Does ' mean inverse or mirror?

[malcolm]

I saw a sequence the other day, something like (RUR'U')*2 (RUR'U')' , And was wondering whether the ' means mirror or inverse? like for U and U' its the same thing. But what about for long sequences?

 

[Johannes91]

Inverse. So that example cancels out to R U R' U'.

 

[AvGalen]

So (RUR'U')' means (U R U' R') and not (R'U'R U)?

 

[TheBB]

Yes.........

 

[abbracadiabra]

Why do they have to make it so complicated? And while we're at it, could somebody please explain the usage of parenthesis to me? Thanks.

 

[hdskull]

Why do they have to make it so complicated? And while we're at it, could somebody please explain the usage of parenthesis to me? Thanks.

You can do the set of moves as 1 finger trick.

 

[TheBB]

Why do they have to make it so complicated? And while we're at it, could somebody please explain the usage of parenthesis to me? Thanks.

Complicated? Excuse me, it makes perfect sense. It's like math, the tools you have at hand must be up to the task of solving the problems you need to solve.

 

[Johannes91]

Why do they have to make it so complicated?

Who is "they" and what's "it"?

 

[abbracadiabra]

Johannes91, "they" is the person who wrote "it," which was (RUR'U')' leaving us to wonder whether the latter apostrophe meant mirror or inverse.

Thanks, hdskull, for the explanation of the parenthesis.

BB, just my humble opinion and I'm certainly not all knowing, but I think the tools at hand can't be up to the task of solving the problems you need to solve unless they are readily understood. To me, (URU'R') seems easier to understand than (RUR'U')'. Again, I don't know it all, which is why I asked.

 

[Johannes91]

... whether the latter apostrophe meant mirror or inverse.

It's very well-known and not complicated at all. I can't really see how a single apostrophe could be used to mean mirroring, because there's more than one way to mirror a move sequence.

To me, (URU'R') seems easier to understand than (RUR'U')'.

But if you have both R U R' U' and U R U' R' in the same alg, using (R U R' U')' makes the connection more obvious and can help understanding how it works.

 

[AvGalen]

It's very well-known

No, it is not. This notation used to be somewhat common when most algorithms were found by hand and based on commutators. It is not common at all at this moment.

The purpose was indeed to explain how/why an algorithm worked, but if you cannot even execute the algorithm, how are you supposed to understand it?

An easy example of how it could work:
(URU'R') L' (RUR'U') L could be written as (URU'R')(L') (URU'R')' (L')'
If you write it like this it becomes clear that you do four moves (A), do one move (B), then undo four moves (A)', then undo one move (B)'.

This notation can be very useful
FRUR'U'RUR'U'RUR'U'F' is hard to learn F (RUR'U')*3 F' is easy

 

[Johannes91]

So people seriously don't know what U', F' etc. mean? I thought inverse is a very basic concept. There have to be some pretty bad notation guides out there.

 

[AvGalen]

malcolm wasn't wondering what ' meant in R'. He was wondering what it meant in (RUR'U')'.

I agree that it is strange that he thought it could mean mirrorring, but as you can see by my question

So (RUR'U')' means (U R U' R') and not (R'U'R U)?

it is difficult to determine what the meaning of that ' is. I really don't think that is very well known.

 

[Johannes91]

malcolm wasn't wondering what ' meant in R'. He was wondering what it meant in (RUR'U')'.

It means exactly the same thing... Inverse, i.e. the move(s) backwards. So X X' is identity, no matter what X is. This has been clear to me ever since I learned the notation, but I see that if it's not explained well then it can seem confusing.

 

[TheBB]

BB, just my humble opinion and I'm certainly not all knowing, but I think the tools at hand can't be up to the task of solving the problems you need to solve unless they are readily understood. To me, (URU'R') seems easier to understand than (RUR'U')'. Again, I don't know it all, which is why I asked.

That's why practice makes perfect, I guess.

 

[malcolm]

Yeah, i thought it was inverse, but wasn't sure. And no its not common notation, I have only ever seen it once, and before I saw it i just knew ' to mean anticlockwise, but obviously i can't perform a sequence anticlockwise...