But one small complaint is I'm not sure if he's quite exactly worked out his audience. Early in the book, I was starting to fear it would be a rehash of stuff I already knew. It's not. But there were some elementary rehashes that, frankly, I think if someone went into the book not having that knowledge already, they aren't going to be able to grok the rest. This is not a mathematically demanding book, but it is a conceptually demanding book, and I am not sure if someone who doesn't have some limited grounding in the mathematics side will be able to make it through the conceptual side without missing a lot.
Carroll spends a good chapter or two explaining the rudiments of general relativity. At one point, he expends a few paragraphs for the benefit of people who don't know what a logarithm is. And then on page 176, he tosses this out:
Boltzmann has told us a compelling story about why entropy increases: There are more ways to be high entropy than low entropy, so most microstates in a low-entropy macrostate will evolve toward higher-entropy macrostates. But that argument makes no reference to the direction of time. Following that logic, most microstates within some macrostate will increase in entropy toward the future but will also have evolved from a higher-entropy condition in the past.
Emphasis is mine. Now, Carroll has been hinting at this for dozens of pages, and I've been anticipating it... but it's also been kinda bending my mind. Perhaps I am being a bit elitist, but I don't see someone who does not already have a deep gut feeling for mathematics understanding the profundity of that statement.
Now, I'm not saying I think someone needs to be an expert in general relativity, or a pro at computing logarithms, to understand this book. The treatment Carroll gives them is quite sufficient for his aims. Nevertheless, there is a certain math-y way of thinking which Carroll seems to take for granted, and I am skeptical that there are many people out there who are able to follow along with that assumed paradigm and yet who don't already know (at least conceptually) what a logarithm is.
It's not like the simpler material is entirely unwelcome: For me personally, I can always use a review of the rudiments of general relativity, as it's a concept my educational background unfortunately has given me very little time to explore. I can't exactly call curved spacetime "old hack", y'know? I'm just sorta wondering, does Carroll really think that someone who doesn't already have a firm grounding in basic math and physics is going to follow along with some of his more esoteric philosophical explorations of the nature of entropy? I'm skeptical.