THE CALCULUS OF DISTINCTIONS
TABLE OF CONTENTS
Calculus of Distinctions
Non-Numerical Arithmetic
The Algebra of Distinction
Types of Distinctions
Logical Interpretations of the Calculus
INTRODUCTION
The Calculus of Distinctions, a mathematical tool needed for the expansion of classical and modern physics into the broader domain of transcendental physics, is an adaptation and expansion of G. Spencer Brown's calculus of indications. The difference between the calculus of distinctions used in transcendental physics and Brown's laws of Form is both simple and profound: In transcendental physcis, based upon infinite continuity, consciousness is recognized as a subtle form of the universal substance, and time, space, matter and energy are derived from it by one process of differentiation--ie., the drawing of distinctions. Thus, different from Brown's calculus of indications, where the question of existence is superfluous to the logic of the calculus. In transcendental physics, the existence of consciousness as an integral part of reality is implied from the beginning with the assumption of infinite continuity.
Definition 1: CALCULATION
Calculation is the logical transformation of one form or expression into another equivalent but different form.
Definition 2: CALCULUS
A logical system developed for the purpose of calculation.
In order to understand how the various forms of the universe might arise in an infinitely continuous reality, it is necessary to develop a logical system, or calculus, to describe the process of drawing distinctions. We will first concentrate upon the logic and consequences of the making of distinctions. (For the purpose of developing the calculus of distinctions, it is not necessary to define exactly how or why distinctions are made. These questions will be considered when we apply the calculus to the distinctions of individualized consciousness, matter, energy, time and space.)
Definition 3: VOID
The void is an infinite expanse of undifferentiated substance; a state where there are no distinctions.
Without distinctions there can be no boundaries. Therefore, the void is, by definition, infinite and continuous.
Step 1. Contemplate the Void.
Definition 4: DISTINCTION
A distinction is the differentiation of a region or part from the rest of the infinitely continuous void.
Step 2. Make a distinction.
Let a region differentiated from
the rest of the void be represented in our calculus by the symbol 
.
Since voidness is a concept that arises prior to
enumeration and is, therefore, different from the value zero, we need a way to indicate
this state. In many transformations, the void state will not need representation since it
is the lack of any distinction whatsoever. However, in instances where we need to call
attention to it in order to avoid confusion, the void state will be denoted by
.
We shall use the following terms to denote the two states:
: distinct; 
: void Ex. 1*.
We must avoid using language, symbolism or concepts that may limit the calculus of distinctions since our purpose here is to develop the calculus in as general a sense as possible. Recognizing, however, that we operate in a world of at least three dimensions plus time, we will use the word region to denote the extent of a distinction.
*NOTE: "Ex." stands for "Expression", a general term that includes statements of equivalence or equations, along with other expressions.
Definition 5: REGION
A region is the extent over which a distinction operates.
Thus the making of a distinction involves the differentiation of a given region from the rest of the infinitely continuous universe.
Step 3: Call the distinction made in Step 2 the first distinction.
The region differentiated by the
distinction , including everything
within it, exhibits a form. This form may be considered the content of the distinction.
Subsequent distinctions (either within or in
relation to the region differentiated by the first distinction, since they are also
distinctions) may be represented by iterations of the symbol . Any arrangement of symbols may be called an
expression.
Any region of the universe is either differentiated or undifferentiated. Thus, at this point, we have defined two states: 1.) the state distinguished by the drawing of a distinction, and 2.) the void, which is the background or matrix containing all distinctions.
For the purposes of calculation, the state of a
region may be called its value. There are only two intrinsic or primary values for the
state of a region, one symbolized by ,
distinct, and one by , the void.
Prior to enumeration, regions of the same value
are, for the purposes of calculation, equivalent. Therefore, the size or shape of the
distinction, at this point, is irrelevant since there is nothing with which to compare it.
We shall use the symbols 
and 
to denote equivalence and the direction of
transformation.
The primary expressions of the calculus of distinctions are:
Ex. 2.
and
Ex. 3.
We may call Ex. 2 the form of condensation and expansion, and Ex. 3 the form of creation and cancellation.
Definition 6: SIMPLIFICATION
The value of an expression is equivalent to the value to which it can be simplified.
For example, given the expression
x = 
x may be simplified as follows:
x = 
by Ex. 2.
by Ex. 3.
Therefore, x =
We have discussed the need for a non-numerical language to describe the concept and the consequences of making distinctions in an infinitely continuous reality. Having defined two logical expressions that enable us to describe the basic processes of the making of distinctions prior to enumeration in an infinitely continuous reality, namely condensation/expansion (Ex. 2) and creation/cancellation (Ex. 3), our next task is to develop a non-numerical arithmetic for the calculus of distinctions.