V

The Patterns...

• • INSOLUBILIA • •

To further examine the problem of paradox, we will employ the ‘Neither, either, both’ and ‘apart/together’ language models described earlier. Because these models described the path of coagulation in terms of isolation(1/9), integration(4/6), and the five ways of being, they will be useful when examining opposites that create paradox.

However it should be noted here that it is not my desire to ‘write the book on paradoxes,’ but only to show how their influence can be found within the stages of our model as an additional proof of paradox as a ruling force, and converging opposites as a pattern in nature. The examples given will be brief and perhaps not as complete as possible, so for a thorough analysis, independent study might be suggested.

Two Singularities in One!

By joining two points of absentia together, the resulting mobius effect creates a yin/yang unity between this impossible pair, with the universe as their impetus of connecting flux (see harry ball analogy). At the same time, the absentia remains a binding force between any two sides of that very same universe, as all sides converge upon the inner absentia, creating a yin/yang unity of their own (see convergence and divergence, and angular momentum). When we begin to examine the question of paradox, and the two points of absentia that create paradox, this unique form of reciprocity starts us off.

The stages of the model connect the two points of absentia, like intermediaries between the divine and mundane. The absentia unites the opposites of the model like the binding of a sacred book.

In our model, we see the two points of absentia as reciprocal in nature, due to their identical need to be excluded from any universe, and the ‘point-to-sphere’ fashion the model uses to maintain this condition. The fundamental difference between the two points of absentia comes from the fact that one is contained by the defined form - the point of convergence, while the other remains beyond the outer sphere. Because of this unique relationship, we can conclude that the essential sameness of a point and a sphere comes from the identicalness of these two points of absentia, while at the same time, we can see that the essential difference of the two points of absentia comes from the differences between a point and a sphere!

Given the point to sphere differences between our two points of absentia, it would seem logical to conclude that paradoxes that are influenced by the effects of the inner absentia would typically deal with contradictions between opposites that overlap while converging upon the final point of absolute definition. While conversely, paradoxes influenced by the outer absentia must deal with conflicts between opposites that compete over the absolute totality beyond the outer sphere. In both cases, each of these points of absentia will represent an attempted passage into an impossible state of one sidedness (or singularity), while at the same time maintaining an illusion of two sides (a split absentia) - just like the mobius band.

Because of the tendency of converging opposites toward coagulation, the outer absentia is seen as a characteristically yielding absence - a yielding absence from which the universe emerges and cannot return until the end of its homing cycle. In this way we see how the outer absentias impossible, uncontained state actually contains the universe that results. While conversely, the inner absentia becomes the impossible state of squelched exclusion from that universe by becoming an excluded middle between converging opposites.

The absentia of the excluded middle completes the point to sphere mobius-like cycle of absentia to absentia. In observing this absentia to absentia path we find yet another example of cosmic reciprocity; i.e. exclusion yields totality (universe from outer absentia), while totality is reduced to exclusion (infinite definition to inner absentia). Together these two points of absentia represent the two sides of onesidedness!

As the two points of absentia influence opposites on the one dimensional number line, they create different kinds of paradoxes characteristic to the isolation to integration spectrum. First, the outer absentia typically deals with opposites that never meet, due to the isolation and extreme separation at that end of the spectrum. Here, one sided exclusion yields a two sided totality, consisting of mutually exclusive pairs. On the other end of the spectrum, the inner absentia deals with the face-to-face antagonism of the mass, as our two sided universe is reduced, back to one side. Thus, as one final expression of this divine symmetry, we observe that;

Only through the impossible state of being ‘neither’ (outer absentia/sphere) are you able to become ‘all’ (inbetween universe). While at the same time, the equally impossible state of being ‘all’ (conflicts in a two sided universe), only makes you ‘neither’ (inner absentia/point)

• Reductio ad Absurdum •

Neither = Exclusion = V

In our first paradox example we encounter a phenomenon known as ‘reductio ad absurdum’ (reduced to absurdity). Reductio ad absurdum is also known as the law of the excluded middle because paradoxes of this type, in dealing with the inner absentia, typically reflect the different forms of exclusion it is subject to.

Because the inner absentia lies at the heart of the defined form it becomes the ultimate ‘neither’ on our spectrum of ‘neither, either, both’ and beyond. Here, at the center of the model or midpoint of the number line, the exclusionary nature of the absentia is reflected in conflicts between opposing forces that can converge no further. It is here where the pursuit of absolute definition becomes completely reduced to absurdity.

