Well, I'm certainly no expert, but I did have a novel idea for how to begin this process. Lately, any thought and application of higher dimensional surfaces has been coming very easily to me. I'd like to apply it to a real world scenario.

So, my idea is this: we begin with the notion that there are 26 dimensionless constants of nature. These are pure mathematical ratios and do not require a measurement system. So, let's start off with constructing a 26 dimensional plane, where origin has 26 axes intersecting at right angles. This is a euclidean space, no curvature. Now, let's take each axis and assign a constant of nature to it, making a point along a line. It's value will be at this point. Now, we end up with 26 points each on its own axis.

My theory is this: we connect all 26 points together into a single object with a complex surface. This surface is the topological equivalent to our universe, and thus the equation. This way, we apply what we know beforehand, THEN derive the surface features. The way it folds and laces may show undiscovered relationships within physics. We'd be exploring mathematical space, shining a light on the intricate surface features that are hidden in the dark.

At least, that's how I see it. Could be way off.