The Origin of Algebra, Introduction

Dynamical historiography uses the concepts of bifurcation theory to analyze historical trends and their transformations. Three major bifurcations of world cultural history,
  • from the paleolithic to the neolithic
  • the discovery of the wheel
  • the chaos revolution
have been so analyzed, in recent writings. (See the book and articles in the Bibliography.)

The origin of algebra, in comparison, is a minor bifurcation in the history of mathematics. However, due to its key role in the paralyzing epidemic of math anxiety in the United States, together with our conviction that concepts are most easily learned in historical order, we have selected it for a dynamical historiographical analysis.

Our analysis, in this case, uses (tacitly) the paradigm of the reaction diffusion equation, which has been developed to model some of the mysterious natural phenomena of biological morphogenesis, such as,

  • How does the leopard get its spots?
  • How does an egg turn into a chicken?
This paradigm is the source of the peculiar metaphors we will use, namely, those of:
  • chemical reactions, as for example, 2H + O -> H2O, and of
  • hydrodynamical diffusion, as water through sand.
We are going to locate the origin of algebra in a chemical reaction beween different layers of cultural reactants diffusing through the geocultural medium:
  • the writing system (literatic) layer
  • the number system (arithmetic) layer
  • the spiritual system (kabbalistic) layer
Revised and Copyright 07 August 1998 by Ralph H. Abraham