Pseudo God's Algorithm Human nxnxn Rubik's Cube Solving Method Created

[Christopher Mowla]

Agreed, people who just talk about how awesome what they did is but never make anything available for others are usually lying and just want to get the recognition without actually doing the work. For reference, see every thread started by unsolved ever.

Having been around as long as you have, I'm surprised you don't remember a similar situation I had in the past. (I deleted a lot of my posts from that thread from pure frustration, but you can see what I wrote because people quoted me.) Then I finally released my work in my thread Methods for Forming Parity Algorithms.

I pursued my work even further to make the 4x4x4 parity algorithms wiki page what it is today.

In short, I've been in this situation before. I claimed to do "the impossible", people doubted me and called me a liar, and then when I did the impossible before their eyes, no comment and no apology.

If anyone thinks the amount of work it took for me to find all of those parity algorithms by hand was a lot, it was nothing in comparison to what I have done in the last two years of solid research. It was very hard work, considering that I was writing a proof for which every word I am responsible for.

Before inventing this method, I regret to say that I first effectively solved half of all 3x3x3 corner and edge positions by hand. (Ponder on that for a moment.) I literally saw the nature of every possible position. After that point, I eventually stumbled upon this solving method. It's bittersweet really.

I started this thread in a help sub-forum asking for help. If anyone wants to continue to post claims of me lying or begging me to release my method on the web (when I specifically said in my post that I do not wish to do so), I will ignore you without any thought. (I hope you can understand now why.)

However, if someone wishes to actually post help of how I can obtain my goal (like cmhardwk and rowan have), I will appreciate your effort.

 

[blade740]

Having been around as long as you have, I'm surprised you don't remember a similar situation I had in the past. (I deleted a lot of my posts from that thread from pure frustration, but you can see what I wrote because people quoted me.) Then I finally released my work in my thread Methods for Forming Parity Algorithms.

I pursued my work even further to make the 4x4x4 parity algorithms wiki page what it is today.

In short, I've been in this situation before. I claimed to do "the impossible", people doubted me and called me a liar, and then when I did the impossible before their eyes, no comment and no apology.

The negative feedback before was no different than it is now. Posting claims about your work, but refusing to post any of the work itself, is not the way cubing discoveries have traditionally been handled. Given your previous posts, I don't doubt that you've done what you claim, but the way you're going about it rubs many people the wrong way.

For comparison, see the work done by Rokicki, et al, at http://cube20.org/. All of the information is posted, freely available. Source code, tables of results, and a wealth of information.

However, if someone wishes to actually post help of how I can obtain my goal (like cmhardwk and rowan have), I will appreciate your effort.

What exactly is your goal? To teach a university course on your work? To publish a paper? Write a book? Your first post isn't completely clear to me.

More importantly, how does withholding information help you achieve this goal? Your posts seem to indicate that you have a large amount of material already written. Is the work not complete? Is there some sort of assistance that you need in order to finish it? What is stopping you from publishing the work yourself online?

 

[tseitsei]

Yeah. This is BS... If you actually have a great new method just release it already like everyone else does in the cubing community if they come up with something new and cool .

That's IMO one of the best things about cubing community. Nobody is trying to hide their findings and profit from them, but instead publicly release those findings and try to help others to get faster with it too...

EDIT: I'm not calling you a liar or anything like that. I know that you have done some impressive stuff before and I believe that you have a method that does what you say it does. I just find it stupid that you don't actually post the method here for us to freely learn and experiment with it. Why do you want to keep it as a secret?

 

[stoic]

@cmowla: have you had any success or feedback from anyone you have contacted so far?
Are any of the publishers of books on the cube of any use to you? What about the authors?
I'd also consider those luminaries of cubing who have links to education - Singmaster, Kociemba, Fridrich?

 

[qqwref]

Having been around as long as you have, I'm surprised you don't remember a similar situation I had in the past. (I deleted a lot of my posts from that thread from pure frustration, but you can see what I wrote because people quoted me.) Then I finally released my work in my thread Methods for Forming Parity Algorithms.

I pursued my work even further to make the 4x4x4 parity algorithms wiki page what it is today.

In short, I've been in this situation before. I claimed to do "the impossible", people doubted me and called me a liar, and then when I did the impossible before their eyes, no comment and no apology.

To be fair, if what you are claiming here is real, it is an order of magnitude more impressive and important than your parity algorithm work.

Before inventing this method, I regret to say that I first effectively solved half of all 3x3x3 corner and edge positions by hand. (Ponder on that for a moment.) I literally saw the nature of every possible position. After that point, I eventually stumbled upon this solving method. It's bittersweet really.

