Thomas McFarlane

With an Introduction by Joel Morwood

Holos: Forum for a New Worldview

Vol. 2, No. 2 (2006)


Thomas McFarlane is the author of Einstein and Buddha: The Parallel Sayings. He studied physics at Stanford University where he graduated with distinction in 1988. He also has a Master's degree in mathematics from the University of Washington, as well as a Master's degree in philosophy and religion from the California Institute of Integral Studies. He has written a number of articles on the philosophical aspects of physics, mathematics, and mysticism which are available online at his Integral Science website. McFarlane also serves on the board of directors of the Center for Sacred Sciences and is the editor of its online journal, Holos. This document is a revised version of an article originally published in McFarlane's 1995 book of essays Sacred Science and is copyright © 2006, 1994 by Thomas McFarlane. The introduction is written by Joel Morwood, spiritual director of the Center for Sacred Sciences, and is copyright © 2006 by Joel Morwood.

Introduction
by Joel Morwood

In this issue of Holos we are presenting a rather unusual article. In order to help our readers appreciate how it fits in with our mission to foster a new worldview in which science and mysticism can be seen as compatible ways of comprehending the same underlying reality, we are including this short introduction.

Let’s begin with the question: What exactly is a worldview? One answer, first suggested by Thomas Kuhn in his seminal work, The Structure of Scientific Revolutions, is that a worldview is determined by the paradigm to which individuals and/or members of a community are committed. According to Kuhn, a paradigm is a kind of map which helps those who adhere to it understand and manipulate the phenomena they encounter. More specifically, a paradigm is characterized by the following components:

  1. Symbolic generalizations. These are formulas expressed in the paradigm’s technical language which state its fundamental principles. Thus, E=mc2 is a symbolic generalization of science, expressed in its technical language, mathematics. Similarly, Tat tvam asi (That Thou Art) is a Vedantic formula, expressed in the technical terminology of Hinduism.
  2. Ontological models. These are the metaphysical assumptions or beliefs about the ultimate nature of reality which are held by members of a community adhering to a common paradigm. The axiom that the speed of light is a constant in all reference frames, for instance, is a cornerstone of modern physics, while all dharmas are empty is a basic ontological tenet of Mahayana Buddhism.
  3. Shared values. Kuhn used this phrase to refer primarily to those aesthetic standards, like simplicity and elegance, which guide scientists in their selection of competing theories. But it can also refer to moral and spiritual values which guide members of a religious community in their daily lives, such as the Judeo-Christian admonition to love thy neighbor.

  4. Exemplars. A paradigm’s exemplars are usually its creators or (in the case of religious paradigms) revealers, who are then held up as pedagogical models for later generations to emulate. Thus, Isaac Newton was the exemplar par excellence for classical physics, while the legendary sage, Lao Tzu, is the primary exemplar of the Taoist tradition.

In addition to these four components identified by Kuhn, we may add a fifth component:

  1. Epistemological criteria. These criteria determine what a community accepts as being valid ways to gain knowledge. In scientific communities the scientific method, which tests conceptual theories against experiential evidence, is considered the only valid way to acquire knowledge. Mystics, on the other hand, insist that, while concepts and experience may produce relative knowledge about the relationships between things, there is another direct way of knowing—a realization or gnosis—which discloses absolute knowledge about the ultimate nature of things.

One advantage of applying Kuhn’s analysis to our task of constructing a new worldview which can unify science and mysticism is that it immediately suggests a systematic, three-pronged approach:

  1. We need to determine if mystics from different traditions adhere to a single paradigm.
  2. We need to determine which of science’s paradigms is the most fundamental—i.e., the one to which all other paradigms must conform.
  3. We need to compare the components of these paradigms to determine which ones are already compatible, which ones contradict each other, and how the contradictions might be resolved.

As to the first part of our task, many scholars have argued that mystics do, indeed, adhere to a single, esoteric paradigm—or perennial philosophy—which is embedded in, but transcends the exoteric paradigms of their respective religious traditions. Although this is still a matter of some debate (e.g., see the Holos interview with David Loy), one point is clear: If such a meta-paradigm does, in fact, exist, it will almost certainly contain the following components:

  1. A nondual ontology that, in particular, holds the subject/object distinction to be imaginary.
  2. Epistemological criteria that recognize the validity of a gnosis which discloses the nondual nature of reality.
  3. Exemplars who have in common the fact that they all claim to have attained such a gnosis.
  4. Moral values which emphasize a life of selfless love and compassion, because, ultimately, there is no real distinction between oneself and others.
  5. A technical language whose statements about the nondual nature of reality are inescapably paradoxical, because language, itself, creates duality by distinguishing one thing from another.

