Which notation do you prefer?

Its easier to remember with (r) or (u) or whatever.

I still don't know what you intend to do with something like (r u'). Is that a cube rotation or a fingertrick of double-layer turns only? Clearly you can't have both lowercase letters for turns and lowercase letters for cube rotations at the same time. As much as x, y, z is confusing to some I don't think this notation is any better, and in fact it is more confusing in the long run because parentheses now have multiple meanings.

And I never understood the value of Rw. It takes up much more space, isn't intuitive or expandable to bigger cubes (if you are going to use a letter it should stand for double layer or something like that, emphasizing the double), and also makes slice turns very long to write, something like (RwR').

I keep the straight using the "left hand curl" rule.

Anyone who's taken physics is probably familiar with Fleming's "right hand rule" for induced electromagnetic fields. You take your right hand, stick your thumb out and allow your fingers curl around like you'd hold a can of Red Bull. If current is flowing through a conductor in the direction your thumb your thumb is pointing, then the induced magnetic field flows around the wire in the direction your fingers would wrap around it. See: http://www.diracdelta.co.uk/science/source/f/l/flemings right hand rule/source.html

The x/y/z rotations conform to a left hand rule. If you're used to drawing Cartesian coordinate graphs, then the x axis on a piece of paper would be horizontal, increasing positively away from zero to the right, the y axis would be vertical, increasing in the up direction and the z axis would come out of the paper towards your face. If you hold your left hand as described above and point your finger in the direction of the axis in question, a regular turn is in the direction your fingers curl and a ' twist is the other way.

That's how I kept it straight in my mind before it became natural to me, so if it makes sense and is useful to you, you're welcome to refer to it as "Brunson's left hand rule of cube rotations".

Thank you very much, I'll be here all week.

Well I'm going to admit that I know them more by what they are associated with than anything else. y is the cube rotation I use a lot for F2L, and x is the nice easy one you use to do fingertricks on B and F. Once I saw those associations it was always pretty easy for me to know which is which.

x, y, and z. Not that they are easier; it is just that I learned notation that way from Macky's site. Plus I always just imagine a graph with a 3D line sticking through(for z) and when I do that it is very easy to figure out what to do.

brunson said:

The x/y/z rotations conform to a left hand rule. If you're used to drawing Cartesian coordinate graphs, then the x axis on a piece of paper would be horizontal, increasing positively away from zero to the right, the y axis would be vertical, increasing in the up direction and the z axis would come out of the paper towards your face. If you hold your left hand as described above and point your finger in the direction of the axis in question, a regular turn is in the direction your fingers curl and a ' twist is the other way.

Click to expand...

Oh yes! Comparing these x, y, and z rotations to the Cartesian coordinate graphs is a really easy way to remember this! Thanks a lot! I don't understand what you're trying to say for the other things but the Cartesian coordinate is great!

If you know what the Cartesian coordinate is but don't know how to use it with your cube rotations, here's another explanation. In the Cartesian Coordinate system, the x axis runs in a horizontal line (runs through the center of the left and right faces). So a x turn would be turning the cube around the imaginary horizontal line running through the center of your cube in a clockwise direction. In the coordinate system, the y axis runs vertically (an imaginary line running through the up and down faces). So, thinking that an imaginary line runs through your center of your cube vertically, rotate your cube around that line in a clockwise direction to get y. Lastly, the z axis is an imaginary line that runs through the center of the front and back faces of your cube (I don't know how to explain it like horizontally or vertically.) Then, you rotate your cube around the z axis in a clockwise direction to get z.

If you understand the Cartesian Coordinate system, remembering which way to turn the cube during the cube rotations is SUPER easy. If you don't, I'm sorry, you'll just have to remember that..

x = turning the whole cube R
Y = turning the whole cube U
z = turning the whole cube F

I like qqwref, lucasgarron, and avgalen's ideas.
I too have thought about it and arrived at something similar to avgalen's.
I hate the right hand rule for physics!
I find xyz very intuitive. I understood how to turn them as soon as I figured out that they are whole cube turns. I confused (r) as an optional double layer r at first. But now I can read both well.
i do hate the inconsistencies between puzzles. especially r can be double layer for 3x3 yet be inner for big cubes and tips for pyraminx.

I think for the 3x3x3, an extra "w" at the end of a notation is best for signifying double layer turns. It conforms better to the whole line of notations for the other puzzles.

It is also easy to understand. Whenever I see, for example, Rw, I say to myself, "R-wide" which tells me to turn two layers because two layers are "wide."

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.

dChan said:

It is also easy to understand. Whenever I see, for example, Rw, I say to myself, "R-wide" which tells me to turn two layers because two layers are "wide."

Click to expand...

Two layers might be wide for a 3x3, but as I said the notation doesn't work for anything bigger. Two isn't that wide for a 4x4 (isn't 3 layers wider?) and it certainly doesn't cut it on a 7x7.

I hope you will all support me at this new notation I just came up with, for large cubes. It covers every possible move for cubes up to 7x7.
Rxs - one layer (R extra shallow)
Rs - two layers (R shallow)
Rm - three layers (R medium)
Rw - four layers (R wide)
Rxw - five layers (R extra wide)
Rxxw - six layers (R extra extra wide)
You can't get any more intuitive than that. It works just like clothing sizes, which everyone is already familiar with. Everyone should start using this method immediately. I suggest we all make a formal request to the WCA to adopt it. (Or maybe you see my point. Also, it's cumbersome.)

pcwiz said:

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.

