On 31 Jan 2014, at 21:39, Craig Weinberg wrote:
On Friday, January 31, 2014 2:47:01 PM UTC-5, Bruno Marchal wrote:
On 31 Jan 2014, at 03:23, Craig Weinberg wrote:
> Maybe it will help to make the sense-primitive view clearer if we
> think of sense and motive as input and output.
>
> This is only a step away from Comp, so it should not be construed to
> mean that I am defining sense and motive as merely input and output.
> My purpose here is just to demonstrate that Comp takes so much for
> granted that it is not even viable as a primitive within its own
> definitions.
>
> Can we all agree that the notion of input and output is
> ontologically essential to the function of computation?
Bad luck Craig!
Not only the notion of input-output is not essential for computation,
but we can argue in many ways that input-output are inessential.
A deep one is the discovery of the combinators, which provides a way
to do math and computers without variables. You still need some
variable at the metalevel, but all formal objects, program and
computations are object without variables. This is exploited in
compilation theory, and in some proof theory.
Then there is the SMN theorem, which says basically that you can
simulate a function with two variables (two inputs) by mechanically
enumerable collection of functions of one variable.
Here too, the S90 particular case says that you can simulate functions
of 9 variables with effective enumeration of functions of 0 variables,
that is without input.
Recursion theory is fundamentally non dimensional.
Take the UD.
A UD dovetailing only on the programs without input is equivalent with
a UD dovetailing on the programs having infinitely many inputs
(streams).
And, to finish, the UD itself is a program without input and without
output. It computes in an intensional very complex way, nothing from
nothing.
The UD has this in common with the common aristotelian conception of
the physical universe. A physical universe cannot have input nor
output, without stopping being *the* physical universe.
This does not mean, than in the relative computation, some input can't
help.
> Is there any instance in which a computation is employed in which no
> program or data is input and from which no data is expected as
output?
The UD.
Isn't everything output from the UD?
No. The UD has no output. It is a non stopping program. "everything
physical and theological" appears through its intensional activity.
In fact it uses an intensional Church thesis. Not only all universal
machines can compute all computable functions, but they can all
compute them in all the possible ways to compute them. The intensional
CT can be derived from the usual extensional CT. Universal machines
computes all functions, but also in all the same and infinitely many
ways.
> This would suggest that computation can only be defined as a
> meaningful product in a non-comp environment, otherwise there would
> be no inputting and outputting, only instantaneous results within a
> Platonic ocean of arithmetic truth.
A computation of a program without input can simulate different
programs having many inputs relative to other programs or divine (non-
machines) things living in arithmetic
How does the program itself get to be a program without being input?
OK. Good question.
The answer is that the TOE has to choose an initial universal system.
I use arithmetic (RA).
Then all programs or number are natural inputs of the (tiny)
arithmetical truth which emulates them.
You need to understand that a tiny part of arithmetic defines all
partial computable relations. The quintessence of this is already in
Gödel 1931.
> Where do we find input and output within arithmetic though?
It is not obvious, but the sigma_1 arithmetical relation emulates all
computations, with all sort of relative inputs.
It seems to me though, and this is why I posted this thread, that i/
o is taken for granted and has no real explanation of what it is in
mathematical terms.
It is the argument of the functions in the functional relations.
If phi_i(j) = k then RA can prove that there is a number i which
applied to j will give k, relatively to some universal u, (and this
"trivially" relatively to arithmetic).
> What makes it happen without invoking a physical or experiential
> context?
Truth. The necessary one, and the contingent one.
Does truth make things happen?
Yes. truth('p') -> p.
If "Obama is president" is true, then Obama is president.
>
> As an aside, its interesting to play with the idea of building a
> view of computation from a sensory-motive perspective. When we use a
> computer to automate mental tasks it could be said that we are
> 'unputting' the effort that would have been required otherwise. When
> we use a machine to emulate our own presence in our absence, such as
> a Facebook profile, we are "onputting" ourselves in some digital
> context.
The brain does that a lot. Nature does that a lot. Ah! The natural
numbers does that I lot.
There doesn't seem to be a clear sense of what it means for numbers
to exert effort.
Of course I was speaking loosely, to avoid too much long sentences. It
is not the number which makes the effort, but the person emulated by
the number relations which makes the effort.
Think about the number relation which emulates the Milky way (by
computing the evolution of its Heisenberg matrix, with 10^1000 exact
decimal, at the subplack level. Of course that is already a toy mulit-
galaxies. It owns a Craig doing the effort to read this post, and omp
prevents that you can distinguish your self from that one. the effort
are the same. (Of course with non-comp, you can made him into a zombie).
If, as you say, truth itself makes things happen, then it would seem
that effort is an incoherent concept.
My poor car followed the schroedinger equation without effort, but at
a higher level, it tooks her a lot of effort to climb some steep
roads. Well, she died through such effort, actually.
Numbers have no reason to make other numbers do their work, as they
don't seem to have any basis to distinguish work from play.
Sigma_1 arithmetic, alias the UD, emulates all possible interactions
between all possible universal machines. All sorts of interactions are
emulated, but with different relative probabilities, and that depends
locally partially on them.
Computers will evolve in two ways: users' self extensions, like a neo-
neo-cortex (+GSM, GPS, glasses, etc), which is a semi-delegation, and
the total delegation (the friendly, and not friendly, AIs).
Those are ways that our use of computers will evolve. I don't see
that computers have any desire to extend themselves or to delegate
their work.
All universal machine are incomplete. Of course "desire" is a high
level feature which requires probably deep computations, but that
desire is a logical consequence of the basic frustration of any
machine when she grasps the difference between what she can obtained,
and what she can dream about.
Bruno
Craig
Bruno
http://iridia.ulb.ac.be/~marchal/
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