Re: [-empyre-] multi-perspectival / cultural hegemony of space

[John Klima <klima@echonyc.com>]

of course i am aware of non-euclidean geometries, jim. what i find
interesting about demonstrations of non-euclidean systems is that when
lets say, a box is drawn, it simply appears to me as a box with curved
sides. i don't see the box from inside the sphere it is based on, i see
it from the outside. i see it as cartesian regardless of how it was
mathematically produced. the same holds true for hypercubes. i sorta
don't beieve anyone who claims to see the fourth dimension, just the
same as i don't believe the versimilitude of fortune tellers and
clairvoiants. where non-euclidean geometries may be very useful in
science, i'm not sure how useful they are for an artist.

to the best of my knowledge, there are no non-euclidean renderers, at
least not in general use. the main point i'm trying to make here, not in
anyway undermined by non-euclidean spaces, is that the space that we are
working with is decided euclidean, and *that* is what it is best at
representing. i'm not talking about limiting its use to the realm of a
poor copy of reality, i'm saying its use, by its mathematical nature, is
restricted to a euclidean spatial representation regardless how much one
tries to confound that space. this is particularly true if you consider
what the machine "knows" about what it is doing. conversely, a
non-euclidean renderer, if such a thing existed, would have no
"knowledge" or understanding of euclidean spaces. in theory, the machine
can be told to "believe" in any system we tell it to believe in.
however, we as humans have a much harder time "believing" in a space
that does not equate to the one we walk around in every day.

best,
j



Jim Andrews wrote:
> 
> there are such things as non-euclidean geometries, john. are you familiar with non-euclidean
> geometries? they generally preserve the notion that a 'straight line' is the shortest distance
> between two points, but if the space is, say, only the points on the surface of a sphere, then a
> 'straight line' turns out to be part of a great circle, ie, the shortest distance between two
> points on the surface of a sphere is part of an 'equatorial' circle.
> 
> the geometry of the universe in some cosmologies is supposed to be non-euclidean. in the big
> bang theory, there's an origin point to the universe, the beginning of time, and the universe is
> supposed to be an expanding four-dimensional sphere.
> 
> when we look out into the sky at night, the further we see, the further back in time we see. so
> that no matter what direction we look, if we could see far enough, we would glimpse the same
> point, the origin of all things, the beginning of time. the meeting place. all lines intersect
> in this geometry. there are no parallel lines.
> 
> pretty non-euclidean.
> 
> is it non-cartesian? uh huh.
> 
> western philosophy has a history that has involved philosophers such as kant and locke looking
> into our notions of space and time. kant supposed that any notion of space that did not involve
> the parallel postulate of euclidean geometry would result in an unintelligable notion of space.
> but that postulate often does not hold in non-euclidean geometries. in other words, kant thought
> that the parallel postulate was an a priori truth, and various famous western philosophers have
> done the same, supposed that some version of the parallel postulate is a priori true. indeed it
> is the most common example in the history of western philosophy of an a priori truth.
> 
> the parallel postulate says that, given a straight line A and a point b not on A, there is one
> and only one line through b parallel to A.
> 
> but on the surface of a sphere, given a straight line A and a point b not on A, there are no
> lines through b parallel to A.
> 
> in other non-euclidean spaces, there are infinitely many.
> 
> non-euclidean geometry was rather important in bringing into question the idea that a priori
> truths exist.
> 
> ja
> 
> PS: Here is a fascinating 'space' by France's Frédéric Durieu:
> http://www.lecielestbleu.com/media/oeilcomplexframe.htm . The nature of this space is discussed
> in http://turbulence.org/curators/Paris/durieuenglish.htm . To make a long story short, this
> piece by Durieu called "Oeil Complex" is using a mapping of 1/(a+bi), ie, is using imaginary
> numbers.
> 
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