On 09 Oct 2015, at 22:22, John Clark wrote:
On Fri, Oct 9, 2015 at 7:12 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
> In Turing minds, the potentially infinite tape is just
modeling
Exactly, A Turing machine is just a model, a model of something
real, it's a toy, a analogy, a parable, a tool to aid in
understanding, but is not supposed to be taken literally.
On the contrary, all the point is that a Turing machine is a formal
object, and we can arithmetize it, and see that computer science is
embeddable in elementary arithmetic at its basic level.
When physicists say electrons are in shells outside the nucleus they
don't mean there are tiny mollusks at the center of atoms that
excrete layers of calcium carbonate.
I hope so.
But the notion of Turing machine is a mathematical discovery. It is
the discovery by Turing that in any universal enumeration of partal
computable function phi_i there is a u such that phi_u(x,y) = phi_x(y).
Robinson arithmetic or quantum computers defines such universal
numbers computing universal function.
A physical computer is a machine which implements such universal
number in the (most probable) physical reality around us, a bit like
you can implement the simple addition laws with pebbles, or
multiplication with a ruler.
It is necessary to distinguish between a program x and its
implementation by a universal number y.
> the papers and ink that a human can use when doing a
computation by hand.
And the ink and papers and the human hand that moves them around and
that human brain that directs the hand are all made of matter that
obeys the laws of physics.
In the aristotelian theory, but it does not work when we assume
digital mechanism, alias computationalism, comp in this list, c for
the very intimate.
>> There is no evidence a Turing machine, or any abstract
entity for that matter, has a memory at all;
> That is false. It has the tape
Show me the Turing Machine's tape!
It is a mathematical notion. They are famous for living in the unseen.
I cannot show it for the same reason that I cannot show you the number
3. I can only hope that you get the idea about it, enough to agree on
some formula so that we can take them as axiom, and reasoning rules.
> where it can store previous calculation result.
Store the entire contents of Wikipedia on the tape of your Turing
machine and then retrieve that information or explain to me why you
are unable to do so.
It is a trivial theorem of arithmetic that there is a Turing machine
which store the contents of wikipedia. Indeed, for all finite piece of
information there is an infinity of turing machine storing that
information, and this in all finitely describable ways, accepting the
usual classical thesis of Church, Turing, ...
> the tape is not a physical thing though.
Bingo! The tape is an analogy, a simple idea that helps humans
understand how real and far more complex physical computers
work.
It depends on the mathematical structure you describe the Turing
machine, and the segmebt of the tape that it uses during a computation.
Just read any book on the subject. I already gave you the definition
by Davis. Nothing physical is assume, and indeed that is used to make
the theorem feasible, and translatable in the language of arithmetic.
>> its memory is not infinite and it's not unlimited either but
is in fact very limited indeed, limited by zero . A Turing machine
has ZERO memory.
> That is false. It has a potentially unlimited memory (but no
actual infinite memory).
A Turing machine has no memory of any sort.
It has different state which do the office of the theory. Also, I
don't use the Turing machine formalism, but arithmetic and the
combinators in my illustration. The theoretical theology of the sound
universal machine is the same for all sound universal machine and
extension. It describes the realities accessible from the different
points of view.
But it would be easy to prove me wrong, all you need to do is store
the entire contents of Wikipedia on your Turing machine and then
retrieve it and put all the disk drive manufacturers out of
business. How hard can that be? And after that I will concede defeat
and thank you for correcting my errors.
There is no error. You just use a no standard not well defined notion
of physical computation. When you define it, you use the mathematical
notion, and add that you take only the physical computation as
existing. But for the mind body problem, especially in the frame of
the computationalist hypothesis, we mlmust use the standard, purely
mathematical, original discovery of Turing, Post, Church, Kleene,
Markov, etc. The UDA shows that a primary physical universe cannot by
itself select the consciousness of the machine, making comp entailing
that physics is a special statistics on the computation/sigma_1
sentences. We have three candidates for the "physical certainty", the
G* level of the logic of
[]p & p
[]p & <>t
[]p & <>t & p
with p sigma_1, that is p -> []p must be added to G (G1).
You can make a physical Turing machine with toilet paper and pebble,
or ropes and strings.
Yes that is true, a physical Turing machine would be VERY slow but
you could actually make calculations in that way, it won't work
nearly as well as a silicon microchip but at least it would work;
but then toilet paper and pebbles and ropes and strings are all
made of matter that obeys the laws of physics.
It helps to understand that all what matter is that a computation is
implemented by some universal u.
It happens that there is an apparent stable physical reality which
offers many variate universal systems. They all exist in arithmetic,
and there, they all compete to generate your more probable next
states. The probabilities "one" obeys the logic of the definition
above, and so we can test them.
Purely abstract things like analogies or parables or stories have
no need to conform with the laws of physics, even Turing machines
don't need to do that but unlike abstract things in general Turing
machines do conform with the laws of logic, and that's why they help
us understand.
The whole point is that such an Aristotelian view is refuted, when
assuming digital mechanism.
Your use of materialism is similar to the use of God when people
misuses it for preventing the research of the solution of a problem.
You just try hard to let the mind-body problem, and serious theology,
under the rug.
Doing so, you de facto protect the traditional charlatans, and you
confirm for the nth time that non-agnostic atheism sides with
religious fundamentalism.
Bruno
John K Clark
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