Can we really solve big cubes?

[Christopher Mowla]

..

 

[blade740]

If someone did find an odd parity alg which is done by reason, how would this change cubing as it is today?

Not at all. I am completely confident that I can solve the single edge group flip on any odd cube without messing up the puzzle.

 

[Jake Gouldon]

HOW ARE YOU A MACK DADDY?

 

[Christopher Mowla]

If someone did find an odd parity alg which is done by reason, how would this change cubing as it is today?

Not at all. I am completely confident that I can solve the single edge group flip on any odd cube without messing up the puzzle.

Well I am sure that you are confident that you can do an algorithm to the cube (which you have memorized), but I am talking about not memorizing some unbvious algorithm to do that task.

Sure we become confident in doing an algorithm which we have done over and over again, but what about if we actually understood what is happening (not just the moves, but what is actually happening to the cube throughout the entire process).

What I was implying is understanding of the pure edge flip, not confidence or memorizaton.

 

[Me]

I usually don't come in this part of the forums, but is this thread is turning on a big philosophic issue, much like ones Descartes came up with in his meditations. Can we really say that reality around us is true? Is there God? He wrote quite a few pages on that.

Having said this I think that we would say yes we can solve big cubes, a single edge flip is possible. However:

Do not try and flip a single edge, that's impossible.
Instead only try and realize the truth... there is no edge.

 

[nitrocan]

Sure we become confident in doing an algorithm which we have done over and over again, but what about if we actually understood what is happening (not just the moves, but what is actually happening to the cube throughout the entire process).

As far as F2L goes, we cubers are pretty intuitive. For the last layer we just don't want to waste our time.

But FMCers are intuitive on that too.

Besides, why do you need to know how an algorithm exactly works? Just memorize it and do it. It's an algorithm. You don't need to investigate how the piano makes its sound in order to play it. And I don't see many cellphone users wondering around about how their phone was programmed so that they can use it more efficiently.

 

[cmhardw]

If someone did find an odd parity alg which is done by reason, how would this change cubing as it is today?

I think I know what you mean by this statement, that people don't understand how exactly they are transposing two edge pieces (nothing gets flipped in this case by the way). However, based on how you worded your statement I think you believe that finding an intuitive algorithm is difficult to do. I completely disagree.

Here's a completely intuitive algorithm to transpose two edges (the "flipped" edge parity case). I choose to swap two different edges, rather than two edge pieces adjacent on an edge of the cube:
r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2

--edit--
A slightly more speedsolve friendly, and still completely intuitive, parity algorithm:
r' U2 r' U2 r2 F2 r' B2 r F2 r' B2 r2 U2 r' U2 r'
--edit--

There's also this one if you want a transposition that swaps two adjacent pieces on an edge of the cube:
r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2 D' r2 D r' U2 r D' r' U2 r' D

I know these algs are longer than the standard speedsolving algs, but they are completely intuitive. If you understand what "parity" is, and a little bit about commutators, you will see exactly what I am doing in both of these algs.

I'm not trying to come across as arrogant, but you should realize that an intuitive way to handle "parity" is not difficult to do.

Chris

 

[Christopher Mowla]

If someone did find an odd parity alg which is done by reason, how would this change cubing as it is today?

[...] Here's a completely intuitive algorithm to transpose two edges (the "flipped" edge parity case). I choose to swap two different edges, rather than two edge pieces adjacent on an edge of the cube:
r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2

There's also this one if you want a transposition that swaps two adjacent pieces on an edge of the cube:
r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2 D' r2 D r' U2 r D' r' U2 r' D

I know these algs are longer than the standard speedsolving algs, but they are completely intuitive. If you understand what "parity" is, and a little bit about commutators, you will see exactly what I am doing in both of these algs.

I'm not trying to come across as arrogant, but you should realize that an intuitive way to handle "parity" is not difficult to do.

Chris

I understand what you are trying to say, and I don't take offense. However,
the first portion of the one-edge perm. which you gave:
r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2
is not very intuitive to me. I know perfectly well what odd parity is, but that just doesn't seem to ring a bell. To me, that is just repetition of moves which all of a sudden can be manipulated in such a way to edge with two opposite diagonal edges, once removed. The second portion of that alg is fairly intuitive because it can be achieved, as you said, with commutators. I fully understand that.

Therefore, what I am really concerned about not being intuititive is the first portion of the algorithm which you presented.

 

[cmhardw]

Therefore, what I am really concerned about not being intuititive is the first portion of the algorithm which you presented.

What does r' U2 r' U2 r' U2 r' U2 r' do to a cube? You can use any non-supercube bigger than 3x3x3. Brainstorm. Tell me anything and everything it changes if you apply it to the solved state.

Chris

 

[Christopher Mowla]

Therefore, what I am really concerned about not being intuititive is the first portion of the algorithm which you presented.

What does r' U2 r' U2 r' U2 r' U2 r' do to a cube? You can use any non-supercube bigger than 3x3x3. Brainstorm. Tell me anything and everything it changes if you apply it to the solved state.

