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

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

#21

Post by dvt »

JKCalhoun wrote: post #10

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…

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

If extending the number line bothers you, you should also have a problem with negative numbers. And, in fact, many ancient mathematicians did, so you're in good company :)

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

#22

Post by acer4666 »

JKCalhoun wrote: post #10

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…

The problem isn't you! "Imaginary" numbers are terribly named, and I can see why that would put anyone off engaging with them. They are just as "real" as 2d co-ordinates are.

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

#23

Post by alkonaut »

Does the limitations of 3D physics just mean that the thing can't really be connected, and you are responsible for making a subset of the moves by free hand, and if you screw up you either cheated, or made the equivalent of a corner twist on a Rubik's cube, leaving the resulting configuration unsolvable?

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

#24

Post by rendall »

GoldenRacer wrote: post #9
rendall wrote: post #8

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?

He starts out showing a 2x2x2x2 and doesn't get to the 3x3x3x3 until just after the 10 minute mark.

Oh yes, I see now. Thank you!

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

#25

Post by voldacar »

JKCalhoun wrote: post #10

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…

I suspect that what threw you off was the dumb term 'imaginary', not the idea that the real numbers could have an algebraic closure.

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

#26

Post by skupig »

maxbond wrote: post #11
JKCalhoun wrote: post #10

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…

I think it's less about some people being especially good at math than mathematics education being especially terrible and uninspiring. 3blue1brown's approach to math pedagogy had really changed how I'm able to see math and to understand it's profundity (as someone who didn't get any further than you, it sounds like, in formal math education [I never took calculus in school.]). https://youtube.com/playlist?list=PLZHQ…

The second playlist is great, thank you! As someone with near zero math knowledge, it was very exciting learning that imaginary numbers are a beautiful and intuitive concept. Really makes me want to start playing with frequency domain stuff. Also, the reveal of the mapped video visualization... the whole series is worth watching just for that moment.

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

#27

Post by maxbond »

skupig wrote: post #26
maxbond wrote: post #11

Earlier quoted context omitted.

I think it's less about some people being especially good at math than mathematics education being especially terrible and uninspiring. 3blue1brown's approach to math pedagogy had really changed how I'm able to see math and to understand it's profundity (as someone who didn't get any further than you, it sounds like, in formal math education [I never took calculus in school.]). https://youtube.com/playlist?list=PLZHQ…

The second playlist is great, thank you! As someone with near zero math knowledge, it was very exciting learning that imaginary numbers are a beautiful and intuitive concept. Really makes me want to start playing with frequency domain stuff. Also, the reveal of the mapped video visualization... the whole series is worth watching just for that moment.

That's lovely to hear!

If you're interested, here are some videos about Fourier analysis:

https://youtube.com/watch?v=spUNpyF58BY

https://youtube.com/watch?v=h7apO7q16V0

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

#28

Post by skupig »

maxbond wrote: post #27
skupig wrote: post #26

Earlier quoted context omitted.

The second playlist is great, thank you! As someone with near zero math knowledge, it was very exciting learning that imaginary numbers are a beautiful and intuitive concept. Really makes me want to start playing with frequency domain stuff. Also, the reveal of the mapped video visualization... the whole series is worth watching just for that moment.

That's lovely to hear! If you're interested, here are some videos about Fourier analysis: https://youtube.com/watch?v=spUNpyF58BY https://youtube.com/watch?v=h7apO7q16V0

I was hoping one of those links was Reducible! :-) His videos on image encoding are fantastic.

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

#29

Post by verteu »

JKCalhoun wrote: post #10

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…

Don't be intimidated! The person who first invented complex numbers called them "useless" and "mental torture."[1] Subsequent mathematicians have simply gotten used to them.

You'd invent them, too, if you spent a few weeks building a computer program to output the values of `t` that make `t^3+pt+q=0` (when `4p^3 + 27q^2 [1] https://en.wikipedia.org/wiki/Complex_number#History [2] https://en.wikipedia.org/wiki/Cubic_equation#Cardano's_formu...

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