Doing a mathematically elegant definition of complexity is easy. I've done it. Dealing with the messy real world is much harder. The first step, Dr. Gell-Mann proposes, is to identify a system's regularities. The schema for a language, for example, is its grammar, the rules for using it.
More complex languages have longer grammars than do simple ones.
Incoherent babbling cannot be described by a grammar. Measuring the length of a schema does not capture everything customarily meant by complexity. A genome, the sequence of genetic information coded in the form of DNA, can be thought of as the schema for an organism. The genome of a bacterium is shorter than that of a salamander. But the genome of a human and a chimpanzee are almost the same.