File spoon-archives/heidegger.archive/heidegger_2003/heidegger.0306, message 46


Date: Tue, 10 Jun 2003 21:18:56 -0400
From: Ed Wall <ewall-AT-umich.edu>
Subject: RE: The dimension of a manifold


It is clear that somehow I assumed more was obvious in my reference 
than there actually was. Apologies. I take Eves as saying something 
very different than a reduction of the world to numbers or tuples - 
in fact, just the opposite. My understanding, and I could be 
incorrect, is that when he speaks of geometers he is not speaking of 
analytical geometers, but of geometers more or less in lineage of 
Euclid. For them such space is not given by a 3-tuple and, hence, 
four dimensions are not given by a 4-tuple. However, space is somehow 
known and navigated, for example, via solids, planes, and lines. This 
is still a way of thinking and doing mathematics and is understood, 
among most mathematicians, as not something that reduces or should 
reduce to arithmetic. What I thought interesting (and I seem to be 
alone in this thought - smile) is that the dimensionality, in a 
sense, increases when space is characterized in terms of lines or 
spheres.

The other thing and this is not meant as a criticism: is that your 
mapping to the reals has some interesting problems. Consider (and, of 
course, there is the interesting question if .9 (repeating) is what I 
say it is - smile).

1, 1, 1 = .9 (repeating), .9 (repeating), .9 (repeating) -> 
.9(repeating) = 1 -> 0, 0, 1

Here  -> corresponds to your map. One can, of course, quibble about 
what .9 (repeating) represents, but it is clear that your 
digitization of space (smile) is more arithmetical than mathematical. 
Having said all this let me note that your method nicely epitomizes 
something that seems mathematically other than a Cartesian reduction. 
There is an interesting way in which it has, one might say, 
non-Euclidean aspects (smile). However, it is a reduction that is not 
atypical (for a number of interesting reasons) of the zero/one world.

Ed Wall

>However, I am not sure about where the decimal point
>>  goes. For example does 1,0,0 correspond to 100 and 0, 0, 1 correspond
>>  to 1?
>
>x=3.141529 y=2.718281 z=1.414213
>
>give the number r=321.174411184522281913
>and for x=13.141529 we would have r=100321.174411184522281913
>
>and so on, for if any number (or so) can be written (with approximation) in
>binary, then our number is a complicated way of counting three numbers in
>one, in the base 1000.
>
>It is a simple way of putting R and R^3 in a bijective relationship. So, it
>seems that all our digital casting does, is to reduce the qualities of our
>world to numbers, and this is made possible by the fact our world is
>one-dimensional (yet tri-drectional spatially plus Minkowskian spatialized
>time, four directions) and its dimension is distance, which is being put in
>a bijective relationship with R (the set of real numbers).
>
>Therefore, one may play all his life with multi-directional spaces, yet not
>know how a (really) two-dimensional or three-dimensional space looks like.
>But, we have a hint in our thoughts and emotions, to which we cannot simply
>attribute distantial numbers. Of course, one could measure their intensity,
>yet the same way a computer makes no sense of a Charlie Chaplin DVD (though
>it is expressed in numerical quantities), but we do make sense of it through
>watching it, the same way would he be unable to say (while having access to
>such numerical input) what is really going on in one of us, who is being
>measured. It takes awareness to make sense of awareness.
>
>Gigantomachia peri tes ousias!
>
>Tudor Georgescu
>
>http://intellect-club.nl.eu.org
>
>Fax +1-775-245-5922
>
>
>
>
>
>
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