Just trying to figure out how rigorously people have thought about this. A computer with an undefined instruction set seems somewhat useless as a computer.
If you don't know how something works, do you assume it is magic? Why? It's a wildly irrational assumption to assume that it is magic rather than assume absent evidence to the contrary that it works according to known physics.
Well, that's essentially a logical tautology. Everything works according to the known laws of physics but it's certainly true that everything must also work with unknown laws of physics because of basic human ignorance.
No it is not. The argument is that absent any evidence of the existence of such unknown physics happening in the brain the most logical assumption is to assume there isn't any, rather that presuming the existence of something we've never observed any hint of.
Rule 110 can be specified with a rewrite system, also known as cellular automata: https://arxiv.org/abs/0906.3248. Cellular automatons have a correspondence with contextual grammars: https://www.cis.upenn.edu/~cis5110/notes/tcbook-lang.pdf. Each is equivalent to a Turing machine, another way of saying that there is a program for it which can be specified on a Turing machine with the usual Turing machine instruction set for writing, reading, and erasing binary digits on a tape. This usual program can then be "compiled" into a rewrite system corresponding to the instruction set for rule 110.
The reason rule 110 is said to be Turing complete is because someone went through the trouble of specifying an instruction set for rule 110 so that other people could verify that it would be possible to write programs with it. This is not the case for the people who claim that they are computers. They always leave the instruction set undefined which makes their claims hard to believe.
I personally have no problem with people who think they're computers but if they're not programmable then I'm not sure what the point would be of calling themselves computers.
> This is not the case for the people who claim that they are computers. They always leave the instruction set undefined which makes their claims hard to believe.
What is your alternative? Can you explain to us how the brain could possibly do something - down to the atomic level - that would allow it to do something that not only is not possible to simulate, but that also does not still constitute computation?
We don't even have language for talking about such "operations" that are so different from all forms of computation that it is not just another form of computation.
Just try to describe one such hypothetical state change that can not be reproduced with a Turing computable function.
At the same time, your insistence on "instruction sets" is meaningless. An "instruction set" the way we tend to consider them is not necessary to parameterize a function. A neural network with input/output used to provide the "tape" can trivially be made Turing complete. If you consider the weights or connections of the network an instruction set, then there you go - that we don't know how to measure and extract all the details of the neural network of a brain does not mean we can't observe their presence. And it also does not mean we haven't done a vast amount of measurements without observing any hint of unknown physics affecting state transitions.
To simplify it: Even a simple mechanical thermostat is parameterized - the dial provides "an instruction set" in the form of an ability to set a single threshold that alters the behaviour of the function computed.
But if you expect something that looks like what we typically talk about when we talk about an instruction set, then that is a very limiting view of computation, and one I've already pointed out to you is just one part of the multiple types of computational devices we've built. Including heavily parameterisable ones.
I expect claims to be backed by evidence that is consistent with our current state of knowledge. I have seen no such evidence so that's why I asked for references. In any case, this discussion has run its course, best of luck to you and your future computations.