally, it is important to remember that when Diaconis flips a coin there is no randomness involved at all.