As to the second part of our task, identifying science’s most fundamental paradigm, this remains a challenge for several reasons:

  1. Quantum mechanics and relativity, the cornerstones of modern physics, have resisted all efforts to unify them into a single paradigm with a consistent ontology.
  2. Quantum mechanics is, itself, open to several different ontological interpretations that contradict each other. Thus, despite the spectacular practical success of modern physics, there is no consensus on what it tells us about the fundamental nature of reality.
  3. The epistemological validity of the scientific method hinges on an assumption that facts have an objective existence independent of the subjective theories we formulate about them. But, as Kuhn himself showed, when old paradigms are supplanted by new ones, it is not just the theories that change, the facts do as well. Moreover, this coincides with observations from other fields, such as psychology, sociology, and anthropology, which suggest that even our most basic perceptions are “theory-laden.”
  4. Scientific values, such as simplicity and elegance, cannot be derived either from science’s ontology or epistemology. They are apparently grounded in nothing more than the pure subjective preferences of scientists themselves.
  5. Finally, while mathematics remains the undisputed technical language of science, some physicists, like the Nobel Laureate Eugene Wigner, have puzzled over its “unreasonable effectiveness” in describing natural phenomena.

One answer to this last mystery (which, as we shall see, is particularly pertinent to our article) might be that the concept of symmetry is essential both to mathematics and to one of the few ontological assumptions which has survived the quantum carnage, namely, that the complexity we witness in the universe at large is the result of broken symmetries. And yet, this still leaves unanswered the question, why should this be so?

In any case, what all this confusion and controversy signifies is that science is presently in the throes of a paradigm crisis—a situation which greatly complicates our third task of comparing scientific and mystical paradigms. With no single paradigm governing all of science, we cannot set up a simple one-to-one correspondence between their various components to see which are compatible, which are contradictory, and why. This, however, has not stopped interested investigators from fruitfully exploring many aspects of the relation between these components, even if they have had to go about it in a somewhat piecemeal fashion.

For example, some thinkers have tried to demonstrate similarities between a mystical ontology and the ontology implied by one or another of quantum mechanic’s interpretations (see Fritjof Capra’s The Tao of Physics and Thomas McFarlane’s Einstein and Buddha). Others have tried to show that science’s epistemological criteria and mysticism’s epistemological criteria are not necessarily incompatible (see, for example, our previous contributors Alan Wallace and Harold Roth). Still others—including one of the fathers of quantum mechanics, Werner Heisenberg—see the quantum revolution as establishing the ancient Greek philosopher-mystics, Pythagoras and Plato, as the original exemplars of modern science. But as far as we know, very few of today’s thinkers have examined the technical languages of science and mysticism and asked, can the symbolic generalizations of mystics of different traditions be translated into the mathematical language of science? And if so, what would that tell us about the nature of science, the nature of mysticism, and the nature of the underlying reality both claim to disclose?

In this issue of Holos we are excited to introduce the work of someone who has done just that. He is our very own editor, Thomas J. McFarlane. In the following article, Mr. McFarlane offers not so much an argument for the possibility of such a translation, but an actual demonstration of it. We hope this inspires others to pursue these investigations further.


The Play of Distinction

By Thomas McFarlane

The Fundamental Nature of Distinction

The one and many … run about together, in and out of every word which is uttered.
Plato, Philebus, 15D

Every word uttered and every thought conceived directs attention and thereby carves out a portion of the world. It is in the very nature and purpose of words and thoughts to specify and delimit, to distinguish something from other things, to create a many from what was previously a one. Every idea contains an implicit distinction between that which it indicates and that which it does not indicate. Indeed, if any thought or word did not direct our attention to one thing as opposed to another, it would be entirely without meaning.

