You have to admit pulling a sphere out of your ass is a pretty neat trick when you don’t even have real numbers to play with, so how did you get to spheres. Ok, the taxi-cab universe only goes so far, but this octahedral thing is based on spheres and close packing, isn’t that just a bit of a leap … even for you (or me).
This is the gap we have to cross. The whole point is that 3(3 – 2√2) is such a cute thing to play with, I mean its not even a counting number, it’s a ratio. So let’s start with the idea of the validity of the ratio in the first place. The ratio occurs in our minds, it doesn’t have to be real in the context of the counting numbers themselves. This is a meta analysis and I’m allowed to use tools that are too complex to express in the context of the thing being studied. So, what I’m saying is, I can derive a ratio between any two things, even counting numbers as long as the ration stays as an expression of analysis and does not play a role in the mechanics of the theory.
Here we have an analytical ratio, the “end game” ratio which would only be true at the end time that never comes. As the ratio of densities approaches this value what does it mean for universes derived from it. As an aside, let’s think of the ratio of densities as the 1st differential of the signal to noise ratio between generations. That is, its the rate of signal diminution over generations.
Now those bloody spheres, if the unit sphere represents the notional parent generation signal strength, and the small sphere the child generation signal strength then is this a model that contains any analytical meaning that could lead to the bringing forth of native spatiality.