On 20 Sep 2016, at 06:18, Brent Meeker wrote:



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

Just finished watching Norm's video, and one thing really struck
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.

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

OK.



and their computation is irrelevant.

?

Their computations are among the relations which just ARE, and they are relevant.

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.





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.

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.

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.

That's a simple consequence of the inability of the first person to detect relative delays in the computations which support them (in arithmetic).

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.

A genuine ultrafinist will never argue for ultrafinitism.

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.

Bruno







Brent

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