1 + 1 = 3: Synergy Arithmetic in Economics

Abstract

Counting has always been one of the most important operations for human beings. Naturally, it is inherent in economics and business. We count with the unique arithmetic, which humans have used for millennia. However, over time, the most inquisitive thinkers have questioned the validity of standard arithmetic in certain settings. It started in ancient Greece with the famous philosopher Zeno of Elea, who elaborated a number of paradoxes questioning popular knowledge. Millennia later, the famous German researcher Herman Helmholtz (1821-1894) [1] expressed reservations about applicability of conventional arithmetic with respect to physical phenomena. In the 20th and 21st century, mathematicians such as Yesenin-Volpin (1960) [2], Van Bendegem (1994) [3], Rosinger (2008) [4] and others articulated similar concerns. In validation, in the 20th century expressions such as 1 + 1 = 3 or 1 + 1 = 1 occurred to reflect important characteristics of economic, business, and social processes. We call these expressions synergy arithmetic. It is common notion that synergy arithmetic has no meaning mathematically. However in this paper we mathematically ground and explicate synergy arithmetic.