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

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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_UJust finished watching Norm's video, and one thing really struckme. The process of factoring numbers of the form 10^n+23 isgeneratingvast 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 longtime to find some large prime factor, but the program is fairlysimple. 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 unltrafinitistarithmetic - that's essential what computers do. Then those "darknumbers" 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

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