V

The Patterns...

• • BEYOND OPPOSITES • •

One of the most important ideas to remember so far, is the idea of a universe on a mobius strip - or sphere. When combined with the concentric stages of homing, this idea shows how our finite universe is not only limited, but self contained, i.e. a system from which there is no escape!

Another important concept to remember is the sliding scale of relative definition as seen in the successive stages of coagulation. Moving from a locationless concept like paradox to the finite mass of the model, shows how we are all in fact born from nothingness as well as limited by nothingness. In other words, when our contemplative minds venture out of our finite world, we find that we actually ‘melt’ back into the very nothingness that contains us, as relative levels of comprehensibility become increasingly complex and less tangible, or increasingly INcomprehensible (see solve et coagula).

As the contemplative mind attempts to think outside its ‘box’, each sphere of our model represents a point of transition, beyond which we we encounter ever increasing levels of incomprehensibility. As we grope to understand these concepts we encounter a very real and relatable example of diminishing returns as each stage of development becomes just a bit less comprehensible than the last.

Because of this limiting condition, that of being contained by relative levels of comprehensibility, we might well conclude that in fact any and all attempts to enter the realm of the infinite with a finite mind, will causes all tools of finite perception to dissolve, thus effectively creating a condition of diminishing returns within the stages of concentric containment that surround any entity/event.

Likewise, if we explore this condition of diminishing returns, and pursue it to its logical extreme we find that we eventually encounter the effects of our split absentia and the mobius twist of paradoxical enclosure. As we are about to see, paradoxical sufferings take many forms and as you might expect, those forms can be described with the stages of our model. This is the focus of our next series of patterns.

• INFINITY VS. THE ABSENTIA •

Earlier, we addressed the question of different types of paradoxes, let's go back to this idea of absentia outside the universe. By existing outside the universe, we see the absentia as a theoretical ‘container’ of infinity. By having a concept like paradox as a container to infinity we can see how, for us and our finite minds, the problem with infinity will be in our attempts to make it finite, while the problem with the absentia will be in trying to make it not be a paradox, and dealing with the unresolvable contradictions it creates.

As we examine the differences between these two conditions, we find that as our minds move beyond our finite reality and into infinity, our finite tools of perception begin to fail us, creating a condition of diminishing returns with respect to our ability to maintain comprehensibility amid complexity. While on the other hand, we find that attempts to resolve the paradox of the absentia, seem to take us a step beyond futility. In other words, by moving in on the absentia, we actually begin to chase our own tail, as we are ultimately lead around and around the two sides of our one sided mobius/universe...or the one side of the two sided mobius/universe!

The difference, then, between problems of the absentia and problems of infinity, comes from the necessary exclusion of the absentia, from the universe that is attempting to perceive its form. In other words, infinity is a concept our finite minds will never understand, but the absentia is ‘no concept at all.’ Thus, by definition, it becomes totally unobtainable as an element of discussion. In other words, the absentia does its best work by being absent! So that means that to even bring it up as a topic of discussion is a pointless act of futility because that only makes it not absent, and to make the absentia not absent is to dilute its relative truth! Or, to put it another way:

Diminishing Returns

For a visual representation of diminishing returns we can use a creative analogy involving an imaginary bed sheet, stretched tight, across a mattress of infinity - The "fabric" of spacetime!

The bedsheet analogy is a good metaphor for describing the fabric of space-time as it relates to our model’s stages of development.

In the bed sheet analogy, we find that if you pinch a sheet somewhere and twist it, wrinkles will radiate out from your fingers. If your eye follows one of those wrinkles, the wrinkle will eventually fade away and blend back into the flatness of the sheet. Because the wrinkled parts and the flat parts are made of the same stuff, we can conclude that the wrinkles become visible, taking on a definable appearance, only because the ‘twist’ of your fingers has caused them to be different than the rest of the sheet. Determining where this difference begins and ends is the job of our model, the number line, and the conditions of diminishing returns that they attempt to describe.

The Bed Sheet analogy is roughly equatable to the warping of spacetime around a mass of existence. Warping, twisting... tomato, tomato.

But the real fun begins, when we contemplate what happens beyond the infinite bed sheet, and between the fingers that hold the twist together. This is where we find the elements of the single absentia split into its two locations, pulling this two sided figure into a one sided form. This is of course another two dimensional analogy attempting to describe something (or a non-thing) that, technically speaking, is beyond the ability of any human to accurately visualize or diagram!

