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Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106190] Re: algebraic numbers
  • From: Vince Virgilio <blueschi at gmail.com>
  • Date: Mon, 4 Jan 2010 06:01:31 -0500 (EST)
  • References: <200912290620.BAA02732@smc.vnet.net> <201001011036.FAA05287@smc.vnet.net>

On Jan 3, 3:38 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:

SNIP

> Philosophically speaking, we cannot be sure that that is not exactly
> what we do in our own minds when we thing of "real numbers" - our brains
> are quite possibly only finite state automata and our reals are also
> approximations to "reals" most of whose digits always remain unknown. So
> I am not convinced that there is in this respect any fundamental
> difference between humans and computers.

SNIP

On the other hand, perhaps our intellect does work with the Reals. (If
the mind can handle some precision, why not all precision?)

Which would suggest, at least, a different order of computation.

Not merely Super, but Hyper.

(
In debt to Stephen Wolfram's latest novelty essay for this concept.

http://www.stephenwolfram.com/publications/recent/fqxi09/
)

Vince Virgilio


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