A New Kind of Science
Many books I like to read with a yellow highlighter, reading Stephen Wolfram’s ANKOS I was compelled to whip out a red pen. While his 1,000-plus page field-guide to cellular automata and complexity theory is brimming with fantastic examples of all shapes, sizes, and dimensions, Wolfram’s writing and failure to acknowledge accomplishments in the field beyond his own research make this book a difficult read.
Wolfram violates the rule of science writing that you must disassociate yourself from your research. I was skeptical of the importance of this principle, until I saw what happens when you don’t follow it:
Just over twenty years ago I made what at first seemed like a small discovery: a computer experiment of mine showed something I did not expect. But the more I investigated, the more I realized that what I had seen was the beginning of a crack in the very foundations of existing science, and a first clue towards a whole new kind of science.
This book is the culmination of nearly twenty years of work that I have done to develop that new kind of science. I had never expected it would take anything like that long, but I have discovered vastly more than I ever thought possible, and in fact what I have done now touches almost every existing area of science, and quite a bit besides.
Wow! Stephen Wolfram considers his book an Earth-shattering iconoclasm that will revolutionize science, and it’s all on Wolfram himself and his 20 years of research; however, despite his repeated use of “I” and casual dismissal of all the research preceding him, Wolfram is not publishing in a vacuum, and that hurts his efforts profoundly.
Put simply, Wolfram believes he has discovered Emergence, the idea that complex systems and patterns can arise out of simple processes or rules. Wolfram mentions searching for patterns in primes, but never mentions Ulam’s spiral. Mentions seeking patterns in pi, but never mentions Carl Sagan’s Contact, which entertained the idea first. Chaos/Complexity Theory gets mentioned in a footnote. A footnote!!! Wolfram never acknowledges that he is standing on the shoulders of giants like Alan Turing, John Von Neumann, or Edward Lorenz.
Lines of Prime Numbers in Ulam’s Spiral
Maybe Wolfram isn’t ignoring all the history behind his subject, maybe in the 15 years of writing his book, he simply never noticed that it’s all been discovered without him, before he even started writing. If we were to lose Einstein’s Theory of Relativity today, someone else would uncover it within a few years. That’s the nature of truth, everyone can arrive at it independently.
The problem is that Wolfram’s failure to explore the near century’s worth of work by his peers on this subject cripples his presentation. Instead of a broad, eclectic overview of ideas from across the field of research shedding light on each of his examples, we are forced to look at them with Wolfram’s blinders on, and given only his insights alone. This is a frustrating treatment, teasing at enlightenment, but never yielding any depth.
Wolfram hasn’t invented anything. Speculation isn’t invention. In the end nothing has been discovered. There is only more wonder. People speculated on these patterns before Wolfram, and they will speculate after him.
Cellular automata, emergence, chaos theory, and other incredibly complex mathematical wonders produced by basic rules allowed to play out over time are absolutely fascinating concepts. You can lose yourself for hours staring at fractals. You can wonder at the increasing wave function of unpredictability produced on a system by something as seemingly mathematically insignificant as a butterfly flapping its wings. You can ponder infinitely complex numbers like pi and phi impossibly running away forever, while appreciating the way they somehow manifest in nature. It defies logic.
Luckily, Wolfram’s book repeatedly appeals to his readers to take up this subject, to explore the phenomena of which he provides so many wonderful examples. Anyone experiencing an Ionian Enchantment from Wolfram’s book will continue his train of thought and discover Turing, Neumann, and myriad of mathematicians and computer scientists immersed in this field. They will discover the whole realm of mighty minds who have also immersed themselves in these puzzles.
Then they will return to A New Kind of Science, and appreciate that Stephen Wolfram has put together a very good coffee table book on cellular automata, just not a revolutionary one.