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    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.

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    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.