File spoon-archives/phillitcrit.archive/phillitcrit_1997/phillitcrit.9711, message 944


From: Patsloane-AT-aol.com
Date: Sat, 22 Nov 1997 17:02:18 -0500 (EST)
Subject: Re: PLC: Spinoza's Ethics


> Pat, I've got to say, I think you are stone wrong here. You can't, and
>  oughtn't visualize numbers. In the final analysis they exist _only_ as
>  abstractions. I knew an elementary school teacher who had students cut
>  number shapes out of plastic and cardboard and sandpaper so they could get
>  a "feel" for them, to involve the "whole" child. " Except numbers are
>  precisely not tactile (and have no color indeed, do not "exist at all),
and
>  I have to agree with your mathematician cohort. The visual interferes with
>  the conceptual in the case of mathmatic (not however, with geometry in
>  which modeling has always been encouraged.
>  
George,

Maybe I'm a left-over Pythagorean. If I have to do math in my head, I imagine
a blackboard with the answer written on it. If you tell me I have to get rid
of the blackboard, it would take a heck of a lot more time to get the answer,
if I could get it at all.

I think it was Hilbert who wanted to get rid of anything visual in
mathematics, and it isn't very consistent.  If you want to get rid of
anything visual, why write numbers down? I see no difference between a "5"
written or printed on paper or on a computer screen and your friend cutting a
number "5" out of paper.  

The urge to sever math from sensory experience comes from the mistaken (I
think) assumption that this will make it more "pure"  or "intellectual."  But
it actually can't be done.

pat sloane


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