You need both. I think I would recognise a solution to global
problems if I saw one. However, I can't for the life of me think it
up. I don't have the compute power to generate enough alternatives
and evaluate them.
In some problems, the evaluation is the easy part: e.g. does this
transmission line design violate any of the safety design criteria?
How expensive would it be to build.
The hard part is fishing around in the sea of all possibilities
looking at the most promising possibilities since you don't have time
to consider them all. One technique for doing this is called dynamic
programming. I used it in Optow. We also used it managing water
levels in interconnected dams.
I think that the density of good solutions in all possible guesses (or
mutations) is key to how we even exist at all. If it took too many
mutations for an organism to hit on an advantageous one, too many
evolutionary "guesses", then evolution could not work; organisms would
degenerate back into random noise. The space of possible mutations has
to be to some degree "dense" with advantageous mutations.
It must be therefore to some degree "not too hard" to randomly come up
with an advantageous mutation. But if that's the case, this should apply
also to learning.
Moreover, we would be sunk if solutions hit upon early on did not tend
to last, did not tend to keep being useful beyond changes in
environment. If every little change in environment invalidated all our
adaptations, then life would be a fragile thing, like a computer program
that utterly breaks down if a single bit is misplaced. Clearly our
adaptations need to be robust. But this means that they need to be
general. I.e., we evolve in one environment, but the features we gain,
or the things we learn, remain applicable and useful, maybe with minor
adjustments, in new environments. This robustness is the same as
generality. Our lessons are general. We learn, or evolve, in specific
surroundings, but the specifics of our classroom (or primordial
environment) are not the only environments in which our lessons apply.
In short, the lessons we learn tend to be general. But that is certainly
not due to any special virtue on our part; the adaptations successful in
one environment simply happen, often, to be successful generally.
This means that not only is the space of possible mutations dense with
advantageous mutations, but the space of advantageous mutations for a
given environment is dense with advantageous mutations for more general
environments.
Or in other words, a given environment is in a way a model, a microcosm,
of the wider world. If one can learn lessons applicable to the wider
world merely by focusing on one particular, limited environment, then
that limited environment clearly is acting as a fairly useful model of
the wider world. This means that the world is filled with self-
similarity. It means that modelling tends to be successful, or tends to
be more successful than we might have any right to expect a priori. It
means that we can expect that by toying with models of the world we are
surprisingly likely to hit upon truths that apply to what we were
modelling. It means that modelling is curiously effective. Mathematics
is a kind of modelling. So it means that mathematics is curiously
effective.
Einstein asked,
"At this point an enigma present itself which in all
ages has agitated inquiring minds. How can it be that
mathematics, being after all a product of human thought
which is independent of experience, is so admirably
appropriate to the objects of reality? Is human reason,
then, without experience, merely by taking thought, able
to fathom the properties of real things?"
It's not just mathematics that admirably appropriate in helping us to
fathom the world outside of mathematics; but environments are,
generally, admirably appropriate in preparing organisms for the world
outside of those limited environments.
To be sure, an animal adjusted to a particular environment does not
necessarily do well outside of it. But when we consider the similarity
of animals that have adapted to all corners of the world, then it
suggests that while animals are not prepared for the wider world EXACTLY
as they are, nevertheless they're at a point where minor adjustments are
sufficient to launch them into a new habitat.