The root of all things is difference.
Ibn Arabi (William C. Chittick, The Sufi Path of Knowledge, SUNY, 1989, p.67)

Everything has at its root an implicit distinction. If they were not distinguishable, letters of the alphabet could not form different words and digits could not form different numbers. With no distinctions, there could be no inside of a house distinct from an outside, no red distinct from blue, no me distinct from you. There would be no difference between apples and oranges, men and women, subject and object, existence and non-existence.

In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by it; and without it was not any thing made that was made.
John 1:1-3

Thought and language can get no more fundamental than to make a distinction, for whenever we have any thing at all we have at least one distinction: the distinction between that thing and no-thing. No matter what it is, whether it be a fleeting thought in the mind, an irritating itch on the arm, a puffy cloud in the sky, or heavy sadness of the heart, all things depend on that one implicit distinction. Indeed, if there were no distinction at all, then there would be no thing at all.

If God stopped saying his Word, but for an instant even, heaven and earth would disappear.
Meister Eckhart (Whitall N. Perry, A Treasury of Traditional Wisdom, Quinta Essentia, 1971, p.787)

There is something precisely because there is distinction—all things are created by distinctions, by the power residing in the Word to divide something from nothing, existence from non-existence, heaven from earth, and day from night.

The Ground of Distinction

The Tao that can be told is not the eternal Tao. The name that can be named is not the eternal name. The nameless is the beginning of heaven and earth. The named is the mother of ten thousand things. These two spring from the same source but differ in name; this appears as darkness. Darkness within darkness. The gate to all mystery.
Lao Tzu (Tao Te Ching, Chapter 1)

Any thing made is made by distinction. But if all of creation rests upon distinction, then upon what ground does distinction rest? Since distinction is the foundation of all concepts and definitions, it cannot be defined or conceived by anything more fundamental than itself. So if we seek a source of creation more profound than distinction and its worldly progeny, we must surrender all powers of conceptual representation and definition—thus we enter the realm of the ineffable.

The ultimate truth transcends all definitions and descriptions, transcends all comments and disputations, transcends all words.
Nagarjuna (K. Venkata Ramanan, Nagarjuna’s Philosophy, Motilal Banarsidass, 1966, p. 272)

However we may try to describe, define, conceive, or imagine That which is prior to distinction, such efforts necessarily involve distinctions and will at best produce only a distorted reflection of it. The best description of it is silence, the closest definition is nothing, the most precise concept is the concept of non-distinction. Yet even the word silence rests on its distinction from the speech, even nothing depends on its contrast with something, and even the concept of non-distinction is defined in contrast with distinction. So, in the end, we must surrender even the distinction between distinction and non-distinction, between form and emptiness, something and nothing. True Reality comprehends the way of distinction as well as the way of non-distinction, and neither way as distinct from the other can comprehend the non-exclusive Reality embracing them both.

The Unfolding of Distinction

The world is what would be if distinction could be.
G. Spencer-Brown (AUM Conference, Esalen Institute, 1973)

We cannot perfectly describe or define Reality in its indescribable, ineffable completeness. Yet the describable, definable aspect of Reality is exactly what we can describe and define. So if we are to think or talk about anything, we must think or talk about what is thinkable and sayable, i.e., what is distinguishable. So, let us distinguish and describe the realm of distinction and description. At the same time, however, let us not forget that the thinkable world created by distinction is a world of imagination and leaves out the indescribable realm prior to distinction. The describable, definable world is thus only a part of Reality, an imperfect expression of its uncreated, ineffable Source.

The ultimate reality is unmade; it will never be other than what it always is.
Nagarjuna (Nagarjuna’s Philosophy, p.268)
The unreal never is: the Real never is not.
Bhagavad Gita II, 16

The most fundamental of all distinctions is the distinction between distinction and non-distinction. For, as we have just seen, this distinction makes distinction itself possible. That is, the first created thing necessarily consists of the distinction between distinction and non-distinction. Thus, out of the mysterious depths of Reality, distinction apparently creates itself, and provides the seed for the elaboration of all form. From this original principle arises all form. Yet the principle of distinction is not the ultimate principle of Reality, for distinction is only the basis of form, and not the basis of Reality, which is beyond both form and formless, existence and non-existence, one and many.

