Claude Code token cost explorer

If you want to pay less for the same type of Claude Code usage you have, you need to optimise your token production. To optimise your token production, you need to start from good data on when tokens are produced and why.

The Claude Code token cost explorer gives you enough details to use it as the basis for rational optimisation. There's lots of other tools that claim to do the same, but they don't.

Full article (4–10 minute read): Claude Code token cost explorer

Flashcard of the week

From Elements of Information Theory, by Cover and Thomas:

(Sidenote: this author duo is confusing because Cover's first name is also Thomas. I knew of Thomas Cover before reading this book, from his explorations of the Kelly criterion. I had to look up the other author – Joy Thomas – who apparently worked with information theory at Google.)

(Second sidenote: when I looked up Joy Thomas, I also learned that both Thomas Cover and Joy Thomas are dead. This affects me, because I do this weird thing where I email people I admire when I run into complicated problems I think they might enjoy. That doesn't happen very often, because my problems mostly aren't complicated, so it's not like I expected to ever email either of the authors. Yet when I discover people I admire having died I feel a weird sort of regret that I couldn't come up with a fun problem for them to think about before it was too late.)

Anyway, back to the flashcard.

What is a binary symmetric channel?

The reason we care about this definition is that it's one of the basic primitives of fundamental information theory, and results derived from binary symmetric channels can be used as approximations for many other situations.

But as is often the case with these terminology or definition questions, it's kind of hard to figure out the meaning of the definition from the question alone.

One might be able to guess that a channel is a communication channel, where a symbol is indicated on one end, with the intention of the other end receiving that same symbol. A binary channel is one where the symbol indicated is either 0 or 1.

The symmetric part is the one that's difficult to guess. It might have something to do with both 0 and 1 being treated equally in some way, but there's nothing in the question itself that reveals in what way.

Well, a binary symmetric channel is

A noisy channel where each bit is inverted independently of the others with probability p.

So it's a noisy channel (not obvious from the question itself!) where the probability of error is equal for both 0 and 1, and that's the symmetric part.

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