"if we lived in 1,000,000-dimensional space. I guess there's a lot of evidence that life can't exist in such high dimensions,"
Max Tegmark wrote a 1997 paper that was an excellent exploration of that, although it had D > big, not D = 1,000,000
"On the dimensionality of spacetime", M Tegmark 1997, Classical and Quantum Gravity, 14, L69-L75
Splash page that links to paper, because it has a nice graph that serves to summarize at a glance (# time dimensions versus # space dimensions versus viability/nonviability for life and indeed matter):