A ‘Random’ Classic!
True randomness is just plain hard to replicate. Recently, an interesting discussion came up on George Hrabís Geologic Podcast about whether it was possible to have levels of randomness. Few folks realize that what most people perceive as random is actually more ordered than one would think. Throw the dice long enough, and biases due to tiny imperfections will present themselves in the stats.
This week, we take a fascinating look at all that is random in The Drunkardís Walk by Leonard Mlodinow. Mr. Mlodinow starts off with some classic mathematical conundrums straight out of statistics 101 and demonstrates just how ill-equipped our brains are to handle the world from a mathematical stand-point. For example, did you know that in the ďLetís Make a DealĒ scenario, you have a better chance of winning if you switch doors on your second choice? Or that if the sex of one fraternal twin is known, the odds that the other twin is the same sex is not 1-out-of-2, but 1-out-of-3? Or that in a room of 30 people, the odds are pretty good that two people share the same birthday? Some of these we had heard before (A great many are wonderfully illustrated in the CBS TV series NUMB3RS) and some were new to us. Great companions to The Drunkardís Walk would be The Calculus Diaries and Proofiness.
While the author doesnít back away from the ďMathinessĒ to quote Buffy the Vampire Slayer, he also presents it in an engaging and accessible way. We live in a mathematically-based society, and whether its calculating batting averages or interest paid on a mortgage, math illiteracy can doom us to being deceived by numbers. The book mentions one of our favorite recent run-ins with randomness in recent years; when Apple 1st presented the IPod, folks began to complain that the shuffle mode would occasionally play the same song twice. And thatís just what you would expect from true randomness; play your IPod long enough, and you could expect to hear Iron Maidenís Rime of the Ancient Mariner 2, 3, even a dozen times in a row. Apple had to insert an exception into the software, and our skewed view of random mode was restored.
As noted in the book, astronomers are also not immune to seeing patterns in the chaos, sometimes gaining deep insight, other times only to wind up chasing false chimeras. Keplerís quest to link the five perfect solids with the classical planets and attempts to find physical underpinnings to the Titus-Bode law are some key examples in astronomical history. Our hunter-gatherer brains are great at seeing patterns, but sometimes this backfires making us see correlations out of mere circumstance. How many paranoid delusional individuals have fallen prey to an asserted hidden pattern in their lives?
Today, randomness or something close to it can be had through advanced algorithms or analysis of static or white noise. But even these have a slight bias that will show up over time. Itís sobering to think that the only true but unobtainable perfection in reality may be absolute randomness. The author also explains the often maligned concept of sample space and the gamblerís fallacy, which is the idea that a player or slot machine must be ďdueĒ after a certain run. The untold history of western mathematics and the understanding of the concepts of randomness alone make for an interesting read. Do give The Drunkardís Walk a browse both before setting foot in a casino or a statistics 101 class. Iím also happy to report that this book was my first successful experience with downloading something onto our Kindle Fire from the local libraryÖ an experience worth repeating!