Computational reducibility may well be the exception rather than the rule: Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be formally undecidable.
I had a very selfish reason for building Mathematica. I wanted to use it myself, a bit like Galileo got to use his telescope four hundred years ago. But I wanted to look, not at the astronomical universe, but at the computational universe.
It's always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex. Well, I think we found its secret. It's just sampling what's out there in the computational universe.
Could it be that some place out there in the computational universe, we might find our physical universe?
I'm committed to seeing this project done. To see if within this decade we can finally hold in our hands the rule for our universe, and know where our universe lies in the space of all possible universes.
I think Computation is destined to be the defining idea of our future.