There is in reality neither truth nor error, neither yes nor no, nor any distinction whatsoever, since all—including contraries—is One.
Chuang Tzu (A Treasury of Traditional Wisdom, p.979)
The cosmos is not a unity here and a plurality there, but a unity and a plurality at the same time throughout its whole being.
Proclus (Morrow and Dillon, Proclus’ Commentary of Plato’s Parmenides, Princeton, 1987, p. 130)

Insofar as the formless is distinguished from form, it has no possibility for the development of form. Within the realm of form, on the other hand, there is the possibility for infinite development of form. The worlds of form thus flower from the single seed of distinction sprouting from the ground of Reality, freely branching out in a self-similar manifestation of diverse possibility. This is the great tree of life.

Systems of Distinction

The particular world you experience in each moment is just one branch of all possible ways for form to unfold. If we look inward toward the root of all diversity, we find growing unity, worlds merging in a single trunk. If, on the other hand, we look outward, away from unity toward the branches, we find growing diversity, worlds multiplying endlessly. These two faces of distinction, one reflecting inner unity, the other reflecting outer diversity, illustrate the nature of the first distinction, which distinguishes a prior non-distinction from a posterior distinction, a fundamental unity from a derived diversity, an original one from a created many. This dual nature of distinction is mirrored at every level of the self-similar tree of form. Looking inward is a straight path to the one, looking outward are multiple branches into the many. Yet, lest we forget, this whole tree is ultimately not distinct from the mysterious ineffable One transcending both one and many.

The One … is there before every oneness amid multiplicity, before every part and whole, before the definite and indefinite, before the limited and the unlimited. It is there defining all things that have being, defining being itself … . It is there beyond the one itself, defining this one.
Pseudo Dionysius (Paul Rorem, Pseudo Dionysius, Paulist Press, 1987, p.129)

At the base of the tree are few distinctions; and where there are few distinctions there are few limitations and conditions, and hence a high degree of universality and comprehensiveness—this is the subtle realm of the archetypes, cosmic laws, and universal principles. At the very root of the tree is the single, most universal seed of all—the first distinction. Emerging from this most subtle of all things are branches of additional distinctions, further restricting and delimiting worlds of form in particular ways unique to their specific branches. Yet, prior to this most subtle of distinctions, there is neither distinction nor non-distinction.

When difference is not evident, there is neither difference nor identity.
Nagarjuna (D. Kalupahana, Nagarjuna: The Philosophy of the Middle Way, SUNY, 1986, p.227)

This is no dead and inanimate tree but an alive and growing one. In some places branches break off, and in other places new ones grow. Flowers bloom, leaves fall, and fruit ripens. The branches of distinctions are alive and dynamic, forming and reforming. Yet they are always recreated as manifestations of the first seminal distinction, with the one and many running in and out of every distinction made—the one leading back to the root, the many leading out to more branches. In fact, this whole tree is recreated every moment, emanating and unfolding, then retracting and returning to its ground, the pulsation of the universal heartbeat, the great ebb and flow of the cosmic ocean, the harmonic vibrations we hear as the music of the spheres. Still, prior to sound and silence is the great One comprehending both.

The One transcends all antithesis, rises above all relation, is pure from all duality.
Proclus (Proclus’ Commentary of Plato’s Parmenides, p. 429)

Any system of thought is limited by the very fact that concepts distinguish, define, and thereby implicitly limit and exclude. Just as no branch of a tree is the whole tree, no conceptual system is an all-inclusive theory of everything. Yet it takes only a slight act of ignorance to consider one manifestation of form real and true, while considering the other possible manifestations of form false or merely imaginary. This prejudice, however, results from a limited view within one branch of the tree. Tracing the roots of any world back far enough, and freeing ourselves of the structures that limit us exclusively to one particular world, we then recognize the common basis of the worlds that we previously saw as distinct. And the ultimate such recognition is the recognition that all worlds of form are really no different from formlessness.

Within Consciousness-Without-An-Object lie both the Universe and Nirvana, yet to Consciousness-Without-An-Object these two are the same.
Franklin Merrell-Wolff (The Philosophy of Consciousness Without An Object, Julian Press, 1973, p. 104)

Can we find the most basic unified theory near the trunk of the tree of life? The closest one may get to a theory of everything is the first distinction itself. To say any more serves only to further limit and exclude things from the class of everything we wish to comprehend. But even a theory of everything would only be a theory of things, and not a theory of Reality, which includes nothing as well as everything.

