On Saturday, February 1, 2014 4:54:47 AM UTC-5, Bruno Marchal wrote:
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> On 31 Jan 2014, at 21:39, Craig Weinberg wrote:
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>
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> 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.
>
"Appears" = output.
> 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.
>
How do we know they compute anything unless we input their output?
Craig
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>>
>>
>>
>> > 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.
>
>
>
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>
>>
>>
>>
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>> > 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.
>
>
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>
>>
>>
>>
>> >
>> > 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.
>
>
>
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>
>>
>> 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
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>
>>
>> Bruno
>>
>>
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>>
>>
>>
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