During my 2 years as a grad student at MIT, we (my family and I) lived in a rural part of the Town of Lexington, several miles west of Cambridge. My then wife had a job in Waltham, to the south, and drove there and back on Waltham Road whose name changed to Lexington Road when you crossed the town line. We made a few friends there and one of them asked one evening how we were enjoying New England. Having come from the gridiron of Detroit suburban streets we replied that we enjoyed it but the winding roads with changing names were a bit confusing. “Well, yes,” she replied, “it is easy to get lost around here, but you don’t mind, because it’s so beautiful!”
One of the true benefits of longevity is that you often get a chance to relive some pleasurable experience from the past, even if it’s in a slightly different venue, and I had one of those this past couple of weeks, of wandering about in a confusing but beautiful environment. I had stumbled on to an announcement by Stephen Wolfram, of Mathematica fame, of the release of his book, A New Kind of Science, for the iPad. Not having one of those yet, but intrigued by its description, I sought out a used copy of the original book, a 1200 page, 5-1/2 pound tome that in its beginnings excited me no end. For one thing it gave thousands of examples of how programs with simple beginnings and simple rules could generate incredibly complex outcomes, one of the principal themes of the model of the cosmos in my own book, the picnic at the edge of the universe. I had derived parts of that idea on the very simple, by comparison, The Game of Life, by John Conway, and a follow-up book, The Recursive Universe, by William Poundstone. Wolfram had built the idea of cellular automata into a powerful argument with thousands of experiments and rigorous mathematical arguments that seemed to support my own intuitions. The book and the ideas truly do create a beautiful world, but one that I as an amateur mathematician found it not easy to navigate. This is not yet the place for the details of his thesis, except to say that it carries these ideas through a set of analyses that show the methodology to be a simpler but still universal equivalent of Turing machines and many other computing devices and systems in their application to science and mathematics, with just a few intractable exceptions.
I must confess to a brief moment of concern, in the middle of Chapter 9, where the author lays out his belief that his system promises to provide simpler answers to the structure of the universe. My doubt came from his apparently residual entanglement with the complexities of relativity and quantum mechanics, much of which seem to go beyond complexity into an almost mystical realm of paradoxes. I gave him a pass for this, since most of our experts seem to suffer from the same entanglements (one of quantum theory’s favorite terms).
It was near the end in Chapter 12, however, when I ran into a greater sense of dismay, when it turns out, in spite of his apparent early encouragements, that cellular automata can’t come close to explaining everything, where there arise all of these complex behaviors, like turbulence, I presume, that may never be explainable, except by a set or rules at least as complex as the phenomena they are designed to explain. I agree that this may be true, though it’s disappointing just the same.
I’ll want to come back to Stephen Wolfram, in another post, down the road, but first, back to New England. There’s a well-known story, meant to illustrate the dour, down east flavor you find in the people there, some of whom I came to know.
It seems that a couple, driving through the countryside in Vermont, find themselves confused and stop to ask a farmer on his tractor by the roadside for directions to their destination,
“Glad to help”, he says and gives them an elaborate itinerary to follow, which they set off on. After an hour of travel through the beautiful countryside, with glimpses of mountains, streams and fall color, they find themselves back at the farmer’s gate.
“Did we make a mistake?” they ask.
“No,” he says, “but I first had to find out if you could follow directions.”
My experience with Mr. Wolfram’s book suggests, perhaps, a new punchline.
The couple finds themselves, speechless, back at the farmer’s gate. “Purty drive, warn’t it,” he says, “and you sure can follow directions!”
“But what about where we want to go?” they ask.
“Well, I been thinkin’ on that,” he says, “and I guess I don’t think you can get there from here.”