Here's an excerpt from section 4.7 of The Lifebox, the Seashell, and the Soul which I was revising yesterday. The book will be out in Fall, 2005.
Consider the following bit of dialectical analysis.
• Universal automatism proposes a thesis:
Your mental processes are a type of deterministic computation.
• Your sense of having a free will entails a seeming antithesis:
Your thoughts and actions aren’t predictable.
• Wolfram advocates a beautifully simple synthesis:
Your mind’s computation is both deterministic and unpredictable.
The synthesis is supported by the following conjecture, implicit in Wolfram's A New Kind of Science.
• Principle of Computational Unpredictability (PCU). Most naturally occurring complex computations are unpredictable.
The workings of your mind are unpredictable in the sense that, when presented with a new input of some kind, you’re often quite unable to say in advance how you’ll respond to it.
Someone offers you a new job. Do you want it or not? Right off the bat, there’s no way to say. You have to think over the possibilities, mentally simulate various outcomes, feel out your emotional responses to the proposed change. Someone shows you a painting. Do you like it? Hold on. You have to think about the image, the colors, the mental associations before you decide. Someone hands you a menu. What do you want to eat? Just a minute. You need to look into your current body feelings, your memories of other meals, your expectations about this particular restaurant.
We say a computation is unpredictable if there is no exponentially faster short-cut for finding out in advance what the computation will do with arbitrary inputs. When faced with an unpredictable computation, the only reliable way to find out what the computation does with some input is to go ahead and start up the computation and watch the states that it steps through.
Once again, suppose I’m presented with some new input. Since my thoughts are unpredictable, the only way to find out what I’m going to end up thinking about the input, is to go ahead and think until my mind is made up. And this means that, although my conclusion is in fact predetermined by how my mind works, neither I nor anyone else has any way of predicting what my conclusion will be. Therefore my thought process feels like free will.
I seem to be a fluttering leaf.