A genuinely natural information measure

TL;DR

This paper introduces a new, genuinely natural measure of information called gnats, addressing the arbitrary choice of logarithm base in traditional entropy, and advocates for its adoption across various fields.

Contribution

The paper proposes a new measure of information, gnats, which removes the arbitrariness of the logarithm base used in entropy calculations.

Findings

Gnats provide a more natural measure of information.

Advantages of gnats in information theory are demonstrated.

Proposal for widespread adoption of gnats methodology.

Abstract

The theoretical measuring of information was famously initiated by Shannon in his mathematical theory of communication, in which he proposed a now widely used quantity, the entropy, measured in bits. Yet, in the same paper, Shannon also chose to measure the information in continuous systems in nats, which differ from bits by the use of the natural rather than the binary logarithm. We point out that there is nothing natural about the choice of logarithm basis, rather it is arbitrary. We remedy this problematic state of affairs by proposing a genuinely natural measure of information, which we dub gnats. We show that gnats have many advantages in information theory, and propose to adopt the underlying methodology throughout science, arts and everyday life.