[manyoso]

#1 Not easy. Prove it. Show a Turing machine programmed with ZFC that can not be modeled by a Turing machine programmed with PE. You can not do so because Turing machines are universal. The fact that you claim this is easy tells me you do not understand what a Turing machine is.

#2 See fundamental level. Penrose claims that what sets us apart from Turing machines is fundamental. But whatever, you've refuted whatever point you wanted to make by saying human's are not logically consistent. Your snark about Penrose not understanding is as empty as whatever point you were trying to make.

#3 Cite a paper showing that objective collapse gives these supposed algorithmic speedups or go home. NOTE: objective collapse theories are an active area of research and are not limited to Penrose by any means. Your claim that they are inconsistent with QM begs for evidence. Cite some or stop spreading nonsense.

#4 Your answer here is completely void of any context to the question: where Penrose says that microtubules are limited to humans. I take it you concede that he did not say any such thing?

You treat Penrose as an idiot missing obvious problems. I think it far more likely that you've misunderstood. Pity your lack of humility might make it impossible for you to understand what he actually argues rather than your strawmen.

[Chronos]

Also: before I bother building a Turing machine that implements a proof-generator for statements in ZFC, you should do me the courtesy of showing your investment by building me a Turing machine that multiplies two integers.

Turing machines suck. Building a Turing machine that implements ZFC proof-generation is a project appropriate to a graduate-level paper, not something to toss off in an Internet pissing contest.

[manyoso]

You were the one who used the phrase "easy" with regard to Turing machines and feasibility of showing them.

[Chronos]

Fine. "Straightforward, if menial and tedious".

[pdkl95]

> You can not do so because Turing machines are universal.

Just because Turing machines are universal making it possible to write a program that asks a question about another type of Turning machine doesn't mean that question is decidable.

[manyoso]

Show a Turing machine programmed with ZFC axioms that can do something that a Turing machine programmed with PE can not do. If a Turing machine programmed with PE can simulate the Turing machine with ZFC and thus give the same answer, then I state that the program with ZFC is nothing of the sort.

[pdkl95]

The paper[1] I linked to in my other post shows that you cannot perform such a simulation because it is undecidable. (Specifically, BB(N >= 1919) is provably undecidable in ZFC).

[1] http://www.scottaaronson.com/blog/?p=2725

[manyoso]

I read that when it came out, but I don't see how that is relevant to this question. The link provides a program for a Turing machine that probes ZFC. So can you create a Turing machine that probes ZFC, but can't be proven not to halt? The link emphatically says yes! And it also puts some bounds on the number of states necessary to program such a machine.

Please show how that paper describes a Turing machine 'programmed with PE' can't simulate a Turing machine 'programmed with ZFC'?

Perhaps we are arguing over what 'programmed with PE' or 'programmed with ZFC' means? The parent post seemed to claim that it was possible to construct a physical computer with the axioms of ZFC built-in so to speak. As opposed to one with PE built-in. Which obviously calls into question the parent post understanding of what exactly idealized Turing machines are.

[Chronos]

Show me a paper proving that what Penrose argues for and what quantum physicists call "objective collapse" are the same thing.

[manyoso]

https://link.springer.com/article/10.1007%2FBF02105068 https://link.springer.com/article/10.1007%2Fs10701-013-9770-... https://en.wikipedia.org/wiki/Objective_collapse_theory -- See Penrose' as canonical example of objective collapse

There is just tons of reading on this if you care to scour the literature. Penrose' objective collapse theory is usually given as the prime example of the whole genre.

[Chronos]

I already read through https://en.wikipedia.org/wiki/Penrose_interpretation when I was trying to figure out what nonsense you were spewing. The article does not mention the Church-Turing thesis, hypercomputation, Gödelian incompleteness, or the Lucas-Penrose argument.

People can be known for more than one thing. Those two things can be unrelated, even if they're in the same field.

[manyoso]

In Penrose book that introduced his thoughts on this argument he devotes an entire chapter to his objective collapse theory and quantum gravity. You asked for a paper and I gave you many. You want to know more pick up his book.

[Chronos]

None of the papers you listed address hypercomputation! They are irrelevant to the Lucas-Penrose argument.