The Metaphysics of Distinction

At the beginning of the beginning, even nothing did not exist.
Chuang Tzu (A Treasury of Traditional Wisdom, p. 26)

To begin with no distinction at all is to begin prior to thought. Indeed, we cannot consistently conceive of there being no distinction since in so doing we would be implicitly distinguishing non-distinction from distinction. Thus, at this ineffable point of ultimate simplicity, there is no difference between distinction and non-distinction, between subject and object, or between any opposites whatsoever. There is no difference between emptiness and form, between substance and void, between something and nothing.

For the wise all “things” are wiped away and even the state of imagelessness ceases to exist.
Lankavatara Sutra (D. Goddard, A Buddhist Bible, Beacon Press, 1970, p. 302)
God dwells in the nothing-at-all that was prior to nothing, in the hidden Godhead of pure gnosis whereof no man durst speak.
Meister Eckhart (A Treasury of Traditional Wisdom, p. 41)

Following the notation of G. Spencer-Brown (Laws of Form, Julian Press, 1977), let us symbolize form with a circle, O, and the absence of form with an empty space,   . We may then symbolize the identity of form and formlessness by the equation O =   . The equation asserts the identity of form and void, universe and nirvana. And when all objects are identified with the void, they are then identified with each other as well. There is no distinction whatsoever. Recognition of Reality at this level is totally comprehensive of both form and emptiness, one and many. All things may appear, and yet they are recognized to be identical with nothing, so that, no matter how objects may appear and disappear, Reality itself is unchanged.

The energy which moves [the universe] is the principle of rupture of equilibrium. But, nevertheless, this becoming, composed of ruptures of equilibrium, is in reality an equilibrium because the ruptures of equilibrium compensate each other. —Simone Weil (Intimations of Christianity Among the Ancient Greeks, p.185)
An object exists as a tension. Although, in the ultimate sense, every tension is balanced by its opposite phase, so the equilibrium is never actually destroyed, yet consciousness, taken in a partial aspect, may comprehend only one phase, or may be only imperfectly conscious of the counterphase. For this partial aspect of consciousness, equilibrium does not exist. —Franklin Merrell-Wolff (The Philosophy of Consciousness Without An Object, p.228)

If the identify of form and emptiness is ignored, breaking the original symmetry and equilibrium, the illusion of a real distinction between subject and object, form and void arises. Since everything is, in fact, identical with Reality, such a distinction—although imagined—is not real, for Reality cannot actually be other than what it truly is. Moreover, for something to appear distinct and real apart from Reality, its true identity with Reality must be ignored. It is only through this ignorance of the imaginary nature of distinction that anything attains an appearance of its own independent reality. Thus begins the development of what would be if distinction could be, or what appears to be when we ignore what is.

The whole of existence is imagination within imagination, while true Being is God alone.
Ibn Arabi (A Treasury of Traditional Wisdom, p. 94)

The veil having thus dropped, Reality is eclipsed by an illusion, and the play of distinction appears real. With Reality hidden, we become half-blind, ignoring the non-dual and knowing only the dual. Thus, it is the exclusive knowledge of duality that precipitates our fall; and in this state of ignorance of the One, we see only a manifold world of separate things, and are thereby in bondage to them.

For what is here is there, and what is there is here;
From death to death hastes he who here another knows!
In spirit shall ye know, here is no manifold;
From death to death is he ensnared who difference sees.
Katha Upanishad (Paul Deussen, The System of the Vedanta, Dover, 1973, p. 53)

Under the spell of duality, every object, every conception, every imagination, every this and every that is falsely seen as a self-existent reality. But the true Reality is not any imagined form or object.

neti, neti! [not this, not that!]
Brihadaranyaka Upanishad II, iii, 6

Just as ignorance of the Non-dual binds, recognition of the Non-dual liberates. The final realization is the complete recognition of the Absolute Non-dual which is not even distinct from the dual. Here it is immediately known that one is already identical with Reality, and that there is nothing to be attained. Indeed, the identity between subject and object, knower and known, seeker and sought, is recognized as the true Reality that always is, always was, and always will be.

