Like the Eiffel Tower or Burj Khalifa, the algebra tower only has 4 levels (Real, Complex, Quaternion, Octonion) before it shrinks to degeneracy, and level 2 (

Like the Eiffel Tower or Burj Khalifa, the algebra tower only has 4 levels (Real, Complex, Quaternion, Octonion) before it shrinks to degeneracy, and level 2 (Complex) has the best balance of dimensionality and power. Adding dimensions adds power, but linking the dimensions adds constraints on allowed structures. https://en.m.wikipedia.org/wiki/Composition_algebra https://en.m.wikipedia.org/wiki/Composition_algebra