The Normal, the Natural, and the Harmonic

TL;DR

This paper explores the concepts of normality, naturalness, and harmonic growth using rigorous definitions, revealing complex relationships and conditions necessary for harmonically sustained natural growth.

Contribution

It introduces precise definitions for normal, natural, and harmonic, and analyzes their interplay in growth processes, highlighting conditions for harmonic natural growth.

Findings

Gaussian distribution alone cannot determine normality

Fluctuations around natural-growth curves may or may not be natural

Harmonic growth requires limited overlap during substitution processes

Abstract

Use is made of rigorous definitions for the terms normal, natural, and harmonic to reveal a number of unfamiliar aspects about them. The Gaussian distribution is not sufficient to determine who is normal, and fluctuations above or below a natural-growth curve may or may not be natural. A recipe for harmonically sustained natural growth requires that the overlap during the substitution process must be limited. As a consequence the overall growth process must experience good as well as bad 'seasons'.