Is cubing mathmatical?

[kirtpro]

just saying they have similarities,

i remember pythagoras in the sentence, "a squared plus b squared equals c squared."

 

[Cubenovice]

If with 'cube theorist' you mean people like yourself, Lucas, Chris, Per, Cmwolla etc then I agree

They're all certainly theorists in the wider sense that they pose puzzle-theoretic questions and attempt to answer them, but not all of them use much that's actually theoretical, and I'm sure some don't know much group theory. To pick on Cmowla, he's much more of an experimentalist. Not that I have any problem with that in itself; doing often produces more useful things, and he's definitely done some cool stuff. But ad-hoc constructions and computations barely qualify as theory. More theory could help him become a more productive experimentalist, if only by pointing out provably fruitless paths of exploration....

[edit]Stuff

To summarize, many interesting problems for speedcubers are hard and more computational than theoretical because they're mathematically unnatural. There isn't much theory to know for cubing, say some group theory (say enough to fully understand the above) and some standard counting tools, and otherwise large computations will often be necessary. But knowing this much theory will help you organize and effectively carry out these computations. In other words, cube theorists are by nature be more experimentalist than theorist, but the best experimentalists are those well-versed in theory.
[edit]

Good stuff!

Note however that my post was a response to qqwref's "A good cube theorist will typically have a very strong intuitive grasp of the group theory that applies to twisty puzzles. "
Neither of us claimed that they use much that's actually theoretical and / or know much group theory.

Seriously, I think your post can be considered a thread closer. Very well put

 

[The Bloody Talon]

IMO, speedsolving doesn't involves math,
but discovering algorithms involves math.

Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, space, structure, and change.
-wikipedia

 

[Gabo]

IMO, speedsolving doesn't involves math,
but discovering algorithms involves math.

Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, space, structure, and change.
-wikipedia

Agree... if you do math you MUST understand what you are doing, and most cubers don't understand it at all. Thats why when you learn math you start with the basic stuff and don't learn the whole bunch of formulas at once, while you can go and learn the whole friedich method and solve the cube with no to much problem (it will be realy slow, but you can ). You could use the math formulas, but if you don't know what those mean, it's barely useless.

 

[dada222]

Yes. Cubing is mathematical because it involves thinking logically and solving problems. You don't actually calculate anything but it's not about that. Everyone thinks mathematically every day - whether they knew any math or not. For example choosing the fastest way to work or school is mathematics. Please read this and see for yourselves: http://en.wikipedia.org/wiki/Algorithm

Oh come on, maths is a humanly defined branch of science - saying that everything we think involves maths is beyond overt. So is suggesting that everything that involves change is based on maths (to the posts above me).

but discovering algorithms involves math.

Wrong. I've "discovered" several algs in my two year "career" and even if I didn't know how to count I'd still have done it. For example, solve F2L and orient the last layer, make some random turns, then fix it so the first two layers are solved again. There, there you have an OLL. It's not rocket science.

Sort answer: no.
Long answer: nooooooooo
It just sounds cool to non-cubers.

My knowledge of group theory specifically is severely lacking. I've never really needed it on my adventures and therefore never bothered to educate myself on the subject. Any maths that I'm required to do for cubing activities is almost always trivial.

Just curious and you don't have to answer lol: "adventures"?

 

[The Bloody Talon]

Wrong. I've "discovered" several algs in my two year "career" and even if I didn't know how to count I'd still have done it. For example, solve F2L and orient the last layer, make some random turns, then fix it so the first two layers are solved again. There, there you have an OLL. It's not rocket science.

Sort answer: no.
Long answer: nooooooooo
It just sounds cool to non-cubers.

lol
well, nooooooooooo to you.
how come you discovered an algorithm and you don't know what change it does to the cube? do you know when to use that algo?

if you discovered an algo, you should know what certain change it do.

math is not all about counting.

 

[Christopher Mowla]

how come you discovered an algorithm and you don't know what change it does to the cube?

He made it very clear how: "random turns." When one does random turning, he or she does not care about the details (the cycles) he or she is actually doing to the cube.

Also, with all of the algorithms I have discovered, I never used math to find anyone of them. One who does not know mathematics well can very well interpret every move in every algorithm I have made strictly in terms of moving pieces. I don't consider the definition of math from Wikipedia you posted earlier to have any grounds whatsoever in an argument that says we use math to create algorithms because, whenever anyone says they use math to solve any type of problem, they are using equations, inequalities, relations, functions, arithmetic, and some branch of mathematics (e.g. Discreet Math, Calculus, Linear Algebra, etc.).

