William Pearson wrote:
On 07/10/2007, Richard Loosemore <[EMAIL PROTECTED]> wrote:
William Pearson wrote:
On 07/10/2007, Richard Loosemore <[EMAIL PROTECTED]> wrote:
The TM implementation not only has no relevance to the behavior of
GoL(-T) at all, it also has even less relevance to the particular claims
that I made about GoL (or GoL(-T)).
If you think the TM implementation does impact it, you should
demonstrate exactly how.
The TM implementation has no impact *itself* to any claims, and its
removal equally has no bearing on the properties of the whole system.
The impact it does have is to demonstrate the system it is implemented
in is Turing Complete. Or computationally universal if you wish to
avoid say the word Turing.
Lets say I implemented a TM on my laptop, and then had my operating
system disallow that program to be run. Would it stop my laptop being
computationally universal, and all that entails about its
predictability? Nope, because the computational universality doesn't
rest on that implementation, it is merely demonstrated by it.
Well, I have to say that you have made a valiant effort to defend the
idea, but nothing seems to be working.
You argue that Game of Life is Turing Complete even when we exclude all
the cases in which the initial cells are arranged to make a Turing
Machine. You then try to justify this strange idea with an analogy.
But in your analogy, you surrepticiously insert a system that is ALREADY
a Turing Machine at the base level (your laptop) and then you implement
ANOTHER Turing Machine on top of that one (your TM program running on
the laptop). This is a false analogy.
To do your analogy properly, you would have to say this: "Lets say I
notice that my laptop is equivalent to a Turing Machine, and then I
drill a one-inch diameter hole in the CPU, so that the laptop can no
longer act as a Turing Machine. Would this stop my laptop being
computationally universal, and all that entails about its predictability?"
To which the answer is: well, yes it would!
If the laptop were repaired, or if the atoms in the laptop were
rearranged, then it would become a Turing Machine.
Similarly, if the atoms in a lump of dirt were rearranged, the lump of
dirt could be turned into a Turing Machine.
So the logical extension of your argument is that a lump of dirt is
Turing Complete just because the atoms have the POTENTIAL to be
rearranged to make a Turing machine.
In exactly the same way, the cells in Game of Life have the POTENTIAL to
be rearranged to make a Turing Machine.
But in both of these cases (lump of dirt and GoL) the sense in which
"Turing Completeness" is being used is completely meaningless. Nothing
follows from the conclusion that lumps of dirt are Turing Complete.
Which was my original point.
Richard Loosemore
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