Content
@
https://warpcast.com/~/channel/math
0 reply
0 recast
0 reaction
Thomas
@aviationdoctor.eth
It's fascinating to me that most of the 2D plots that we use in algebra are deceptively hiding the true behavior of functions, which only becomes visible once we start mapping them in 3D space, by switching from real to complex numbers. So many people's understanding of mathematical behaviors are based on a flawed and incomplete low-dimensional premise —much like seeing only the 2D shadows of 3D objects on the walls of Plato's cave. Extrapolating, it makes me wonder how much deep intuition we're missing out on by operating most commonly on the real number line (1D), or at best in the complex plane (2D), but almost never using the quaternion (4D), octonion (8D) or sedenion (16D) numbers — our puny brains probably couldn't take it anyway. This is an area where I'm hopeful that AI, being free of our low-dimensionality bias, can help us make strides. Watch just 30 seconds of https://youtu.be/92wXQYcYLMg?t=1469 to see how much depth is lost by switching back from 3D to 2D plots of familiar functions
2 replies
3 recasts
20 reactions
Rod Mamin
@ionrod
Wish I'd be able to visualize the full complex->complex plain not just a projects :( How to imagine 4th dimension?
1 reply
0 recast
1 reaction
Thomas
@aviationdoctor.eth
Short answer: shrooms Long answer: mushrooms
1 reply
0 recast
1 reaction