In the beginning was Allah, and beside Him there was nothing,—and He remains as He was.
Muhammad (A Treasury of Traditional Wisdom, p. 804)

Here we have traced the play of distinction from Reality, O =   , to the first stage of illusion, O ≠   , and back, from vision to half-blindness and back. We have created a world and destroyed it, been born and died. Note, however, that this return from creation does not involve any real destruction of a world but a realization that the world had never actually been created, and this death reveals not a dead state but an unborn one. Just as the One transcends both one and many, the True Uncreated comprehends both created and uncreated, and the True Unborn transcends both birth and death.

Both the Absolute and the Relative belong to one and the same Reality.
Ramakrishna (A Treasury of Traditional Wisdom, p. 807)

Worlds may evolve much further beyond this one single step into form. Thus, we may find ourselves not just half-blind, but nearly completely blind. Not only is the unity beneath the diversity of subject and object ignored, but we also ignore the unity of objects in the world at more complex levels of manifestation. Not only is the identity of emptiness and form broken, but the identity of form and form is broken, apparently breaking symmetries and giving birth to complex worlds of form. Let us follow this descent into form more explicitly, not forgetting, of course, that this is an imaginary play of distinction.

The world of Nature is many forms in One Mirror; nay One Form in diverse mirrors. Bewilderment arises from the difference of view.
Ibn Arabi (A Treasury of Traditional Wisdom, p. 782)

From the Reality that identifies form and void, O =   , we first imagine distinction between form and void, O ≠   . If this distinction is taken to be real, then all form is mistaken to be truly distinct from formlessness. This mistake represents an ignorance of the fact that the dual is not ultimately distinct from the non-dual. Now with ignorance veiling this Nondual Reality from view, distinction comes to the foreground and dominates non-distinction. As yet, however, there are no distinctions between various forms. All form is identified as form only. Here we reside on the universal level with the seed of all creation. On the one hand, this seed is the origin of the multiplicity of all things; on the other hand, this seed is, in Truth, identical with the original Unity.

He in his unity is all things: so that we must either call all things by his name, or call him by the names of all things.
Hermes Trismegistus (A Treasury of Traditional Wisdom, p. 783)

The structure inherent in this seed is reflected in the development of all form. Explicitly, the structure of this seed is to distinguish and produce multiplicity. Implicitly, this seed joins and produces unity. When we ignore the unity implicit in distinction, we are, as it were, only looking at one side, the side of division. On its other side, on its other face, is unity. This first distinction thus implicitly contains its opposite, non-distinction. If taken as real, the distinction itself becomes the veil that hides non-distinction from view. But although this distinction divides, it also connects; while it separates, it also binds.

Each thing hath two faces, a face of its own, and a face of its Lord; in respect of its own face it is nothingness, and in respect of the Face of God it is Being. Thus there is nothing in existence save only God and His Face.
Al-Ghazali (A Treasury of Traditional Wisdom, p. 986)

Prior to distinction we have no choice in development except to create the first distinction. Once there is a distinction, however, we have choices. One choice, as seen above, is to return back from form into emptiness. That appears as creating distinction and dissolving it. On this path, we first ignore Reality to obtain distinction, then surrender distinction to recognize Reality.

Another path is to fix the first distinction and build upon it. Once the first distinction is reified, form and emptiness are seen as completely separate. A second action or distinction may then be considered in relation to the first distinction as an instruction to cross from one side of the first distinction to the other side while still maintaining the first distinction. Thus, this second distinction, combined with the first, takes us between reified form and reified formlessness. Note, however, that this formlessness is a formlessness contrasted with form, and is not the Reality prior to distinction that transcends and comprehends both form and formlessness. We could express this second distinction taken with the first as a circle around the first circle, (O).

Alternatively, a second distinction may be construed as an instruction to make another distinction like the first. Since we are retaining the first distinction, this creates a second distinguished distinction. Thus we have two similar distinctions, which may be represented as OO. The second distinction is distinct from the first form, and from the void, and is, as it were, a copy of the first distinction. The first distinction created the world as distinct from void. But the world itself is not more than a potential world until the second distinction arises, making it explicit. Making this second distinction or not is a mirror or image of making the first distinction or not.

The second distinction, therefore, can be a symbol for crossing the first, (O), as well as for creating an additional distinction similar to it, OO. Thus there are exactly two ways to make a second distinction.

