Physical 3x3x3x3 hypercube and other physical 4d twisty puzzles [video]

I understood 0% of what he was saying but I'm happy for him

Unbelievable. I used to be a collector of twisty puzzles and there was quite a few levels of challenging puzzles beyond my ability, but seeing this is just astounding! I only have barely a clue what each of the moves are doing but it makes me smile knowing someone cared enough to make this. Science has gone too far

Yeah even though the moves are all the same in 4d space, some of them get complex in 3d space.

I don't understand how that's a 3x3x3x3. While there are some 3x3 elements, there are only 2 layers and 2 side by side. What am I missing?

I trust the math. I trust the manipulator.

But it drives home the reason why I parted ways with advanced math. There just came a point when the math no longer resonated with the natural world that I was comfortable living in.

Imaginary (and complex) numbers were the first real schism where my mind repelled the very idea.

Nonetheless, decades later, I would be talking with a friend who is much smarter than me. We were talking about the lossy nature of converting audio from the time domain to the frequency domain and back. I understood that phase information was lost in the translation (I also thought it was curious that the human brain seemed to be phase-agnostic and so could not perceive the difference when audio was round-tripped through the frequency domain).

"Oh," he said, "when you do a Fast Fourier transform to move audio into the frequency domain the phase information is represented by the imaginary part of a complex number."

Wait, what? So complex numbers have a real-world analog in constructing an FFT — a "real" algorithm that does real work?

I see now that the really smart people just understand the natural world much better than I do — or perhaps see it differently than I do.