atddta 32: math in transit or complex topography

[grladams at teleport.com]

Mathematics involved.. So many really good posts in the past on this. Can't
find them. But this chapter begs for some math nod, and I'm just throwing
in a few cards, 

Changes of sign. http://en.wikipedia.org/wiki/Astrological_transit

Valences.

The train going from one way to the other way, Kit's mission folding back
at once as Shambhala has been sighted, Dally leaving her mission to join
Kit.

Chasms, on unpredictable surfaces. Moebius strips, Riemann surfaces, Klein
Bottles, come to mind.

(The Millenium Problems/Keith Devlin) "The story begins in Italy during the
Renaissance where mathematicians began to talk about doing the unthinkable:
introducing into algebra a number whose square root was -1.. p 222 In the
early twentieth century mathematicians generalized the idea of a Riemann
surface to the highly abstract concept of a complex manifold, a
multidimensional analogue of a Riemann surface with a complicated topology.
Such a manifold is equipped with a structure that ensures that the concept
of a complex analytic function mades sense." p 226 

I like this, that we need "equipment" like this to, well, to understand ATD
really. Like why in ATD does New York city seem to be destroyed in 1900? Is
there some flip? Are we on the one side looking straight up seeing the
other side looking back at us? Aren't the visitors who with their cyborg
voices bemoaning their times, aren't they us? 

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