Uh, what?

 

[StachuK1992]

I believe he's claiming to have gone through half of the 8! * 3^7 = 88M corner cases.
This may be lowered by some symmetries though, which would make it less cray.

 

[TDM]

I believe he's claiming to have gone through half of the 8! * 3^7 = 88M corner cases.
This may be lowered by some symmetries though, which would make it less cray.

Yes, by choosing one corner as fixed you can reduce the number to 7!*3^6 (or is it 7!*3^7 still?). But that's still a huge number. I'm sure there are still ways to reduce the number further.

 

[Christopher Mowla]

What exactly is your goal? To teach a university course on your work? To publish a paper? Write a book? Your first post isn't completely clear to me.

The paper/book is already written and all supplement material is written and all Mathematica code (which is well documented and commented) is written.

I did think about publishing a paper, but I was told that no journal will publish such a long paper.

Therefore, I wish to create a university course. I also clearly wish to publish my book to accompany the course.

The only item which remains is instructional videos.

@cmowla: have you had any success or feedback from anyone you have contacted so far?
Are any of the publishers of books on the cube of any use to you? What about the authors?

I have sent out many emails and have gotten few responses. The typical responses thus far are basically "I don't know", "I'm not interested in the cube anymore to help you", and "your work goes far beyond the scope of my course".

I'd also consider those luminaries of cubing who have links to education - Singmaster, Kociemba, Fridrich?

I haven't sent emails to them yet. I'll give it a shot.

I believe he's claiming to have gone through half of the 8! * 3^7 = 88M corner cases.
This may be lowered by some symmetries though, which would make it less cray.

Exactly. I am referring to my single commutator proof. I reduced the number of even permutation corner positions to a mere 1002 cases and the even permutation middle edge positions to 3351 cases. (I have mentioned this in the past in Per's thread.) I show all of the work in my book about how I did this, and I have Mathematica code which proves this true from more than one direction (when only one direction is necessary). However, it can also be verified by hand in a "reasonable" amount of time, as I also explain in my book.

EDIT:

Yes, by choosing one corner as fixed you can reduce the number to 7!*3^6 (or is it 7!*3^7 still?).

This would only apply to the even nxnxn cube. I handled the nxnxn, and thus I had to tackle the full number of positions.

 

[qqwref]

The paper/book is already written and all supplement material is written and all Mathematica code (which is well documented and commented) is written.

I did think about publishing a paper, but I was told that no journal will publish such a long paper.

Therefore, I wish to create a university course. I also clearly wish to publish my book to accompany the course.

Well, of course no journal will publish a book-length paper. They want people to read what they publish in a reasonable amount of time, and to not have one paper completely overshadow the rest of the issue's important research papers.

As far as actually publishing your results, I recommend writing a detailed but *short and concise* paper for some kind of journal publication, and then releasing the full details somewhere else - arXiv, personal website, self-published book, and so on. Having seen some of your earlier text on speedsolving, it seems like you spend a lot of space giving examples, going through relatively straightforward derivations or algebraic transformations, and showing casework. That is, details and explanations designed to show your work and to make retracing your steps easier. While this stuff is interesting and worth publishing somewhere, the vast majority of it doesn't really belong in a normal research paper. I'm no published

As for the university course, I feel like this is completely the wrong way to go. The raw amount of content may match up, but it is not an appropriate subject for a university course. The work isn't even peer-reviewed, and as it's not published you certainly can't expect a professor to understand it well enough to teach, especially since it's completely unrelated to the field of almost every professor out there. In my experience, relatively new discoveries would be taught by the discoverer or someone who knows their work very well (such as one of their students or research associates), and they are taught to graduate students who may end up doing research in that field. Random university students, even if they are interested in cubing, have far more important and applicable things to be spending a semester of effort (and money) on.

I am referring to my single commutator proof. I reduced the number of even permutation corner positions to a mere 1002 cases and the even permutation middle edge positions to 3351 cases. (I have mentioned this in the past in Per's thread.) I show all of the work in my book about how I did this, and I have Mathematica code which proves this true from more than one direction (when only one direction is necessary).

Surely this can be shown by a quick list of commutators, which can be generated from a program, no? I feel sorry for you if your first instinct was to do it by hand.

 

[Christopher Mowla]

I thought of this, but think about the "well-rounded" educational requirement. Why is an engineering major forced to take English literature? Haven't they had enough of that in high school? Why not require them to take a technical writing course (or a second technical writing course, if they are required to take one)?

