DIALECTICS: INFINITY AND MATHEMATICAL OPPOSITION

By Fendersen
Dialectics is the science of the most general laws of development of nature, society, and thought. Its principal features are as follows:

1) The universe is not an accidental mix of things isolated from each other, but an integral whole, wherein things are mutually interdependent.

2) Nature is in a state of constant motion:

"All nature, from the smallest thing to the biggest, from a grain of sand to the sun, from the protista to man, is in a constant state of coming into be­ing and going out of being, in a constant flux, in a ceaseless state of movement and change." --Friedrich Engels, Dialectics of Nature.
3) Development is a process whereby insignificant and imperceptible quanti­tative changes lead to fundamental, qualitative changes. The latter occur not gradually, but rapidly and abruptly, in the form of a leap from one state to an­other.
"Merely quantitative differences, beyond a certain point, pass into qualita­tive changes." --Karl Marx, Capital, Vol. 1.
4) All things contain within themselves internal dialectical contradictions, which are the prima­ry cause of motion, change, and development in the world. - wikipedia.org
The first three points do not diverge from Epicurus' notions from around 367 B.C. as re­vealed by Lucretius (On the Nature of Things) in 50 B.C. The divergence or unique­ness of Dialectic Materialism is seen in the fourth point, where we have a platonic or cartesian notion of opposition and conflict operating throughout the universe.

In a one or two dimensional mathematical universe, two points an equal distance from a central point along an axis are said to be opposed or "opposite". Move the cen­ter point and the opposition of any two points disappears, or must be thought of as gra­dients of opposition. If there are an infinite number of points on this line, and the cen­tral point is therefore arbitrary, the concept of opposition is rendered meaningless. The notion of infinity demands rela­tivity.

In a three or more dimensional universe, two or more facing geometric structures (matters) existing in space (arbitrarily imposed universe) are said to be opposed. If the possibilities of space (the uni­verse) and matter (structures) are infinite in time, dimension and number, then opposition can only be thought of as points of comparison. That is, all things com­pared are in opposition and may be said to be two sides of an equation or statement of relative equivalence, and multiple sides in ad­vanced mathematics. Opposition is rendered academic, since everything will be seen to be comparable and therefore anything compared will be in opposition. It does not follow that everything is in op­position and therefore, is comparable. Comparison does not necessarily imply a cause-effect relation.

Opposition and dichotomy can now be stated as "true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, true and false and meaningless in some sense"1.

If the universe or space is infinite, the beginning of universe, space, or the infinite "contain­er" of everything can be found at the end of the individual geometric structure. If "you" are that structure, then the universe is "you" and "everything else". It branches out from "you" in all directions forever. It is big, infinitely. This idea lead god to the mis­taken idea that s/he is the beginning and the end. Many philosophers have themselves entertained this mistaken notion. If the quantum folks are on the right track, that is, the universe is also small, infinitely, then the individual structure, or "you" is a finite struc­ture (with a definite boundary) which nev­ertheless contains infinity branching in every direction toward the infinitely small. Thus spoke Lao Tse 2500 years ago:

"The Tao is like a well: used but never used up. It is like the eternal void: filled with infinite possibili­ties. It is hidden but always present. I don't know who gave birth to it. It is older than God."
If everything which exists, that is, "existence", actually does exist, then the only sen­sible dichotomy or opposition is between the individual structure (such as you or me, or this rock), which begins at your edge and continues to the infinitely small, and every­thing else, which be­gins at your edge and continues to the infinitely big. If the tau (or totality, or universe [U]) is "you" plus "everything else", then it is precisely twice as large as infinity (¥): U = 2 x ¥. This statement is linguistically unreasonable. If space-plus-time is a foldable fabric, then inside can be outside and even this dichotomy breaks down: U = U. Existence is a pure redundan­cy. Sense and nonsense are now reducible to each other and the only sense left is "humor", which may be described also as "pleasurable".

