Message #3946

From: Joel Karlsson <>
Subject: POLL: Positive rotation convention
Date: Wed, 10 Jan 2018 21:33:17 +0100


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,

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 –
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.


These pages use the notation as defined here,

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).