The Rubik's Cube is a Calculator

This video is an exploration of ways to apply modular multiplication to twisty puzzles.

Reference: Contemporary Abstract Algebra - Gallian

[EvilSandwich]

Man. Abstract Algebra is a hell of a drug.

[excelmaster]

0×0
"Remove the stickers"
*removes the stickers*
"Remove the stickers"
*starts panicking*

[.]

when you can't bring a calculator to a test

[danielleidulvstadpereda]

I've been speedcubing for quite a few years, and this is by far the coolest thing involving Rubik's cubes I've come across!

[DarkAlgae]

by tricking me into being entertained by modular arithmatic, you earn my subscription.

[thegnugod]

My gosh doing 3*67 and watching the cube turn back to its starting position was amazingly satisfying

[memetech-]

1:05 hey, I *AM* thirsty, I should drink water.

[rarebeeph]

is this just a sneaky introduction to group homomorphisms?

[ProactiveYellow]

Working through this is an interesting exploration of the normal subgroups of the rubik's group. It must be a challenge to make sure the algorithms for the larger cyclic group elements end up commutative.

[PaulFisher]

I’m not very skilled with the Rubik’s Cube so I couldn’t handle the complex algorithms for 10, but I have found one for modulo 2:

1: do nothing

and the decoding process:

• cube has been destroyed: 0
• cube exists: 1 (orientation unimportant)

[romywilliamson]

I love that you are teaching the essenece of group theory and elementary number theory to cube-enthusiasts, without ever saying that's what you are doing :)

[voliol]

Ah, the cliffhanger. Looking forwards to the next video!

[art-of-imagination]

I'm a cuber as well as a math student but I've never thought anything like this. I appreciate you for giving this kinda mind-boggling aspect to see or use the mod. ❤

[vaughnp]

I've spent far too much of my life watching cubing videos on youtube, and this has to be one of my all-time favorites! Thank you for making this - it's excellently done :)

[kyanilcauli]

When the obscure theorems in Dummit and Foote finally appear to you in a visual form. Bless you. You just made my day.

[tl_dragonstars]

I was brushing teeths while watching, this :
=> 1) I have to watch the video a second time
=> 2) Iwon't be able to sleep because of too intense curiosity

[SamuelLiJ]

Interesting video. You can actually do all four elementary operations (addition, subtraction, multiplication, division) mod 10 on the 3x3, where defined and invertible, for the dumb reason that the symmetric group S10 embeds into the Rubik's group. So you just perform the action corresponding to how the elements 0 through 9 permute. (Actually S12 fits as well.)

Note that you can add or subtract any number, but only multiply and (modular) divide by units.

[amogus]

This is why Rubik's cubes are loved by many. They are more than some toys.

[Higgsinophysics]

A math video that also reminds you to drinks water. This is just the summit of youtube. Loved the video

[MooImABunny]

I'm relearning group theory right now and I'm delighted that this video came out right now 😁
Also, embedding an Abelian group within the Rubik's cube in order to multiply numbers mod n is stick is a wild idea. I know these (non-trivial) subgroups exist, I know how group isomorphism works, but there's a whole other set of steps I'd need to do to come to the idea "I'll use the Rubik's cube to compute ab mod n"