I have a weird hunch that it is *not* possible to make solid
predictions about chaotic systems without prohibitive amounts of
computation power in the general case. It may be possible to prove
this assertion (or may not -- "does P=NP" has held for a very long
time without a proof.) The related question of "is it possible to make
solid predictions in interesting specialized cases" may be more
tractable.
I don't make any predictions about what the great discoveries of the
next century will be, given that if we really truly hit exponentially
self-feeding intelligence enhancement its unlikely that we'll have
even a tiny shot at predicting what the next hundred revolutions of
the earth around the sun will hold -- probably more changes for
ourselves than we have experienced thus far in our whole existance as
a species, and perhaps more change for life than it has undergone in
its entire existance on the planet.
However, I can easily name something on my "most wanted" list of
information.
What do I want to see? A theory framework that answers (in a
meaningful way) the question "why does the electron weigh as much as
it does" or, in the same vein, "why is the speed of light in a vacuum
what it is?"
Similarly, the framework should answer (in a meaningful way) the
question "why is the formula relating velocity, mass, and energy of a
body in motion what it is?"
For years now, we have built up this large coherent body of equations
and constants that give us answers to physics questions. What I want
to know is -- why *these* equations? Why *these* constants?
The answer may turn out to be unknowable, or there may be an
underlying answer to what gives rise to particular bits of the physics
bestiary. I suspect that some of the questions (like why the charges on
the electron and proton are what they are) may have better answers
than others. At this point, even coming up with coherent ways to
phrase some of the questions is hard...
Perry