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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]

#11

Post by maxbond »

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=PLZHQObOWTQDPD3MizzM2xVFit...

This is also a great series of videos about how, like it says on the tin, the imaginary numbers are real:

https://youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJ...

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

#12

Post by Y_Y »

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…

(In the following, mathematical uses of terms are given in "quotes".)

So many of the names of mathematical objects are arbitrary and I think that can be harmful. "Real" numbers are just as imaginary as "imaginary" ones! They both have use in physics as models for natural phenomena, but neither are real like an atom. You may still argue that "natural" numbers are real because we really can have n of something, but general real numbers can't be written down or computed or used to divide physical space and time as we understand them now. The names are mostly historical artefacts that serve as mnemonics, nothing more.

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

#13

Post by wheels »

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 numbers are important in a lot of real world applications. One of the most important ones at the moment is in quantum mechanics and quantum algorithms. You can't model quantum algorithms without imaginary numbers.

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

#14

Post by [deleted] »

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…

[deleted]

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

#15

Post by whatshisface »

ummonk wrote: post #7

Not exactly "physical" in the same sense as a normal Rubik's cube, since there isn't any physical restriction that makes illegal moves of taking it apart and putting it back together anymore difficult than performing legal moves.

The magnets are pretty complex, I am not sure if that's true. (I can see the imprints of at least four magnets per side.)

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

#16

Post by [deleted] »

wheels wrote: post #13
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 numbers are important in a lot of real world applications. One of the most important ones at the moment is in quantum mechanics and quantum algorithms. You can't model quantum algorithms without imaginary numbers.

[deleted]

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

#18

Post by 123pie123 »

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…

this help me a little (a lighter easier intro) https://www.youtube.com/watch?v=cUzklzVXJwo by veritasium

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

#19

Post by friendzis »

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…

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

No. Complex numbers are "simply" neat construct to represent 2D coordinates algebraically - i.e. without matrices.

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

#20

Post by maxbond »

friendzis wrote: post #19
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…

> Wait, what? So complex numbers have a real-world analog in constructing an FFT — a "real" algorithm that does real work? No. Complex numbers are "simply" neat construct to represent 2D coordinates algebraically - i.e. without matrices.

Complex numbers behave quite differently than vectors/matrixes, and their discovery wasn't motivated by needing to represent coordinates. They were discovered (or invented, for the nonplatonists) in the process of resolving the paradox that 3rd degree polynomials must have at least 1 (real) root (because they always stretch out in opposite directions, and so cross 0), but you end up needing to square root a negative number to solve for it (the paradox being, this was thought to be impossible, since the square of any real number is positive).

Their existence is a natural consequence of the rules of the algebraic operations (addition, subtraction, multiplication, division, powers and logarithms); they aren't incidental, they are integral. Without imaginary numbers, the algebraic operations aren't closed.

(This being a brief summary of the thesis of the videos I linked in a sibling comment.)

That being said, they are useful as coordinates, as well.

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