On 10 Jan 2012, at 18:48, meekerdb wrote:

On 1/10/2012 7:48 AM, Bruno Marchal wrote:
In a way, that strong form of CT might already be false with comp, only in the 1p sense as you get a free random oracle as well as always staying consistent(and 'alive'), but it's not false in the 3p view...

Yes. Comp makes physics a first person plural reality, and a priori we might be able to exploit the first plural indeterminacy to compute more function, like we know already that we have more "processes", like that free random oracle. The empirical fact that quantum computer does not violate CT can make us doubt about this.

I don't think that is so clear. Nielsen has written some papers on computations in QM that are not Turing emulable, essentially relying on the fact that QM uses real numbers. He suggests that QM should be restricted to avoid this kind of hypercomputation by dropping the assumption that all unitary operators are allowed.

Yes. e^i * OMEGA *t is a solution of the SWE. With OMEGA = Chaitin's incompressible real number. But are the real numbers "physically real"? Open problem in comp, and in our "observable universe". Nielsen is aware that, would we met such a quantum wave, we would be unable to recognize it or to distinguish it from quantum noise. Which follows from comp indeed.

More interestingly e^i * POST *t, with POST = Post "creative number", which decimal codes the stopping problem, would be a quantum universal dovetailer. Here the wave will have the computations redundancy needed to give sense to the measure problem. With the incompressible OMEGA you get a shallow description of all there is by doing a highly non constructive reduction of the measure. OMEGA evacuates the redundancy of POST. POST is deep (in Bennett sense).

But I am not sure that the decimals in the wave plays any relevant computational role. Unless some very low level number conspiracy?

The UD is dumb enough to dovetail all program executions with their "products" with *all* approximations of all real numbers, so, so some exploitation of the continuum is what to be expected for the most stable realities configuration, and it is hard to avoid, logically, that some infinite non computable constant might play a role, but why would we postulate something like that?



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