Earlier I mentioned the issue of representing space as a 3-dimensional array and light as a propogation of data from each cell in the array to its neighbors - namely that in such a representation, the number of steps between any two points is X + Y, whereas in the real world we have measured this distance to be C^2 = A^2 + B^2.

Here is a picture I drew of that representation, to refresh your memory:

The simplicity of this arrangement appeals to me - I see it as a kind of 3-dimensional lambda calculus -  so I'm hoping there is some kind of transformation by which a 3d array could be the underlying representation of our universe, even though, when measuring distances, we still end up with A^2 + B^2 = C^2.

At the forefront of my thoughts is algorithmic complexity - or Big O; basically the measuring of the number of steps to complete a task.

Beware:  Gross oversimplifications incoming! 

In the diamond diagram above,  it takes 4 steps for the light to iterate a distance of 4 pixels horizontally or overtically, and 8 steps for it to iterate a distance of on the diagonal.  So in the worst case it would be something like O(N).

But if we're going to do things over a set of things in discrete steps, pythagoras would seem to indicate that we're looking for something that's O(N^2).

I went over the wikipedia to see what kind of algorithms fit that description:  http://en.wikipedia.org/wiki/Big_O_notation

The examples it gives:  

Multiplying two n-digit numbers by a simple algorithm; bubble sort (worst case or naive implementation), Shell sort, quicksort (worst case), selection sort or insertion sort

This encourages me to imagine that our observation of distance might be somehow constrained in an algorithmic way, wherein our measurement of distance could be in "visits" to the cells, rather than a difference in the x and y coordinates of the cells. 

Just throwing some ideas out there:

• Perhaps the wavefront is like a number thrown into a randomized stream of numbers, and undergoes something like a Bubble Sort or Selection Sort before making its way to the end.  In this case, we are measuring the number of steps to sort, rather than the number of cells sorted over.
• Possibly relating to the notion that each point on a wavefront is the source of a new wavefront - it could be that each of the points between the original source and destination need to have communicated to every other point along the axis, like in an n-body-simulation (which I read about here:  http://en.wikipedia.org/wiki/N-body_simulation ).  The light sensor isn't triggered until all these points are in sync, resulting in N^2 steps.