On the origin of ambiguity in efficient communication

TL;DR

This paper explores how ambiguity naturally arises in communication systems due to logical irreversibility and symmetry in coding and decoding complexities, explaining Zipf's vocabulary balance.

Contribution

It provides a formal framework linking ambiguity to logical irreversibility and symmetry in information processing, offering a new perspective on natural communication.

Findings

Ambiguity is a necessary feature of effective natural communication.

A symmetry equation relates coding and decoding complexities to ambiguity.

Logical irreversibility underpins the emergence of ambiguous codes.

Abstract

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.