On 23 Sep 2011, at 19:13, Pzomby wrote:

On Sep 23, 8:41 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
Hi Roger,

On 23 Sep 2011, at 07:37, Roger Granet wrote:


    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?


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

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!



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