And why I will never be one . . . witness nostalgic memories of the Rubiks Cube:
It took me 3 weeks the first time, about 1 week the second time. I remember setting my alarm to 5am so I could work on the cube for two hours in the morning before going to school. Eventually I got my time down to a little over 2 minutes (which is just about the longest I can concentrate on anything). There were two kinds of cube solvers: those who held the cube in a stationary orientation and spun the edges around, and those who kept turning the cube around in their hands to get just the right orientation for each move. I was of this second type, which I think kept my efficiency down. One of my math professors in college told me that he'd solved the cube in theory--he taught abstract algebra--but had never bothered to do it in practice. This impressed me to no end. A guy down the hall from me had a 4x4x4 cube, which at one point we tried to see if we could solve using only 3x3x3 operators. I don't think we succeeded.It's been years since I've done the cube. Last time I tried and tried and tried and got stuck. If I ever want to do it again, I think I'll have to figure out some operators again from scratch.
It came out when I was in grammar school. I solved it once, by extremely long trial and error, and had the wisdom to put it down and never tried to repeat the stunt again. An acquaintance took a more direct method, pulling off the plastic pieces and reassembling them in solved formation. But no one I ever met had a Rubiks Cube theory.
My friends in engineering grad school solved it with a combination of tensor manipulation and experimentation, but I never got into it. They also found a particular solution to a 4x4 cube, but not a general solution. 5x5 was too much though.
I did play with a Rubik's Magic in elementary school. One year I came home from college and performed the solution in less than 30 seconds from muscle memory. That really freaked me out.
I got my first one when I was 16. It took me a week to solve it, but after solving it the first time, it never took more than 2 minutes to do so. For a time afterwards, I timed myself with a stopwatch to see how quickly I could solve it- the shortest was 29 seconds, however, times this short only happen by accident (after solving the first two layers, the pieces in the top layer have a minimum amount of rearranging required).
I never got one of the 4x4x4 cubes, but it always seemed to me that the principles involved should be the same as for the 3x3x3 cube- you just treat any two layers as one whenever performing an operation.
I cheated and bought the book that told you how to do it. I'm pretty sure I was under a minute once I got the hang of it. I don't remember all of it now, though. There were 5 sections to do, and the first 3 are straightforward, but the last 2 require you to remember certain patterns, and they've been forgotten.
I learned to do some tricks with it, but I quickly figured out how to disassemble the cube and reassemble it correctly. That way I didn't have to worry about the stickers falling off and I "solved" it with the color faces in the correct relationships.
OK, nerd alert here:
My first exposure to group theory was when I developed a very simple operator algebra to for the Rubik's cube. Secret Asian Dad decided that this was a good time to teach me group theory.
Later in high school I found my Rubik's cube and notes. After a while writing programs that did operator compacting, I wrote programs that would try to find the optimal solution for a given cube. Then I sat around for days at a time wondering if there was indeed an algorithm to generate a provably optimal solution.
Then I got a girlfriend, and all that stopped.
Think what beautiful results I could have had!
Could be worse. I could have gotten in a duel.
I learned to do a Rubik's cube off the internet a few years ago. But, I've forgotten since then.
If you want to drive someone crazy, switch exactly two stickers on any one of the corner pieces (or physically rotate the corner one-third turn in either direction). The cube can no longer be "solved".
Yancey Ward, wouldn't anyone who knows how to solve it be able to quickly figure out that it can't be solved?
The "theory" (group theory) of the Rubik's cube is really no more complicated than the "theory" (calculus) used to solve physics problems like computing work or flux. It's only because calculus has lots of applications to science and engineering (and economics too!) that we expect students who want to obtain a degree in these fields to learn this particular theory. It turns out that group theory has applications in more advanced physics, in chemistry, and in computer science (and probably other fields as well), so some more mathematically advanced students learn this theory as well. Someone who has learned group theory well can solve the Rubik's cube without much trouble -- and in fact will likely come to a solution faster than someone who tries the trial and error method.
Not appreciating that (even if you don't want to learn the details) is akin to someone saying about economics "I don't know why they bother with collecting all this data and doing statistical analysis, because I just know *insert random belief about how the economy works*" (But maybe your post was less a dismissal of this thought process and more a statement of where your academic interests lie.)
The beauty of the theory of solving the Rubik's cube is that, in principle at least, you could do the same type of calculations (though much more time consuming) to solve a 100x100x100 Rubik's cube or any size cube you can dream of. (And a mathematician will also naturally try to imagine what it would be like to solve a Rubik's cube in higher dimensions, e.g. a 3x3x3x3 cube.)
It is these kind of generalizations which allow mathematicians to see a world that is much more complex and much more beautiful than the mundane world of three spatial dimensions that we happen to inhabit. That is what makes mathematics such a sublime pursuit.
Hei Lun Chan,
I think it depends on how one learned to solve it. Someone that learned it from a book by rote memorization will likely not understand why it can't be solved, and won't then be aware it can't be solved.
But I had in mind someone who was learning to solve it, not someone that already knew how.
Here's my question - I keep seeing mention about solving it more than once. How do you suitably re-randomize it before beginning again?
I could twist it two or three times, then twist it back and claim to have solved it in "two weeks the first time, 15 seconds after that" but I assume those here are a bit more rigorous...
Geoff,
I always considered it rerandomized when it would take me longer to determine how to exactly reverse the moves used to mix up the colors than it would take me to systematically resolve it. For me, that usually meant turning all the faces at least one quarter turn through at least 2 random cycles (I could mess it up in about 5 seconds doing this).
I hope readers/somebody realizes, after reading this post/thread, that many of the 'problems' we face have already been solved from an Engineering POV..our existing Economy, broadly predicated on Waste, is a Political construct that, obviously, serves us none too well..
Somewhere from my time fiddling with Rubik's Cubes I remember that 7 random 90-degree rotations was enough to scramble it sufficiently randomly.