Chris

1) It rotates the top composite center 180.
2) It puts the [top front left' edge in the [back bottom right] edge slot.
3) It puts the [top back left] edge piece and moves it to the [top front left]
4) It takes the [back bottom right] edge and moves it to the [front bottom right] edge slot.
5) It takes the [front bottom right edge] and puts it in the back top left slot.


I understand where you are going, but how is that logic? It is just taking repeating moves until the centers are restored and a few edge pieces are swapped. Combining this with another piece causes another thing to happen, ..., which is then combined with a commutator and then the one edge correction. However, the very pieces that are combined here are only found by experimenation. I do admit that it does take logic to combine these pieces in such a way to accomplish a specific result, but still that makes the algorithm incomplete, in terms of fully being derived from logic.
Here is an unobvious algorithm that I found on my own which rotates all 4 edge complimentary edge pieces, in two opposite composite edges, counter clockwise

S l2 S' [preliminary moves]

l' U2
l' U2
l' U2 "intuitive algorithm"
l' U2
l'

S l2 S' [reverse of preliminary]

This is probably the easiest algorithm to memorize to accomplish this task (not to mention brief). I did need to use logic to do preliminary moves to prevent discoloration of the centers and restrict the edges affected to only two composite edges, but the "intuitive algorithm" was not found by reasoning, but by experimentation.

Here is another example, using the same base algorithm which you have provided for me:

S' r2 S [preliminary moves]

r' U2 r' U2 r' U2 r' U2 r2 B2 r F2 r' B2 r F2 "intuitive algorithm"

S' r2 S [reverse of preliminary moves]

This is more "intuitive" than even the commutator you attached to the end of the base (not to mention shorter). It prevents discoloration of the centers and restricts the edge swapping within the same edge.

My point is, I understand what you are saying about adding pieces together to achieve a desired result, but this is still not fully logical: it does require experimentation and experimentation is equivalent to computer-generated algorithms.

Please continue to comment. I am honestly interested in what you have to say.

 

[AvGalen]

those 9 moves chris gave are actually a perfectly understandable parity fix that messes up some other pieces as well though. In order to solve parity you need to perform an odd number of slice turns. If you don't understand why then you don't understand what parity is yet. So just a single "r" turn fixes parity but messes up the rest of the cube. Doing "r U2" 5 times is an intuitive way to not mess up the cube too much while still doing an odd number of slice turns.

 

[Christopher Mowla]

Doing "r U2" 5 times is an intuitive way to not mess up the cube too much while still doing an odd number of slice turns.

I understand that completely. However, it is not obvious that the cube's centers will be restored until after one has done those 9 moves to a big cube. That is experimenation.

Algorithms such as:
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

is:
a) Done by a computer
b) Done by experimenation

However, my aim is to not involve experimentation at all in order to make an algorithm.

 

[AvGalen]

actually it is perfectly obvious to me that centers will be restored after doing that 5 times and this is why:

normally doing r 4 times would restore the centers. Think of this as passing down the right centerrow r times
now before you do the first r move, add a U2 move. this changes things because now 1 left centerrow is passed down as well, now requiring 5 (odd!) r turns for all those centerrows to return to their centers

( i actually changed the alg to U2 r * 5 to make this easier to understand)

 

[Christopher Mowla]

I do not mean to be annoying, but be honest here. Are you telling me that because of that reasoning which you just gave, you knew what would happen before you even did that algorithm the first time? No matter how brief an algorithm is, if it was first done by experimentation and then was reasoned later why it works, that is still pure experimentation.

If I wanted to write a computer program to, for example, search a string (just as microsoft word searches a document). I could not by any means lean on experimentation to write such a program. A small fraction of experimentation might be required to learn the commands of the computer, but the algorithm itself needs to be understood in full. Otherwise the program would malfunction (have bugs), and never be reliable.

Experimentation can be more of an illness than a source of understanding.

Here's another analogy. Think of the weathermen (and women). They still do not understand hurricanes after countless years of scientific experiments. They have a say so on where hurricanes might go, but even with the best computer systems, hurricanes still stupify their "expertise".

Cubes are kind of like this. We develop a chart of algorithms in our heads through gained experimentation. We subconciously fuse these trial and error algorithms in our heads and, when we say that they are intuitive to someone who has never played with a cube before, those persons look at us like we are crazy. What happened there? Are they dumb or are we so experienced with cubes (when I say experienced, I am saying "we know what moves produce a positive result and which ones do not") that we don't realize that what we are doing is unobvious to an unexperienced cuber.

An intuitive algorithm is one that can be understood by just about anyone. The process for their understanding might take a while to process, but should be provable without experimentation.

 

[blade740]

I do not mean to be annoying, but be honest here. Are you telling me that because of that reasoning which you just gave, you knew what would happen before you even did that algorithm the first time? No matter how brief an algorithm is, if it was first done by experimentation and then was reasoned later why it works, that is still pure experimentation.

