Hyper-spacial ray-tracer

[Rouslan Korneychuk]

On 10/04/2013 04:23 PM, Tony the Tiger wrote:
> On Wed, 02 Oct 2013 17:05:32 -0400, Rouslan Korneychuk wrote:
>
>> game
>
> Sorry, but that sounds awful. I hate games.
>

This... isn't a game or even related to gaming. Is it because of the use 
of Pygame that you thought it was. I use Pygame because it's a wrapper 
for SDL, which gives you cross-platform graphics, input and even thread 
support, and because the additional drawing and font modules are useful 
for prototyping and implementing user-interfaces for navigating 
higher-dimensional space.

The point of this was to explore the concept of hyperspace, which is a 
mathematical curiosity and also has relevance in theoretical physics.

One idea I had for this was to simulate some sort of 3D scene involving 
physics (probably in another program, such as Blender), take the 
resulting coordinates of the geometry at every time interval and plot it 
as one 4D static scene. Every pair of connected vertexes would be 
extruded from one instant in time, to the next, so each object is a 
continuous 4D extrusion. When viewing with your local XYZ axes aligned 
with the global XYZ axes, you would see one instant of the scene as 
normal. Moving along the fourth axis, which I'll call T, will let you 
see the same, earlier or later in time, but if you rotate parallel to 
the T axis, you will effectively replace one of X, Y or Z with T. In 
essence you will turn the time axis into a spacial axis and the spacial 
axis into a time axis.

Looking at a scene with space and time lumped into one 4D space might 
help in trying to better understand time, why it's different, and its 
relationship with space.

I was also wondering about general relativity. I'm not going to go into 
too much detail, but basically: if an object with synchronized clocks on 
either end of it, passes by a static observer while traveling near the 
speed of light, to the outside observer, the object will appear shorter 
and the clocks will appear desynchronized, and from the object's 
perspective, it is the outside observer that becomes distorted this way. 
I was wondering if this seemingly strange effect is actually the natural 
consequence of a simple geometric transformation, such as rotation into 
the time axis.