Rex,
Well here I disagree (with Wikipedia, not with Turing, although he is
responsible for this widespread misconception).
The discovery of the universal machine by Turing is the discovery of a
finite Turing machine capable of emulating all the other machine from
a number description (a program).
Turing machine are finite object. Their tape plays a role of always
finite, but unbounded memory space. You personal computer is a
universal (Turing) machine, and then this explains why, regularly, it
asks for a supplement of memory, and the user usually obliged by
buying a bigger hard disk.
Universal numbers and universal machine are finite objects. All
machine are finite objects. Human universality shows up when humans
used walls and papers to process their calculation. Universal entity
are typically growing self-extending entities. They always want more
'memory-space-time'.
I can argue that bacteria (like Escherichia Coli) are universal
machines, even if you need viruses to build read and write instructions.
Bruno
On 29 Jan 2011, at 04:54, Rex Allen wrote:
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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