Ambiguity, Invisibility, and Negativity

TL;DR

This paper explores how limited knowledge causes ambiguity and invisibility in various fields, requiring negative values to represent inherently positive quantities, with analysis across perception, mechanics, and quantum measurement.

Contribution

It introduces a unified mathematical perspective on ambiguity and invisibility, highlighting the role of negative values in different scientific contexts.

Findings

Ambiguity relates to limited knowledge in diverse problems.

Invisibility can be modeled using negative quantities.

Negative values are essential for representing certain physical and perceptual phenomena.

Abstract

Many widely different problems have a common mathematical structure wherein limited knowledge lead to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for quantities that are inherently positive. Here I analyze three examples taken from perception theory, rigid body mechanics, and quantum measurement.