It strikes me as quite arrogant to assume that those are the only possibilities. People, even experts in a field, disagree about topics and the implications of evidence all the time. Arguing that honest disagreement must reduce down to one of the three categories you list is basically saying "my point of view is so obviously correct that only bad thinkers or bad people could disagree". But that's almost certainly not the case.
It is vacuously true that a Turing machine can simulate a human mind - this is the quantum Church-Turing thesis. Since a Turing machine can solve any arbitrary system of Schrodinger equations, it can solve the system describing every atom in the human body.[1]
The problem is that this might take more energy than the Sun for any physical computer. What is far less obvious is whether there exist any computable higher-order abstractions of the human mind that can be more feasibly implemented. Lots of layers to this - is there an easily computable model of neurons that encapsulates cognition, or do we have to model every protein and mRNA?
It may be analogous to integration: we can numerically integrate almost anything, but most functions are not symbolically integrable and most differential equations lack closed-form solutions. Maybe the only way to model human intelligence is "numerical."
In fact I suspect higher-order cognition is not Turing computable, though obviously I have no way of proving it. My issue is very general: Turing machines are symbolic, and one cannot define what a symbol actually is without using symbols - which means it cannot be defined at all. "Symbol" seems to be a primitive concept in humans, and I don't see how to transfer it to a Turing machine / ChatGPT reliably. Or, as a more minor point, our internal "common sense physics simulator" is qualitatively very powerful despite being quantitatively weak (the exact opposite of Sora/Veo/etc), which again does not seem amenable to a purely symbolic formulation: consider "if you blow the flame lightly it will flicker, if you blow hard it will go out." These symbols communicate the result without any insight into the computation.
[1] This doesn't have anything to do with Penrose's quantum consciousness stuff, it just assumes humans don't have metaphysical souls.
> It is vacuously true that a Turing machine can simulate a human mind - this is the quantum Church-Turing thesis. Since a Turing machine can solve any arbitrary system of Schrodinger equations, it can solve the system describing every atom in the human body. The problem is that this might take more energy than the Sun for any physical computer.
Feynman on "Simulating Physics with Classical Computers" [0] goes beyond that to posit that any classical simulation of quantum-mechanical properties would need exponential space in the number of particles to track the full state space; this very quickly exceeds the entire observable universe when dealing with mere hundreds of particles.
So while yes, the Turing machine model presupposes infinite tape, that is not realizable in practice.
He actually goes further:
Can a quantum system be probabilistically simulated by
a classical (probabilistic, I'd assume) universal computer? In other words, a
computer which will give the same probabilities as the quantum system
does. If you take the computer to be the classical kind I've described so far,
(not the quantum kind described in the last section) and there're no changes
in any laws, and there's no hocus-pocus, the answer is certainly, No! This is
called the hidden-variable problem: it is impossible to represent the results
of quantum mechanics with a classical universal device.
In particular, he takes issue with our ability to classically simulate negative probabilities which give rise to quantum mechanical interference.
bigstrat2003|1 year ago
WhyOhWhyQ|1 year ago
aithrowawaycomm|1 year ago
The problem is that this might take more energy than the Sun for any physical computer. What is far less obvious is whether there exist any computable higher-order abstractions of the human mind that can be more feasibly implemented. Lots of layers to this - is there an easily computable model of neurons that encapsulates cognition, or do we have to model every protein and mRNA?
It may be analogous to integration: we can numerically integrate almost anything, but most functions are not symbolically integrable and most differential equations lack closed-form solutions. Maybe the only way to model human intelligence is "numerical."
In fact I suspect higher-order cognition is not Turing computable, though obviously I have no way of proving it. My issue is very general: Turing machines are symbolic, and one cannot define what a symbol actually is without using symbols - which means it cannot be defined at all. "Symbol" seems to be a primitive concept in humans, and I don't see how to transfer it to a Turing machine / ChatGPT reliably. Or, as a more minor point, our internal "common sense physics simulator" is qualitatively very powerful despite being quantitatively weak (the exact opposite of Sora/Veo/etc), which again does not seem amenable to a purely symbolic formulation: consider "if you blow the flame lightly it will flicker, if you blow hard it will go out." These symbols communicate the result without any insight into the computation.
[1] This doesn't have anything to do with Penrose's quantum consciousness stuff, it just assumes humans don't have metaphysical souls.
vitus|1 year ago
Feynman on "Simulating Physics with Classical Computers" [0] goes beyond that to posit that any classical simulation of quantum-mechanical properties would need exponential space in the number of particles to track the full state space; this very quickly exceeds the entire observable universe when dealing with mere hundreds of particles.
So while yes, the Turing machine model presupposes infinite tape, that is not realizable in practice.
He actually goes further:
In particular, he takes issue with our ability to classically simulate negative probabilities which give rise to quantum mechanical interference.[0] There are a number of PDFs shared as handouts for various grad classes; https://s2.smu.edu/~mitch/class/5395/papers/feynman-quantum-... was the first that I came across.
unknown|1 year ago
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