On 28 Jan 2011, at 18:52, Brent Meeker wrote:

On 1/27/2011 10:08 PM, Rex Allen wrote:
On Thu, Jan 27, 2011 at 7:58 PM, Brent Meeker<meeke...@dslextreme.com> wrote:

But if the
emulation attempts to be local then it must include inherent randomness -
which I think is not Turing computable.

The Turing machine could draw the required randomness from a tape of
random bits, couldn't it?

The question might then be asked:

"Where did the tape of random bits come from?"

To which I guess a response of sorts might be:

"Well, where did the Turing machine come from?  Probably from there."

If you can have unexplained order, then you can have unexplained
randomness, can't you?

Sure, but then you've gone beyond Turing emulation. A tape providing the random numbers would have to be a realized (not just potential) infinity.

I hope Rex doesn't mind, but I don't understand Brent's remark.

Anyway, the UD compute all machines on all inputs, and big inputs acts like oracles from the first person point of views. We cannot enumerate the reals, but the dovetailer dovetails on all the finite sequences as parameters, and from the first person views, which abstracts from the UD-time delays, it already makes a background random noise. A priori.

Think about the iterated self-duplication. In that case it is easy to define a notion of normality, like when a laser beam split in two a sheaf of photon prepared in the complementary base.


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