I cannot speak for all universities, but I can say that they make exceptions to "applicable" courses with no justification on the customer's (student's) behalf. So why rule out such a course as this which would give technical students another perspective on the world (the concept in my book emphasize to keep and opened mind) and give non-technical students an appreciation for mathematics that other math courses simply don't provide?

EDIT:

Surely this can be shown by a quick list of commutators, which can be generated from a program, no? I feel sorry for you if your first instinct was to do it by hand.

Even if I would have thought of this (if it is indeed feasible), I consider the elegance of a proof more valuable than some number crunching. In addition, my book doesn't just merely prove this theorem. It is how it proves it which makes it special.

 

[blade740]

The paper/book is already written and all supplement material is written and all Mathematica code (which is well documented and commented) is written.

I did think about publishing a paper, but I was told that no journal will publish such a long paper.

Therefore, I wish to create a university course. I also clearly wish to publish my book to accompany the course.

There are hundreds of resources on self-publishing, so I won't get into that. As for teaching a course - this is going to be highly dependent on finding an institution that has room for a newcomer, teaching a single course on a single obscure problem.

I think qqwref is right - the best course of action would be to try to write a condensed paper to publish in scholarly journals, and in the meantime, work on self-publishing the larger work either digitally or on paper. It may be several years (if at all) before you find an institution willing to offer you a chance to teach, but in any case, having your work published and available can only help this case.

 

[Christopher Mowla]

As for teaching a course - this is going to be highly dependent on finding an institution that has room for a newcomer, teaching a single course on a single obscure problem.

I took a Java course at my university, and the book talked about the Nim game throughout the entire text. That is, it constructed a complete program during the entire scope of the text where in each chapter, it added more features and sophistication to the software.

So I thought, why can't such a course, which does address many components of abstract algebra and several components of computer science (and a collective knowledge of many other technical subjects and concepts) into a course which focuses on another "game"?

 

[qqwref]

I thought of this, but think about the "well-rounded" educational requirement. Why is an engineering major forced to take English literature? Haven't they had enough of that in high school? Why not require them to take a technical writing course (or a second technical writing course, if they are required to take one)?

Well-rounded means they know multiple subjects. Your discoveries are not a subject or a field of study, they're just your personal work. In addition, "well-rounded" in practice usually implies basic STEM requirements and a bunch of Humanities/Social Science courses, and since your proposed course is an extremely in-depth look at a very specific subfield of (what I assume would be considered) abstract algebra, it would be neither of these.

I cannot speak for all universities, but I can say that they make exceptions to "applicable" courses with no justification on the customer's (student's) behalf. So why rule out such a course as this which would give technical students another perspective on the world (the concept in my book emphasize to keep and opened mind) and give non-technical students an appreciation for mathematics that other math courses simply don't provide?

This is kind of ridiculous. Has any university ever had a class like this, based entirely on unpublished and extremely in-depth research on a niche subject that maybe a few students will be interested in? And how could methods of finding Rubik's Cube algorithms, or solving the cube efficiently, possibly give people "an appreciation for mathematics that other math courses simply don't provide"? Keeping an open mind is irrelevant if the topic has nothing in relation to your interests, career, or subject. The fact is, even on this forum, a class like this would be a huge waste of time for all but a few people who are extremely interested in cube theory. Outside of a cubing community, it would be pretty much everyone.

In addition, my book doesn't just merely prove this theorem. It is how it proves it which makes it special.

I think other people would have to see your proof and decide that for themselves. Your techniques may well represent a standard approach in some field of mathematics. If the techniques themselves really are new, that should itself be a paper, as it could be useful for people who have not dedicated years to cubing and thus are not going to wade through many hundreds of pages of cube theory to figure out how you proved things.

I took a Java course at my university, and the book talked about the Nim game throughout the entire text. That is, it constructed a complete program during the entire scope of the text where in each chapter, it added more features and sophistication to the software.

So I thought, why can't such a course, which does address many components of abstract algebra and several components of computer science (and a collective knowledge of many other technical subjects and concepts) into a course which focuses on another "game"?

Nim itself has a huge amount of history - many courses have been taught, papers written, generalizable results gotten, etc. In fact, the game itself is one of the fundamental concepts of a major field of study (game theory). The analogy doesn't work IMO because programming is all about learning to construct something (a program), and the book's approach was surely to give students something to construct that was easy to follow - Nim could have been replaced by a lot of other things, and really has nothing to do with Java (or indeed programming) other than its simplicity. Abstract algebra is not about constructing a useful program to give to users, it's about the theory and theorems built up around certain mathematical objects, and spending dozens of hours going through cube theory casework surely isn't the best way to teach that.


