You may be conflating [Bernoulli's solution to the Brachistochrone curve](http://www.math.rug.nl/~broer/pdf/ws-ijbc.pdf) with the optimal path for light. [Fermat's Principle](https://en.wikipedia.org/wiki/Fermat%27s_principle) states that, when traveling between two points, light will always take the path that minimizes the time taken from the first point to the last. In a medium of constant refractive index (which includes free space), this results in a line.
>So if you're looking for ways to distribute partitions or encode invariants in your models, data or otherwise, the geometrical aspects of elliptical and cycloidal curves are a good place to explore.
How do you mean? What sort of data can be encoded this way and how?
> NB: Consider this, two seperate impulses of light beginning at different distances away from the observer, both impulses of light traveling along the optimal path at the optimal speed, and both arriving at the observer simultaneously, without bending time. And as shown above, on a cycloidal curve, this phenomenon is not unique to light.
Two separate impulses of light beginning at different distances away from a stationary observer will necessarily arrive at different times, otherwise you violate the basis of special relativity: the speed of light is constant and invariant of reference frame.