
As usual, ideas float around in my head for sodding ages (about 3 years in this case) before someone asks the right question and they get written down...
In this case, the question was "Exactly how do you describe intelligence?"
Basically: The ability to recognise patterns and extrapolate from them.
Of course, these patterns can be mathematical, social, spacial, etc.
I also believe there are two kinds of intelligence:
Inductive: Subconsciously learnt through repetitive exposure to a situation. This is how we learn that "That thing over there" is a "Dog" and "When I let go of things, they fall".
Deductive: The part of the brain that forms rules such as "Dogs have four legs" and "Gravity follows the inverse square law".
All creatures have inductive learning, deductive learning is much less common and humans have the highest level of all animals. Deductive seems to be more complex and difficult to do for people, I suspect because it's being "emulated" using inductive systems, much as when computers want to induct they have to emulate it using deductive systems.
What makes human thinking special is our ability to convert our inductive learning into deductive rules and then pass them along to other people (via speech, writing, etc.). This means we can take our inductive knowledge of "That's a dog and so's that, that too, not that, but that definitely is.", work out the defining characteristics "has 4 legs, goes woof." and then tell other people about those definitions. Then we can communicate using those definitions and be fairly sure that we're talking about the same things.
(This, of course, leads off into areas to do with mistaking the deductive definition with the thing itself, infinite definition regress problems and possibly Godel's incompleteness theorem if you're dealing with logic and language. Not going there right now)
Artificial Intelligence systems are either deductive(for instance, rules-based expert systems) or inductive(neural networks). I believe the next big breakthrough in AI will come when we develop inductive systems that produce rules for deductive systems, followed by the combination of those into a more closely knit whole. I think that the forebrain in humans is primarily concerned with deductive reasoning and acts as a feedback loop/monitoring system for our induction systems, correcting them when they are contradictory and allowing us to make much larger leaps on understanding than would otherwise be possible.
Ever heard someone say "I wasn't thinking." or "What were you thinking?". That's because, while the inductive parts were working fine, the deductive bits were on hold, because they take far too long to come to a conclusion. The more instinctive, inductive parts of the brain can make good first order guesses, usually using heuristics to short-cut to 'reasonable' guesses, and in an emergency you don't have time to do more than that.
The deductive parts of the brain also seem to be those parts that deal best with the abstract - mathematics, philosophy, physics, programming, etc. Deductions necessarily work with abstract concepts, slightly divorced from the more 'real' inductive pictures we have of reality. Some people have a much greater grasp of these abstract ideas and others can't see why people would be interested in topics that don't apply to their daily life and can't see how these topics do apply.
Oh, and sleep is an important part of this - you learn a lot while you're asleep, as your brain processes things you've experience recently and produces the inductive (and possibly deductive) results for you. Studies have shown that (for instance) if you learn to play something on the piano, you'll advance a certain amount in any particular day and then hit a brick wall where practice doesn't help. Sleep on it, however, and try again the next day, and you'll be up to 20% more proficient, because your brain has been processing the learning overnight.