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MathGroup Archive 2012

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Re: Landau letter, Re: Mathematica as a New Approach...

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  • Subject: [mg127923] Re: Landau letter, Re: Mathematica as a New Approach...
  • From: John Doty <noqsiaerospace at gmail.com>
  • Date: Sat, 1 Sep 2012 02:29:07 -0400 (EDT)
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On Friday, August 31, 2012 2:03:01 AM UTC-6, djmpark wrote:
>  I claim that the natural numbers arise from a PHYSICAL counting
>
> process but infinite ascent and induction require ABSTRACTION and that is
>
> where mathematicians especially come in. It takes both.

Nunez addresses the problem of conceptualizing infinity (and much else) in this wonderful paper:

http://www.cogsci.ucsd.edu/~nunez/COGS200/nunez%2Bpdf.pdf

This may be of interest to educators.

I also note that experimental psychologists, notably Macfarlane and Tolman back in the 1930s (!), have established that even laboratory animals are capable of constructing abstract models, specifically "maps" of mazes. Their experimental results are inconsistent with the idea that in learning a maze, the animals merely learn the sequence of steps needed to solve it. Abstraction is a useful mental ability that is hardly confined to mathematicians.  Of course, like other biological capabilities, it comes more naturally to some people than others, and it can be enhanced via training and practice, or degraded by disuse.



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