The only "math" one has to really know to make algorithms is to know the difference between an odd number and an even number, which is so simple, it's redundant to use it as an example of how one uses math to create algorithms.

Like dada222 said, we can even use less effort than even considering an odd number of turns or an even number of turns by simply doing random moves.

Don't get me wrong, it's always better if we have at least an educated guess to build on so that we are more productive in creating algorithms, and we definitely have to be knowledegable to find algorithms efficiently and systematically. However, even at that level, no math is really required.

As some have probably already said, math can be used for calculating case counts, creating formulas describing a puzzle, etc.

 

[cubecraze1]

more memorisation but is memory linked to maths

 

[The Bloody Talon]

He made it very clear how: "random turns." When one does random turning, he or she does not care about the details (the cycles) he or she is actually doing to the cube.

"trial and error". very important in mathematics
but if you discovered algorithm X by trial and error, you should study what it do.
If you don't, you couldn't use it again.

for example.
I discovered R U R' U R U2 R' by trial and error.
and by studying that I learned that it rotates three edge pieces clockwise.
and by that, with proper orientation, I discovered that you could properly orient all the edge pieces of the last layer by performing at most two R U R' U R U2 R' algorithm.

expanding my knowledge by starting with trial and error, clearly, It is math.
or are we discussing different things?

what is your definition of mathematics?
you don't believe wikipedia?

Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation.
- Britannia Concise Encyclopedia

mathematics, deductive study of numbers, geometry, and various abstract constructs, or structures; the latter often "abstract" the features common to several models derived from the empirical, or applied, sciences, although many emerge from purely mathematical or logical considerations. Mathematics is very broadly divided into foundations, algebra, analysis, geometry, and applied mathematics, which includes theoretical computer science.
-Columbia Encyclopedia

 

[Christopher Mowla]

"Trial and error" is nothing more than a "science experiment," not mathematics. What you described is nothing more than the scientific method. As for my definition of mathematics, I'll stick to defining only applied mathematics because you are claiming to apply skills of mathematics to solve a real world problem.

Mathematics is the tool by which one can model a real life phenomena. Once the phenomena is modeled with mathematics (see the different branches of applied mathematics if you need a specific example), it is "translated" into mathematical language. Once we have translated a problem properly to the language of mathematics, we do not need to refer back to the object we modeled to help us solve the problem we wish to solve about that object. Rather, we refer back to the object after we have made calculations with the math, and we want to see how the mathematical solutions can be interpreted back in the real world. That is, we "translate" the math solutions back to reality.

We know we are using a branch of applied mathematics to solve a real world problem when, after we have successfully modeled _ with mathematics, we are able to use that branch of mathematics we modeled _ with (which does not involve experimentation, rather, a clear list of axioms, theorems, algorithms, and arithmetic) to find any solution we wish. Since _ is now in mathematical language, we can even consider how the other branches of mathematics are related to the initial branch of mathematics we chose to model _ with, and possibly discover something new about _ which we didn't know from experimentation already.

If we have properly modeled _ with some branch of mathematics, then we can calculate everything possible there is to calculate with that branch of mathematics. Once all calculations have been made, we can then look back at _ and try to interpret what the math is telling us about _.

As a simple example, I can model what my grade will be in a class by modeling the restrictions and conditions the teacher enforces in his/her syllabus with an equation. From this equation, I can calculate my grade with zero experimentation. With this equation, I can calculate every grade that a student can possibly get if I want to. I can exchange what is a variable and what is a given.

On the other hand, relating to "trial and error," if I didn't know how to express my teacher's grading system with an equation and I have a C average before the final exam, I would have to experiment to see exactly what I would have to make on the final to make an A, B, or keep the C.

In summary, using mathematics to solve a problem _ , relieves one from having to experiment to find solutions. In effect, mathematicians dream of being able to model a real life situation with an equation because it not only relieves them from having to experiment, but it gives them assurance (assuming that they properly modeled the situation with math) that any conclusions which can be drawn from the results of the math are correct (that is, if the solutions the math yielded can be translated back to reality).

See the difference?

 

[The Bloody Talon]

this will end this topic.

http://en.wikipedia.org/wiki/Group_theory

 

[Christopher Mowla]

this will end this topic.

http://en.wikipedia.org/wiki/Group_theory

No. You in particular are NOT using group theory to find algorithms. Group theory is based on very abstract concepts and theory, quite contrary to raw experimentation.

Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation.
- Britannia Concise Encyclopedia

What is meant by "logic" is a systematic approach using truth tables to determine whether a statement is true or false (or compositions of statements are true or false). When you experiment with moves on the cube, you are unsure of whether something is true or false: you have to experiment first to see if it is true. I don't think you used truth tables to find out what you did about the <U,R> algorithm, did you? Here's a better question, did you even know that "you could properly orient all the edge pieces of the last layer by performing at most two R U R' U R U2 R' algorithm" before you experimented with R U R' U R U2 R'? No, you used conclusions of your experimentation. You're not even using "if this is true, then that is true" from mathematical logic in your observations of the <U,R> algorithm. Why?

If A, then B. Okay, well, if A = R U R' U R U2 R', then what is B? Do you know what B is before you experiment with A? No, you didn't. Math is used to figure out a clearly defined problem.

Mathematics is very broadly divided into foundations, algebra, analysis, geometry, and applied mathematics, which includes theoretical computer science.
-Columbia Encyclopedia

Analysis is referring to Advanced Calculus, not simply "analyzing what you have from experimentation."

 

[The Bloody Talon]

what's with your self interpretation of every fact I post?

I don't think you used truth tables to find out what you did about the <U,R> algorithm, did you?

duh! do I really need to make truth tables? lol


Let me know what you think of this sentence:
If Rubik's cube is not mathematical, no robot could ever solve it.

 

[ric d]

In a month or two I am talking with a college math professor about how it is mathimatical. I'm not sure how it's mathimatical yet, but i'll come back to this thread after I talk to him.

 

[xabu1]

Let me know what you think of this sentence:
If Rubik's cube is not mathematical, no robot could ever solve it.

so, if I make a robot to open a cupboard, and nothing else
opening cupboards is mathematical?

 

[The Bloody Talon]

so, if I make a robot to open a cupboard, and nothing else
opening cupboards is mathematical?

hahahaha!
bwahahaha!

cool cupboards!
what is that? a puzzle cupboard?
does it involve much thinking to open it?!
LOL

 

[Christopher Mowla]

what's with your self interpretation of every fact I post?

I'm surprised no one who actually knows math hasn't told you that I am not "self interpreting" anything about what I mentioned.

duh! do I really need to make truth tables? lol

Of course you don't. That was a rhetorical question illustrating how little (none in fact) math YOU, me, and most others use to solve a puzzle.

Let me know what you think of this sentence:
If Rubik's cube is not mathematical, no robot could ever solve it.

1) I never argued that the cube isn't mathematical, and anyone (well, others besides you, obviously, since you have gotten the idea that I have somehow) can see that since I didn't edit my posts like you did. You first were absolutely determined that a human must know how moves change a cube before he or she could make an algorithm, even when dada222 mentioned (not that he even was debating whether or not a person needs to understand moves before he or she makes an algorithm) that he did random moves once for an OLL, which in turn definitely did not require any mathematical skill (not that he doesn't have mathematical skills, rather he did not need to use any that he has to do what he did). (I'm sure he has used more constructive trial and error on other occasions, however). I happened to also mention in that post that humans do not need to use math to make any algorithms (post47). The only time that a human could possibly need to use math is when he or she is trying to find an optimal solution and creates an optimal solving algorithm (e.g., like the 2-phase algorithm like Herbert Kociemba made).

2) I defined what applied mathematics was in the following post and explained that when humans use trial and error in the manner you did with your <U,R> discovery, they are not using any form of mathematics whatsoever.

3) A robot does not need to know a bit of group theory to solve a cube, as it can be programmed to select a pre-made algorithm from a table of thousands (probably more) algorithms based on the cube position it senses with its sensors. Its actions are governed by programming and nothing more. That being said, yes programming directly corresponds to mathematical logic, but, as I've said, that's just to get the robot to move and to match the scrambled cube case with what was put in its database: it does not necessarily need to be an optimal solver itself or know any math behind the cube.

I have programmed my Ti-83 plus calculator to solve an orbit of wing edges in the last layer of a big cube (K4 style) doing just this. Did I or the calculator have to know any math that may be associated with the cube to do this? Well my calculator sure didn't, and the little math that I needed to know had nothing to do with the algorithms I typed into it for it to select for specific cases.

