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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
Get started now by creating a new collection.
Please stand up and make one step forwards, left, backwards, right. If you are not standing in the same place in the end where you started, then you and I are not living in the same world :)
A more computer-oriented analogy would be pairing up parentheses for example. In that case, there is a difference whether you are trying to simplify "(){}" or "({)}". In the map example, there are no such differences. I'm sorry but I can't explain it better than this.
I'm sorry, but stepping through "NORTH", "WEST", "SOUTH", "EAST" one will arrive exactly at the same position where one started, as a result of any reasonable thought process.
The analogue may be wrong and may not cover what you are after, but in this form this is a seriously flawed exercise. If you were thinking about chemical reactions then rewrite the exercise.