Something that I always found fascinating is how DNA is a base 4 information format. There's this thing called radix economy, which is basically an expression of how efficient a number system is. Base e is the theoretical maximum, and so base 3 is the closest integer.

Obviously if you have a special use case, then that may dominate your radix economy (like hex, b64, etc...), but for general purpose information purposes, the order base 3, base 4, then base 2.

This present a lot of interesting questions to me. Like, why didn't DNA end up as base 3? (probably because 4 naturally lends itself to pairs of 2).

Also, this idea of radix economy goes beyond just the encoding of information and is represented in logical economy as well. So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant.

To that end, I have always wondered how nature has exploited this 4-state number system logically. Like, are there all sorts of exotic logic gates that come from a 4 state system?