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

["Jim Andrews" <jim@vispo.com>]

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.