## How many tweets are possible?

Randall Monroe's latest "What If?" explores the total number of possible English-language tweets:

Based on the rates of correct guesses—and rigorous mathematical analysis—Shannon determined that the information content of typical written English was around 1.0 to 1.2 bits per letter. This means that a good compression algorithm should be able to compress ASCII English text—which is eight bits per letter—to about 1/8th of its original size. Indeed, if you use a good file compressor on a .txt ebook, that’s about what you’ll find.

If a piece of text contains n bits of information, in a sense it means that there are 2n 2^n different messages it can convey. There’s a bit of mathematical juggling here (involving, among other things, the length of the message and the concept of unicity distance), but the bottom line is that it suggests there are on the order of about 2140×1.12×1046 2^{140\times1.1} \approx 2\times10^{46} meaningfully different English tweets, rather than 10200 10^{200} or 10800 10^{800} .

Now, how long would it take the world to read them all out?

Reading 2×1046 2\times10^{46} tweets would take a person nearly 1047 10^{47} seconds. It’s such a staggeringly large number of tweets that it hardly matters whether it’s one person reading or a billion—they won’t be able to make a meaningful dent in the list in the lifetime of the Earth.