The membership roster of the SU(3) non-Abelian homology (gauge) group was used to (as it turns out, apparently correctly), predict the existence of the top quark in QCD, which helped to bring about the marshaling of greater effort to find it -- ephemeral, because it doesn't hadronize like the others, but part of the group, so the QCD theorists assiduously sought it.WOW... sudden realization!! This is exciting!! For the last 20 years I meandered around them mysterious quantum formulas (without understanding anything, but fascinated on how cute they look) people would talk about SO(2), SU(3), etc... and refer to Lie algebra, multiplicative groups, ... ah!!!... no way someone with under 30 trillion neurons can understand any of that!!
Now I see - SO(2) is the same thing as a 2D rotation in ℝ2, and SO(3) is a 3D rotation in ℝ3. Hooray! So SO(4) may be related to 4D rotations? Or something else.. the wording is really difficult to translate a human English. Also I guess SU(3) too must be related to some other transformation-thingie with some particular property-thingie-thingie.
So SO(2) is related (related-sy, however the proper Mathematish phrase for that) to z ∈ ℂ such that ||z|| = 1! I learned something!!!