Does anyone know why a maximal chain in the lattice of subspaces of a vector space is called a flag? A chain of increasing subspaces doesn’t look anything like a flag!
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An Ergodic Walk 
Because like the flag of a country, it holds together several disparate entities? Just speculating after 9 double espressos and exam preparation here.
It kinda does for n = 2.
Yeah, but R^2 is for losers, yo.