On 9/19/2016 7:26 PM, Russell Standish wrote:
On Sun, Sep 18, 2016 at 11:54:04PM +0200, smitra wrote:

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 and their computation is irrelevant. 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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