To be honest, the core of Penrose’s idea is pretty stupid. That we can understand mathematics despite incompleteness theorem being a thing, therefore our brains use quantum effects allowing us to understand it. Instead of just saying, you know, we use a heuristic instead and just guess that it’s true. I’m pretty sure a classical system can do that.
I'm sure if you email him explaining how stupid he is he'll send you his Nobel prize.
Less flippantly, Penrose has always been extremely clear about which things he's sure of, such as that human intelligence involves processes that algorithms cannot emulate, and which things he puts forward as speculative ideas that might
help answer the questions he has raised. His ideas about quantum mechanical processes in the brain are very much on the speculative side, and after a career like his I think he has more than earned the right to explore those speculations.
It sounds like you probably would disagree with his assumptions about human perception of mathematical truth, and it's perfectly valid to do so. Nothing about your comment suggests you've made any attempt to understand them, though.
I want to ignore the flame fest developing here. But, in case you are interested in hearing a doubter's perspective, I'll try to express one view. I am not an expert on Penrose's ideas, but see this as a common feature in how others try to sell his work.
Starting with "things he's sure of, such as that human intelligence involves processes that algorithms cannot emulate" as a premise makes the whole thing an exercise in Begging the Question when you try to apply it to explain why an AI won't work.
"That human intelligence involves processes that algorithms cannot emulate" is the conclusion of his argument. The premise could be summed up as something like "humans have complete, correct perception of mathematical truth", although there is a lot of discussion of in what sense it is "complete" and "correct" as, of course, he isn't arguing that any mathematician is omniscient or incapable of making a mistake.
Linking those two is really the contribution of the argument. You can reject both or accept both (as I've said elsewhere I don't think it's conclusively decided, though I know which way my preferences lie), but you can't accept the premise and reject the conclusion.
Hmm, I am less than certain this isn't still begging the question, just with different phrasing. I.e. I see how they are "linked" to the point they seem almost tautologically the same rather than a deductive sequence.
And you do it again, you apologise while insulting me. When challenged you refuse to defend the points you brought up, so that you can pretend to be right rather than be proved wrong. Incompleteness theorem is where the idea came from, but you don’t want to discuss that, you just want to drop the name, condescend to people and run away.
Here are the substantive things you've said so far (i.e. the bits that aren't calling things "stupid" and taking umbridge at imagined slights):
1. You think that instead of actually perceiving mathematical truth we use heuristics and "just guess that it's true". This, as I've already said, is a valid viewpoint. You disagree with one of Penrose' assumptions. I don't think you're right but there is certainly no hard proof available that you're not. It's something that (for now, at least) it's possible to agree to disagree on, which is why, as I said, this is a philosophical debate more than a mathematical one.
2. You strongly imply that Penrose simply didn't think of this objection. This is categorically false. He discusses it at great length in both books. (I mentioned such shallow dismissals, assuming some obvious oversight on his part, in my original comment.)
3 (In your latest reply). You think that Godel's incompleteness theorem is "where the idea came from". This is obviously true. Penrose' argument is absolutely based on Godel's theorem.
4. You think that somehow I don't agree with point 3. I have no idea where you got that idea from.
That, as far as I can see, is it. There isn't any substantive point made that I haven't already responded to in my previous replies, and I think it's now rather too late to add any and expect any sort of response.
As for communication style, you seem to think that writing in a formal tone, which I find necessary when I want to convey information clearly, is condescending and insulting, whereas dismissing things you disagree with as "stupid" on the flimsiest possible basis (and inferring dishonest motives on the part of the person you're discussing all this with) is, presumably, fine. This is another point on which we will have to agree to disagree.
