Transitions and transpositions

This is just a little taxonomical lesson for our omniscient participants and international masters who somehow were unable to understand it. 

I = Initial position; A and B any 2 legal chess positions in databases.

Every position A has the standard sequence of moves I-->A called the main line. Any other sequence of moves I-->A is called a transposition. If there is a sequence I-->B-->A, by abuse of language, it's called a transposition from B to A. However, correctly, it should be called a transition (or transfer) from B to A. 

"He/she who has ears to hear, let him/her hear" (Jesus Christ). 

Great explanation! Good job as there are some people that doesn't understand something as simple as this.

What problem do you have with the normal terminology? ie. when a transposition occurs (the move order of some opening is changed, for example two moves are exchanged, changed in order, "transposed" for each other eg. 1. Nf3 and 2. e4 is played rather than 1. e4 ,2. Nf3 but we end up in a normal position.) What is incorrect about saying (as we normally do) that we have transposed into that position?

The sequence  I-->B-->A presumably is of some interest to him, for some unclear chess as stamp collecting reason. It is not terribly interesting for people who play chess.

It's not me but the standard terminology

https://en.wikipedia.org/wiki/Transposition_(chess)

U explained it yourself: a transposition is a permutation of 2 moves in a sequence of moves. It concerns intermediate moves, not a passage from one position to an other. Just think about it carefully in order to understand. 

One more omniscient participant knowing evrything about chess and what is interesting. 

I'm still not understanding the problem. A transposition does not have to be the simple switch of only two moves. I only used that example because it is very easy, in that case, to understand why that term is appropriate. It seems you feel that when a transposition becomes more complex we should prefer another term. If that is what you feel, I don't see why this should be the case. It would be one thing if you were explaining a concept for which we don't already have a term. It's another thing for all of us to go out of our way to change the terms we've been using for decades. It's a lot of work/it makes old texts obsolete, etc... That's not to say it should never happen, but when it does I want to hear a particularly compelling reason.

tmkroll and DeirdreSkye: U are unable to understand the definition. I can do nothing for your anymore. 

Yigor, are you sure you are not misunderstanding the conventional definition somewhere? I explained a simplified case and you seemed to agree there. Can you tell me where it is you think we are beginning to disagree?

I'm sorry, ghost_of_pushwood, but I take some offense that. I was legitimately trying; I hope you can see that.

Hope can see that Vigor wasn't, and just fancied a bit of patronising.

In general (including mathematics and chess), a transposition is a permutation of things. In chess, U don't permute positions (!) but moves leading to a given position changing the move order.  So, when someone says a position B is transposed into position A, it's an abuse of language (or the word "transposition" is used as a synonym of "transfer"). What really happens is that U complete a diagram I-->B into I-->B-->A which is normally a permutation (in the strict mathematical sense) of the standard path I-->A.

In conclusion, we don't disagree, there is just a little abuse of language happening in chess. 

There is a bit of humour in all my threads, though it was mathematically strict. 

Something like that. 

N.B. There are 2 meanings of the verb "to transpose":

1. cause (2 or more things) to exchange places
2. transfer to a different place or context

Normally, chess players use the 2nd meaning while the formal definition in wikipedia uses the 1st meaning. It creates a little mix-up. 

Now that is TRUE

The wikipedia's definition of transpositions in chess is okay. It's more general and consistent with the notion of transpositions in mathematics. It's worthy to understand it. 

Oh boy, U are so ... unsmart.  U haven't understood yet the wikipedia's definition. Transpositions are not from one position to an other. They are always from the initial position to a fixed one, let's say Nimzo-Indian. There is the standard path: 1. d4 Nf6 2. c4 e6 3. Nc3 Bb4. All other move orders (leading to the same Nimzo-Indian position) are called transpositions. 

Well, it's just a little terminological issue. I didn't pretend that it has any tremendous practical usefulness. 

Yigor, what you're saying would make sense if you took position A and then moved pieces (not making chess moves just changing the position) in order to arrive at position B. This would not be a transposition, it would just be one position being changed into another. When people use the word "transposition" to describe something like a game beginning as a Caro-Kann but then reaching a Queen's Gambit position or something like that what they mean is that a Queen's Gambit position has been arrived at via transposition from the Caro-Kann. E.g. what we are looking at momentarily is a position from the Queen's Gambit that can be continued in that opening but the moves order is not a Queen's Gambit move order, 2. d4 was played instead of 1. d4 etc... If you want to be strict about the meaning of the word in that sense the "transposing" we are talking about the permutation of the moves and the move order of the Queen's Gambit not something the process of changing from one opening to another. As Deidreskye has pointed out, however, the use of transposition to go from one opening to another is pretty much always the way it comes up in the literature as it is useful. You can also transpose to known positions from garbage move orders, but there's generally no point to talking about those. I have, however, sometimes seen very old games analyzed and a few of the first moves explained by annotator with something like "well chess theory then was not what is was now; now we would play ___ first" followed by at point in the game something like "but already here we have transposed into a Slav which is still played today." Perhaps Deirdreskye does not like it when annotators do that, or when they explain that one game (not opening or position) transposes into another game but I feel those are valid uses of the term. If you think about it the way you are thinking about it instead, as transposition being only the process of changing from one opening to another, then I guess you can imagine some abuse of language is happening to get that word to mean that thing; that's not really happening, though. If you look at it the other way, you will notice transposition (even by your mathematical definition) is occurring in order to arrive at your position B.