Paradoxes involving a reduction to absurdity usually involve conflicts of self-reference, self-exclusion or incompleteness, all of which center around a vocabulary designed for absolute singular one sided acceptance in a binary universe of opposites. Here are some examples.

THE BARBER - A clean shaven man who only shaves all men who do not shave themselves. The question is, who shaves the barber? If the barber shaves himself he violates the rule of shaving all men who do NOT shave themselves. If does not shave himself he violates the rule of shaving ALL men who do not shave themselves. The Barber paradox is a problem of set theory. We have two sets, men who shave themselves and men who are shaved by the barber. The question is, which set does the barber fall into? The answer is neither. By trying to be ‘all’ he has become ‘neither’.

SETS - Deals with sets that include themselves as members, and sets that don’t include themselves a members. The question is, is the set of all sets that are not members of themselves a member of itself...by virtue of not being a member of itself? Once again attempts to include ‘all’ possibilities, leads to exclusion and a one sided hypocrisy.

As the effects of the inner absentia radiate out to successive stages of development, paradoxes of absolute definition begin to focus on relative truth value.

Either = Alternation = 5

In the ‘neither, either, both’ model, the five is the ultimate ‘either,’ as in either yin or yang. Here the alternating action of the five, and its eternal in-between state, creates a paradox of logic similar to the visual examples already given of Figure ground, Nekar’s cube, and Retinal rivalry. Here, truth value seems to alternate back and forth without resolution, as conflicting attempts at singular one sided acceptance, compete for the last remaining point of the model. Here are some examples.

THE LIAR’S PARADOX - Associated to Eubulides and Epimenides, takes many forms. In the case of Epimenides, the fact that he himself was a Greek poet from sixth century Crete made the statement “All Cretans are liars” a paradoxical sensation. Other examples of this same paradox include the simplified version; “I am lying,” and “This sentence is false.”

In each of these examples we are offered a statement whose apparent truth value stands, until such time as the content of the statement is allowed to be applied to itself. Once this is done, a re-evaluation produces an alternate result which, when re-applied, changes things back to the original. In other words; If everything I say is false, then what I just said is false, which means everything I say is really true. If everything I say is true, then what I said before must be true, which means everything I say is really false. In these paradoxes the speed of the alternating effect is usually governed by how fast your mind can apply and reapply the content of each statement.

Another example of the liar paradox, which also creates this condition, involves two statements which change each other. For example

In this paradox, each statement is allowed to stand, only until the next statement is read, whereupon the content of the first is changed by the content of the second, which then changes the second..... which changes the first back again! Once again the alternating speed is governed by how fast one can apply and reapply the content of each statement.

Both = Reciprocity = 4/6

The 4/6 mass is described as a combination of both yin and yang sides. In this stage of the model, we find paradoxes who’s opposing sides carry truth value of equal validity, toward opposite conclusions. In other words they can’t both be correct, but they are! Something has to give, and never does. Here are some examples.

CROCODILE’S DILEMMA - A crocodile grabs a baby from the banks of the river. The mother asks the crocodile to return the baby. The crocodile says “If you can accurately predict what I will do, I will return the child, but if you guess wrong, I will keep it, to eat later.” The mother says “You will keep it, to eat later.” The crocodile says “I cannot return the child, if I do I will make you speak falsely and I said if you spoke falsely I would keep it.” The mother says “You cannot keep my baby, if you do you will make me speak the truth and you said if I spoke the truth you would return my baby”

Here is a diagram for visualizing the crocodile dilemma

THE LAWYER’S PARADOX - Lawyer ‘A’ teaches a student ‘B’ to be a lawyer, with the agreement that a fee will be paid AFTER ‘B’ wins his first case. ‘B’ puts his interest in law aside. ‘A’ gets tired of waiting for his money and goes to ‘B’ demanding payment. ‘B’ resists claiming he has not yet won a case. ‘A’ decides to sue ‘B’ for the money. ‘A’ argues that if he wins, ‘B’ must pay him the money, while if he loses, ‘B’ will have won his first case and then must pay the money anyway. Both outcomes prove victorious. On the other hand, ‘B’ argues that if he wins, he will not have to pay, while if he loses, he will not have won a case and will still not have to pay. Both outcomes prove victorious!

Together, the neither, either and both stages of this model deal with the mass and the paradoxes of the inner absentia as it radiates its influence from the center of the model. In all cases, reduction to absurdity centers around two sided competition for single sided truth value, as well as the vocabulary of absolute definition and irreconcilable differences that look reconcilable (impossible one sidedness, that looks two sided - like a mobius strip!).