The Mathematics of Distinction

Since there is no other approach to a knowledge of things divine than that of symbols, we cannot do better than use mathematical signs on account of their indestructible certitude.
Nicholas of Cusa (A Treasury of Traditional Wisdom, p. 310)

Let us express this unfolding play of distinction in more symbolic form. First note that the mark, O, distinguishes a blank page from a page with a mark on it. Thus, the mark represents the fundamental distinction between distinction and non-distinction. Without the cognition of a mark, there is no notion of a blank page as distinct from a marked page, and every mark is identical with no mark.

Everything is of the nature of no thing.
Parmenides (A Treasury of Traditional Wisdom, p. 789)

Thus the very existence of the mark implies an implicit distinction between its existence and its non-existence, between the sign and the space in which it is written, between the mark as an object and the void page without the mark. This is how our symbol represents the first distinction.

If we remember what we have done, however, then distinction becomes transparent: We recognize the imagined nature of the distinction, and so there is the possibility of recognizing the Origin in which there is not any distinction even between distinction and non-distinction. Thus while imagination creates and takes us across the first distinction into apparent duality, O ≠   , recognition sees through that distinction by canceling the imagined reality of the original distinction, O =   .

Form is emptiness, emptiness is not different from form, neither is form different from emptiness, indeed emptiness is form.
Heart Sutra (A Buddhist Bible, p. 85)

Depending on how it is viewed, the distinction is a symbol for form as distinct from emptiness and a symbol for form as identified with emptiness. The distinction thus symbolizes both sides of the distinction. But while it consistently symbolizes the side of distinction, it inconsistently symbolizes the side of non-distinction. Distinction dominates over non-distinction in the world of distinction for the simple reason that the world of distinction is based upon distinction, not non-distinction. As objects, symbols presuppose distinction, and so they naturally resist non-distinction, for their very being as objects is in conflict with it. This contradiction, however, is only a problem if we take as given the distinction between distinction and non-distinction, between image and void. In Truth, since there is really no distinction between them, there is only apparent, imagined contradiction, and thus any symbol is itself identical with both distinction and non-distinction. So the same mark of distinction can symbolize both faces of distinction. It is distinction insofar as we reify distinction, and is non-distinction insofar as we don’t reify distinction. The mark thus has two meanings or faces, one dominant or explicit, the other recessive or implicit. Even this duality, however, is not ultimate.

There is not Nirvana except where is Samsara, and no Samsara except where is Nirvana. All duality is falsely imagined.
Lankavatara Sutra (A Buddhist Bible, p. 292)

The two distinct faces of the first distinction may be represented by the inside and the outside of the mark, O. Note, however, that distinction in its abstract purity does not necessarily distinguish a two-dimensional space, or even a space of any dimension at all. We are taking one instance of distinction (a closed curve in a plane) and using it as a symbol for distinction in the abstract. In so doing, we must be careful not to attribute to distinction itself properties peculiar to this particular representation of it.

In this geometrical representation of distinction, the inside represents formlessness and the outside represents form. Thus, marking the outside of one distinction, represented as OO, indicates making another distinction in addition to the first, while marking the inside, represented as (O), indicates crossing back over the first distinction to the void. Note that a pair of parentheses, (), is used here to denote a circle containing the circle O. Thus, by fixing distinctions and making further distinctions we can create ever more complex forms that unfold the implicit potentialities of the first distinction.

The whole development of complex worlds of form can be seen as one gradual attempt to cross the first distinction, to create a perfect image of the original void. But since there really is no distinction, we can never actually make such a crossing, we can never perfectly reflect Reality in an image. Thus the unfolding of the play is endless. It forever elaborates a more refined reflection of Reality. It gets closer and closer, reaching toward infinity, but never ends, for what never really began can have no end.

An understanding of God is not so much an approach towards something as towards nothing; and sacred ignorance teaches me that what seems nothing to the intellect is the incomprehensible Maximum.
Nicholas of Cusa (A Treasury of Traditional Wisdom, p. 723)

Levels of Form

We may now formally outline the development of form in stages.

Level 1

At the first level there is simply the Reality prior to distinction. Whether we mark, O, or do not mark,   , we indicate the same Reality. At this level, form is emptiness and emptiness is form, samsara is nirvana, the named is the unnamed, the object is the subject. The image of this level as seen from later levels of distinction is contradiction and self-reference, for here we have apparently identified opposites. The name “void” names void and is void, so it names itself. We can symbolize this level as O =   , i.e., form is void. This yields a mathematics of unity.