Click to expand...

Funny, despite being a math major at Caltech, I've never heard of it. Do you think you could elaborate a bit more? It sounds interesting.

Even better:

Single-layer: Ri
Double: Rii
Triple: Riii
Quadruple: Riv
Quintuple: Rv
...



Actually, it's not THAT bad, and obvious to generalize. Now we just have to get w compatible with i.

No, I have an even more intuitive system. Forget block turns entirely. Let's just write everything in base 4 notation (1 meaning clockwise) on the R, U, and F axes.

So what's now an Rr move on the 4x4x4 would become R0011. l becomes R0300. An lr antislice move becomes R0310. What is now a y rotation simply becomes U1111. This is clearly a superior notation to all others, since it requires no interpretation whatsoever and no special terms have to be memorized, except for R, U, and F. The size of the cube is also immediately implied in the number of base-4 digits used. If you do not adapt THIS new terminology you will be assimilated by the Borg anyway. Resistance is futile.

I myself think we need a more beautiful and artistic notation system. I propose the use of colors.

R Is the outermost layen on the right.
RRR Would be the 3 rightmost layers
RRRRRR Is the2nd-7th rightmost layers.

qqwref said:

pcwiz said:

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.

Click to expand...

Funny, despite being a math major at Caltech, I've never heard of it. Do you think you could elaborate a bit more? It sounds interesting.

Click to expand...

I don't think the Cartesian Coordinate system is used in math...

I learned it in school like two weeks ago and I'm not exactly sure what it's used for... I just learned what it was and... I don't know.. I learned it when I was learning about robots so... Nevertheless, I know what it is, and if you compare it to the x, y, and z turns of the Rubik's Cube, they are exactly the same. Therefore, if you know what the Cartesian Coordinate system, is, you'll immediately know which direction to turn the cube with the x, y, and z notation.

I'm sorry I didn't explain it because it's hard to explain and I don't know what it's used for. So I myself am not too familiar with the topic so I wouldn't really be able to teach you. Sorry! Maybe you can ask Brunson?

blade740 said:

I myself think we need a more beautiful and artistic notation system. I propose the use of colors.

R Is the outermost layen on the right.
RRR Would be the 3 rightmost layers
RRRRRR Is the2nd-7th rightmost layers.

Click to expand...

Yes, this idea would work PERFECTLY , especially for colorblind people/ people with color recognition problems (like Harris), and for people with monochrome printers. Imagine doing team BLD with that..
"RED BLUE ORANGE GREEN YELLOW!"
"Whoa, slow down there.."
"Oh,no, sorry, I just lost my pencil crayons."

pcwiz said:

qqwref said:

pcwiz said:

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.

Click to expand...

Funny, despite being a math major at Caltech, I've never heard of it. Do you think you could elaborate a bit more? It sounds interesting.

Click to expand...

I don't think the Cartesian Coordinate system is used in math...

Click to expand...

I'm pretty sure qqwref is being facetious, but I can't quite tell if you are or not.

brunson said:

pcwiz said:

qqwref said:

pcwiz said:

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.

Click to expand...

Funny, despite being a math major at Caltech, I've never heard of it. Do you think you could elaborate a bit more? It sounds interesting.

Click to expand...

I don't think the Cartesian Coordinate system is used in math...

Click to expand...

I'm pretty sure qqwref is being facetious, but I can't quite tell if you are or not.

Click to expand...

Wait what? I had to look in the dictionary to understand what "facetious" means. So you mean he's being sarcastic or I'm being sarcastic? I'm confused! :confused: Anyway, I don't know what you mean by this post but I'm being serious and I'm not really sure if it's used in math so...

The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry.

You can extend this system into any dimension. In 3D, the x axis is horizontal, the y axis points toward you, and the z axis is vertical. Now, I'm not going to philosophy about Tetraspace, aka (w,x,y,z,) coordinates.

Cubie Newbie said:

The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry.

You can extend this system into any dimension. In 3D, the x axis is horizontal, the y axis points toward you, and the z axis is vertical. Now, I'm not going to philosophy about Tetraspace, aka (w,x,y,z,) coordinates.

Click to expand...

You made some errors.

x = horizontal axis
y = vertical axis
z = pointing towards you

You don't use z in ordered pairs or do you?:confused:

pcwiz said:

Cubie Newbie said:

The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry.

You can extend this system into any dimension. In 3D, the x axis is horizontal, the y axis points toward you, and the z axis is vertical. Now, I'm not going to philosophy about Tetraspace, aka (w,x,y,z,) coordinates.

Click to expand...

You made some errors.

x = horizontal axis
y = vertical axis
z = pointing towards you

You don't use z in ordered pairs or do you?:confused:

Click to expand...

You also made some errors.

1) x is not any less horizontal than what you call z.
2) z is not pointing towards "you," by most conventions of z-depth I've seen, which make z away from you. (Same applies to Cubie Newbie's y-axis.)
3) Both of you are equally wrong and right. y and z doen't inherently point in a direction, it's whatever you define it as (most orthogonal conventions have x the same way).

See Wikipedia and MathWorld.

1) He did not use z in an ordered pair, but in an ordered quadruple (which I presume contains a typo extra comma).
2) I don't know if he does. But if he does, so? He can use (rubiks, cube) for coordinates if he wants!
(Who's up for rubik geometry? rubiks²+cube²=1 )

Cubie Newbie: Why "philosophy"?