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Original post by Daerax Quote: Original post by AlphaCoder Quote: Original post by ibebrett Quote: Original post by AlphaCoder I could have it run this for random values of n from 10 billion to a trillion and random amounts and directions of connections until I got one that took the text input of some famous math problem and text outputted the correct answer and upon further testing, did this for other problems as well ( to prove it wasn't just a completely random fluke of input/output ). but it was proved about 80 years ago that there literally CANNOT be an algorithm for solving general Diophantine equations and therefore problems in general. (this is in response to you if you are implying that you could create a computer to solve general math problems) If it checked all possible neural networks with more and less nodes than neurons in the brain then it would certainly come across one that could solve problems at least as well as any human in history. You'll have to tell me where you saw this proof and I'm sure it's out of context because the way you describe it, either no human could ever solve general Diophantine equations, or the proof was wrong. No the proof was correct. Perhaps you should look up Hilbert's 10th Problem. You may also be interested in the even more relevant Chaitin's Construction. It highlights one of the reasons why CyC is a silly endeavour. The caveat in all this is algorithims and formal systems. Humans do not operate by algorithims. It is common amongst Mathematicians to think of infinity as an approximation of really big things. It is much easier to deal with infinity than really big things. Thats the real idea behind calculus. Point being a computer with infinite resources is still a stupid computer and will not just suddenly become creative. Neural Networks are not some magical thing, their design requires complex algorithims especially when their intended purpose is vague. Now suppose by some magical luck we were able to find a method for minimization that was just a bit short of impossible and whose kolmogorov complexity was just short of infinite for this computer. Via various incompleteness theorems we can know that there exists problems that will cause it to suddenly halt operation (sounds like a good story... , does it also have infinite time?). We also know that there are an infinite number of things which it will not be able to solve. And that there are some things to which it will give true answers though we know they are false. Finally from a hardware perspective neural networks work better with lots of simple parallel processors than one large one. As stated we do not know where intelligence comes from and it does not seem likely that some inelegant algorithims on lots of what essentially reduce to simple mathematical functions on reals will magically get us there. The brain is more than a 'neural network'. The general consensus is that general AI will likely come from a direction where one is not trying to copy the human brain.

Going to have to disagree with you on that.

The human brain is in my opinion nothing but a neural network.

If you can prove that there is no general algorithm for solving some type of problem that that just means one of two things

there will be problems that the neural network couldn't solve and humans couldn't either

humans don't solve them with "algorithms" per se and neither will the neural network.

I'm sorry but given all possible configurations of neural networks we WILL stumble upon some that work in the same manner as human brains. Or far better.

You suffer from what I believe to be a common misconception that there is something magical and mystical about human intelligence that transcends what can be described by an adequately large neural network. I don't feel the brain differs from that at all. If the brain is a neural network that can change it's structure (well it is of course) then that could be engineered into the neural network as well.

Are you forgetting that the human brain is just a finite volume that contains finite matter that follow simple finite rules? Anything that satisfies those criteria can theoretically be simulated by a computer with sufficient resources and hence create an intelligence capable or more capable than a man's.

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Original post by AlphaCoder Going to have to disagree with you on that. The human brain is in my opinion nothing but a neural network.

You are under the misguided, though common, belief that CS Neural Networks have something to do with the brain.

The human brain is made of neurons. It is not, however, a neural network as implemented in CS algorithms. The latter is is only very loosely based on how the various parts of a brain actually. There are a myriad of other influences in a biological brain which are not present in CS neural networks (hormones, synapses, Na/K pumps, synchronizing neurons, some neurons are analog processors not digital ones, etc, etc, etc).

So, sure, if you exactly modeled the human brain you'd get a human intelligence. That's obvious. The problem is we have no idea how all the details of the human brain work out so you cannot model it.

-me

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Original post by Palidine Quote: Original post by AlphaCoder Going to have to disagree with you on that. The human brain is in my opinion nothing but a neural network. You are under the misguided, though common, belief that CS Neural Networks have something to do with the brain. The human brain is made of neurons. It is not, however, a neural network as implemented in CS algorithms. The latter is is only very loosely based on how the various parts of a brain actually. There are a myriad of other influences in a biological brain which are not present in CS neural networks (hormones, synapses, Na/K pumps, synchronizing neurons, some neurons are analog processors not digital ones, etc, etc, etc). So, sure, if you exactly modeled the human brain you'd get a human intelligence. That's obvious. The problem is we have no idea how all the details of the human brain work out so you cannot model it. -me

I am not under that belief. I do know that a neural network as it is defined is probably (actually no.. i'll get back to this) an inadequate approximation of a human brain.

To be honest, I would say any of the other factors of the brain that aren't exactly analogous to a neural network could easily be simulated by.. neural networks.

I don't think the neural network is the same as a human brain. But I do think a neural network could model everything about the brain that's worth modeling.

So maybe it would take a trillion node neural network to model the 100 billion node brain. So maybe 90% of the network's complexity would be devoted to making up for the key differences between brains and networks.

Still, a neural network could simulate human and superhuman intelligence.

You're of a contrary opinion because you live in a time where cpu-resources are inadequate for neural network solutions to problems.

I am well aware of this and that's why this was a hypothetical scenario.

again though, the ANNs that we talk about in computer science really have almost nothing to do with the nueral nets in our heads. Its an extremely loose model thats useful because of some basic pattern recognition you can do with it, not because it acts like our brain.

first you would have to figure out how the brain actually works. this might depend on some very confusing principles, and in fact it could be that there is literally no way to simulate it. the universe doesnt have to express itself in totally deterministic terms. who knows whats actually going on in the brain?