The 3-d Order Stream of thought on the impossibility of a discourse on the dialectics of disso­nance:

disordered ® disorganized ® disagreed ® negated ® denied ® discredited ® argued ® deluded ® delusioned ® disillusioned ® disallowed ® deprived ® econo­mized ® deject­ed ® rejected ® ejected ® neglected ® subdued ® vanquished ® enslaved ® entangled ® sorted ® arranged ® ordered ® organized ® accorded ® included ® classified ® opposed ® disordered ® disorga­nized ® disagreed ® negated ® de­nied2
It is a circle, here starting with "disordered". If any other point in the circle is selected as a starting point, for example, "argued", a new circle of meanings may be drawn which might in­clude: fought, discoursed, dialogued, communicated, intercoursed, kama su­tra'd etc., etc. The com­parison of any two points in the circle will exhibit 'fuzzy' rela­tions. Intersecting circles are also related this way. Any point may have emotional markers such that we view them more or less negatively or positively. In "Information processing", emotional attachments help us fo­cus and remember. Where can there be a dialectical synthesis where oppositions are select­ed arbi­trarily, where there are so many shades of meaning and intent, where the map itself changes depending on where we are standing?

We can communicate so well because we can make nearly unlimited semantic distinc­tions. The distinctions we make derive from associations, not oppositions. The brain, which is the parent of language, functions to make associations. That is what it does. In "classical conditioning", and even "operant conditioning", pleasure (reinforce­ment) is associated with a behavior or an idea. When we repeat that behavior, it is said we have learned. By the same token, when the reinforcement re-occurs, we also tend to repeat the behavior whether or not we have notions of a pay-off. When some­thing is associated with pain or deprives us of our plea­sure, we overcome it or avoid it. "That is the way things are!", said Old Lodge Skins3.

We, the civilized, have been taught to submit because we are deprived of any alterna­tive to over­come or avoid our pain (or misery). Fortunately, dis­sent among the civilized who are only exposed to systems of punishment is guaran­teed. The fly-swatter is never as efficient as hon­ey when catching flies. This was the essential notion of B. F. Skinner (as in, "Hey, stop beat­ing on your kids"). He has since been totally discredited and satanized by both main­stream and califor­nia-chique psychology. But goat-herders have always known this to be true.4

We respect the person whose actions reflect her ideas. He whose actions and ideas are in opposition is called a hypocrite. Distinction is an expression of uniqueness and a measure of diversity, not opposition. Those distinctions we collectively agree on are rehearsed and re­peated - learned as language, given by our culture and history. We are not always in agree­ment because we each draw our individual circles in a unique way. We only relate to each other in a fuzzy sort of way. This guarantees uniqueness and diversity. Thus, without diversi­ty, there can be no communication and without common ground, there can be no community. A community is an association, not a collection of oppositions. That is a prison. A language based only on a logic of dialectics would be extremely limited. It would lead to an information culture - a culture where everyone is in formation. Its language is a well-ordered machine lan­guage. The individual is expressed as a one or a zero. It is the language of Vulcan.

Alternately, there is the parable of the two hunters.

There were once two hunters, Hordrik and Edelgraff, disagreeing as to which direction the injured deer went, west or east. The Shaman was called from the village south of the hunting-ground to mediate. Many of the people fol­lowed her to see what was the trouble. Her dialectical synthesis provided the answer: "North, up in the hills", an elegant choice of a middle path. "How can this be?" asked the hunters. "The tracks lead to the west and to the east!" After putting on war paint and hav­ing a dance the people decided to split up. The spiritually-inclined went north, the left-enders went west, the right-enders went east.
All things being equal, can you predict who did not find the deer?
At dusk, the three groups returned to the camp-fire, each with a deer. All the people congratulated the shaman and thanked the grandfather, Abundance, for this miracle. They went out and collected the people from the other vil­lages and celebrated with a feast. The people were happy. The original injured deer, however, after leading Hordrik and Edelgraff west, and then east, had cir­cled around the village on a difficult rocky path and went to the south. There he met many other deer who took him in and col­lected herbs and healed his wounds. Over time, he met a beautiful maiden among them, and the two had many children who grew and had their own adventures wan­dering the four directions.
In nature, which is abundance, all things are never equal, and nothing is opposed. They were all right, and they were all left. They were all up, and three deer were downed. The question is rendered meaningless, but the truth is made abundant: danc­ing celebration, taste­ful venison, healing herbs, skillful hunters, beautiful maidens, and plentiful children.

