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.
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
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.
What makes it happen without invoking a physical or experiential
context?
Truth. The necessary one, and the contingent one.
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.
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).
Bruno
http://iridia.ulb.ac.be/~marchal/
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