You aren't suggesting that statistics as a field defined a notion of "order", prior to thermodynamic entropy or Shannon entropy, are you? To me, that would be circular.

Based on my knowledge, it seems likely the first published quantification of disorder arose in the study of thermodynamic entropy. Later, Shannon defined entropy in information-theoretic terms, independent of physics. It can be interpreted as a notion of 'surprise' or what he called information.

My claims:

First, the field of statistics is _not_ historically rooted around concepts such as: "order/ordering" or "information/surprise".

Second, the field of statistics, as a directed graph of abstractions, is not rooted in ordering nor surprise.

Third, in teaching statistics, practically or conceptually, the concept of surprise isn't foundational. The idea of _variation_, on the other hand, is central.

I'll add a few more comments. To talk meaningfully about 'surprise', there has to be a stated or assumed baseline or 'expectation' about what is _not_ surprising. For Shannon, if the probability of an event is certain, there is no surprise. Probability and statistics work together, but they are conceptually separable. This is particularly clear when you compare descriptive statistics with, say, probabilities over combinatorics problems.

> The field of statistics is not organized around concepts relating to "order" or "ordering".

Sure but reduced to the simplest form, statistics are used to predict things, the most basic thing in the Universe being "is this particle gonna stay put or move a little in a given direction", which is related to entropy, so to me intuitively these two things seem very related. The fact that in statistics we don't use the words "order" and "disorder" doesn't mean it doesn't reduce to that.

Btw I'm an electrical engineer that isn't amazing at statistics or thermodynamics so beware I might just be talking nonsense.

> ... reduced to the simplest form, statistics are used to predict things

Inferential statistics is not the simplest kind of statistics. Descriptive statistics are both simpler and foundational for inference.

P.S. I should say that I am a bit of a stickler regarding discussions along the lines of e.g. "these things are related". Yes, many things are related, but it is really nice when we can clearly tease things apart and specify what depends on what.