X-Message-Number: 27574 Date: Sat, 4 Feb 2006 16:49:34 -0500 Subject: Mythbusting 102 From: <> Peter, >> Unfortunately on the way it melted and all the water spilled into the atlantic. I used your definition to explain to him he need only look out at the breakers to admire my statue. << Did you actually understand my definition? At some point during the melting of the ice sculpture, and certainly when nothing remained but a pool of water, the predicate 'P(x) = x is an ice sculpture of a Nordic beauty' ceased being true, and the statue stopped existing. You can do better than this, Peter. I know you can. >> c) Being in jail I found myself with time on my hands so I studied physics and discovered there are no infinitely continuous functions observable by humans. << The definition I gave used the criterion of infinite continuity because no one knows yet whether space is quantized (the only thing we know is you can't measure distances beyond a certain scale). It's not required but it's much cleaner than an alternative definition that assumes the discretness of spacetime. >> Similarly any gas may be regarded as a quantum and molecular computer, consisting of quatrillions of atoms, impracticable to simulate. And yet Avogadro's Hypothesis enables us to simulate gases in calculations with a pencil and a piece of paper. << And if by simulating a brain, you mean predict short-term macroscopic observables (such as, how long it would take your brain to cool to room temperature if it were ripped from your skull by an axe-wielding Pomeranian), then yes, we can 'simulate' a brain, in the same way we can 'simulate' a gas. You are engaging in prevarication and I think we both know it. >> A convincing argument against the existence of phenomes. Plainly neither you nor I exist; "we" require the interpretation of genome and proteome, and interpolation of that interpretation across billions of interacting cells. << We are lumps of matter. Lumps of matter don't require the subjective interpretation of a conscious mind to exist. We're like rocks, which simply exist---unlike the upside-down, bearded grandfather in a puff of clouds that a kid sees, who, no matter how realistically portrayed, exists only in the mind of the kid, and does not possess a factual existence of his own (what exists are water molecules). In any case, you engage in two fallacies with the above analogy. I can't force myself to believe you don't see them. I think you believe you are on the right side, but are more concerned with persuading people reading Cryonet than actually saying something substantive. Believing you're right is dangerous because it means you will use any means (fallacious reasoning, ad hominems, etc.) to justify the end (converting the masses). >> A neuron has the function of mapping signals received biochemically from its dendrites onto biochemical signals, via the axon, to the dendrites of other cells. Neurons may have a few other functions too. << Like most people familiar with IT, you like to think of the neuron as having N electrical inputs, and 1 electrical output. Nothing could be further from the truth. A vast amount of neural functionality occurs not through transmission of electrical signals, but through biochemistry---chemical interaction between neural membrane glycoproteins and binding complexes, for example. In any case, let me join you in your make-believe and pretend that neurons have N electrical inputs, and 1 electrical output. For the average neuron, N is about 2000. So in order to model a neuron, all we need to do is come up with a black box equation that tells us the output of the neuron given each of its inputs. Sounds simple, eh? Everything does to an armchair engineer---but real life is infinitely less tractable. First, there is the problem of simultaneity. This problem is easier understood in a concrete context, so let's take the example of gravity. The earth exerts a force on the moon, which affects the acceleration of the moon; however, the moon also exerts a force on the earth, which affects the acceleration of the earth. This leads to a problem of infinite recursion: because, for example, the acceleration of the moon is going to affect the acceleration of the earth, which is in turn going to affect the acceleration of the moon again, and so on. It turns out this problem can be solved for the earth and moon. Add another body, however, and you're out of luck (in the general case). We can't solve the equations, and can only approximate them; with increasing numbers of bodies, our approximations become increasingly poor, and because these systems are fundamentally chaotic, with enough bodies our best approximations are worthless. This same problem is everywhere in physics (pretty much anywhere you see a differential equation). It's at the lowest levels and the highest; quantum, molecular, electrical, astronomical. Simulations attempt to sidestep the problem by dividing time into discrete units---pretending for that unit of time, one part of the system exists in isolation and is not affected by any other part of the system. Of course, it's a big fat lie---but a necessary one, as without it, we would be unable to do any useful simulation whatsoever. What it means, however, is that there is an upper limit to what we can know about an N-body system. So even if a neuron can be modeled perfectly as a mathematical black box with 2000 electrical inputs, and 1 electrical output, we would not be able to perfectly simulate more than (say) two of them together. At what point our simulations become so grossly inaccurate as to render the result useless, I can't say, but until someone can demonstrate otherwise, there's no reason to believe that limit is anywhere near ONE TRILLION (which is the number of neurons you need to simulate if you want something like a human brain). The second problem is the inherent complexity of mathematically modeling an equation with 2000 inputs. Right now we assign each input a weight and say the neuron fires if the weighted sum exceeds a threshold. If you're not laughing you should be, since the complexity of a neuron dwarfs the simplicity of this toy model I've just described. This function with 2000 inputs depends intimately on the state of the neuron at that time: the number and position of the billions of molecules floating around in the cytoplasm; the position and configuration of the millions of microtubules; the genetic expression of the neuron; the size, shape, and length of the dendrites and axon. I could go on and on, describing all of the factors that influence the shape of the 'neural function'; pointing out that these are changing with time, and, as with all truly interesting problems, are self-dependent. But I won't. Instead, I'll point you to one of the many available neural simulators available on the net (start here, if you're interested: http://leenissen.dk/fann/). You want to put your money where your mouth is? Then use one of these simulators to produce something more than a toy. Hundreds of thousands of researchers and software engineers have tried over more than three decades, and you know what? Neural networks are still regarded as mere curiosities. A blip on the history of computer science. The burden of proof is on you. You want me to believe, in spite of the evidence to the contrary, that neurons can be modeled and simulated using neat little mathematical equations? Then knock yourself out. Until then, you should acknowledge the fantastical nature of your own beliefs (and by 'fantasy', I mean, truly from the pages of a fantasy book, and completely and utterly divorced from this thing called 'reality' that we live in). >> If you accept that, let's go ahead and replace one of your neurons with our model. Are you still yourself? << I have objected only to the idea that neurons can be modeled mathematically and simulated on computers at a level necessary to support the emergence of human-like intelligence. Don't read more into what I say than what I say. You will be wrong. I don't doubt that it is possible to create artificial structures that serve the same functions as biological neurons. I am even open to the idea that, should such artificial neurons be based on the same principles of operation as biological ones, certain configurations of these neurons might be capable of subjective experience. Going one step further and supposing artificial neurons could interoperate with biological neurons (which implies much more than electrical compatibility), I do believe it would be possible to upgrade my brain, with my identity preserved (this is implied in the definition of identity I laid out some messages ago). But that is quite a different subject altogether. Richard B. R. Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=27574