Group theory 101: How to play a Rubik’s Cube like a piano - Michael Staff

Mathematics explains the workings of the universe, from particle physics to engineering and economics. Math is even closely related to music, and their common ground has something to do with a Rubik's Cube puzzle. Michael Staff explains how group theory can teach us to play a Rubik’s Cube like a piano.

Lesson by Michael Staff, animation by Shixie.

[RacecarsAndRicefish]

I'm a musician and I can solve a rubik's cube and I understand what you're saying but I don't understand what you're getting at

[abouttime]

I don't understand any of this but the animation is pretty

[ronk]

It would be really cool to have a cube that plays music as you solve it.

[pianoaround]

Very informative. Now I'm going to try and figure out how to play my piano like a rubix cube :-)

[ZoggFromBetelgeuse]

No wonder so many commenters are confused! This video mixes up two distinct things:

1) Positions of the Rubik's cube (or its 2x2 equivalent)
2) Turn actions which change positions. (Simple or combined actions, modulo identical results.)

Also, the word "group operation" is applied to turn actions (for ex. at 0:44), but in the context of Group Theory, it means the addition of turn actions.

I am aware that you *can* identify the turn actions with positions, if you chose a "start position" and identify each turn action with the result of applying said action to the start position. But by implicitely doing so without telling, you only confuse the viewer.

[kevingao]

If the chords get more harmonious the closer the cube gets to being solved, could we make software that analyzes how dissonant a chord is for every turn action, and then display a progress bar that updates every turn? That way a cuber could know how close he is to finishing or if he made a wrong move. (I guess he already knows this by looking at the colors, but it would still be cool!)

[EdsCollegeLife]

I have always told my friends about this and they have always thought in crazy! Music is always linked to math in some way and personally for me it's so difficult to explain in theory but this video explains it so well!

[famsu]

So a talented pianist can solve random rubic cubes to creates random melodies, and eventually become the next Mozart.

[kcwidman]

You need to animate all your videos this way. It's so visually appealing!

[luisvillegas]

This is a brilliant video. It probably is the best thing I've seen in a while! Kudos for introducing lesser known mathematical concepts through examples anyone can relate to.

[DiggOlive]

This has to be the most effort that has ever been put into an introductory explanation of group theory. 🙂

[azureorbit]

Best comment community I've found in a while. Piano players, rubik's cube solvers, mathematicians, and people who are just hilarious

[ankurbanerjee]

4:18 - Hold on programmers, it's C# written on top of the cube

[tatianatub]

i want to make a program to do this now

[andrewdodo]

Am i the only one who didn't understand anything?

[victordelmastro]

I loved the way you broke it down and included chord theory. Way to go.

[ParisDorn]

All these non-cubers rubin, rubic, rubic's cure, rubix's, anarubik, robik   C'mon guys

[nept]

He makes associativity sound like a commutativity condition by pronouncing
(1+1)+1=1+(1+1) as "one plus two equals two plus one" which I think is
very misleading. And then he also defines a general group with a plus,
as if it was commutative. Granted, the rotation group of a square is
abelian (indeed, it is cyclic) but I have a hard time believing that the
full rubiks group is. And a general group (which is what he claims to
define!) is certainly not.

[ajeeshmk]

So there are 43 quadrillion configuration of musical manipulations which can be made, But still some songs seems to be same.

[late_arvie]

The animations were just.. I can't even explain.
Smooth, beautiful, professional. Amazing.
Great video.