[TML] Noncanonical TU 3D.

[Jerry W Barrington]

On 1/9/08 4:04 PM, "Jens Rydholm" <jens.rydholm at bredband.net> wrote:

> Jerry W Barrington wrote:
>> 
>> Drop tanks can add a jump to anything though.  :)
> 
> When I built a 3D map (on hold for now, but I will resume or restart at
> some point), I used a special rule to guard against this. If you allow
> drop tanks and several jumps in sequence, all sorts of odd problems
> start to appear with the maps (mostly that you cannot visualize them in 2D).
> 
> My rule stated that you need to jump to a significant gravity well.
> After I finished writing, the idea evolved so that space is essentially
> the surface of a sphere (in 4D), and the gravity wells point in towards
> the center of the sphere. Jumpspace is using shortcuts between the
> gravity wells.
> 
> Do I make sense? I am very tired, and I must sleep now. But that was the
> general idea. Feel free to require clarifications :-)

It makes sense, but...

The tiny scales of the gravity well and of the overall bending of space,
compared to the humongous 4-sphere, are trivial.  They really wouldn't
shorten the distance noticeably.

Imagine it this way: Go to the Earth's equator.  Draw a box on the ground
that is a perfect 1 meter square.  Now take 2 points a meter apart on the
equator and draw 1 meter lines from them towards the North Pole.  The
northern end of that box will be *slightly* closer than 1 meter, but if you
compare it to the first box you drew, the difference is unnoticeable (on the
order of 25 nanometers!).  The comparison of 1 parsec to the circumference
of the universe is *at least* that extreme.

> I have made a program that creates 2D maps of jump routes in 3D space,
> using Graphviz (www.graphviz.org) to create the graphics. Works quite
> well, and enables maps to be printed to paper as something more visual
> than a table of coordinates. The program is not finished, but it should
> be easy for any programmer to generate Graphviz input from coordinate
> distances.

I've used a similar method before with a grapher called yEd.  Never really
went beyond playing with it though.