# Re: Numbers in Space

```On 9/21/2012 4:18 AM, Bruno Marchal wrote:
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On 20 Sep 2012, at 19:16, Craig Weinberg wrote:

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On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:

On 20 Sep 2012, at 17:02, Craig Weinberg wrote:

> Here's another reductio ad absurdum illustration of comp.
>
> If the version of comp we are discussing here is independent of
> physics, then shouldn't it be possible for us to program universal
> machines using only empty space?

You are quite quick here, but have a good insight, as comp makes
space
non clonable, indeterministic in the details, and plausibly Turing
universal, as QM confirms. The 0-body problem (the quantum
vacuum) is
already Turing universal (I think). For classical physics you need
three bodies at least).

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What about an ideal vacuum? Just lengths multiplying and adding enumerated bundles of lengths. No quantum.
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It would not be Turing universal.
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Dear Bruno,

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How so? What is the proof? Craig is allowing for N, + and *. So why not?
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> Length can be quantified, so why can't we just use millimeters or
> Planck lengths as the basis for our enumeration, addition, and
> multiplication and directly program from our mind to space?

Who we? In the universe nearby it costs a lot of
energy/money/time to
handle matter already gigantic compared to the Planck length.

Or are you suggesting we are already simulated by the quantum
vacuum.
Very plausible, but comp asks for justifying this in arithmetic.

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I'm saying that whatever program we access when we choose what we think about should be able to run just as easily in space as it does through the brain.
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Or just arithmetic. You don't need space. Only addition and multiplication of integers. Or justapplication and abstraction on lambda terms, etc.
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What do Integers represent? Are they just primitive "objects" with "inherent" properties?
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I should be able to pick an area of my house and leave a bunch of memories there and then come back to them later just be occupying the same space.
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Not at all. You are distributed in the whole UD*. You can go back to your memory only if the measure on computations makes such a persistence possible. This needs to be justified with the self-reference logics, and that is what is done with S4Grz1, Z1* and X1*.
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You lost us ... "Eyes glaze over" No explanation is being offered as to how the measure comes to be. I am asking you about the measure. Why do you avoid my questions? I will not stop until you answer me coherently!
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That's if we define space as relative to my house and not the rotating planet, revolving sun, etc.
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So it sounds like you are not opposed to this idea of computation with no resources whatsoever besides space,
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No need for spaces. To invoke it is already too much physicalist for comp.
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So all "spaces" are physical? What about a Hilbert space? Is it not a mathematical object?
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provided that it could be justified arithmetically (which I don't understand why it wouldn't be. how does comp know if it's running on matter or space?)
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By UDA. Anything physical must be justified with the "material hypostases". Up to now, this works, even by giving the shadows of the reason why destructive interference of the computations occurs below our substitution level.
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What determines the "substitution level"?

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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