English Language & Usage Asked by John Cooper on September 1, 2021
Is there a term that describes how far removed or how many change steps are between two given states or configurations?
Complexity is a term to describe that something is intricate or complicated, but it does seem to reflect the number of steps required to make the change. Degrees of change may be closer, but that doesn’t seem to be a common term.
As an example, a star has a great many components, parts, currents, etc., and could be considered complex. In comparison, a child’s toy is much less complex, but the number of proceeding steps required for a toy to exist (a planet to form, complex life to evolve, etc) is far greater. A child’s toy made from refined uranium, while of the same complexity as one made from wood, requires again more steps to create.
I am looking for a term to describe that the toy is far further removed from the universal base configuration than (for example) a star due to a greater number of steps required for the thing to exist.
It's doubtful that you'll do better than complexity for a situation as general as you describe. You are talking about steps, but what's a 'step'? The closest thing that comes to mind is a string metric, a measure of how different one string of symbols is from another, of which there are several (see e.g. here). One of these, for example, is the Levenshtein distance, which, roughly speaking, is
the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
In physics, particularly quantum mechanics, there are various ways to quantify the 'distance' between quantum states (see e.g. here). This seems quite close to what you are asking—except that, as far as I know, they do not involve the notion of 'steps'.
In probability and statistics, there is a notion of statistical distance. But again, the various kinds of statistical distance don't involve the notion of 'steps'.
Correct answer by linguisticturn on September 1, 2021
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