revolution and cognitive dissonance: Cognitive dissonance is not, or should not be viewed as stress resulting from con­flicting ideas. We all hold conflicting ideas, and they rarely cause a problem. Surely, when we criti­cally look within and discover conflict, we make adjustments, or at least ra­tionalizations, and this is pleasurable. Pleasure should be the basis of real edu­cation.

The stress we usually attribute to cognitive dissonance (which is itself a dialectical ap­proach to understanding "thinking"), appears when that which defines us as an indi­vidual, or an individual member of a group is attacked. To use John Lilly's term, when our "metapro­gram" - the filter through which we view the world - is attacked, we experi­ence stress. If the attack is not strong, we fight. "Them is fightin' words!" If it is strong enough to actually dam­age us, that is, we acknowledge some portion of its logic, we re­treat. There we fall back on Freud's "defense mechanisms" and possibly even shut down: "this does not compute". If the attack is successful, it is said to be a revolution. Someone is escorted to the guillotine.

But, while human beings employ logic, they are not logic machines, as the A-I crowd pre­sume. The metaprogram relies on basic assumptions which usually lie at an uncon­scious lev­el. They need not be in a state of formal agreement. They are not ques­tioned. An aris­totelian metaprogram, especially as formulated by Descartes, renders the world as composed of opposites. If one side is good or true, its opposition must be evil or false. At the very least, every idea has its opposite. "All things being equal" (that is, in a state of machine perfection), if part of a thing or idea is offensive it discredits the whole system, structure or idea. We want to "throw out the baby with the bath-water".

This underlies all our notions of dualism. Either or. The world is either perfect ("It is as it should be") or imperfect. Thus, "enlightened" humans strive toward perfection. The old dis­course between Epicurus' atoms and Plato's essences became Descartes' idealism and Lock­e's materialism. Now we have mind/body, sacred/mundane, science/philosophy and waves/particles. The old evolutionists told us "everything strives toward perfection". Their cousins, the revolutionists, told us "the revolution must be permanent". To this day, this grates on the nerves of the enlightened, who, wanting to feel "special", tell us our imperfection (sin) is our special gift from a perfect god so we alone can endlessly strive toward perfection. Life becomes impossible. Progress through struggle. Dialecticians sought to quiet the argument by eliminating the con­flict rather than the oppositions themselves. Borrowing from the utilitarian epistemologists, 'Truth' be­comes "whatever works". But this liberal attitude does not jive with the conservative who would strike the child who ar­rives at the correct answer through her own intuitive logic rather than through the pre­scribed steps. Intuition is often mistaken.

Finally, we have the opposition, "Man is either basically good or basically evil". Enlight­ened conservatives like the "evil" side. It accounts for our special gift, sin. We therefore need rules and leadership. Liberals may choose the good side, but do not con­sider perfection. Rather, we are considered weak and incompetent. We therefore need benefi­cent rules and wise leader­ship - a Fidel Castro, but certainly not a Che Guevara. We need liberated. Purist anarchists seem to be the only crowd who see humans as basically good and competent. "Screw your rules and your leaders! We will liberate ourselves!" Nihilist skeptics share this same senti­ment, but also throw out the opposi­tions altogether. They keep the baby but throw out the bath water. (Or is it the other way around?)

Dialectical synthesis (which we get not from Hegel, but from Plato, Aristotle's teach­er) at­tempts to discover the most basic oppositions and rectify them by throwing out that which does not conform to the metaprogram (paradigm) and merging what remains on both sides. It is "Middle Road" philosophy and conservative analysis. The truth of the equation ( = ) lies within the lines of the symbol, not on either side of it. It is an ap­proach toward unity and con­formity. "Let there be no question about this!" What a limit­ing approach to a world which might otherwise be seen as a source of novelty, humor and adventure.