Look, honestly, when I have seen your previous work, even I don't have the patience to read through all of the details, and I really care about cubing and have put a ton of time into it. I can't imagine how uninteresting this would be to college students who don't care about cubes and who are paying a lot of money for each course they take.

 

[irontwig]

I can't imagine how uninteresting this would be to college students who don't care about cubes and who are paying a lot of money for each course they take.

Being from a country where education is free, I didn't even think about that. But really, cmowla, you're a smart guy. How can you not realize that it's very improbable that this will be taught at any university?

 

[Christopher Mowla]

qqwref, make no mistake, just because you haven't found interest in my previous works, this doesn't mean that you will not find interest in my book; and it certainly doesn't mean that everyone else has your taste if it turns out that you won't.

Why do I say so? Because you haven't even seen my work to judge it. This book is not like my previous works for the most part (except for prerequisite information, and the like). I spent a lot of time writing it to make it easy-to-understand, and despite the amount of content, I have written it almost like a "novel". I also hyper-linked my book for easy navigation on electronic devices. It's not 350 pages of solid text: it has many accompanying figures, tables, and examples. It even has links to wolfram alpha on occasion.

However, thank you (and everyone else) for giving me another perspective regarding making this a university course. When I see courses like this arising, it makes me think, why not give it a try?

It won't break my heart if this doesn't become a university course, but yes, a course of some form it shall become. I am still requesting contacts.

EDIT:
Quick fact. Having written and read my book, I can tell everyone without a doubt that the current content on the commutator wiki page really over complicates commutators. (I never fully read through that page because I simply cannot believe how much it over complicates this subject.)

Therefore, if anyone assumes that my book is much more sophisticated than that page, since I claim that I give the tools needed in my book of how to construct every possible commutator for any nxnxn Rubik's cube position, this could not be further from the truth. My book is nothing like that, nor will my course be.

 

[qqwref]

Why do I say so? Because you haven't even seen my work to judge it.

And whose fault is that?

EDIT:
Quick fact. Having written and read my book, I can tell everyone without a doubt that the current content on the commutator wiki page really over complicates commutators. (I never fully read through that page because I simply cannot believe how much it over complicates this subject.)

I've never looked at this page, but I quickly skimmed it, and... WOW it is bad. I certainly hope nobody takes that as an example for their writings on cube theory!

 

[AlexMaass]

so... updates?

 

[Damien Porter]

I spent a bit of time last semester researching uses of differential equations / calculus in cubing that have been used in the past. I found absolutely nothing. How do you find a use for the continuity of calculus in the world of finite, discreet permutation groups. Or are you using some form of calculus like proposition calculus. In my mind those aren't really calculus.

 

[Christopher Mowla]

@Alex, nothing has changed since my last comment.

Or are you using some form of calculus like proposition calculus. In my mind those aren't really calculus.

I never heard of propositional calculus before, but I looked it up, and it looks neat.

I spent a bit of time last semester researching uses of differential equations / calculus in cubing that have been used in the past. I found absolutely nothing. How do you find a use for the continuity of calculus in the world of finite, discreet permutation groups.

At the end of June, I wrote a post on twistypuzzles which shows how I used the limit, derivative, and integral in puzzle theory. Of course, I found that the derivative has the most applications so far and not integrals (i.e., differential equations). Most of my works that I link to in that post have been on speedsolving for at least a year--most longer--but I didn't post them anywhere else on the web. Therefore, I just decided to compile a post for twistypuzzles members, because most do not view these forums.

Since you mentioned permutation groups, I believe the last bullet in that post should get your attention (i.e., nth derivatives can be used to calculate sub factorials, which are what make up permutations). That is, I found (with "assistance") that, we can express n! as a sum of a product of a binomial and the kth derivative and (k-1) for positive integers n:

So calculus and permutations are directly related, as we can count the total number of permutations using calculus.

EDIT:
And of course I forgot to mention the well-known fact that the gamma function (which is an integral) can be used to compute the factorial. However, clearly the formula above is a more concrete approach to compute the number of permutations using calculus versus using gamma.

 

[Damien Porter]

Thanks for the prompt reply. They are some interesting relationships. I would be very interested in reading your book and seeing how these relationships lead to practice uses. I hope that you release your book soon as in the coming year I will be deciding the topic for my PhD and your research may influence my choice.