• Cassatio •

Same = Simultaneity = 3/7

The next step on the isolation to integration spectrum is the point at which opposing sides are not separate and converging and not yet spiralling together, they are the same, or without separation. Here, paradox comes from the simultaneity of no separation between opposites. At this stage, paradox involves conflicts between opposites that never even get off the ground! In other words, as each predicate is put forth, it simultaneously and inclusively annuls itself, as in the examples; “I do not speak,” “I am silent,” “Never say never” and my personal favorite.

I AM SILENT - At first, this paradox might appear to be an alternating type, like the liar paradox - they both seem to be a bit hypocritical. These paradoxes, however, do not alternate, but instead create a condition of simultaneous and inclusive annulment. This simultaneous breaking down of a system as it is being created, typically leaves the victim of the paradox with something that is nothing, reflecting the metamorphically transitional condition of the 3/7 sphere and its state of neutrality between definition and infinity.

• Contrarius ad absurdum •

Outer Absentia = Exclusion = V

At the other end of the isolation to integration spectrum is the outer absentia. In the grand design of the ‘neither, either, both’ model, the outer absentia is also seen as an ultimate ‘neither,’ in fact the same neither - a companion of impossible association. Here, at the outer absentia though, isolation and infinity, combine to create the outer absentias characteristic absence from any universe. ‘Existence through absence’ or ‘totality through exclusion,’ is what causes any chosen reference frame to be its own universe. In other words, the universe is here only because the absentia isn’t. Here are some example of ‘existence through absence.’

MARX’S PARADOX - Woody Allen opened his movie ‘Annie Hall,’ with a quote he attributed to Groucho Marx “I would not want to belong to any club that would have me as a member”. This is a good example of an outer absentia paradox, wherein one sets up a condition which leaves you ‘nowhere’. Nowhere, then, becomes the reciprocal equivalent to the ultimate ‘neither’ found in overlapping paradoxes of the inner absentia.

CHARLIE THE TUNA - Marx’s paradox shows how the absentia sees the universe, Charlie the Starkist Tuna shows how the universe sees the absentia. Wanting to belong to a club that would snuff you as a member, shows the impossibility and pointlessness of ever obtaining the absentia.

Non-model = Displacement = 0

As the outer absentia yields to coagulation, paradoxes involving the almost equally incomprehensible characteristics of infinity take over. Paradoxes of the outer absentia dealt with the universe that was born from it, and the necessary exclusion of the absentia from that universe.

Paradoxes of the non-model deal exclusively with the manifestation born from it, and the almost equally unstable state that infinity holds along the spectrum of coagulation. Here, on the isolation to integration spectrum, the extremes of separation between opposites are between the very ideas of manifestation vs. non-manifestation, the two sides of the universe side.

In these paradoxes displacement of non-manifestation by manifestation, creates a dichotomy that paralyzes its victim into his chosen reference frame or point of view, creating a paradox of non-action or pointless, contradictory action, much like the example already given of untwisting a mobius band, only to find that you have twisted what was untwisted. In these paradoxes we find that the grass is typically greener...until you’re over there! Or as stated previously, “wherever you go, there you are.”

In these paradoxes, the model displaces the non-model like a fish swimming through the vast volumes of water in the oceans of the earth. Wherever that fish goes, water is always surrounding him, and he is always at the center of the continuum of oceans. That’s how non-model paradoxes usually work. They combine the similarities of infinity, and paradox, to reveal the necessary exclusion, or displacement of each, in relation to manifestation - the perpetual viewpoint and center of any universe. Here are some examples of displacement paradoxes.

MIRAGE - The paradox of a mirage combines the exclusion of the absentia, and the displacement of non-manifestation, to create a formula for paradoxes that show the yielding action of both toward manifestation. It shows how all attempts to find the absentia fail. And it also shows how all attempts to be anywhere but where you are, fail.

As a paradox, a mirage becomes a concept that can only be perceived from a vantage point that excludes finite possession. In other words, when you put yourself in the location of a mirage, it disappears - it’s no longer there, this of course is because you ARE. It is for reasons similar to this that any discussion of ‘the absentia’ only replaces the absentia, with the discussion of it!

