By Edward B. Burger and Michael Starbird, W.W. Norton & Company, 2005
Coincidences, Chaos, and All That Math Jazz
By Edward B. Burger and Michael Starbird, W.W. Norton & Company, 2005
My father-in-law is a physicist, my brother-in-law a grad student in mathematics at Harvard, and yet, despite my unusually close exposure to people who make their life’s work out of playing around with numbers primarily for the sake of playing around with numbers, I’ve never been able to understand people who have a passion for math. Coincidences, Chaos, and All that Math Jazz didn’t quite turn me into a budding mathematician, but it did make just a bit clearer the alluring beauty of numbers and the way they dance around and interact with one another in very often surprising ways. A funny and admirably accessible introduction to some of the coolest mathematical concepts out there, Math Jazz will be entertaining for anyone short of the most inhibited mathphobics.
I know, I know. You don’t believe me. But it’s true. Mathematicians Michael Starbird and Edward B. Burger (who used to moonlight as a stand-up comedian) have done a remarkable job of making some really, really esoteric ideas into light (well, maybe middle-weight) reading. They have wisely started out by writing a couple of chapters that show the ways math affects how we live our daily lives and perceive (often incorrectly) the world around us.
Starbird and Burger tackle the notion of coincidences, for example, by revealing the statistical underpinnings of apparently miraculous chance. They debunk the old gem of the long list of coincidences between the lives of Abraham Lincoln and John F. Kennedy (Lincoln’s secretary was named Kennedy; Kennedy’s secretary was named Lincoln; etc.) by pointing out one statistical tidbit that should be obvious but isn’t: given the huge number of facts that can be known about a person’s life, it shouldn’t be surprising that a handful of those facts might coincide in the lives of any two randomly chosen individuals. That there are 10 or so coincidences in the biographies of Lincoln and Kennedy isn’t astounding when you realize that there are thousands of facts that don’t coincide. There are correspondences, for example, between the dates of election of the two presidents and the birthdates of their vice-presidents, but there is no correspondence in the presidents’ dates of birth, graduation, marriage, death, birthdates of mothers, fathers, brothers, sisters, children, cousins, grandchildren or pets. When you look at it that way, it doesn’t seem like such a big deal that Lincoln was elected to Congress in 1846 and Kennedy in 1946.
Starbird and Burger give the same treatment to the concept of chaos, in which tiny variations in initial conditions vastly affect the outcomes of complex systems. This is the famous butterfly effect: a butterfly flapping its wings in Africa (or South America, or any place far away from where you are) starts a chain of atmospheric events that eventually creates a hurricane in the Caribbean (or any place far away from where the butterfly is). The authors clearly explain how the limits on human understanding make it impossible for us to predict the future in any significant way or even to know with any reasonable degree of certainty whether it will rain next week or not. Math could explain it all if only we could get a firm grasp on math - all of it, without exception, even the trickiest of its secrets. But no one, not among all the grad students at Harvard and MIT or the physicists at Los Alamos, understands all of it, and that’s the problem.
When the authors get to that revelation - that even the sharpest of mathematicians are stumped by some seemingly simple math problems - the book gets really fascinating. We all thought that we were the dummies, but Starbird and Burger admit that the universe is perplexing even to the geniuses. Take prime numbers. Those are numbers that are evenly divisible only by themselves and one. The first few prime numbers are 2, 3, 5, 7, 11 and 13. It seems like there infinitely many prime numbers, but no one knows if that’s true; when numbers get big enough, even the super-est of computers can’t figure out whether or not they’re prime. In 1742, a mathematician named Goldbach conjectured that every even number greater than 2 is the sum of two prime numbers; it looks like it’s true for small numbers (4=2+2; 6=3+3; 8=3+5; etc.), but no one has been able to prove mathematically that it’s true for big numbers up to infinity. And the list of math puzzles without answers goes on and on, itself probably to infinity, although it’s impossible to know for certain.
Speaking of infinity, Starbird and Burger get to that, too. They also discuss mathematically explainable patterns in nature, the math of internet security, the fourth dimension, and the ideal height of a bellybutton. They reveal the surprising answer to the question “How thick would a piece of paper be after you fold it in half 50 times?” (Hint: It would be really, really, really thick.) They also explain how to take off your underwear without removing your pants, even if your feet are tied together. I’m not sure if this bit of knowledge would ever come in handy for anyone, but there you have it.
A couple of years ago, David Foster Wallace wrote a book about the concept of infinity. The book’s publisher claimed that it was supposed to make a difficult idea digestible by regular people. All Wallace’s intentionally convoluted prose did, however, was reinforce the perception that those who understand complex math are inscrutable geeks. Starbird and Wallace, bona fide mathematicians both, but anything but inscrutable, have done what Wallace was unable or unwilling to do: throw a little light on murky concepts in an intelligent and entertaining manner.
/P>Copyright 2006 Ad Media Inc.