Information, Physics and Computation (2009)

But they're not three entirely different concepts. Regular-capital-X, the random variable, is the object. Italic-X is its range, and lowercase-x is often something like an iterator over that range.

It might be a little clunky in isolation, but it lets you talk about multiple random variables and their properties in a fairly compact way.

You could write X, codomain(X), and possibleValue(X), but this would be pretty verbose.

This is the standard notation used in most probability theory books and courses.

Once you've famiarized yourself with the notation, which is standard, it's easy to understand and very efficient.

The set script-X, the random variable X, and the value x refer to three different but interrelated concepts. Using entirely different letters would likely make it harder to understand.

They are not distinguished by font: there is an an upper-case "X" (to mean a random variable) and a lower-case "x" to mean a sample from that radom variable. This is a very reasonable and useful case convention.

Finally there is the Greek letter Chi to mean the set over which that self-same RV varies. Chi seems deliberately chosen because it resembles "X". That might not be a good idea, but there is a defensible argument for it:

The domain Chi is a piece of mathematical machinery that is logically needed, but is not very important to the main disucssion. He wants to note it down, but also let it fade into the background. It's precesly because you want to pay too much attention to it that you are getting upset.

(I'm more worried that he seems to elide the distinction between the domain of an RV and the underlying sample-space. But then, sample-spaces are also mathematical machinery that aren't needed once the rubber hits the road.)

Very different. Their text focuses on the connections between stochastic systems, information theory, and machine learning/discrete models in mathematics, whereas the one you linked is purely about statistics and machine learning from a classical perspective.

btw, you've linked to a 2012 version of the book. Since 2012, they've added another author and changed the name of the book. I have no idea how much the content changed.

Anyway, here's the latest version of the book: http://www.cs.cornell.edu/jeh/book2016June9.pdf . (I got the link from http://www.cs.cornell.edu/jeh/)

I'm personally struggling to find a way of answering this that doesn't sound ridiculous on account of the fact that I've been obsessing over this stuff for several decades. These subjects address the heart of what it means to be able to make decisions and use language effectively. This subject matter is essentially a continuation of a broad attempt at a modern conceptualization of meaning, and as such it's value is immediately obvious to me... You should value this material because it is this kind of material that describes what 'value' is, why it is important, and what limitations it has.

But this is all absurd when I try to apply it to a specific book. It's a low rung on a ladder so tall nobody has seen the top.