What Is Entropy?

I'm not sure I understand the distinction between "high-entropy macrostate" and "order". Aren't macrostates just as subjective as order? Let's say my friend's password is 6dVcOgm8. If we have a system whose microstate consists of an arbitrary string of alphanumeric characters, and the system arranges itself in the configuration 6dVcOgm8, then I would describe the macrostate as "random" and "disordered". However, if my friend sees that configuration, they would describe the macrostate as "my password" and "ordered".

If we see another configuration M2JlH8qc, I would say that the macrostate is the same, it's still "random" and "unordered", and my friend would agree. I say that both macrostates are the same: "random and unordered", and there are many microstates that could be called that, so therefore both are microstates representing the same high-entropy macrostate. However, my friend sees the macrostates as different: one is "my password and ordered", and the other is "random and unordered". There is only one microstate that she would describe as "my password", so from her perspective that's a low-entropy macrostate, while they would agree with me that M2JlH8qc represents a high-entropy macrostate.

So while I agree that "order" is subjective, isn't "how many microstates could result in this macrostate" equally subjective? And then wouldn't it be reasonable to use the words "order" and "disorder" to count (in relative terms) how many microstates could result in the macrostate we subjectively observe?

I think you need to rigorously define your macrostates. If your two states are "my friend's password" and "not my friend's password" then the macrostates are perfectly objective. You don't know what macrostate the system is in, but that doesn't change the fact that the system is objectively in one of those two macrostates.

If you define your macrostates using subjective terms (e.g. "a string that's meaningful to me" or "a string that looks ordered to me") then yeah, your entropy calculations will be subjective.

That's better than how I was going to say it:

In one case you're looking at the system as "alphanumeric string of length N." In another, the system is that plus something like "my friend's opinion on the string".

Also, as the article says, using "entropy" to mean "order" is not a good practice. "Order" is a subjective concept, and some systems (like oil and water separating) look more "ordered" but still have higher entropy, because there is more going on energetically than we can observe.

I guess part of my question is, are there any macrostates that are useful to us that can't be described using more abstract human-subjective terms? If a macrostate can be described using human terms, I'd say the state is somewhat ordered. And if a state can't be described using human terms, then wouldn't it be indistinguishable from "particle soup" and thus not a useful macrostate to talk about?