In the model, diminishing returns is what keeps the finite and infinite apart in our binary universe. In other words, in this universe you not only “can't take it with you” (the finite into the infinite), you also cannot bring it (the infinite) back, into the finite world. Together our coagulating, homing and converging analogies show us how all attempts to bring the infinite into the finite world, without causing it to coagulate (or wrinkle) into a finite form no longer representative of its true nature, is about as possible as bottling an emotion. Thus by acknowledging the unobtainable presence of this ‘other world’ (the world beyond diminishing returns), we develop a balanced mind capable of traversing a mobius shape without anxiety.

As we continue though, the temptation to finalize infinity will always taunt us. When this happens, we must remain strong in our commitment to allow unresolvable concepts to remain so. We must restrain ourselves from constantly asking, in Henry Higgins fashion, “Why can't the infinite, be more like the finite?”, and instead recognize the fact that it can’t. Only then can we accept the differences, marvel at the symmetry, and find our place in it all.

Diminishing returns describes the effects of a universe containing infinity and definition as opposing elements. The notion of paradox, however, is how we identify the presence of absentia and mobius influence upon those elements. But because the absentia is; ‘no concept at all,’ ‘not possible,’ ‘unobtainable’ and ‘absent’ from any universe, it cannot be identified as an element of that universe. Because of this, a study of paradox becomes the only way of identifying or describing its mobius-like form. For us, paradox is the paint we pour over the absentia to see where it is.

• PARADOX •

In our tarot universe, the absentia, and the mobius effect it creates, become the bottom line form for all paradoxes, antinomies, oxymorons, and conundrums. The spherical mobius idea, and the ‘chicken and egg’ qualities of its beginnings, create varying types of paradoxes within the opposing sides of our binary universe. Left alone, these paradoxes create frustration in a world of finite beings attempting absolute definition of their world.

Whether or not the examples of paradox that follow are a result of a mobius effect upon a binary universe, is of course another speculation for the open mind to ponder. To me, the unresolvable contradictions of paradox become simple manifestations of logic upon a mobius band (or in our case sphere). By theorizing that a mobius effect is universal, logic becomes but one possible coat of paint to pour over this unspeakable form. How the elements of common language and logical thought manage to find there way into expressing this universal trap of infinite regress is another questions I leave open for speculation. However, given the fact that these situations occur, it becomes an interest of mine to look for the patterns created by paradoxical conflict within the elements of the model.

When I set out to study paradoxes of logic, the first thing I noticed about them was that they didn't all use the same exact trick to achieve the endless looping effect so common to them all. Because the source of the looping effect was so obvious to me (whether it is correct or not), I began to focus my attention on the subtle differences in how this loop was formed in each example I found.

In examining the looping effect of paradox, I found that even though some paradoxes involved more (or sometimes fewer) than two elements to their form, they seemed, inevitably, to all arrive at the same place somewhere down the line. To me, this ‘place’ always appeared as some kind of inevitable conflict between opposites. In other words, regardless of how many elements were used to create the paradox in question, paradox would not occur until the logic involved “took up sides” as it were. Upon closer examination, it became apparent that these ‘sides’ did not always confront each other in the same way. Some would seem to overlap in conflict, i.e. two things trying to be in one place at the same time. While other times the conflict seemed to resemble a more disparate dilemma, i.e. one thing trying to be in two places at once.

As I continued to ponder the idea of opposites that are either overlapping or in diametrical conflict, a pattern of my own came to mind - the apart/together model! As I contemplated the idea of placing these paradox examples on this spectrum as an organizational device, I began to toy with the idea of looking for other examples that could fit appropriately into the remaining stages of the this model. Upon successful completion of that task, I decided to include these examples as yet another tool of analogy that can be used to visualize the supposedly universal form of our theoretical model of existence.

Pretzel Logic

In creating a device for examining paradox, the isolation to integration spectrum of the apart/together model revealed a possible culprit to the conflict found within the examples of paradox I encountered. Within the confines of this spectrums influence, one could easily conclude that it is in fact the impossibility of squelching the inner absentia, combined with the equally impossible task of containing an outer absentia, that offers the resistance to absolute acceptance within all paradoxes - inasmuch as all paradoxes insist upon absolute acceptance of one solution over another - which they do.

If this condition of absolute acceptance is true, it is not difficult to reason that, within the limits of this spectrum, all possible attempts to be absolute will produce a paradox of absolute impossibility! Thus, within the grand design of our home-made universe, we find that the only way to be absolute is to be impossible, thereby making it impossible to be absolute! Or to put it another way...

This, as I see it, becomes the ruling logic of paradox, as well as the ruling paradox of logic - a ‘logical equivalent’ to the mobius sphere and its visual twist.

