My point is that you seem to think neurons in the sense of artificial neural networks and neurons in the human brain are equivalent because:
(1) Neural networks are Turing complete, and hence can do anything brains can. [debatable anyway; We don’t know this to be the case since brains might be doing more than computation. Ask a philosopher or a cognitive scientist. Or Roger Penrose.]
(2) Neural networks were very loosely inspired by the idea that the human brain is made up of interconnected nodes that ‘activate’ in proportion to how other related nodes do.
I don’t think that’s nearly enough to say that they’re equivalent. For (1), we don’t yet know (and we’re not even close), and anyway: if you consider all Turing complete systems to be equivalent to the point of it being a waste of time to talk about their differences then you can say goodbye to quite a lot of work in theoretical computer science. For (2): so what? Lots of things are inspired by other things. It doesn’t make them in any sense equivalent, especially if the analogy is as weak as it is in this case. No neuroscientist thinks that a weighted sum is an adequate (or even remotely accurate) model of a real biological neuron. They operate on completely different principles, as we now know much better than when such things were first dreamed up.
The brain certainly could be doing super-Turing computation, but that would overturn quite a bit of physics seeing as how not even quantum computers are more powerful than Turing machines (they're just faster on some problems). Extraordinary claims and all that.
As for equivalency, that depends on how that's defined. Real neurons would not feature any more computational power than Turing machines or artificial neural networks, but I never said it would be a waste of time to talk about their differences. I merely pointed out that the artificial neural network model is still sufficient, even if real neurons have more complexity.
> No neuroscientist thinks that a weighted sum is an adequate (or even remotely accurate) model of a real biological neuron
Fortunately that's not what I said. If the neuron indeed has more relevant complexity, then it wouldn't be one weighted sum = one biological neuron, but one biological neuron = a network of weighted sums, since such a network can model any function.
The original comment you were in defence of was suggesting that artificial neurons were somehow very close to biological ones, since supposedly that’s where their inspiration came from.
If you’re interested in pure computational ‘power’, then if the brain is nothing more than a Turing machine (which, as you agree, it might not be), fine. You can call them ‘equivalent’. It’s just not very meaningful.
What’s interesting about neural nets has nothing to do with what they can compute; indeed they can compute anything any other Turing machine can, and nothing more. What’s interesting is how they do it, since they can ‘learn’ and hence allow us to produce solutions to hard problems without any explicit programming or traditional analysis of the problem.
> that would overturn quite a bit of physics
Our physics is currently woefully incomplete, so… yes. That would be welcome.
(1) Neural networks are Turing complete, and hence can do anything brains can. [debatable anyway; We don’t know this to be the case since brains might be doing more than computation. Ask a philosopher or a cognitive scientist. Or Roger Penrose.]
(2) Neural networks were very loosely inspired by the idea that the human brain is made up of interconnected nodes that ‘activate’ in proportion to how other related nodes do.
I don’t think that’s nearly enough to say that they’re equivalent. For (1), we don’t yet know (and we’re not even close), and anyway: if you consider all Turing complete systems to be equivalent to the point of it being a waste of time to talk about their differences then you can say goodbye to quite a lot of work in theoretical computer science. For (2): so what? Lots of things are inspired by other things. It doesn’t make them in any sense equivalent, especially if the analogy is as weak as it is in this case. No neuroscientist thinks that a weighted sum is an adequate (or even remotely accurate) model of a real biological neuron. They operate on completely different principles, as we now know much better than when such things were first dreamed up.