Apparently (I am no expert) there are sequences of patterns in different dimensions based on: even-odd, powers of two, prime numbers and surely others. In some

Apparently (I am no expert) there are sequences of patterns in different dimensions based on: even-odd, powers of two, prime numbers and surely others. In some cases ±1 to get some effect. There is the uniqueness of the 3D cross-product, even though various generalization do occur in higher dimensions. One of the most obvious is the 1,2,4,8 sequence for normed division algebras: real, complex, quaternion and octonion. At each step you lose one mathematical property (commutative, associative, etc.). There cannot be any more, but there is a certain repetition, with factoring (doubling) known as Bott Periodicity: https://math.ucr.edu/home/baez/week105.html https://math.ucr.edu/home/baez/week105.html https://math.ucr.edu/home/baez/octonions/conway_smith/conway_smith.pdf https://math.ucr.edu/home/baez/octonions/conway_smith/conway... https://math.ucr.edu/home/baez/octonions/ https://math.ucr.edu/home/baez/octonions/ String Theories occur in 10, 24, 8+8, 32, ... dimensions, based on various symmetries and dualities. And some solutions need the extra increment, say 10+1, for the actual theory in spacetime. There are various theorems that seem to be trivial in 0D, 1D and 2D, then difficult in 3D, but perhaps eventually solved. In parallel, the upper limit existence proofs descend from infinite dimensions down to finite, then some impossibly (and apparently random) large finite number. Then a reasonable number less than 1,000, brought down to 100, and perhaps to less than 8. After a long struggle, and a Ph.D. for each number 7..6..5, it comes down to just 4, and 4D remains unsolved.