Re: Two Mathematicians in a Bunker and Existence of Pi

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On 09 Mar 2012, at 01:47, Stephen P. King wrote:```
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```On 3/8/2012 1:43 PM, Bruno Marchal wrote:
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On 07 Mar 2012, at 18:36, Pzomby wrote:
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```Yes, but even the symbols =, +, x, *, are notations that are
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substitutes for words. Eg. Equals, addition or union, multiplication.
```The operational notations are words used to describe the formulation
of the model.
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Hmm... OK.
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In logic they are symbol associated with axioms and rules, and they have (standard) semantics, for exemple the mathematical "meaning" of + is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2) .... (6,7, 13), ..., (1, 23, 24), ....}.
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I could not resist! So they are infinite after all!
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Who ever doubt this? Comp is based on N, the phi_i and the W_i (most of which are infinite). Church thesis needs infinities, and the first person view on the (infinite) arithmetical reality is beyond the nameable infinities.
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The confusion might come from the fact that those infinities are epistemological, but the epistemology does exist. Yet the ontology, although finitistic, is not ultrafinitistic and so needs too a potential omega.
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Yes. Then it is Ok to use it for that. eg. 1stness, 2ndness, 3rdness
```in sport races gives a quality of feeling to the participants,
observers/bettors.
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OK. But I would say the "quality" of being the first is more in the mind of the machine winning the competition, or in the mind of the machines members of the jury, than in the ordering relation itself.
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Are these not equivalent in the Platonic sense?
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After all, we are considering universal machinery that ignores any kind of local gauge symmetry.
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?

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```Are numbers (ordinal) necessarily qualitative descriptions?
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Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
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akin with the human conception of quality as being a lived experience.
```But what you say might make sense in some other contexts.
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It is the “lived experience” that is reality as I understand.
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OK. That is the reality of subjective experience, but we can bet there is something independent of that reality, and which might be responsible for that reality.
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It seems to me that any one that would bet against that "there is something independent of that reality" would be a sucker or a solipsist
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OK.

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or some superposition thereof! How does this tie into 1p indeterminancy?
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What is the problem?

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The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process.  eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001.  In nature: January in central Europe exudes certain
environmental qualitative conditions.
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Once universal numbers are in relation with other one, many qualitative conditions can happen, assuming digital mechanism.
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Wait a second, does not digital mechanism assume a fixed substitution level?
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OK. What is the problem?

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Numerals symbolize number position (as in particular instants in the
```sequence of the continuum of time).
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OK. But that's quantitative for me, or at least a "3p" type of notion.
```Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.

Bruno
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Duration of time is quantitative. Existing conditions in the duration
```are qualitative.
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I doubt this. I would bet that if time can be quantitative, and objectively measured by different observers, the duration notion is more qualitative, and subjective.
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How can a "measure of change" be anything but quantitative?
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What about change of mood, or change of taste?

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Given that we are seriously considering that all of our 1p and 3p tropes are, literally, nothing more than numbers and relations between them, what else is there?
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The machine 1p are (provably) not "number relations". They are qualitative modalities of relative number self-reference, related to non sharable truth that machines can be aware of. The physical reality has to be among them by the UD-Argument, except for a part of them being first person plural sharable.
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The 1p are what the machine talk about when looking inward. That sorts of things have just no 3p description at all, neither number or anything 3-mathematical. They do have only 3p meta-logical accounts, like this very paragraph, but this should not be confused with what they are.
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You state: “Quality is more 1p” but it is not exclusive to 1p. Humans
```observe and have  empathy for others qualitative conditions and
states.
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I agree.

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It could be that "qualities" are just spectral ranging over local gauges... THink of how we can associate even an infinite field of continuous transformations with a single point using fiber bundles. I strongly suspect that this is exactly equivalent to "infinite computations running through each 1p"...
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Vague analogy with too much precise terms. Look a bit "1004" to me. We might have a notion of quantization, but a lot of work remains before we get arithmetical linear operators and spectra, if ever.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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