This question has been killing me for the last week or so. As I understand it, there's a possibility that human intelligence relies on a hypercomputer/super-Turing computer in as much as it processes quantities with theoretically infinite precision, and if that were true, human-like intelligence would be provably impossible on Turing-equivalent computing machines.

It appears to me that the inputs to the system would, assuming spacetime is not quantized, be of infinite precision in either the spatial dimensions, the temporal dimension, or both; and that the chemical interactions within the mind (same assumption of a non-quantized spacetime) would have infinite precision, again in one or many dimensions. Say, a photon striking a photoreceptor in the eye-- obviously the intensity of this input is quantized, and its source becomes quantized, but its position in time is theoretically not quantized. The time at which any one signal begins to propogate through the neural network would also, theoretically, not be quantized. Then, the interactions between these signals within the mind would be occuring at infinite precision until they reached a threshhold (that was probably variable and of infinite precision itself) that triggered a neural cascade or hormonal signal to a muscle / gland / what have you.

If those two assumptions hold true, though, that spacetime is not quantized and that the temporality of the mind is not quantized, obviously any attempt at general AI modeled in the form of human intelligence is a waste of effort.

Anyone know any more about this? I can't find any particularly convincing arguments for either side of this, but generally that just means I haven't looked hard enough. Enlighten me, kthx.

5/2/2006 12:05:33 PM

This is just an absolutely surface, first reaction response, but I would have to say no, organic intelligence is not turing compatible.

I think you could make an EXCELLENT case for organic instinct being turing compatible. That is, involuntary and unconscience decision making.

But intelligence, human intelligence especially is not in any way state based, so I don't see how you could apply any state-based automaton to human thought or processing.

With vision for instance, there really isn't any objective correlation between the photons that actually hit our retinas and go into the visual cortex, and the stored memory of that event. Any new event, input or process can change the entire conscious brain in an instant, or be lost completely.

We don't experience something and react based on a set of rules. We experience something, try to place that experience in context with previous experience, create a set of rules to mimick or change the previous experience, look for instinctual reactions, and then start processing the actual response.

And even that isn't regular. A slight change in brain chemistry can throw it all out the window and become a completely different circumstance.

I can't recall where I read it, or who wrote it (I'll look tonight), but back in 98-99 I read about a theory of understanding consciousness. It basically came to the conclusion that a being cannot understand the mechanisms of it's own awareness, but it can do for other previous evolutions of beings. It was a pretty interesting read.

5/2/2006 12:36:27 PM

Even though these things are infinite, couldn't the finite approximation be so good that the difference couldn't actually be detected by humans anyway?

5/2/2006 12:39:05 PM

please refer to insaneman for all "correct" answers - hahaahahaha

5/2/2006 2:25:22 PM

^
Where did he go?

^^
You begin placing limits on the system/environment you are in, game over.

5/2/2006 2:32:25 PM

There are limits on the resolution of my eye versus the next persons eye, I don't see the problem.

5/2/2006 2:44:28 PM

Quote :

"Even though these things are infinite, couldn't the finite approximation be so good that the difference couldn't actually be detected by humans anyway?"

Well, you can't take an infinite space time and quantize it to suit your suitable approximation idea. That simply can't be done.

In the movie "A Beautiful Mind," recall the scene where Nash is trying to extract an algorithm for pigeon movement. In essence, a complex algorithm, or a simple one for that matter, is a turing machine. The limitless possibility of a pigeon's movement based upon it's infinite supply of senses around it cannot be finitely determined and made into an automaton.

What you're trying to do is fit a square block through the circle hole. But on a larger scale. You're trying to cram infinity into a box with finite dimensions.

5/2/2006 3:20:26 PM

Quote :

"Even though these things are infinite, couldn't the finite approximation be so good that the difference couldn't actually be detected by humans anyway?"

I suppose that could be possible. However, IF human intelligence processes information with theoretically infinite precision, then you could foreseeably have a regime where certain processes are chaotic in nature, where arbitrarily small perturbations in the inputs could produce markedly different outcomes. If that's the case, then a finite approximation, no matter how fine in resolution, would fail for those certain processes; that's not to say that they couldn't pass for other processes or other situations, though.

I'd also like to profess ignorance to most of this thread, however; my comments are based solely on nonlinear dynamical systems and chaos theory applied to my base interpretation of what's been said. I freely admit I don't have the background in theoretical computer science or information theory to really discuss this, and don't have the time right now to read up on it.

5/2/2006 4:07:23 PM

Quote :

"There are limits on the resolution of my eye versus the next persons eye, I don't see the problem. "

Exactly why any finite limit you impose would be completely arbitrary and would have failure cases eventually.

5/2/2006 5:40:31 PM

The question isn't really "is a finite approximation good enough?" because the computability theory this reasoning is based on has been logically proven in various forms by Turing, Godel, et al. The question is, are these systems really of infinite precision? If so, there's a good chance our understanding of intelligence as neural networks is missing a lot of the picture, as Shadowrunner noted. The system could respond to infinitesimally small variations with wildly varied results. I think there was a project somewhere with the intent of simulating then entire brain of some simple slug as a virtual neural network, now that I remember that I'm gonna see if they have any published results that illuminate this question any further.

Speaking of InsaneMan, where is that cat when you need him? He's crazy but last I heard he was still playing with neural networks... I wouldn't mind hearing his opinion on this.

State409c- I didn't at all claim an infinite resolution for the eye, I allowed for the source of the photon emittance to be quantized by the resolution of the eye, and the intensity to be quantized by the nature of a photon... however, the signal remains unquantized in the time domain unless you can prove the quantization of spacetime right quick for us, or provide some insight into the chemistry of the photoreceptors, the neural cascade that follows, and how it might quantize the signal in the tiem domain. If the signal is unquantized in the time domain, that is equivalent to a neural network with infinite weights, which is one of the models of computing that is accepted to be super-Turing in computational order.

[Edited on May 2, 2006 at 9:52 PM. Reason : *]

5/2/2006 9:46:15 PM

shit, double post.

[Edited on May 2, 2006 at 9:52 PM. Reason : *]

5/2/2006 9:51:34 PM

When I was doing research at NASA this guy, Dr. Dennis Bushnell, gave a talk about this shit. All I can say is everybody left there freaked out . He was talking some crazy shit --growing brains in labs--computer based. The guy reminds me of the Professor Farnsworth on futurama.hehe
If you see a picture of him online you'll know why.

Anyway I'll see if I can find some of his stuff online.



Well here goes the first link that popped up. Try googling his name with terms like artificial intelligence. He does a lot of shit so you got to get to the relevant info.
http://www.imagination-engines.com/




[Edited on May 2, 2006 at 11:45 PM. Reason : comments]

5/2/2006 11:39:04 PM