Re: Star Trek Astronomy


Joe wrote:
I was watching an old rerun of Star Trek TNG and I noticed something I had
never seen addressed before. It was an episode where the Enterprise received
a distress call from a scientist out in space. The scientist gave his
position with two floating point numbers.

They would be better off represented as fixed point or integers.

My question is if there is any system of geometry that would allow for
giving the exact position in 3 dimensional space with only 2 coordinate
numbers.

Yes a countable infinity of them but they are potentially confusing
unless sender and reciever both know the convention used to encode it
as a single number. (But that is true of all coordinate systems -
unless you know the rules they are just meaningless numbers)

A normal 2D grid coordinate ABCDEF, GHIJKL can be written AGBHCIDJEKFL
for instance. You therefore need a longer symbol or you lose precision
when the 2 dimensions are rolled into a single numeric representation
and then truncated.

And just for fun you could also give your coordinate in 3space as one
long number.

A pure but inefficient method using a single long coordinate would be
to specify your distance(s) from the origin along one of the various
space filling fractal curves.

These will not survive in ASCII art so here is a link to the pretty
space filling Hilbert curve on Wolfram's mathworld showing the first
few generations of the family.

http://mathworld.wolfram.com/HilbertCurve.html

Space filling curves were thought to be impossible until 1891 when
Hilbert discovered them. There is a 3D space filling curve example
drawn at the bottom of that page...

There is a zoo of other ones if you follow the Lindenmayer system
link.

Thanks for any answers in advance.

Regards,
Martin Brown

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