George Spencer Brown
Only Two Can Play This Game

Bantam Books 1974

pg 111
Other Books:

G. Spencer Brown, Laws of form,

An account of the emergence of physical archetypes, presented as a rigorous essay in mathematics.

Starting with nothing and making one mark, we trace first of all the eternal forms. From these we obtain two axioms, and proceed from here to develop theorems.

The word angel, as we find if we look it up, means messenger, and the algebraic consequences that spring from any mathematical system are always the "Angels" through which the mathematics, which is basically structured in the eternal regions may be interpreted or applied in everyday life.

In this particular system, the consequences enable us to construct logic and to build computers. They turn out to be, in other words, the principles underlying Boolean algebra. It thus appears that accounts of the creation of the world, from Genesis back to Yin-Yang and beyond, turn out to be more or less evident, if incomplete, accounts of certain fundamental properties of Boolean mathematics.

Having arrived, then, at a point where we have reconstructed Boolean algebra, we then proceed to take it considerably further than the ordinary textbooks, into equations of the second and higher degrees, which Boole found no way of doing. What in fact we do now is extend the disciplines of Boolean algebra as in the ordinary numerical algebras, to include both real and imaginary values, thus introducing into Boolean mathematics what turns out to be an exact analogue of the arithmetical i = root(-1).

In the Boolean form, of course, the imaginary value is not in any way numerical, but does behave in all other essentials like its numerical counterpart, enabling us to solve equations and to reason in ways we could not manage without it.

Most astonishing of all, the use of this imaginary value reproduces, in the forms necessary to represent it, recognizable archetypes (what I calI "precursors») of particle and quantum physics, thereby constructing, without any outside help, the ground of what we call material existence.

It is constructed from nothing other than an unbroken sequence of argument whereby we see that,
if we distinguish anything at all, then "all this" - including in the end the physical universe - is how it must eventually appear. In short, what I prove is that all universes, whatever their contents, are constructed according to the same formal principles.