Having successfully developed a non-numerical arithmetic, we may proceed to another level of expression that will enable us to investigate the role of distinction in an infinitely continuous universe. In order to describe the possible forms arising from the making of a distinction, we need to develop a formal procedure for dealing with expressions regardless of their value. Such a formal procedure would be an algebra based upon the non-numerical arithmetic. Algebraic expressions are functions of a variable or variables. Therefore, in order to develop an algebra, we must define relationships of variance and invariance or constancy.

As a result of the proving of the distinctness of all expressions with respect to transformation to and from simplicity, we may replace the transformation symbol,

by , which is identical in meaning to the customary mathematical symbol of equivalence, the equals sign: = .

We shall, therefore, take

  (invariance) Ex. 7.

as the initial equations of the algebra of the calculus of distinctions.

A great number of algebraic theorems may be proved using only these initial equations. Many of them may also be demonstrated by substituting the arithmetic values as we did in the proofs of Theorems 3, 4 and 5.

Since the object of this presentation is to apply the calculus of distinctions to understanding the nature of physical reality and its interaction and relation to consciousness, we will only develop the theorems and relationships necessary or appropriate to our needs as we proceed.

Recognition of the infinite continuity of reality brings with it a subtle shift of perspective. Our senses and cultural conditioning have led us to believe that appearances are real and that nature is built of discrete units like atoms, bodies, and planets. Recognition of the underlying continuity and unity of all things dispels this illusion. By contemplating the drawing of a first distinction in a void, we may begin to see how all the forms we perceive and the laws of natural science, especially those of physics, arise. Cosmologists try to visualize the origin of our universe in the "big bang", but the beginning of our perception of the universe lies in the conscious drawing or recognition of perceptual and/or existential distinctions.

The algebra we are developing is the symbolic representation of the making of a distinction and the logical consequences of this act. Let us use the calculus of distinctions to trace the consequences of making a distinction in the substance of the void.

The primary distinction may be visualized
as a perfectly symmetric contraction in a
uniform infinite expanse.

We have no reason to assume that the primary distinction is anything more than, or different from, the simplest possible existential distinction. Therefore, consider the primary distinction to be a perfectly symmetric contraction of substance. This perfect symmetry is consistent with the infinite continuity of the void. Since asymmetry would require a prior distinction in the void, any asymmetry would constitute a violation of the assumption of the continuity of the void. Therefore, asymmetry has no basis and is not allowable as part of the primary distinction.

We now return to the calculus of distinctions, bearing in mind the definition of the primary distinction as a simple, symmetric contraction of the universal substance of the void.

Now, Ex. 3, is the archetypical expression of Newton's Third Law and the Law of Conservation of Matter and Energy. It expresses the truth that with the contraction of substance, a corresponding expansion must occur because of the natural symmetry of the void. It also states that they are equal and opposite, resulting in a total effect equivalent to non-distinction. Thus nothing is created and nothing is destroyed on the universal scale.

As we developed complex expressions, we arrived at more general expressions, Ex. 7 and Ex. 8:

which, in terms of distinction as contraction of substance, state that the sum total of all the distinctions in the universe is always equivalent to the void and the existence of universal substance is invariant and unaffected by distinction. Thus nothing is ever created or destroyed. However, the infinity of the universe allows the illusion of creation and dissolution on any finite scale of perception.

The second law of thermodynamics, which states that the entropy of the universe is increasing with time, implies that order is disappearing from the universe. However, if the order we see around us is the result of a primary distinction drawn in an infinitely continuous void, as we have posited, then it will be helpful to have a term for decreasing entropy.

Definition 7: EXTROPY

Extropy is the organizing force existing prior to relative motion, or entropy.

"Ex" = before or beyond, "tropy" = turning or relative motion.

Extropy is order, or structured substance in the universe. This order is perceived in consciousness as distinctions and patterns of distinctions in time and space. Entropy is defined in physics as the degree of uniformity of a system, or of the universe. Thus, the void is a state of maximum entropy. Science has noted that all physical systems appear to tend toward greater entropy, i.e., toward the undifferentiated void. This observation prompted Bertrand Russell, in his book A Free Man's Worship to remark that all the works of man, however wonderful, are destined to end in the entropic death of the solar system.

A similar pessimistic attitude is reflected in Nobel Prize physicist Steven Weinberg's opinion that the more the we know about the universe, the more pointless it seems to be. Such views are the result of looking only in one direction: outward, toward what is assumed to be a physical world totally separate from the inner world of consciousness. This approach is not valid in the self-referential universe of infinite continuity.

The missing element in the entropic view of the universe is consciousness. Traditionally, physicists have not considered consciousness as part of the substance of reality. In an infinitely continuous universe, consciousness must be considered as a more subtle form of the same substance which comprises mass and energy. Then we must consider the order associated with conscious, organic forms in the total extropic-entropic picture. In an infinitely continuous universe, the contraction of the substance of the void into forms exhibiting order and organization is analogous to the conscious drawing of distinctions. This suggests that consciousness is the organizing force in the universe and the calculus of distinctions describes the process by which order is introduced.

Due to the perfect symmetry existing in the state of maximum entropy, i.e., the void, and the natural tendency of any system to return to a condition of equilibrium, the sum total of all forces in the extropic-entropic energy field we call the universe will always equal zero. The most general interpretation of Ex. 7 in an infinitely continuous universe expresses the law underlying all the laws of physics.

THE LAW OF EXTROPY/ENTROPY:
Entropy equals extropy.

Entropy is simply the outward manifestation of the universal law of extropy/entropy. There would be no universe for entropy to operate in were it not for extropy. The very fact that entropy operates in finite systems reveals the necessary condition that extropy has to precede it and co-exist with it.

In order to establish a logically consistent theory based upon the assumption of infinite continuity, we shall adhere to the parsimonious rule allowing nothing to enter the universe, arising from the primary distinction, without reason. Our algebraic expressions do not yet explicitly involve the notion of time. The expression x may represent a whole universe consisting of millions of distinctions without any reference to time. We might visualize this as our own universe, frozen at some specific point in time. We will only introduce time into our universe of distinctions when it becomes necessary.

We must also limit the scope of our treatment of the calculus of distinctions to the consequences and theorems that are needed for our purpose: application to relativity and quantum physics. While a number of useful theorems may be proved with the initial equations, (Ex. 7 and Ex. 8), we will only develop a few of them here.

As demonstrated in the previous section, of the two forms of our calculus, and , is always dominant, since represents the void and may be dropped from any expression without affecting the form of the expression. We have seen that if a distinction is affected in universal substance, an equal and opposite distinction inevitably exists due to the natural symmetry of the void. Thus we would expect the dominant form in such a universe to be an infinite pattern alternating between opposite and equal distinctions of contraction and expansion. Such a pattern may be visualized as a standing spherical wave pattern originating at the point of the first distinction and radiating in all directions to infinity. An oscillatory pattern, like that of electromagnetic radiation, is immediately suggested by this visualization.

It is desirable for the reader to develop some facility in following the calculations or logical transformations of the algebra of distinctions to facilitate understanding the arguments presented in this book. The symbols and logical expressions developed so far are summarized below:

: distinct; : void Ex. 1.

Ex. 2.

Ex. 3.

Ex. 4.

THEOREM 1.

Any finite expression may be simplified.

 

THEOREM 2.

The simplification of any finite expression is unique.

THEOREM 3.

Ex. 7

THEOREM 4.

X Ex. 8