On Fri, Jan 28, 2011 at 12:52 PM, Brent Meeker <meeke...@dslextreme.com> 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.

Going beyond Turing emulation?  Doesn't the definition of a Turing
Machine involve infinite memory and and infinite tape?

"Referring to his 1936 publication, Turing wrote that the Turing
machine, here called a Logical Computing Machine, consisted of:

...an infinite memory capacity obtained in the form of an infinite
tape marked out into squares, on each of which a symbol could be
printed. "

http://en.wikipedia.org/wiki/Turing_machine

OR:

"A Turing machine has an infinite one-dimensional tape divided into
cells. Traditionally we think of the tape as being horizontal with the
cells arranged in a left-right orientation. The tape has one end, at
the left say, and stretches infinitely far to the right. Each cell is
able to contain one symbol, either ‘0’ or ‘1’."

http://plato.stanford.edu/entries/turing-machine/

But, beyond that...you believe that there are no actual infinities?

Why do you believe that?

You believe that space-time is finite?

You believe that there isn't an infinite causal chain behind us?  You
believe that there was a "first cause"?

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