# Message #3946

From: Joel Karlsson <joelkarlsson97@gmail.com>

Subject: POLL: Positive rotation convention

Date: Wed, 10 Jan 2018 21:33:17 +0100

Hello,

While discussing notation (primarily) applicable to 4D-puzzles (including

the physical 2^4) with Marc, we encountered a decision of convention which

we could not decide ourselves. Therefore, I want to start a poll to gather

the community’s opinion.

The question is: should the positive direction of rotation of a cube or a

cell of a cube be clockwise or counterclockwise? The rotation is assumed to

be performed in 3D-space. With the "positive direction of rotation" I mean

the assumed direction of rotation around an axis if nothing else is

specified. Ox is a positive rotation and Ox’ is the opposite negative

rotation; which do you think should be a clockwise rotation and which

should be a counterclockwise rotation around the positive x-axis?

I’ll leave the arguments below. If you have an opinion or preference please

respond to this post with something like "I think that [insert your

preference here] should be the positive direction of rotation… [insert

arguments here if you wish]".

Best regards,

Joel

PS. I don’t know how long the poll should be open, we’ll see when the

reply-rate drops.

PPS. If everyone is fine with that, I’ll leave my vote as a casting vote in

the event of a tie.

*Clockwise (arguments)*

The speedsolvers’ convention: Regarding x versus x’ turns being clockwise,

we speedsolvers have read so many dozens (hundreds) of pages using our

notation that it is wired right into our brains. So, instead of our

criterion for the best notation being "what seems objectively reasonable,

in principle", our criterion is "what will not make our heads explode by

being the exact opposite of what we use daily in a very similar context."

As an example, here are a couple of typical pages from speedsolving.com –

a page for a random beginner method, and one of the most commonly used

reference pages for the last stage of many people’s solves.

```
https://www.speedsolving.com/wiki/index.php/8355_Method<br>
https://www.speedsolving.com/wiki/index.php/PLL
```

These pages use the notation as defined here,

https://www.speedsolving.com/wiki/index.php/3x3x3_notation

and use x, y, and z to refer to clockwise turns of the entire cube around

the relevant axis.

My argument is not that the speedsolving community is our largest or most

important subcommunity, but that it is the group to which this decision

makes the biggest daily difference. If there’s a subcommunity of MC4D who

read lots of recipes in which "z" means a counterclockwise turn around the

z axis, then my argument will be invalid on its face. If not, then we’ll

have to decide whether there is a reasonableness argument that can override

the practical difficulties for speedsolvers in dealing with two opposite

conventions used so similarly.

*Counterclockwise (arguments)*

1) For a mathematician or a physicist, the positive direction of rotation

is, conventionally, counterclockwise. Always, when talking about rotations

in topics ranging from linear algebra to mechanics the axis of rotation is

defined in such a way that a rotation (of a positive number of degrees)

around that axis is a counterclockwise rotation.

2) It follows the right-hand rule. This is a simple rule which helps the

forgetful to remember in which direction to rotate; if your right thumb is

the axis of rotation the fingers curl in the direction of rotation.

3) It’s consistent with MC4D. A left click on a sticker in MC4D rotates the

cell counterclockwise around the axis pointing from the centre of the cell

through the specified sticker. This implies that Ux is performed by

left-clicking on the right sticker on the U-cell and the same goes for all

other twists. The axes (in the notation) can be thought of as specifying a

sticker on the cell (Fx’yz specifying the sticker (on the F cell) in the

negative x-direction (left), the positive y-direction (up) and the positive

z-direction (front)) and the twist is performed by simply left-clicking on

this sticker.

*A third option?*

No, I don’t have a third option but there is something which could

potentially be a game-changer. If an option to swap the behaviour of left-

and right-click would be available in MC4D the third argument for

counterclockwise would fail. This argument could then instead be used by

the clockwise camp since G already breaks the MC4D convention (the axis in

the G moves specify the direction in which the stickers should move and

ctrl+left-clicking on a cell in MC4D rotates the cube in the opposite

direction) and therefore, all moves (including G) would follow the MC4D

convention if clockwise is the positive direction of rotation and the

controls are swapped (or you prefer right-clicking to left-clicking).