On 23 Sep 2011, at 19:13, Pzomby wrote:
On Sep 23, 8:41 am, Bruno Marchal <[email protected]> wrote:
Hi Roger,
On 23 Sep 2011, at 07:37, Roger Granet wrote:
Bruno,
Hi. Yes, I am pretty much a materialist/physicalist.
So, you cannot defend the idea that the brain (or whatever
responsible
for our consciousness) is Turing emulable. OK?
Bruno:
When you state “that the brain (or whatever responsible for our
consciousness) is Turing emulable”…in using the term Turing “emulable”
do you mean that the brain is being imitated, is represented, is an
instantiation, or something stronger such as the Turing machine
actually having inducted number properties of “encoded” information.
Could you clarify why the term Turing “emulable” is used and not
Turing “represented” or Turing “instantiated” or even Turing
“encoded”?
That's an important but not so easy question to answer, especially
without digging a bit in the computer science (and it is hard for me
to guess what you already know about computer), but I will try to do
my best.
Emulation means "exact simulation". That concept makes sense in the
digital world, for digital processes (although many have attempted to
extend it on a variety of analog devices).
People like Post and Turing have discovered a universal machine or
universal program. Such a program is able to emulate the work of any
other program. So we can say that a (general purpose) computer is also
a universal emulator (leaving open if such a machine can even emulate
just one physical process: in fact comp entails that a computer cannot
emulate *any* physical processes, despite it can simulate them quite
well, at least for short period).
The brain functioning, or a physical computer functioning is a
physical process, and *as such* is not emulable by computers.
But a computer computes, and *that* function is emulable by any other
computer.
Let me give an example. If you write a program computing the
factorial, when you execute it on a computer, the computer will go
through a discrete sequence of step, ending up with the result of some
factorial in some register. Now, any other computer, including humans,
can emulate that digital process, that is do exactly the same
computation, going through the same equivalent step (with a very
narrow notion of equivalence). A human can emulate this with pencil
and papers, for example. This does not mean that a human can emulate
the physical working of a physical von Neumann computer: not only he
will not have the time to emulate the quantum wave responsible for the
stability of the atoms of the von Neuman physical machine, but he
cannot probably emulate the infinity of worlds that such a wave really
describe. So when we say that a computer emulate some machine, it is
always with respect to what such a machine is supposed to be doing.
This is the reason why, with comp, we have to make explicit that an
artificial brain emulate a real brain, at the level here we suppose
the real brain acting like a computer. Comp assumes that such a level
exist. Once such a level is chosen, by the notion of universality, we
can choose any computer for doing that task, with silicon, or with
water, air, pebbles, whatever.
The term "emulable" is used, to remind us, that it means simulable in
some exact way, which makes sense for the digital process.
"Instantiate" is not bad, but is a more general term. If a Toby is
ferocious, he can instantiate a ferocious dog, but you would not say
that he can simulate a ferocious dog exactly. But "instanciate" is OK.
In some context, representation can be used too, but the term can also
have less precise, and more precise, meaning according to the context.
It is usually more statical, less dynamical, than simulation and
emulation. Encoded, is a bit too much precise, and is also rather
statical. You can encoded data in a computer, but if you cannot encode
a computation, unless you do meta-programming, and handle a program
which manipulate a representation of some computation.
For a (crucial) example, Arithmetical truth does both. It emulates
computations (meaning that the "natural" true relation between numbers
does exact simulation of the dynamical evolution of computers, with
digital time emulated by the successor function, but it encoded also
the (finite) pieces of computations (which become statical, like *one*
number). Consciousness supervenes on the computations, but not on the
encoding of computations, which are merely description of computation,
a bit like a movie can describe some happening, but is different from
the happening itself.
For those who knows the phi_i, this can be made more clear. let phi_0,
phi_1, phi_2, ... be an enumeration of the computable functions. Let
phi_i(j)^s be the sth step of the computation of phi_i on argument j.
A computation can be described by the sequence phi_i(j)^0, phi_i(j)^1,
phi_i(j)^2, phi_i(j)^3, phi_i(j)^4, phi_i(j)^5, .... Note that such a
sequence describes a computation, but is not the computation. The
computation is what do the universal machine for relating all those
steps. It is necessarily more abstract than the description. A number
or machine u is universal if phi_u(<x, y>) = phi_x(y). Here we can say
that u, when programmed with x, and when y is given as data, emulates
x. Unless x is itself a universal number, usually x cannot emulate u.
I hope this helps a bit. Don't hesitate to ask if something is still
unclear. It is not so easy to grasp, for some people, the difference
between a computation, and a description of a computation. The modal
logic can be used to explain ... why this is difficult!
Bruno
http://iridia.ulb.ac.be/~marchal/
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