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Original post by AlphaCoder Going to have to disagree with you on that. The human brain is in my opinion nothing but a neural network. there will be problems that the neural network couldn't solve and humans couldn't either humans don't solve them with "algorithms" per se and neither will the neural network.

It is good to have conviction. However it is also good to be certain of their veracity. You say the human brain is nothing but a neural network. Have considered approaching professionals in the field and asking them what their opinion of this is? And explaining to them why they are wrong? Have you studied what a Neural Network actually is? Opened texts on cognitive and neuroscience to see what the brain might be?

Your conclusions have a significant impact on the philosophical aspects of the Church Turing Thesis. Consider developing it further and publishing it, the scientific community would be vastly interested in those results.

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I'm sorry but given all possible configurations of neural networks we WILL stumble upon some that work in the same manner as human brains. Or far better.

You underestimate the size of infinity. A similar stance was taken by foramlists of the early 20th century with regards to the mechanization of mathematics. It was quickly found out that only the propositional logic was decidable (as well as surprisingly enough euclidean geometry sans circles) and that any system which can encode the Godel numbering system could not be proven to be consistent from within the same object language. With the advent of computers it was found that unless carefully guided most of what an automated theorem prover can generate is gibberish (not wrong just really large inefficient proofs) and trivial.

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You suffer from what I believe to be a common misconception that there is something magical and mystical about human intelligence that transcends what can be described by an adequately large neural network. I don't feel the brain differs from that at all. If the brain is a neural network that can change it's structure (well it is of course) then that could be engineered into the neural network as well.

Perhaps I suffer from the former but certainly not the latter. But it is almost a tautology that the human brain transcends a neural network. The brain is more than an exercise in mathematical optimization. More than a triple (V,E,f : E -> R) where V is merely a set of mathematical functions on the reals which is essentially what neural networks reduce to. No such compact summary can be given for the brain which could capture even a small percent of its essence.

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Are you forgetting that the human brain is just a finite volume that contains finite matter that follow simple finite rules? Anything that satisfies those criteria can theoretically be simulated by a computer with sufficient resources and hence create an intelligence capable or more capable than a man's.

Exactly. The brain is not made up of 10 ^ 24 hertz processors. It is finite sized but the interaction of its components is infinitely varied. The detailed nature of their behaviour and interaction is unknown to us. It is a mass of electro-bio-chemical-organic cells. There are many types of them. The details of their interaction indeed a small aspect of their mere core - manufacturing of protein is a large problem on its own; with a small aspect how to fold proteins requiring a fair part of the computational power of the machines on the planet. Something more than mere computation is going on there.

Have you thought about how your neural network of near infinite capacity will go about learning? I assume it must train itself? If such is even possible?

[Edited by - Daerax on August 30, 2008 3:23:27 AM]

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Are you forgetting that the human brain is just a finite volume that contains finite matter that follow simple finite rules?

I'd argue that the rules aren't simple at all: The rules are physics. This includes science that we haven't even discovered yet!

I might even argue about the "finite" bit: A particle is a wavefunction, which is an element of an infinite-dimensional Hilbert space.

There are also spatial infinities. Since there aren't any infinite potentials (energy wells) in your brain, every wavefunction will have infinite support. Basically, this means that your brain occupies all of space.

It's just usually where you think of it as being. ;-)

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Original post by AlphaCoder If we were suddenly in possession of computers with cpu frequencies of 10^24 Hz with no memory bandwidth drawbacks, and enough and fast enough RAM to scale properly with it, are there any algorithms that would be best suited for it? Of all the different approaches to and implementations of AI, which would be the best to scale with that type of frequency and get the quickest super-AI results? I'm talking about in the area of general learning and simulating of human or super-human level intelligence in problem solving.

THe speed would make possible eecuting AI logic of great complexity, but the same old problem is building that AI logic (logic as data) into the system for the specific use. A human is involved in either writing that logic directly or with a self-learning machine making correction/directing lessons for the learning. Humans can only do so much so fast.

As for what algoruthms to use, pretty much the same ones would be used (brute force is still inefficient even when the computer is faster..).

The US Govt in cooperation with IBM and a bunch of universities managed to implement enough of the laws of physics inside a mainframe that they don't need to detonate nuclear bombs for testing any more - they can replicate their bombs in a simulation.
If that's possible in this day and age, then I'm guessing that in the far future it will be possible to implement enough of the laws of physics required to simulate a chemical/electric brain, and thus simulate intelligence.

If we can simulate an intelligent brain, then in a fairly indirect way, the proof that Daerax was referring to is wrong (as AlphaCoder was saying) because by that point, we will have created an algorithm (i.e. the laws of physics) that happens to let us solve any mathematical problem by giving it to the virtual brain ;)

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Original post by Palidine Fundamentally, we don't understand how human intelligence works; heck we can't even define it.

I don't even know why some humans DON'T have intelligence. Or pherhaps they do have, but it doesn't work?

Sigh... human brain is too difficult to understand [lol]

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Original post by Barking_Mad Quote: Original post by AlphaCoder Quote: Original post by Hodgman *** Source Snippet Removed *** This is more or less exactly what I meant with my example. Though I was referring to one level of abstraction higher. Monkeys typing forever will eventually type out the design for a good neural network. What if they type out the instructions for self destruction first?

What if the monkey was running on a Debian machine with their giant Random Number Generator Fiasco?
Congratulations! we have a deterministic monkey!

Just cheering up the forum