Quote:
You have three equally massed objects in space.
They are governed by gravity.
Given initial conditions, solve the differential equation which describes their motion.
You can't. It's impossible.
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Sure you can. Get a computer. Have it crunch out the differential equations with some good code. You will find that certain initial conditions give unstable solutions, but it can be done. Next imagine a computer that can solve the problem to an accuracy less than the uncertainty principle. Now you've got something that is operationaly as good as (perhaps arguably better than) an analytical solution. If that seems like an ad hoc solution to the problem consider that the analytical solutions to physics problems are almost always had at the expense of making some simplifying assumptions.
Still, just because you've got the ultimate equation (think: unification of physics) that doesn't mean it's the end of the story. When Maxwell wrote down his famous equations it was not the end of learning about electromagnetic theory; there was a lot of work to be done in understanding all the applications/implications of the new theory. Besides, there is also the issue of emergent properties of many body systems which do not lend themselves well to understanding with the fundamental equations. Just think about thermodynamics. On some level all that we measure is governed by the microphysics (electromagnetic interactions) but instead we talk about things like entropy, pressure, and the like. Thermodynamics stands as knowledge apart from any ultimate theory of reality.
I had an idea while I was reading the posts here. People have noticed that all information has a certain amount of energy associated with it. To prove this to yourself, imagine discovering some new knowledge without expending some energy in the process or try to imagine conveying some information to somebody else without expending energy. If you can buy that, then I bet that information and knowledge are fundamentally limited by the amount of energy available in the universe. There are reasons to believe that the amount of energy in the universe is finite. I can't think of the exact reasons right off the top of my head unfortunately, but I think it is tied to the size and expansion of the universe somehow. Anyway, if the energy is finite and the information is proportional to the energy then the information must also be finite!
On a happier note, there is so much energy out there that I bet we will destroy ourselves with our knowledge before we exhaust our supply.
