OK, this is too cool - while writing about this stuff I received in the mail a book from my friend Todd by Stephen Wolfram called A New Kind of Science. It sort of fits with what I'm talking about, and something I've felt for a long time: That humans are based, just like computers, on what is known in Comp Sci as 'levels of abstraction'. Complicated things grow from a lot of little simple things. Computers have a system that moves around electrons-these get abstracted as ones and zeros, these get abstracted as characters, these are used to write programs, programs make operating systems, on top of operating systems are built MS Word, Internet Explorer and the Ultimate Metal motW forum. This is going to be long sorry....
"...On the basis of many discoveries I have been led to a still more sweeping conclusion, summarized in what I call the Principle of Computational Equivalence: that whenever one sees behavior that is not obviously simple--in essentially any system--it can be thought of as corresponding to a computation of equivalent sophistication. And this one very basic principle has a quite unprecedented array of implications for science and scientific thinking.
"For a start, it immediately gives a fundamental explanation for why simple programs can show behavior that seems to us complex. For like other processes our processes of perception and analysis can be thought of as computations. But though we might have imagined that such computations would always be castly more sophisticated than those performed by simple programs, the Principle of Computational Equivalence implies that they are not. And it is this equivalence between us as observers and the systems that we observe that makes the behavior of such systems seem to us complex.
"One can always in principle find out how a particular system will behave just by running an experiment and watching what happens. But the great historical successes of theoretical science have typically revolved around finding mathematical formulas that instead directly allow one to predict the outcome. Yet in effect this relies on being able to shortcut the computational work that the system itself performs.
"And the principle of Computational Equivalence now implies that this will normally be possible only for rather special systems with simple behavior. For other systems will tend to perform computations that are just as sophisticated as those we can do, even with all our mathematics and computers. And this means that such systems are computationally irreducible--so that in effect the only way to find their behavior is to trace each of their steps, spending about as much computational effort as the systems themselves.
"So this implies that there is in a sense a fndamental limitation to theoretical science. But it also shows that there is something irreducible that can be achieved by the passage of time. And it leads to an explanation of how we as humans--even though we may follow definite underlying rules--can still in a meaningful way show free will.
"One feature of many of the most important advances in science throughout history is that they show new ways in which we as humans are not special. And at some level the Principle of Computational Equivalence does this as well. For it implies that when it comes to computation--or intelligence--we are in the end no more sophisticated than all sorts of simple programs, and all sorts of systems in nature."