God may be called nothing because he is none of all the things that we can imagine or understand; but in himself he is indeed as it were all in all.
Father Augustine Baker (A Treasury of Traditional Wisdom, p. 725)

Level 2

At the second level we have imagined and reified a distinction, we have ignored or veiled Reality. Now the mark is not the void, O ≠   . In other words, form is distinct from emptiness, samsara is not nirvana, the named is not the unnamed, the subject is not the object. This level is the basis of distinction and consistency and all form, and appears as real only insofar as the first distinction is imagined to be real. Note that although we have distinguished something from nothing, O ≠   , we have not distinguished things from each other. Thus, at this level form is form is form, so any combination of multiple distinctions is identical with the first distinction: OO = (O) = O. Because of the instability of imagination, however, we may remember the unity of form and formless. This insight would negate the distinction—which is itself a negation of the original One—and return us to level 1. This return can be represented in form by identifying formlessness with the negation of form, i.e., (O) =   .

The One is a negation of negations.
Meister Eckhart (A Treasury of Traditional Wisdom, p. 789)

On the other hand, another distinction may be used to reassert the first distinction, i.e., OO = O. We thus obtain the equations

OO = O

and

(O) =   .

As shown in Laws of Form, this yields a two-valued arithmetic that embodies elementary logic. In this system, the universe of form is symbolized by a negation of void, O, while the void is symbolized by a negation of this negation, (O). For any value x, the two rules above may be generalized to obtain

xx = x

and

((x)) = x .

Level 3

Note that we passed from level 1 to level 2 by ignoring the equality O =   , to obtain O ≠   . The equality of form and formlessness was then represented by a more complex equation, (O) =   . Following this pattern, it is possible to make further distinctions between forms of distinctions by continuing to ignore certain identities and by equating formlessness with ever more complex forms. At the next stage, for example, we can break the identification of the two nested distinctions with the void so that (O) ≠   . This corresponds to viewing the negation of form as itself just another kind of form rather than as a symbol transparent to the void. With this break in symmetry, we have two distinct values of form, O ≠    and (O) ≠   , both of which are held distinct from the void. If we cling to these distinctions, we are led to create a more complex symbol for the void. The simplest form available is a combination of three distinctions. There are three ways to combine three distinctions, namely, OOO, ((O)), and O(O). The first simplifies to O using OO = O twice. The second simplifies to O using ((x)) = x once. The third, O(O), however, does not simplify. Thus, without violating any existing rules, we may identify O(O) =   , which may be interpreted to mean that the void is both form, O, and not form, (O). Here we arrive at a three-valued arithmetic with values    , O, and (O).

Level 4

Breaking the identification O(O) =   , we obtain four distinct values,    , O, (O), and O(O). If we hold these distinctions, then we are led to a fourth symbol of the void. There are eight possible combinations of four distinctions, but only (O(O)) does not reduce to one of the four values. Thus we may identify (O(O)) =    and obtain a four-valued arithmetic. The interpretation of (O(O)) =   , is that the void is not both form and not form, i.e., that it is neither form nor not form.

In words, these first four levels may be interpreted as follows:

   = O             Emptiness is Form

   = (O)          Emptiness is not Form

   = O(O)       Emptiness is both Form and not Form

   = (O(O))    Emptiness is neither Form nor not Form

Everything is true; Nothing is true; Everything is both true and not true; Everything is neither true nor not true; This is the teaching of the Buddha.
Nagarjuna (Nagarjuna: The Philosophy of the Middle Way, p. 269)

We can continue this process indefinitely to higher levels with increasing diversity. Just as the two-valued level embodies the laws of logic, so the higher levels may embody more sophisticated mathematics used to express the laws of physics. The details of these higher levels, however, are beyond the scope of the present work.

We have seen that Reality manifests in stages with more and more elaborate forms. The levels of manifestation unfold in a dialectical flow from simplicity to complexity. Though it may seem that we live in a world of multiplicity, hidden beneath this veil of multiplicity is an underlying Unity that always is, always was, and always will be the true nature of all manifestation. Because the entire world is stitched together in the form of distinction, by recognizing the true nature of distinction, we can follow this thread of insight back from multiplicity to unity and unravel the net of illusion, revealing the One beyond both the one and the many, and freeing us forever.


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