Luke’s argument

By studies, of course, I mean philosophers (I thought that Sh”k Adm”r Yavin would understand). According to Wikipedia, most of them think that Locke's argument is not successful, but I don't know why. Hofschter in the Gabba also addresses this, but it seems that all he has against it is his personal deterministic view. I couldn't find any argument against Locke there.
“It is common to think that physics can be described by a machine”. Does anyone disagree with this? On the surface, it is clear that given all the positions and velocities of particles at a certain time, it is possible in principle to calculate the positions and velocities (or their distribution) at any other time.
Does the fact that physics can be described by a machine mean that everything physical is a Turing machine? After all, in the end, even if human consciousness is somehow the result of physical activity, it is clear that it is not the activity of the particles themselves. Even when you stay inside the system, it's hard to see, for example, how the activity of particles in the head translates into the Pythagorean theorem. Isn't it possible that the activity of particles in the head somehow translates into Gödel's theorem?

Oh, I should have put: researchers

In my own sins, I thought Mr. was talking about mathematicians. They usually dismiss the words of philosophers and their conclusions from Goel's theorem. By the way, although there are quite a few philosophers who talk nonsense, especially on subjects they don't understand, this dismissal is usually not justified. Mathematicians think that a conclusion that is not logically proven is not a conclusion of Goel's theorem. And apparently their sins caused them to not understand that philosophers are also satisfied with conclusions that are reasonably required from the theorem, and not only those that are proven from it logically-mathematically. And this is what I made sure to write in my previous message.
To your question, John Searle, for example, claims that a physical system can create behavior that is not “mechanical” at the macroscopic level, what was later called “emergentity”. In my opinion, this is a lack of understanding of physics, as I explained in my book.
This is precisely why it is impossible to translate the activity of particles in the head into Godel's theorem. The Pythagorean theorem is a proof within the system (what is called in computer science a “computational operation”), and therefore there is no reason why it could be a translation of physical activity (although the translation mechanism is of course unknown to us and we do not even have a language to describe and study it. Therefore, the epiphenomenalistic assumption is wild speculation). But even if we accept epiphenomenalism (for the sake of discussion), it still cannot be applied to the proof of Godel's theorem. This requires going outside the system, that is, it is not computational, and therefore, in the accepted concepts of physical systems, to the best of my understanding, it cannot be any mechanical translation of physical actions. Therefore, here even if we adopt the assumption of epiphenomenalism (or emergentism), we will fail. It is a contradiction in terms.
I will just comment on another point in your words. According to quantum theory, even if you give me the positions of all the particles (and then of course you can't give me their velocities, according to the uncertainty principle), it doesn't necessarily predict the future state. Physics is probably not deterministic. But quantum theory adds only a random component to physics, and therefore it also cannot explain mental phenomena, and in particular not free will (for those who believe in it. In my book, I explained that this is a third mechanism, different from determinism and different from randomness). That's why I removed quantum theory from the discussion. This is also explained in my book.
As for the arguments against Lucas, this characterizes almost every argument in this field. They all assume what is wanted, or show that the argument is not purely logical (i.e., not valid). I don't think there is a good argument against Lucas, and this is left to everyone's judgment according to their understanding and assumptions. As mentioned, in my opinion, it's not a bad argument at all. By the way, he already appears in my book Two Carts (without his name. I didn't know him then). On various “scientific” websites (like The Reading Deer, Not Accurate, The Daily and various atheist websites you will find mainly expressions of disdain and rejection against Panenros and Lucas, but very few arguments, if any).

No. I actually read that correctly. I understood that's what you meant, except that I realized you were talking about mathematicians or brain researchers and not philosophers.

I wrote a distribution precisely because of quantum theory.
And I already wrote that the argument appears (yes, by name) in the footnote (look in the key).
Incidentally, Hofstadter writes that those who relate to Locke's argument are really divided into those who are enthusiastic about it and those who despise it. He says that he himself does not despise it, but takes it seriously but rejects it (and he presents an incomprehensible rejection that seems to be based only on the assumption of the desired one, and says that there will be more and more in the future).