ognyankulev

Edit: OK, actually there is a separate page for alternatives: https://cborbook.com/introduction/cbor_vs_the_other_guys.htm...

"The starting point is the connection between diversity and entropy. We will discover:

• how Shannon entropy, originally defined for communications engineering, can also be understood through biological diversity (Chapter 2);

• how deformations of Shannon entropy express a spectrum of viewpoints on the meaning of biodiversity (Chapter 4);

• how these deformations provably provide the only reasonable abundance-based measures of diversity (Chapter 7);

• how to derive such results from characterization theorems for the power means, of which we prove several, some new (Chapters 5 and 9).

Complementing the classical techniques of these proofs is a large-scale categorical programme, which has produced both new mathematics and new measures of diversity now used in scientific applications. For example, we will find: [...]"

"The question of how to quantify diversity is far more mathematically profound than is generally appreciated. This book makes the case that the theory of diversity measurement is fertile soil for new mathematics, just as much as the neighbouring but far more thoroughly worked field of information theory"