This is not to say novelty, humor and adventure do not exist in our culture, but only as they are interpreted within the paradigm. Even surrealist art is interpreted in terms of form and col­or use, or a limited view of creativity (that which is obviously 'untrue' is a source of entertain­ment, as long as it conforms to our sense of form and color). The truly novel, humorous and adventurous is relegated to "(drug-induced?) fantasy", "dream", "sin", "crime" and "insanity" - mostly the latter. Associations which derive from a novel logic are labeled "schizophrenia". The first rule of our enlightened metapro­gram is that it is the only one. There is only one logic and it is ultimately mathematics.

I am not suggesting eliminating dialectics. Surely, it is part of my own metaprogram. It may even be necessary from time to time, for example, in choosing situations which give us pleasure over those which produce pain. Nor am I suggesting we should throw out all our analy­ses, some of which are excellent. But we need be mindful that the map is not the territo­ry. Dialectics is not sufficient to over­throw the paradigm or metaprogram. It will always repro­duce it. It is our metaprogram.

But what would happen if we did away with our obsessive insistence on opposi­tion and its synthesis? At the very least there would be a lot less competition and a lot more room for di­versity. Compe­tition is a road toward unity, the ultimate project of the enlightenment: global­ization. More op­tions ul­timately mean more choice and less leadership. What conflict re­mained would be­come both ultimately personal and ultimately useful. We could return to the old Indo-Euro­pean sense of the term "dialectics" displayed by Hor­drik and Edelgraff - "collect­ing together" [from PIE *leg- 'to pick together, gather, collect']. Eliminating opposition and competition is a return to a "primitive" sensibility5. Without a universe of oppo­sitions, anarchy (without authori­ty) is reduced to local (or no­madic), and ultimately individual autonomy.

"Primitivism" (outside the usual connotation of a revolutionary praxis) is not crouching around the fire picking cooties off each other (although that doesn't sound too bad to me), but a logic of abundance and choice, autono­my and coopera­tion ("sharing"). There is no room for unity as conformity to law, which always implies authori­ty. Some will argue the "authority of custom", but both eth­nology and oral tradition suggest that diversions from custom were not only tolerated, but eventually incorporated into the body of custom. The exception is in coer­cive diver­sions, but then the response is not a matter of collective authority, but of self-de­fense against potential tyranny, which crops up from time to time even among other animals.

 


Notes:

1Gregory Hill, Principia Discordia

2.'dis-' separation = apart; 'dia-' transformation = across/through, between; 'de-' origination = from

3Thomas Berger, Little Big Man

4 One could say wage-slavery was the neces­sary (dialectic) response to counter the ever-present slave revolts by co-opt­ing pleasure and replacing it with symbolic reward - the creation of commodity fetishism. The problem with this is that pleasure was already negated by the system of restraint and punishment and we continue to view the wage as an im­provement. Free men were already enslaved by the illusions of property, value and rights to their acquisition and appro­priation. The analysis only reflects the success of the illusion colloquially held that reinforcement and reward are the same beast.

5 I prefer the term "primitive" over "native" or "indigenous" if it refers to primacy, not simplicity. These are the "first peo­ple" - just ask them. "Native" and its synonyms suggest restriction to a locality. This is also to say prevention from other localities. Without our notion of "property", primitive peoples "owned" the universe. That is, it was free to them. The common historical approach which looks at origins in a specific time or place (the three dimensional or cartographic approach) does not answer the question of who-they-were as does an investigation of their metaprogram (the ethnologi­cal approach, which asks who-we-are by asking others "who are you?"). "Native Americans" were not discontented Eurasians who migrated to a new continent, but the first people. The entire planet was theirs. That is why local names usually translate to "The People" or "Human Beings" rather than "Bostonians" or "Eugene Anarchists". The only Eurasian ancestors the civi­lized claim were the discontented, the conquerors. But we, the civilized, are the wayward de­scendants of the first peo­ple.

 


HOME