Hey, thanks for clearing things up! Forgive my misconceptions. And now I’m curious. Can you pare down in a few sentences (they can be incredibly technical and terse, I don’t mind) what you’re looking into as far as hypercomputation? I admit, the extent of my knowledge of hypercomputation is limited to things like letting a Turing machine compute for infinitely long (which then removes concerns of computable reals among other things). Or do you have a paper you’d point me at? So… Any thoughts on the P v NP problem? Equal? Separate? Independent?

“The unique, and smallest, causally connected region including myself”.

As I note, I just have to laugh. This is so a mathematician’s answer! And I can say that, ‘cuz I ar one, too.

In any case I understand Feynman proved that the predictions of quantum mechanics can be computably calculated which I think is enough for the purposes of my argument.,

If you’re simply talking about the predictions being computable in that sense, then I suppose I don’t have too much to quibble about (other than maybe asking whether we’re talking completely computable, or probabilistically computable…). I certainly haven’t researched any into the computability of the laws physics in that regard, but then, your answer suggests you were stating a much weaker proposal than I originally thought.

If I have misused the term Turing computable it is through carelessness not a lack of understanding. Never the less I think that at worst I have failed to specify what I meant rigorously enough.

Well, now knowing that you’re mathematician working within the realm of hypercomputation, it now makes perfect sense why you’re fairly strident at saying “Turing computable”. In my field (resource bounded measure and dimension), all the notions of computability we work with are polynomial-time equivalent, so we tend to just say “computable”. I definitely retract my flippant Montoya comment.

Hmmm, I didn’t really mean to say this. I really ought to have said: But for you to be right would really imply that the physics relevant to the mind is not just a combination of Turing computation and randomness. This doesn’t really effect my argument though.

Well, this comes down to fundamental views of mind/brain interaction. If we suppose that all human thought, intelligence, and whatnot is determined by physical laws, if there’s nothing more than the brain at work, that’s one thing. If there’s a spiritual soul, which we can’t prove or disprove mathematically, but which is a doctrinal statement of the Catholic Church, then there’s more at play than are touched by physical laws. That’s the only point I was trying to make.

Thanks again, Barnaby! Now, I should probably hit my research, as well.

The philosophy of materialism holds that the only thing that can be truly proven to exist is matter, and is considered a form of physicalism. Fundamentally, all things are composed of material and all phenomena (including consciousness) are the result of material interactions; therefore, matter is the only substance.

What I am saying is that we believe that there is more to man than the sum of his biological parts. Our thought processes extend beyond the material world to the non-material world. We possess an immortal soul which gives us this ability, which a purely material creature or construct could not. I suggest that this capacity is a critical component of human intelligence.

Matt

No offense taken. I’m arguing that if AI is impossible then that would imply a revolution in physics. And I am concluding that until further evidence emerges we should assume that AI is possible.

“..AI capable of ANY original thought..”. I would argue that you have not shown that people are capable of any original thought either by the exceedingly stringent definition you appear to be using. I am arguing that by any reasonable definition if people can reach a certain level of intelligence then that level can be reached by a suitably programmed, and powerful enough, computer.

I don’t think the term materialist is very well defined so I wouldn’t call myself one. I do think that the laws of physics are Turing computable where they are relevant to the human brain/mind.

I think there is a much bigger difference between today’s computers and ‘higher’ animals than between ‘higher’ animals and people. But never the less I really am convinced that artificial intelligence is possible! Furthermore my intuition that AI is possible is as strong as my intuition that other people think and feel. I am fascinated by the fact that others lack this intuition or have an opposing one. I try not to be over reliant on my intuitions, however, even when they are this strong.

“If you are arguing from a purely materialist perspective then it would be impossible to demonstrate the impossibility of AI achieving human intelligence.”

This is only true if you think the idea that the universe involves hypercomputation is not compatible with being a materialist. Do you assume a materialist must believe the universe has a finite number of laws of physics? Because if not then a materialist could in principle reject the possibility of AI (realised by faster computers of the type we have today rather than hypercomputers).

Response to Ryan:

“You’ll have to clarify universe in this dialogue”.

I normally use the definition: “Causally connected region” and for ‘our universe’ I use “The unique, and smallest, causally connected region including myself”. I do not try to separate the universe up into domains such as material and spiritual.

“Do you hold to hidden variable theory?”

I meant to add the caveat: OR Turing computable with some random noise added. In any case I understand Feynman proved that the predictions of quantum mechanics can be computably calculated which I think is enough for the purposes of my argument.

“What is your field?”

I am a mathematician working within set theory on hypercomputation. If I have misused the term Turing computable it is through carelessness not a lack of understanding. Never the less I think that at worst I have failed to specify what I meant rigorously enough. I didn’t say at any point that I work in the philosophy of mind (I don’t). I just mentioned the area.

“What specifically do you mean by laws being computable?”

I mean that the predictions of those laws can be calculated (with initial conditions as input) by a Turing computer. Richard Feynman proved that quantum mechanics is computable in this sense. Strictly speaking the same is only true of general relativity under the assumption of a space time like the one we observe in our universe (but this is enough).

“Intelligence, thought, etc. are actually phenomena…”

Hmmm, I didn’t really mean to say this. I really ought to have said: But for you to be right would really imply that the physics relevant to the mind is not just a combination of Turing computation and randomness. This doesn’t really effect my argument though.

Now that was a very long response! I’ve enjoyed this discussion and regret I may not have the time to continue it (I have my research to write up).

I meant no offense by the “snootiness”, but a little sarcasm, and for that I apologize. I guess I was just trying to reject the idea that intuitive ideas ought to be rejected out of hand, or are not worth discussing. It’s my understanding that Einstein developed the special theory of relativity triggered by an intuition that it was the case.

I think Ryan has very effectively placed a lot more intellectual rigor into the points I was trying to make.

Matt

i guess if you put enough artificial constraints then it’s impossible to prove ANYTHING is impossible.

We know that man’s capacity to “engage in abstract reasoning, create new ideas or understand concepts” is not limitless, because that would make us God. But you’ve yet to show that AI is capable of ANY original thought let alone limitless.

It seems to me that AI could achieve the level of intelligence of the highest animals short of humans, and with massive computational power, but that is distinct from human thought.

Just curious, are you a materialist? It seems that you’re treating man as just a higher animal, rather than possessing an eternal soul.

If you are arguing from a purely materialist perspective then it would be impossible to demonstrate the impossibility of AI achieving human intelligence.

Matt
ps. snootiness aside, do you REALLY believe intuitively that AI could ever participate in such a discussion?