interesting reading https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensio...
1. https://www.reddit.com/r/askscience/comments/q8fmo/what_woul...
2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...
Not sure if this is what GP was talking about. But the explanation there is excellent. It's in the chapter where curl is introduced for the first time. After you read it, you'll get annoyed whenever you see curls or cross products.
Also: https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...
In computing applications, if you want to find a vector perpendicular to two or more vectors outside of 3 and 7 dimensions, you would use the QR decomposition to do it. If on the other hand, you want to generalise the "directed area" properties of the cross product, you would use Exterior Algebra, or its elaborations like Clifford Algebra or the theory of differential forms.
Stable is not really the right word. "Well behaved" is better. In 2D all orbits are stable in the sense that escape velocity is infinite, but a consequence of that is that you don't naturally get nice (nearly) circular orbits that keep planets in habitable zones. That only happens in 3D.
So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.
Or you can make the argument that no other universes other than a 3D one can support life, i.e. that 3D is necessary for life. Then you can conclude if life, then 3D.
If you use Bayesian probability, you would in this case start with p(3d) = 1 since there's only one universe which is 3d and then end with p(3d | life) = 1. In other words, there's no explanatory power in the observation that there's life.
If instead you say that p(3d) = 1/1000 because maybe the multiverse has all sorts universes out there but you also say that life is only possible in 3d, i.e. p(life | 3d) > 0, but p(life | not 3d) = 0, then you go from p(3d) = 1/1000 to p(3d | life) = 1. In other words, the observation of life does have explanatory power.