Available online at www.sciencedirect.com _,, ·:;- ScienceDirect ELSEVIER Technological Forecasting & Social Change 74 (2007) 391-404 Technical note 1ed1nokJglcal RJI'ecasling and Social 01ange The normal, the natural, and the harmonic Theodore Modis * Vza Selva 8, Massagno, 6900 Lugano, Switzerla11d Received 16 February 2006; received in revised form 17 March 2006; accepted 16 July 2006 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". © 2006 Elsevier Inc. All rights reserved. Keywords: Nonnal; Gaussian; Natural growth; Fluctuations; Logistic growth; Hannonic; Product substitution; Cascading logistics; Business seasons 1. Introduction The hard sciences have traditionally attached rigorous definitions to common words. Most people are familiar with the physics terms: energy, force, momentum, and power. But more subtle concepts such as action, impulse, natural, and hannonic have also been endowed with scientific rigor. When everyday notions enter the world of science they become subject to natural laws and may occasionally yield unexpected insights. 2. To be normal is to be different Consider, for example, the word "normal". To define normal behavior psychologists use the bell- shaped distribution curve named Gaussian after its creator Karl Friederich Gauss (1777-1855). In * Tel. : +41 91 9212054; fax: +I 801 6506643 . E-mail address: tmodis@compuserve.com. 0040-1625/$ - see front matter © 2006 Elsevier Inc. All rights reserved.