> the :-separated blocks are not fractions, they are two-component vectors up to a multiple Projective coordinates are fractions, or more precisely the ℤ⁺²-pro

> the :-separated blocks are not fractions, they are two-component vectors up to a multiple Projective coordinates are fractions, or more precisely the ℤ⁺²-projective vector space[1] (over the positive integers) is ℚ⁺, the positive rational numbers[0]. You generally want to use ℝ instead of ℤ for obvious reasons, but that's not really "not fractions" in any useful sense. But writing it as vectors does have the benefit of making the generalization from ℝ² to ℝⁿ (n≥2) somewhere between obvious and trivial, whereas fractions are at-least-implicitly specific to the ℝ² case. 0: give or take some issues with 0 and ∞ that we don't care about because 0 and 1 are not probabilities 1: I'm sure someone can out-pedant me on the terminology here, but the point is it's two-dimensional, which (2) is the fewest dimensions this works non-degenerately for (leaving one degree of freedom, versus zero for the ℝ¹ case, and negative one (aka doesn't work at all) for ℝ⁰)