Stephen Wolfram (Wikipedia article) is the child prodigy who went on to invent Mathematica, the ubiquitous software package for mathematical analysis. It’s now been three years since the publication of his A New Kind of Science (Wikipedia article) to much fanfare. The book’s main thesis is that complexity can emerge from extremely simple models, of the type that can be embodied in computer programs. He claims

My purpose in this book is to initiate a transformation in science…making it possible to make progress on a remarkable range of fundamental issues that have never successfully been addressed by any of the existing sciences before.

The book is nearly 1200 pages of dense mathematics, diagrams, and discussion. The notes alone are over 300 pages, and the book is not cheap, so I’m not recommending people read it, but it is nonetheless thought-provoking, regardless of whether you accept his grandiose claims, which many people do not. For one thing, it’s never clear whether he’s claiming that his models might generate behavior which resembles the real world, or that they are the models governing the real world.

At one level, this book is a work of philosophy. So how does Wolfram approach the hoary old philosophical problem of free will? For him, free will is related to “computational irreducibility”, one of his key concepts, which basically means that there are some types of computation which don’t allow shortcuts. Such phenomena permit no predictions about what is going to happen until it actually does. There is no future until the universe has finished computing it.

Wolfram says, “I believe that it is this kind of intrinsic process [complex, unpredictable behavior generated by simple rules] that is primarily responsible for the apparent freedom in the operation of our brains.” A novel definition of “freedom”: “free of obvious laws”, “freedom from predictability”.

In a word, Wolfram believes that free will vs. determinism is a false dichotomy. The world proceeds deterministically, but appears to be (is?) imbued with “freedom” due to its unpredictability.

(Students of language may find it interesting that for this book Wolfram invented a distinct new style of writing which he claims is specifically suited to its material. That style involves starting a large percentage of his sentences with conjunctions: “And” (to show a connected thought), “But” (to show a contrasting thought), or “For” (to show background or reason). He notes that this helps break up extremely long sentences. After a few hundred pages, however, this style becomes extremely irritating.)

This entry was posted on Sunday, January 23rd, 2005 at 18:18 and is filed under computing. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.