4) Yes, Herbert Kociemba and others who made optimal solvers did use math to some degree (predominately programming I presume), and there are ways to interpret each move on a cube in terms of group theory for sure. But again, this wasn't my argument at all.

 

[The Bloody Talon]

"humans do not need to use math to make any algorithms"
-speak for yourself.

learning an algorithm (which can be get by experimentation) and modifying it (it can be "set up" move or performing it twice or thrice) to come up with a new algorithm is already a mathematics.
N perm + a certain set up move = J perm.
doing a certain OLL algo *2 = another OLL algo
G perm *4 = 0
tell me, is it math? or still not?

and please don't expect me to show you numbers and tables.

about the "robot" thingy, it is just an exaggeration of my point. It proves that an algorithms for solving a whole cube can be achieved through mathematics.
so a certain application of mathematics can solve the last layer, or orienting edge pieces.or swapping 3 edges. And yes, human can't compute it by just facing a cube.

 

[Gaétan Guimond]

Have an aptitude and the knowledge of math is two worlds. We can draw comparisons with the cuber and chess gamer. World champion Carlsen does'nt have much interest and knowledge in math

I love this page ....

The effect of math and chess
The Chess Academy, Chicago, USA
Research studies have shown that chess can be used as an effective game-based teaching method. However, all the past studies used chess as a separate instructional tool. There were no math contents in chess instruction provided and there was no math and chess integrated workbook used. This study examined the effect on pupils’ math scores when a truly integrated math and chess workbook was used as an instructional practice workbook. The results show that the integrated math and chess workbook significantly increased pupils’ math scores between pre-tests and post-tests among grade 1 to grade 8 pupils.

Introduction
Research papers have demonstrated that chess instruction improves analytical reasoning, problem solving skills, and academic achievement (Chrisiaen & Verholfstadt (1978); Frank & D’Hondt (1979); Smith & Cage (2000)). Research conducted by Gaudreau (1992) shows no significant differences among the groups on basic calculations. These research studies point to the direction that chess has strong effect on improving children’s cognitive ability than their arithmetic computation ability. By teaching math and chess as two separate subjects, children do not have opportunities to work on basic arithmetic operations using acquired chess knowledge, this may explain why by playing chess, it may not statistically significant improve children’s basic arithmetic computation ability.

How to maximize the benefits of chess instruction in such a way that not only chess benefits children’s cognitive development, but also their computation ability? All the past chess instruction research studies have used chess instruction as an independent teaching tool and it is not truly integrated with math instruction. The author Frank Ho created a math and chess integrated workbook. The theoretical basis of how math and chess are integrated has been published by Ho (2006). We believe that with the creation of truly integrated math and chess workbooks, pupils will be able to increase their computation ability by working on these math and chess integrated workbooks. This is particularly important for those children who have no interest in playing chess, but they could still get benefit of chess instruction by working on math and chess integrated workbooks.

No research has been done before on the effects of using math and chess integrated workbook, this study will compare the effect of pupils’ math computation ability before using the math and chess integrated workbook and after using it to see if there is a significant difference.

 

[Christopher Mowla]

"humans do not need to use math to make any algorithms"
-speak for yourself.

No comment.

learning an algorithm (which can be get by experimentation) and modifying it (it can be "set up" move or performing it twice or thrice) to come up with a new algorithm is already a mathematics.
N perm + a certain set up move = J perm.

People can use math symbols to abbreviate words used to describe many things. For example, I can use this same argument to "prove" that everyone who speaks a language is using mathematics because "one phrase" + "another" = a sentence. Not to mention that many languages use verb conjugations. We have conjugation (set up moves) in cubing too, so language is definitely mathematics, right?

Take cooking as another example. "One ingredient" + "another ingredient" + ...+ "a final ingredient" constitutes a particular food type. Is cooking mathematics?

My (current) point is, by your definition, everything is mathematics, seriously.

doing a certain OLL algo *2 = another OLL algo
G perm *4 = 0
tell me, is it math? or still not?

Yes, those two examples, as well as the ones above can be interpreted mathematically (which I have already said in point #4 in my previous post), but what good, for example, does repeating an algorithm until the identity is reached help you make algorithms? Repeating that OLL alg twice to get another OLL alg is experimentation yet again.

about the "robot" thingy, it is just an exaggeration of my point. It proves that an algorithms for solving a whole cube can be achieved through mathematics.

You are right, but no this is not what I was debating with you, as I HAVE JUST SAID in point #4 of my previous post.