Of course to some, this is not an acceptable conclusion to the study of paradox. To the finite minds of the world who cannot allow the undefinable to remain undefined, paradoxes are an endless source of challenge. In some cases these people attempt to blame the condition of paradox on the two sided nature of the logic employed. They attempt to resolve paradoxes with alternate methods of reason, such as abandoning the notion of ‘sides’ or creating multiple levels of language in hopes of being able to step out of the picture and straighten it out from afar (see spiral). In my opinion, ‘conditional’ solutions to paradoxes cannot be considered real solutions. To my mind, the very essence of a paradox lies in the limitations of its opposing elements and the fact that they cannot be solved of themselves. Conditional solutions can therefore only be viewed as compromises and not real solutions.

Likewise, the notion of a sideless universe does not eliminate paradox for me. Because, the way I see it, a sideless world is not compatible with a sided world, and to alter your mind to be sideless only makes the sided world you leave behind as paradoxical to your sideless mind as a sideless world was to your sided mind! By being incompatible, you are forced to adopt one mindset or another. In being forced to adopt one mindset or another you find that paradox does not ‘go away’ when you are sideless, it simply trades places with your shifting mind, thus continuing to elude your grasp - like the absentia it represents. Yet another expression of mobius-like forces upon our perception of universe, as trading sides with a sideless world is also seen as equatable to untwisting a mobius band, only to find that you have now twisted what was untwisted!

The real beef I have with this sideless approach though, is how it attempts to eliminate or resolve paradox. As we have already pointed out, paradoxes (especially predictable ones) are a very necessary part of the structure of our universe, when viewed through the stages of our model. A single paradox offers the only possible origin to any universe, and therefore should not be resolved, for to do so would catastrophically eliminate that universe! The path from our original paradox to the relative definition of the mass is a gradient spectrum, part of the emergence and deliquescence of manifestation. I believe paradox holds an important place on that path, along with chaos and order, and should not be changed or defeated.

What is Pardox?

Some people use the word paradox to define any kind of conundrum involving any kind of apparent conflict between premises or conclusions. Some use the word paradox to define anything that is beyond comprehension, like the concept of infinity. Some use the word paradox to define any kind of sophistry, false statement or lie. Personally, I take a narrower view in my definition of paradox. In addition to confining my definition of paradox to the limits of the elements that eventually face off in conflict, I also limit my idea of paradox in other ways. To me, I think to have paradox, we need to have sides facing off, even if it is just a self-referential face off, but to be a true paradox, the face off has to be a truly unresolvable conflict. Most definitions I've read of paradox employ the words "contrary" or "contradiction" in them. But, to my mind, it has to be more than just conflict or contradiction, it has to be an interdependent relationship between possibilities that produce mutualy, alternately or unclusively unacceptable, unmanageable and unresolvable impossibilities. It has to be a contradiction where the relative truth value of one side supports the relative truth value of another side whose function it is to oppose the relative truth value of the first side... thereby negating the relative truth value of the first side, which then negates the relative truth value of second side, which of course restores the relative truth value of the first side, which then restores the relative truth value of the second side, which again negates the relative truth value of the first side... etc. etc. Thus, to me, it is not paradox until this uniquely unresolvable looping effect is evident.. or something equally interdependent in unresolvable impossibility with the appearence of possibility intact, like the examples that follow in the next section.

How do we get the looping effect? In the case of "The Absentia" its function is to represent impossibility. That's one half of the two things we need to create a paradox. The Universe (a universe) is the other. The Universe represents all that is possible. But mixing impossible and possible alone doesn't create paradox. The missing ingredient is a "cosmic twist" to make our conflicting and contradicting opposites relate to each other in a way comparable to that of the relationship seen in a Mobius strip, where a two sided piece of paper is made to have only one side! Without the twist, a band of paper is still two sided - representing any type of non-paradoxical opposition or conflict that we might encounter in our binary universe. With the twist, a band of paper can be shown to have two sides... or one side! Is it one sided, yes. Is it two sided, yes. If you think it is two sided, I'll show you how it is one sided. If you think it is one sided, I'll show you how it is two sided. This is paradox..

But the real trick to paradox - and in my mind the real definition of paradox - is how each conclusion is entirely dependent upon the other, and how one conclusion can't happen without the interdependent influence of the incompatible opposite whose function it is to make the other side to not happen!! Paradox is a symbiotic relationship between sides that makes each one be and not be at the same time - like the age-old dilemma of deciding which came first, chicken or egg. Can't have an egg without a chicken, can't have a chicken without an egg. Choose the chicken, deny the egg. Choose the egg, deny the chicken. This is paradox.

If you choose to continue with this study, we will now examine some examples of paradox, and observe how different paradoxical standoffs resemble the stages of our evolving model.