Again, if we don’t go to the mirage, we can drink all we want from it. Of course this means that altho we are allowed to drink from it, we can’t. On the other hand, if we move to where we can drink from it, we are not allowed, because it is no longer there. In the same way, any attempt to discuss ‘the absentia,’ or be anything other than the universe we have chosen to be, causes the absentia to vanish, leaving you right back where you started - not absent.

The crux of this paradox lies in the fact that we already exist within our own mirage, at the same time we are perceiving it outside us. The difference is that the mirage we are in, has been replaced, or displaced, by us and our defined form, while at the same time, it remains apparent to us outside, beyond our capabilities of definition (including the relative definition of infinity, when compared to the absentia).

As a fish in the ocean we may think we are moving to a different location to obtain the absentia we perceive, but when we arrive we find that our condition is unchanged; water still surrounds us, we are still the center of the ocean and the absentia is still ‘over there.’ So as long as we (the universe) are here, the absentia isn’t. And when we are not, the absentia is. This is the essence of non-model paradoxes. Here are some more examples;

CATCH 22 - In the book/movie ‘Catch 22,’ this idea of ‘vanishing presence’ appeared more than once. One of the best examples was that of major Major, an officer who climbs out a window to avoid meeting the Chaplain who has arrived on behalf of Yosarian.

Through a series of hastily given orders, major Major ends up telling his secretary to always say he is NOT ‘in,’ when he is there, and to only allow people to ‘see’ him when he is gone. He then climbs out the window and says “Now you may let the Chaplin in.” The secretary goes to the waiting Chaplain and says “You may see him now.” The Chaplain enters the room, looks around only to find it empty. He then has to relate this experience to Yosarian by explaining that “..yes you can see him, but only when he isn’t there. That is, when he is there, you can’t see him, but when he isn’t there...you...can see him”.

Paradoxes involving Army logic are easy to find because the chain of command usually attempts to hand down orders that are not to be questioned. As a result, simple requests require absolute acceptance, often with absolute vocabulary - fertile ground for paradox.

Isolate = Polarity = 1/9

As the outer absentia and infinity give way to the model itself, paradox begins to involve encounters between opposing viewpoints and contradictory reference frames created by the extreme separation of yin and yang halves on the isolation to integration spectrum. Here, polarity between opposites, creates paradoxes that sort of diametrically orbit a common midpoint. In other words, the condition of one is always diametrically opposed, or mutually exclusive to the other, thus once again freezing each into its separate universe, with an impossible inbetween.

Paradoxes of polarity usually involve some sort of ‘wanting to have your cake and eat it too’ kind of problem, or something like; ‘you can’t do this until you do that, and you can’t do that until you do this’, or perhaps some other ‘can’t have one with the other’ problem, like ‘trying to get a job without experience and trying to get experience without a job’. Here is another example;

NORTON - Another example of the dichotomy of these paradoxes can be found in a particular episode of ‘The Honeymooners.’ Norton tries to comfort Ralph about his hatred of Alice’s mother, by lying to him about hating HIS mother-in-law. Then Trixie enters the room and talks about how much Norton LIKES her mother. Ralph then gets mad at Norton for lying. Trixie gets mad at Norton for changing his opinion about her mother. Norton then finds that if he apologizes to Trixie, Ralph is mad and if he affirms his truth to Ralph, Trixie is mad. Norton has created a condition whereby existence in one frame, constitutes total denial of the other.

In this example, the condition of the other reference frame is not one of exclusion or displacement, but polarity. Both ‘universes’ exist, but not in each other’s frame. The consequence of ‘diametric denial’ is what leads to the question of the tree in the forest, and whether it makes a sound when it falls, if it does so outside your reference frame. The vagueness of this question gives rise to much debate. Most people recognize the need to define the terms given with regard to sound and what it is. But the real controversy is in whether the sound, the tree and the forest itself, even exist outside the frame of a person not present at its alleged fall. In other words, does awareness alone constitute existence? Or is everything we are not aware of, the balanced opposite to existence, making it worthy of consideration, in a different form? - like the differences between analytical vs. wholistic number lines discussed earlier.

Separate = Discrepancy = 2/8

The next form of paradox deals with discrepancies between opposing viewpoints toward the same entity or event. Here many of the paradoxes of relativity come to light.

This is the numerological sphere that represents the axiom of relativity given earlier, about all points of view being equally valid. Because all points of view are equally valid, contradictions are easy to come by and paradoxes are many. Additionally, this stage of development is also a good point from which to perceive the effects of diminishing returns, as it is the element of space/time itself that contributes greatly to this phenomenon. Here are some examples of paradoxes involving discrepant viewpoints and diminishing returns.

