Stephen Wolfram discusses “Computation and the Future of the Human Condition”

As found on the Wolfram Blog, Stephen Wolfram provides a transcript of his talk “Computation and the Future of the Human Condition” delivered at the H+ Summit @ Harvard on June 12, 2010. I found it interesting. Unfortunately for me, just as when I read his book A New Kind of Science (NKS), I think I can grasp the general ideas, but I can’t make the intellectual leap necessary to understand how to apply them to solving problems. I think I can see some of the outlines of what may be involved, but the full outline, and the all-important details of implementation remain beyond my reach. Frustrating.

Below is a brief excerpt dealing with ideas he’s discussed at length elsewhere, so it may not be the best choice of an excerpt. On the other hand, it may be good for piquing the curiosity of those without much exposure to Wolfram’s thinking.

[...T]o make a prediction, we have to be able to somehow out-compute the system that we're trying to predict.

Well, for systems like idealized planets orbiting a star, that's always been possible.

We don't have to trace every point in each orbit; we can just have a little computation that jumps immediately to the answer.

In effect, we can computationally reduce the behavior of the system.

But will that always be possible?

The Principle of Computational Equivalence implies that it won't.

And in fact it implies that even among very simple programs in the computational universe, it's common to find computational irreducibility.

The exact sciences have always avoided systems that work like this.

But they're all over the place.

We've always implicitly assumed for our science that we as observers or predictors of systems are much more computationally sophisticated than the systems we're observing or predicting.

But the Principle of Computational Equivalence says that this isn't true.

And that instead we are just equivalent to the systems.

So that we can never expect to outrun them.

And to find out what they do we have no choice but to simulate each step in their behavior, or in effect just to watch how the behavior unfolds.