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Turing completeness says this isn't true: any Turing-complete digital system can simulate any physical system, including a human brain. What Turing completeness

Turing completeness says this isn't true: any Turing-complete digital system can simulate any physical system, including a human brain. What Turing completeness doesn't address is efficiency - how much energy would it take an artificial neural network to simulate a human brain? If it's "approximately one nuclear reactor" then maybe this will work with some efficiency improvements. If it's "approximately one sun" then it won't work at all. There is a very good Quanta article about this[1] detailing researchers attempt to simulate a rat cortex neuron with an ANN: it took 700 artificial neurons to simulate a single rat neuron, and that was just simulating the "voltmeter" measurements of the synapses, ignoring any genetic effects. If you included genetic effects[2] I would guess it would take several thousand artificial neurons, if not more. And that's just a rat! Even at the level of individual neurons, primates seem to be more sophisticated than other mammals, with apes more sophisticated than other primates. So your friend is onto something: biological computers are astonishingly sophisticated compared to 21st-century transistor technology, and this probably has implications for our ability to emulate biological intelligence even on supercomputers. Think of a neural network that was trained to draw physically-sensible spiderweb patterns across a wide range of geometries. Now think about running this neural network in a computer the size of a spider. And that's ignoring the difficult real-world planning an actual spider would have to do to create a physical spiderweb. [1] https://www.quantamagazine.org/how-computationally-complex-is-a-single-neuron-20210902/ https://www.quantamagazine.org/how-computationally-complex-i... [2] AI is not even close to this level of computational sophistication: https://www.universityofcalifornia.edu/news/biologists-transfer-memory-between-snails https://www.universityofcalifornia.edu/news/biologists-trans...

somewhereoutth 3y ago
No, a Turing complete system can perfectly simulate any other discreet (digital) computation system. What it cannot do is perfectly simulate any analogue system. By Cantor's diagonal argument, there are vastly more real numbers than natural numbers. Any system that is completely definable in the natural numbers (like digital computers) will not be able to 'reach' the vast majority of real numbers (in case you are concerned about the existence of real numbers, what is the square root of 2? What is the ratio of diameter to circumference?). Throw in some Chaos Theory and you can see how far away any Turing complete system is from a biological brain.
- nicklecompte 3y ago
  You are putting words in my mouth. I didn't say "analogue system," I said "physical system." The uncomputable reals don't have any known physical application, but the computable reals like sqrt(2) and pi, which do have physical application, can be perfectly well simulated to arbitrary precision by a Turing machine (edit: in particular, the computable reals form a countable set, though there isn't an algorithm to find the bijection). And when I said "simulate any physical system." I very specifically did not say "perfectly simulate," I meant "to arbitrarily high accuracy." What I said is undeniably true according to modern science, and not especially deep: - the human brain can be described as a massive system of Schrodinger equations. I strongly doubt you actually need the full machinery of quantum mechanics to describe it, but certainly quantum mechanics is sufficient. - a Turing machine can solve any arbitrarily large system of Schrodinger equations - therefore a Turing machine can emulate a human brain
  - somewhereoutth 3y ago
    Seems rather conveniently coincidental that the computable reals might be the only reals found in nature. I'd also suggest that there are plenty of equation systems that in fact cannot be solved, by Turing machine or otherwise. The 3 body problem comes to mind. Perhaps a Turing machine could emulate the human brain, however maybe you'd need all the atoms in the known universe to get to the required fidelity. Of course, the idea that a computer can do anything is rather attractive to those who are experts in computers. It is wrong though.
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somewhereoutth 3y ago

No, a Turing complete system can perfectly simulate any other discreet (digital) computation system. What it cannot do is perfectly simulate any analogue system. By Cantor's diagonal argument, there are vastly more real numbers than natural numbers. Any system that is completely definable in the natural numbers (like digital computers) will not be able to 'reach' the vast majority of real numbers (in case you are concerned about the existence of real numbers, what is the square root of 2? What is the ratio of diameter to circumference?). Throw in some Chaos Theory and you can see how far away any Turing complete system is from a biological brain.

nicklecompte 3y ago
You are putting words in my mouth. I didn't say "analogue system," I said "physical system." The uncomputable reals don't have any known physical application, but the computable reals like sqrt(2) and pi, which do have physical application, can be perfectly well simulated to arbitrary precision by a Turing machine (edit: in particular, the computable reals form a countable set, though there isn't an algorithm to find the bijection). And when I said "simulate any physical system." I very specifically did not say "perfectly simulate," I meant "to arbitrarily high accuracy." What I said is undeniably true according to modern science, and not especially deep: - the human brain can be described as a massive system of Schrodinger equations. I strongly doubt you actually need the full machinery of quantum mechanics to describe it, but certainly quantum mechanics is sufficient. - a Turing machine can solve any arbitrarily large system of Schrodinger equations - therefore a Turing machine can emulate a human brain
- somewhereoutth 3y ago
  Seems rather conveniently coincidental that the computable reals might be the only reals found in nature. I'd also suggest that there are plenty of equation systems that in fact cannot be solved, by Turing machine or otherwise. The 3 body problem comes to mind. Perhaps a Turing machine could emulate the human brain, however maybe you'd need all the atoms in the known universe to get to the required fidelity. Of course, the idea that a computer can do anything is rather attractive to those who are experts in computers. It is wrong though.
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