At which point would such attributions be accurate? Humans are fundamentally just computers too. A different medium, but still transforming electrical signals.
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.
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.
Per the Church-Turing thesis these can all compute the same set of functions, and unless you can demonstrate that brains and only brains can evoke unknown physics that allows brains to compute a set of functions that can not be computed by other means, the most logical assumption is that it holds, including for brains.
Especially given how much we measure brains without seeing any signs of unusual physics.
For it not to hold, there would need to be something unique about the physics of a brain that allows it to compute a class of functions which are inherently impossible to compute by other means. That'd imply entirely new/unknown physics that we're somehow not seeing any hints of.
> Your claim is that the brain is actually a computable function, can you tell me which one it is using your favorite version of a Turing complete instruction set?
No, my claim is that absent evidence of unknown physics or another way of disproving the physical Church-Turing thesis, the rational assumption is that the brain follows the same laws of physics as everything else, and so is limited to computation that is equivalent in power to Turing computable functions, just like everything else we know of.
For the brain not to be a computer would imply "magic" - not just that we don't know how the brain works, but for the brain to work in ways inconsistent with all known physics, and inconsistent in ways impossible to simulate with Turing computable functions. No sign of any such unknown physics happening in the brain has ever been recorded.
I am not the one making any extraordinary claims. Physicists themselves admit there are aspects of reality with no computational basis.
For brains not to be computers would mean the physical Church-Turing thesis is invalid, and proof of that would be extraordinary enough to be Nobel Prize material.
We have built computers without instruction sets, e.g. in the form of mechanical devices to carry out calculations. Fairly complex computations were done that way before general purpose programmable computers, but even many early programmable computers had no fixed instruction set.
There is a rich history of computation through wiring up calculations without any instructions involved. And for that matter of mechanical computation.
Here's an outline for a simple computational device:
A bucket.
Pour predefined quantities of water into a bucket, and you can compute a threshold. Use buckets of different size and overflows, and you can separate a numeral into binary digits. Drain them into containers of different sizes and you can carry out logical operations. (Actual computation has been done this way - fluidics is one way, which dates back to the Tesla valve in 1920).
Every physical interaction is computation, whether or not it is useful computation. The notion computation requires an instruction set is confusing a very limited notion of classical programmable computers with the general concept of computation.
It is also a notion contradicted by the history of computation, which is full of computation without an instruction set, and of implementing computers with instruction sets in terms of computations of fixed function devices without one.
E.g. it's not turtles all the way down - that instruction set runs on a CPU that ultimately is built of fixed function logic.
Instruction sets are an optional high level abstraction.