Uses of math in cubing?

[StachuK1992]

A discussion meant to be along-side this.

Please take note of what a proper definition of 'mathematical' is, and when explaining how mathematical the cube might be, or rather how useful mathematics is when dealing with the cube, note which branch of mathematics is used.

I'm hoping macky or someone will take this thread from me.

 

[Stefan]

This might get rid of the problem of people voicing an opinion based on a very limited understanding of math, but the basic problem remains - debating whether or how much cubing is "mathematical" is about as futile and pointless as debating whether cubing is a sport. There are and always will be different people with different more or less valid viewpoints, so we'll never reach a conclusion and the question itself is moot. Plus I find the objection "but I personally happen to not think of it as math so it's not math" rather irrelevant. So instead, I suggest a one-sided constructive question like "What math can be used/seen in cubing?", eliminating the naysayers. This won't answer the original flawed question, but might lead to more interesting information.

 

[StachuK1992]

Okay then, let's do that.

; New topic: what mathematics can be applied to the Rubik's Cube?

 

[macky]

(I'll delete this post later.)

This isn't what I had in mind, but I hope it'll make an interesting list. Change the title to "Uses of math in cubing" or something.

My question really concerns "The relation between math and cubing."

The public views cubing as a mathematical activity. This is true, but to a limited extent. On one hand, the cube has a group-theoretic description, concepts such as commutators and conjugation are useful for solving, and the cube has as a result sometimes been used to teach basic group theory. On the other hand, speedsolving rarely treats the cube mathematically, the best algorithms often have no clear theoretical interpretation, and even interesting cubing questions of a more mathematical nature have often required large computations.

This much is old news. Now, can we say something more nuanced and get closer to the true relation between math and cubing?

I'll make a separate thread when I have a good opening post.

 

[Stefan]

The public views cubing as a mathematical activity.

Most non-cubers say it is.

I'm not sure about that (I rarely talk with non-cubers about cubing), but ok, let's assume that.

Then I have some questions first:

1) Why do non-cubers think so, and what do they mean with it?
2) Are they right or wrong? (This can be answered once we know/assume what they mean)
3) Do we care? If so, what do we want to do?

My thoughts:

1) If non-cubers think cubing is mathematical, I'm sure they don't suspect group theory and commutators etc, cause they don't know that stuff. More likely what they mean with "mathematical" is that it's a puzzle, a somewhat abstract structured thing, they're supposed to solve it, there's one clear answer, and it's hard. It's not like literature class where anybody can just lalala write some text and then the teacher's mood decides how good it is. It's much more like math class, precise questions with precise answers that can be found systematically. Whether it really *is* "math" depends on the viewpoint and is actually irrelevant. It's just a label, what really matters is what people mean. Simply calling it math or not doesn't help anyone.

2) I think it's indeed similar to what they're used to from math class. Many just seem to overestimate how hard it is or not make a distinction between solving it yourself and just learning from someone else.

3) I don't really care much, but if they tell me that it's so hard and that someone solving it must be some genius then I feel the urge to correct them. I clarify that probably most of us have learned it from someone and that they can, too (though I encourage them to try it on their own first). I tell them that they talking with others is already a much bigger intellectual achievement, proven by the fact that people can learn solving a cube in hours and that it takes much longer to learn a language. That the only reason they don't think so much of their talking ability is that they're used to it. I thought about some more analogies as well, maybe I'll post more later.

Summary:
- What math we can see in cubing is an entirely different question than what math-aspects non-cubers are thinking of.
- They're about right, it does have math aspects. When they say/ask "math", we should ask what they mean. When they think it's too hard and they're too dumb, we can explain they're wrong.

 

[Mike Hughey]

I think another interesting related question is "Why does the cube tend to attract people who like math?"

I remember that a question was asked on this forum about the William Lowell Putnam math competition, and I was surprised by how many people said they had competed before. And many of them were very high scorers on the test! (Not me, I only got 9/120.) Only about 4000 people take the test each year (well, more like 2000 way back when I took it ), and you must be from the USA or Canada and in college to take it. And as tough as the test is, you really need to love math to want to take it. So why is our community so high in Putnam competitors? Don't we clearly skew towards liking math much more than the general population?

 

[Vincents]

I think another interesting related question is "Why does the cube tend to attract people who like math?"

I remember that a question was asked on this forum about the William Lowell Putnam math competition, and I was surprised by how many people said they had competed before. And many of them were very high scorers on the test! (Not me, I only got 9/120.) Only about 4000 people take the test each year (well, more like 2000 way back when I took it ), and you must be from the USA or Canada and in college to take it. And as tough as the test is, you really need to love math to want to take it. So why is our community so high in Putnam competitors? Don't we clearly skew towards liking math much more than the general population?

My theory: Most people taking the Putnam have probably taken a course in Group Theory, where the Rubik's Cube may be an example of a real life application. Some may even learn to solve it, and just want to get faster, possibly looking into university Rubik's Cube clubs to connect with people who know about "speedsolving".