Adjointness expresses a condition that is essentially universal in mathematics, category theory, probability, logic, optimization, machine learning.
What is adjointness? Depends on the context.
This page is really illuminating.
I really like this definition: "adjoint operator ... back-projects information from data to the underlying model."
Essentially, it carries information about possible states at a point in time so that we can go back and forth.
Adjoint functors are the foundation of "category theory". Adjoint functors capture solutions to optimization problems.
The slogan is "Adjoint functors arise everywhere".
— Saunders Mac Lane, Categories for the Working Mathematician
Adjointnes is only a part of the story. One often sees equations
Adjointness is only a part of the story. Norm is the other character.
Check out Kolmogorov's three axioms of probability on Wikipedia. Translated, these mean: 1. 2. you have a norm 3. you have an adjoint
Chu spaces are essentially matrices
Linear logic is a logic
Constructive mathematics is mathematics without the law of excluded middle.