well playmofire, maybe the answer to the question "how then does the arrow get from point A where it started it's flight, to point B, where its flight ends" could be - with some effort.
or even - with some difficulty.
just kidding...

pastifi - the antikythera mechanism is beautiful.

it has that magic round quality that portuguese xvi century astrolábios also have but the fact that it looks so much more like a machine and that it is so much older gives it an extra glare.
although i am an architect, and have therefore some geometrichal skills, i wish i could have paid more attention to my past math classes.
i know just enough to understand most of the explanations but not enough to be able to make some research for myself.
i think mathematics can produce items as beautiful as your antikythera mechanism and also a buildink like this -
http://www.thecityreview.com/london.htm - the spiral daniel libeskind designed for the extension of the victoria and albert museum.
unfortunately it wasn't built for lack of funds.
it is based on a series of fractal equations (i don't know if i spelled the word right) that include the design for the tiles.
i just wish i knew how i could go so far.

one of these days i know i will find the time...