In addition, one can easily argue that “Logic is the most fundamental natural science” using your argument.

http://web.ncf.ca/andre/publications/methodology_of_design.pdf

Poincare quipped about the scientific method “man proposes, nature disposes”. I don’t think it’s very different with software, except that “nature” is replaced by “design specifications”.

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(1) Where does this come from? I mean, “How do you know this?”
(2) Why is it relevant? And who said that TMs must have a blank tape?

If the universe is infinite (even just in Turing Machine-ish sense), it isn’t a TM, since the tape won’t be blank anywhere. But if people are finite, then everything they are capable of can be performed with a TM. Church-Turing thesis should be about the nature of human ability, not the nature of reality (of course, the latter can only be meaningfully conceptualized through the lens of the former).

Yeah, they are utter garbage (not just wrong, but thoroughly and embarrassingly wrong with no redeeming features). I went to a talk of his once and spent some time arguing with him afterwards. Basically, he starts with Hilbert’s 10th problem, about the solvability of Diophantine equations. This is known not to be solvable by Turing machines. He then writes down a Hamiltonian encoding this problem, so that finding a solution of the original equation is equivalent to finding the ground state of his quantum mechanical system. This is easy. He argues that of course you can find the ground state using a quantum computer, which is therefore more powerful than a Turing machine.

This assertion is provably wrong in all previously studied models of quantum computers, but he claims these models are unnecessarily restrictive and that in reality a quantum computer could do this. He ends up spending a lot of time arguing for this position, but it’s all just silly. The fundamental computational issue here is that the solutions to the Diophantine equation may involve enormous numbers of digits (growing not just quickly but faster than any computable function). Even aside from the ludicrous difficulty of engineering a physical system that can handle this level of precision, you never know when you have searched the solution space thoroughly enough. If you could really cool your system to absolute zero, you would get the true ground state, but you can’t actually reach absolute zero, and you never know whether you’ve come close enough to say there’s definitely no lower-energy state.

So what it comes down to is this. If you can create and manipulate an exact Hamiltonian of a certain form (on an infinite-dimensional Hilbert space), and if you can find a guaranteed way to bring it into its ground state, then you can use this to do things no Turing machine can do. In my experience, no expert is surprised or impressed by this, since it’s an easy deduction from grossly unphysical hypotheses. However, Kieu has a lot invested in this idea and has spent the last 10+ years arguing for it. It’s kind of depressing.

@Gustavo The analysis of the performance of real-world implementations is tricky, but not always so tricky that nothing can be said about their asymptotic running time.

OTOH, it seems like we’ve accepted that the asymptotic behavior of PCs is modeled by Turing Machines… although we’ve seen in practice that this is an idealization, and PC performance is in fact slightly worse than that of Random-Access Machines.

Did you take a look at the paper I linked? I haven’t had a chance to read it fully yet, but if you’d like to discuss further, I’d be happy to take this over to e-mail. It’s a really interesting topic that I’d like to learn more about.

Avoid UA (useless acronyms).

from my “Write good papers” page (http://www.daniel-lemire.com/blog/rules-to-write-a-good-research-paper/).

the math appears simple, and occams razor as a tool supports the logic.

I would look at things differently,
can you define physics OR computation of without a systemic construct?

since the primary requirement is that there is a non-monobloc state,

and here things get weird since a monobloc would by definition make the turing machine AND its data a single item/materia/composite?

can we define a plausible algorithm to describe the physics completely?

We may come close but I doubt we will ever describe the universe complete

as being part of the universe would would describe ourselves complete first
(this would lead to a review of religions imho)

So is the BQP really JDIS in the KEWA of the BPP?

Darn acronymania!!!

(Yeah! Strong Church-Turing Thesis but that really pisses me off)

I like the idea of thinking of machine classes (e.g. Turing Machines) as functions from problems to asymptotic complexity classes… but you never know when these classes might collapse (e.g. if someone proves that P=NP)… Moreover, if P=NP, then quantum computers are equivalent to Turing Machines wrt complexity. So you end up collapsing not only problem classes, but machine classes too.

Step 1 of your program is notoriously hard for problems in NP (otherwise we would know that P!=NP).