# Re: Peano Axioms are wrong (at least in our universe)

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On 20 Sep 2016, at 06:18, Brent Meeker wrote:```
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On 9/19/2016 7:26 PM, Russell Standish wrote:
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```On Sun, Sep 18, 2016 at 11:54:04PM +0200, smitra wrote:
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```https://www.youtube.com/watch?v=nK6XawDE8_U

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```Just finished watching Norm's video, and one thing really struck
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me. The process of factoring numbers of the form 10^n+23 is generating
```vast amounts of complexity, as n increases. I hadn't really thought
about things that way before, but I have to say this really
constitutes a direct counter example to my oft stated dictum that
evolutionary processes are the only way to generate complexity.

Food for thought.
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But is the algorithmic complexity high? A program has to run a long time to find some large prime factor, but the program is fairly simple. In Bruno's Platonic view these numbers and relations just ARE
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OK.

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```and their computation is irrelevant.
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?

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Their computations are among the relations which just ARE, and they are relevant.
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Indeed the computations are, basically, the sigma_1 true relation. (They are also probable by any Turing universal theory). They are the domain on which the (8) logics sof self-reference eventually are applied.
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But I see no reason why one cannot axiomatize an unltrafinitist arithmetic - that's essential what computers do. Then those "dark numbers" will not exist.
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Not from the small numbers/machine FIRST person pov: as the small program is also implemented by the infinities of the dark giant numbers, and that might play a rĂ´le in the measure calculus.
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The bodily and practical means of the numbers are rooted in the neighborhood of zero. The fate of the number's soul and experienced are driven in the neighborhood of infinity.
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That's a simple consequence of the inability of the first person to detect relative delays in the computations which support them (in arithmetic).
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But doctrinal ultrafinitism does not make sense even from a pure 3p pov, in the sense that it deprives itself of the means to explain what it means. Robinson arithmetic is consistent with the proposition "there is a biggest natural number", but we get the consistency by adding that biggest natural number above all others in some contrived model.
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A genuine ultrafinist will never argue for ultrafinitism.

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He/she can't do that without betraying that he/she disbelieves in it at the meta-level. He/she will only say "what?" when you name a number too much big for him/her.
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Bruno

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Brent

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