It's fairly obvious, like Arnaud said, why it fixes centers if you think about it a bit. Sure, I heard that alg before I knew what it did, but that doesn't mean I understand it any less now, just because I didn't discover it myself.

 

[cmhardw]

Cubes are kind of like this. We develop a chart of algorithms in our heads through gained experimentation. We subconciously fuse these trial and error algorithms in our heads and, when we say that they are intuitive to someone who has never played with a cube before, those persons look at us like we are crazy.

An intuitive algorithm is one that can be understood by just about anyone. The process for their understanding might take a while to process, but should be provable without experimentation.

I can see where you are going with this, and yes I can kind of see that to most people you might not be sure that the algorithm listed will solve centers after 5 inner slice turns.

However, I still am going to refute your claim that there does not exist a perfectly intuitive algorithm to solve parity. I am going to list one, and I am going to list it without having ever touched a cube.

I will describe the intuition to you as well, to make it obvious. You should be forewarned though, that this algorithm will be quite long.

r' B2 l U2 l' (u2 e2 d2) l U2 l' (u2 e2 d2) B2 l' (f2 s2 b2) l F2 l' (f2 s2 b2) l F2 D' f D' B2 D f' D' B2 D2

Lower case m, e, and s turns mean to turn the corresponding layer as M, E, S for 3x3x3, but only the single inner layer. You can also rewrite the alg with upper case M, E, S turns which imply to turn the triple layers. This rewrite of the alg would be written as follows:

r' B2 l U2 l' E2 l U2 l' E2 B2 l' S2 l F2 l' S2 l F2 D' f D' B2 D f' D' B2 D2

Again, to be clear, the bolded M, E, S turns in this algorithm are triple inner layer turns.

The intuition of this algorithm I hope is completely obvious. I will tell you only that it uses the shortest, most optimal, algorithm to toggle the parity of the inner wing piece orbit. The optimality of this algorithm cannot be called into question, because it is only 1 turn in length! I would hope that we cannot call the intuitiveness of this algorithm into question either, because it is very easy to know beforehand, and track during the application, its effect on the cube. Lastly, after toggling the parity of the inner wing orbit I use commutators to re-order pieces that were destroyed in the side effect of this optimal length parity toggling algorithm.

True to my word I did not even touch a cube in the writing of that algorithm. Everything was done in my head based on the intuition of what I am trying to accomplish. I did not need to do any experimentation of which commutators would be necessary beforehand, as I used the intuition of how to move pieces around with commutators.

I'm sure you could argue that I had to do experimentation in order to learn commutators in the first place, which nulls the intuition of using them afterward, but I would have to disagree with you. Here is why:

Can you ride a bicycle? If so, do you do it while constantly calculating and recalculating your changing center of balance, or do you do this intuitively? Now - were you capable of learning to ride this bicycle purely by your own reasoning abilities about the properties of center of balance of a mass in motion? I think you probably learned it by experimentation ;-) After which, your body developed a "muscle memory" of what worked via the experimentation, and now I would argue that you could ride a bicycle comfortably with very little conscious thought of the act.

I'm also not trying to be annoying, but I think your conditions on what constitutes intuition are excessively strict for cubing related tasks. I would define intuition on a cubing algorithm as being able to explain the purpose for every single turn you do in an algorithm, as well as how it relates to all the other turns. By this I mean you should be able to tell how the algorithm would fail for each turn if it was removed from the algorithm. That is a bit simpler, but also still requires that you know what you are doing - i.e. intuition.

Chris

 

[Stefan]

r
There. An understandable odd parity alg. No lengthy discussion needed.

If someone did find an odd parity alg which is done by reason, how would this change cubing as it is today?

About as much as eating would change if someone today invented the spoon.

the cage method may be used as an example against my reasoning here (since it bypasses odd parity)

No it doesn't.

 

[JTW2007]

I would say that any alg is intuitive, most peoples' cube intuition isn't good enough to see the reasoning behind a single edge pair flip.

 

[AvGalen]

I will be a bit shorter than Chris
After realising what parity actually was I thought of the following way to fix it
r to solve parity (odd)
U2 r U2 r' to restore the first center (even)
x'l' U2 l to restore the second center (even)
x' U2 r U2 r' to restore the last centers (even)
result: parity fixed and centers restored with the most basic moves possible. I will not discuss restoring the edges here. For an intuitive way to do that (without changing parity) see my (AVG) method for edge-pairing

I hope that convinces you and that it satisfies all of your requirements.
p.s. i am one of those FMC guys that solves most of the cube with intuition, but I also use things I discovered by using experimentation and I know some algs that I understand now, but didn't discover myself

 

[Stefan]

I would say that any alg is intuitive

L' D' B2 L' F' L' U B2 R2 F' R2 F' L2 B' F' U L2 R2 B2 F R U' B' F' R D2 L F' D' R2 U' R2 B R' F' D' R U2 B2 L B2 L U2 R D2 R' U2
Explain.