Is Mankind Smart Enough?

[Lestat]

Cooker-

I'm not sure I quite understand what you're saying. Our evolutionary process is actually quite slow. It took thousands and thousands of years for us to adapt to our current habitat. Exactly what is it that makes you think a machine would not be more able to adapt in much less time?

[Piers]

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I am not an expert on Gödel’s incompleteness theorem, but I am fairly sure that it is not far reaching enough to make such statements. Certainly, euclidean geometry is a complete theory, so complete theories do exist. The existence of complete theories is enough to allow for the possibility that there may exist a complete final theory of the universe (although it could not be based on a recursive scheme I believe).

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Basically my understanding of Gödel’s theorem (its about twenty years since I worked my way thorough it) is that you take a sufficiently complicate theory, anything that includes the natural numbers should do.

Then you encode the theory within itself. What this means is that you have a well-formed statements within the theory which have a meanings on two levels:

There is the up front meaning, as given by the logical system itself.
An indirect meaning that you get by decoding the statement.

If the statement is a theorem then both meanings are valid.

You now show it is possible to construct a statement that when decoded has the indirect meaning “This statement is not a theorem of the logical system”.

Clearly the statement is not a theorem, because if it was a theorem that its indirect meaning would be true and hence it would not be a theorem. For much the same reason its negation is also not be a theorem.

So we have a statement that is in a sense ‘true’ but not contained within the system.

Now imagine that we have devised a model of the universe. This will consider a set of rules by which the universe is governed. By their nature it will be possible to express these rules in such a way that Gödel’s theorem can be applied to them.

Statements using the language of our universe model become statements about the real world that can be either true or false.

So what can you say about the statement “I can not be explained using this model”. Both it and its negation map on to a meaningful statement about reality, one of which is true but neither are contained within our theory.

(Or things are really weird, and logic breaks down in some way, which would negate the above argument, but that would also negate any theory we would have knocked up as well.)

[Piers]

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I don't think there's much question that a complete theory of the universe exists. The question is will man ever figure it out?

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You are correct in the sense that the universe is its own model.

What I am saying is that it is not possable for us create a complete model of the universe using a set of axioms plus logic. which is what mankind will have done if it created the OP's "Theory of everything".

The reason Man can not understand everything is not that we are not cleaver enought, but that its not logical possable for us to.

[Cooker]

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Once AI equivalent to the intelligence of a person is developed,

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I don't think you realize how huge a leap this will be considering we know closer to 0% than 5% about how human intelligence works. I think there is a strong chance that bioligical systems adapt at optimal rates already, so beating them will be nearly impossible. I think it may take us longer to develop human level AI than nature took. What intelligence can we make? We can't even make intelligence at the level of retarded bacteria. We are still basically at zero AI. I will grant you that once we get AI at the human level, we will improve quickly, I just don't think we will ever get there. I think the extinction of the human race will come before we see a computer 1 billionth as intelligent as a human. Currently, computers have zero percent of human intelligence so if they improve by a factor of 100000000000000000000 they will still have 100% of the way to go (rough estimate but probably much closer than anyone else will give you).

[Cooker]

But the one key point of Godel's theorem is the type of system. I believe it must have an infinite recursive structure to fall into the class of theories that must be incomplete. If the final theory doesn't have such a structure, then it is possible that it could be complete (like euclidean geometry).

I personally feel as though physics is being overly dominated by a search for a final theory, but I think a final theory is still a possibility (although I entertain many ideas about possibilities here as well). If it is to be complete, then it will have to be much simpiler than the arithmetic of the natural numbers I agree. However, I do not agree that a final theory must be more complex than the arithmetic of the natural numbers, so I think completeness is still a perfectly possible choice. I think this would suggest that the natural numbers are an invention of man and not of nature.

[Piers]

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But the one key point of Godel's theorem is the type of system. I believe it must have an infinite recursive structure to fall into the class of theories that must be incomplete. If the final theory doesn't have such a structure, then it is possible that it could be complete (like euclidean geometry).

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Do you really believe that a complete theory of the universe might not conatin an infinitive recursive structure (such as the natural numbers)? The possibly of the universe not haveing such a recursive structure goes so against my intuition that I really cannot imagine it.

[hurlyburly]

We've only been asking questions for a few thousand years, and (I think) we've come a long way. We don't know how long the road is. We still don't really know what the important questions are.

Sorry you feel that way, but history doesn't bear that line of thinking out.

[Lestat]

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We've only been asking questions for a few thousand years, and (I think) we've come a long way. We don't know how long the road is. We still don't really know what the important questions are.

Sorry you feel that way, but history doesn't bear that line of thinking out.

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There is nothing in history that suggests we must have it in our capacity to eventually figure everything out, even if we survive millions of years into the future. Think of it this way...

How long would you give the species "Dog" to evolve to the point where one could understand the workings of a combustible engine? Never? I agree.

It is very possible (in fact, most likely), that there are things which are completely beyond our capacity to understand. I do agree with some other posters that it is much more likely we will create machines that will get further than us.

[Cooker]

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But the one key point of Godel's theorem is the type of system. I believe it must have an infinite recursive structure to fall into the class of theories that must be incomplete. If the final theory doesn't have such a structure, then it is possible that it could be complete (like euclidean geometry).

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Do you really believe that a complete theory of the universe might not conatin an infinitive recursive structure (such as the natural numbers)? The possibly of the universe not haveing such a recursive structure goes so against my intuition that I really cannot imagine it.

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I take my own intuition with a grain of salt. I give yours (or anyone else's for that matter) no credibility whatsoever. Intuition is not an arguement. I still think completeness is possible. Very simple systems are capable of very complex behavior. I don't put anything past mother nature.

[hurlyburly]

I had a million "Yeah, buts...", but only time will tell. 100 years ago they would have never seen us where we're at now.

As long as the distractions don't capture 100% of our progeny, there will always be someone working to move forward. I agree with you somewhat, but I don't see the mental barriers. We're missing so much information now, we can't even gauge how much is missing.

As far as the dogs go, they are what they are, they're not trying to understand engines. Breed one that cares and is interested and you just never know.