THE TWIN PARADOX - The most well known paradox of relativity, involves the discrepancies between recorded time on earth as opposed to a spaceship traveling at a speed approaching that of light. The clock on the spaceship returning to earth from light speed travel, will always show less time than the clock that remained on earth.

This phenomenon is know as ‘time dilation’. Time dilation occurs because the speed of light, is also the speed of time. In other words, if it were possible to travel at light speed, time would actually stop! Time dilation shows how time slows down when approaching this limitation. When time dilation is incorporated into the stages of our model it becomes another useful scientific analogy, representing to us, the idea of diminishing returns.

Time dilation can also occur in the mind, in the form of ‘Time flying, when your having fun.’ In other words, when a person is exhilarated, his mind is accelerated, and time passing becomes condensed. That is, perception of given time is distorted. When the activity is over, perceived time will always be less than actual time; “I just got started and it’s time to go already?” Time in the accelerated mind has slowed, like the spaceship at light speed, while actual time seems to have gone by faster.

On the other hand, a person who is not exhilarated, is running slower, and time passing is extended; “This has been a short week, eh?” “Are you kidding, I can’t wait for it to end.” When activity ends, perceived time will always be more than actual time “oh god, it’s only 2 o’clock!”.

ZENO’S PARADOX - has to do with a foot race that never ends - or never begins - depending on your point of view. In this paradox a runner at point ‘A’ runs to point ‘B’, at a constant rate of speed. If, after completing half the total race course, we consider that he must also complete half of what is left, then he must also complete half of that again, and again, ad infinitum. Under these conditions it is alleged that the runner will never finish the race, (or never begin) because the number of times the remaining distance can be divided is infinite. In other words, he will always have half of some distance left to go (see scaling).

A paradox like this is important to observe because this condition of diminishing returns, i.e. forever striving and never getting, is exactly the pattern that contains the stages of the model and prevents the tools of finite perception from ever reaching into the realm of the infinite. In other words, as the time, space, motion and energy of manifestation radiate out from the center of our model, to the 1/9 stage of development, the speed-of-light = speed-of-time limitations of relativity gradually slow things down to an ever-symmetrical halt.

Loopius ad Infinitum

In general, all paradoxes lead us around a mobius-like loop. By segmenting these examples into the stages of the ‘neither, either, both’ model we gain an insight into its form as well as learning more about the model itself.

The mobius-like looping of two points of absentia as one, is what creates the endless contradictions that leaves us chasing our tails over the two sides of a one sided issue, or the one side of a two sided issue. The reciprocal, point to sphere condition of the two points of absentia, reinforces the 2 into 1 and 1 into 2 pattern of the mobius shape. The looping characteristics of the mobius is an integral part of all paradoxes and simply plays on the optical illusion of its one sided impossibility.

From these examples, we can see how searching for absolute truth, becomes as pointless as trying to define the infinite. In other words, ‘No concept at all,’ being a concept itself, represented our original paradox, or outer absentia. Now in a similar fashion, we can see how the ‘no absolute truth’ concept stated earlier, represents our final paradox, or inner absentia.

In the end both points of absentia are still the same place (or no place), but because one is beyond the infinite, and the other is within the finite, they create different patterns in paradox. However the one thing that does remain the same, enabling us to confirm their impossible association, is the fact that they both represent and are faithful to ‘that which is not possible,’ the very essence of the absentia.

In other words, no great truth ever stands alone as an absolute singular one sided ‘truth’. Truth only becomes a truth when opposed by an opposite concept that is also true, thereby creating a situation wherein each truth cancels out the other. By cancelling out each truth you are put out of your universe of opposites and put into the realm of the absentia - or as some might call it, the Tao.

Thus the truth, that of the singularity of the Absentia/Tao, is only realized through the utilization of opposites (as in the case of two cancelling truths), just as the one sided effect of the mobius strip became dependent upon the two sided piece of paper that created it. In other words, the ‘one’ (absentia) is dependent upon the ‘two’ (universe of opposites) to be ‘clothed,’ and the ‘two’ (universe of opposites) are dependent upon the ‘one’ (absentia) to separate opposites and create the figure/ground conditions responsible for manifestation and the cycles of life and death

Absolute truth: Without sides, you wouldn’t have a sidless absentia. Without the sideless absentia you wouldn’t have sides. Figure/Ground shows us where the absentia is, and where it isn't, at the same time!

If you choose to continue with this study, we will now explore the meaning of life... !