kind of a weird question

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could there be a computer program that fits equations and algorithms together so they make some kind of real-world sense?

What I mean is basically, have the computer start with "A" and start plugging in random or in-sequence equations, algorithms, theorems and whatnot until it finds something that could be useful like faster than light travel or the formula for limitless energy...

For example, I'm looking for a theory of general relativity.

The computer starts with A, goes on the B then C on to ultimately E where the computer goes, "ah-ha! I can use E! Okay, E equals..." and then it continues its search for something else to complete or add to the equation. The computer searches and minds M and then C, plugs those in and then squares C.

Equation complete. "E=MC2"

Well, for one thing, the letters in "E = mc²" don't represent letters. E represents energy, m represents mass, and c represents the speed of light. You can't have a computer program just line up letters and come up with "E = mc²", since "E = mc²" isn't saying anything about the letters themselves. It doesn't go "A, B, C, D, aha! E!", because E isn't a value, it's a symbol for energy. "E = mc²" is utterly meaningless without the knowledge of what the letters represent in the context.

If you are talking about a formula/proof generating computer, there were attempts back in the '80's, but they weren't terribly successful. I guess the problem is that variables can be combined into an equation and infinite number of ways.

In addition to which, most mathematical theories are recursively undecidable which means one cannot determine whether something that looks like theorem really is a theorem by some simple or finite algorithm. The only way to show that something is a theorem is to come up with a proof for it and this has not been nor can it be reduced to a algorithmic procedure. In formalized arithmetic, Geodel show there are closed formulas such that neither they nor their negations are provable. The Goedel Incompleteness Theorem. Nor can a theory demonstrate its own consistency.

ruveyn

just an example. Don't be so literal

Research Turing Machines, Godel's Incompleteness Theorem (as ruveyn mentioned already), and Theory of Computation in general.

As ruveyn already said, you are essentially asking for a proof generator and as I recall, a general proof generator is impossible. Not impossible as in lacking computer power, but impossible in the same way that 1+1 can never = 3. It is impossible even with a quantum computer. Very loosely, for any proof generator, you can generate the proofs within that system, but there are things outside of the system that you can't "get to" from within the system. Making more proof generating systems and "linking them together", doesn't work because they (again very loosely) all reduce to the same system if you can link them. If you can't link them, they will prove different different, sometime contradictory things. Any Theory of Computation expert would cringe at this explanation, but it gives a bit of the flavor of the problem.

Your example makes no sense. You can't ask a scientific question with a somewhat detailed example to clarify what you're asking for, and then expect people to not take your example literally. Why would you even use such an example if you know such a thing to be impossible?

What you can do, though, is give a computer a whole lot of data and get it to figure out the relationships/laws present in it. This works using genetic algorithms: the computer randomly generates a bunch of formulas and sees how well they fit the data, picks the best, then changes them a little bit, picks the best of them and repeats the process. That can work quite well, from what I know, although I don't know how extensively it's been applied. But a few years ago this process was used to have a computer rediscover all of the laws of motion.

because, smartass, I don't know any of this crap:

http://en.wikipedia.org/wiki/Trinification

nobody likes a know-it-all douche.

Numbers or whatever the eff smart people work with, okay?

(and mods, before you go off half cocked because I was calling someone a name or three, remember he was calling me dumb without actually typing it)

And it should be pointed out there, Einstein that I have what's called dyscalculia. I'm lucky if I can even add fractions. So before you off off being a prick, consider they might not be as smart as you (at least in some areas)!

That's really interesting. I'd be pretty cool to see something like String Theory evolved in this way



Is that due to the fact that no system can prove its own validity? Or is that Turing's idea?

This is where it gets tricky. Even a phrase "no system" has very particular meaning in formal computation theory. The are systems that are complete and consistent, they jut lack any real power. So it is incorrect to say "no system". You even have to rigorously define "validity".The point is that what can be generated by a computational system has strict theoretical limits. Fortunately, those limits are not of much concern to regular usage of computers and software. It does have some interesting implications regarding artificial intelligence. It is possible that sentience is something that can't be computed. Of course, we would need an agreed upon concept of just what sentience is. I don't believe such a universally accepted definition exists.

I am somewhat familiar with the idea of a Formal System; that any sufficiently complex formal system has some propositions which it cannot prove, along the lines of "this statement cannot be proven within formal system A". Validity, in this context, refers to the consistency and completeness of a formal system. Correct me if I'm wrong

I think that Consciousness is ultimately computable, but I am unsure how it arises. Perhaps huge amounts of data and endless layers of self-reference gives rise to the phenomena.

There's a lot that think consciousness is computable. But until it is actually defined you can't even decide what type of problem it is, let alone it's computability.

I am one that doubts the computability of consciousness. Without a workable definition of consciousness, it's all conjecture, but the very layering you describe adds huge complexity to the system. Any mathematical model would be an abstraction of that complexity, and hence less complex. So even if you add a robust mathematical model, something you would need before you could investigate computability, you would be investigating the computability of the abstraction, not consciousness itself.

Another issue is that consciousness is not only thinking. It is also tied to perception. Sometimes perception happens without thinking, or at least any higher order thoughts. How do you even frame this as a computable problem?

I guess we'll have to wait and see.

I have literally no idea how it would be computed. I won't pretend I do.

I agree with the that the "Book of Nature is written in Mathematical Symbols", so that everything can be described exactly in terms of a mathematical model, albeit an almost infinitely complex one. If Quantum Mechanics adds a Stochastic element to nature, then we merely need to write one "master equation", add the stochastic elements, compute every single possible outcome, and we will then definitely have one model that perfectly describes the universe.

I know that it is conjecture, although somewhat guided conjecture. Perhaps I am making the idealistic fallacy of assuming that Maths, the system which shows the interconnection between ideas by stripping away qualia, could actually give rise to qualia itself. Perhaps the gap from abstract interconnections to subjective experience is impossible to bridge using abstract reasoning. Or perhaps I'm just talking s**t again...

Quantum physicists aren't even sure of that. How are you?

Goedel and Turing proved this meta mathematically.

if plain old math (i.e. set theory) is consistent then these theorems are true.

ruveyn