John,
On 22 Mar 2013, at 21:27, John Mikes wrote:
I tried to find FOAR - but failed. You kindly advised to 'show me
how' get subscribed, but it was missing from your post.
Could you repeat it?
You might try this:
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Tell me if it is OK.
Best,
Bruno
John M
On Fri, Mar 22, 2013 at 5:36 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
Hi John,
On 21 Mar 2013, at 21:40, John Mikes wrote:
Dear Bruno,
it is so fascinating to read about "universal machines".
Is there a place where I could learn in short, understandable terms
what they may be? Then again the difference between a 'Turing
machine' and a 'physical computer' (what I usually call our
embryonic Kraxlwerk).
I grew up into my science without computers, got my doctorates in
1948 and 1967 and faced a computer first on a different continent
(USA) in 1980. At that time I had already ~30 patents and a
reputation of a practical scientist.
So I need more than the 'difference' into the universal.
Descriptions I saw turned me off. My chemistry-based polymer
science does not give me the base for most (and mostly
theoretical!) descriptions.
How'bout common sense base?
Actually I quasi-discovered Turing universality by myself when
studying Jacob and Monod 's work on genetic molecular control in
bacteria. But I did not take that very much seriously, until I
discovered (in the literature) the diagonalization technic (Cantor,
Kleene) and Church's thesis, which makes me decide to study math
instead of biology.
May be you could subscribe to the FOAR list, as I will explain all
that there. But if you ask me, I can send it in cc here or provide
other explanations (I think some people are on both list, but this
should not be a problem as it will not be a great number of posts).
I dunno. I will see.
Thanks for telling me your interest,
Best,
Bruno
On Thu, Mar 21, 2013 at 2:02 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 21 Mar 2013, at 02:32, Stephen P. King wrote:
Are physical computers truly "universal Turing Machines"? No! They
do not have infinite tape, not precise read/write heads. They are
subject to noise and error.
The infinite tape is not part of the universal machine. A universal
machine is a number u such that phi_u(x, y) = phi_x(y).
Please concentrate to the thought experiments, the sum will be
taken on the memories of those who get the continuations, and the
extensions.
When a löbian universal number run out of memory, he asks for more
memory space or write on the wall of the cave, soon or later. And
if it does not get it it dies, but from the 1p, it will find itself
in a situation extending the memory (by just 1p indeterminacy).
Universal machines are finite entities. Physical Computer are
particular case of Turing machine, and can emulate all other
possible universal number, and the same is true for each of them.
All universal machine can imitate all universal machines.
But no universal machines can be universal for the notion of a
belief, knowledge, observation, feeling, etc. In those matter, they
can differ a lot.
But they are all finite, and their ability is measured by
abstracting from the time and space (in the number theoretical or
computer theoretical sense) needed to accomplish the task.
That they have no precise read/write components, makes them harder
to recognize among the phi_i, but this is not a problem, given that
we know that we already cannot know which machine we are, and form
the first person point of view, we are supported by all the
relevant machines and computations.
And they are all subject to noise and error, (that follows from
arithmetic). Those noise and errors are their best allies to build
more stable realities, I guess.
Bruno
http://iridia.ulb.ac.be/~marchal/
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