Another equivalent way to represent this diagram would be a rhombus: the point at top, which could be called Apex, is the Good, that of left is the Yang point, that of right-hand side the Yin point, and that of bottom the evil (which could be called the gutter, where all the dirt gathers). According to the situation to be described, the square will be more adapted, or the rhombus, and sometimes only a triangle (the higher rhombus half, or inferior half). We can even consider only the two axes and get back on symbols such as the Christian cross or the Hermes's Caduceus, which may be appropriate with some cases.
Notes: The Yin-Yang as well as the evil/good are both represented in the tradition by black and white. However their significance are completely different and it would be a misinterpretation, see a mind control attempt, to confuse the Yin-Yang with the evil/good. Here, for a clear understanding, we thus represented the Yin-Yang by blue-red, and used the black/white only for the good/evil.
So now we have the rhombus diagram with the white good point, the red Yang point, the black bad point, the blue Yin point, and the grey compromise centre.
We also have the square diagram with red Yang Sephirah, blue Yin Sephirah, dark red ¥ang Qliphah and dark blue ¥in Qliphah.
All the subtlety of the diagram is into the gradations between these influences, which are figured by the gradations between colors. A given situation of reality is on only one spot of the diagram, and thus has an unique color.
So we clearly have now a whole set of places for the quality of an object, which play the same role in reasoning than the two places of the Aristotelian logic. Let us call this the quadripolar logic©, (of which I claim intellectual paternity, except for the above antecedents). Whereas Aristotelian logic exhibits two exclusive values, true or false, quadripolar logic has four poles (enumerated above, in the two equivalent representations) more all the intermediate degrees, represented on a two dimension surface. (We could use the name of phase space, although this is usualy defined with measurable values).
The left-right axis is a Yin-Yang dialectical relation between two opposite or contrary aspects, while the top/bottom axis expresses the degree of this harmonisation or non-duality: null in the bottom (antagonist duality or full exclusion of one of the terms) average in the medium (tedious compromise) strong in top, with a perfect non-duality at the apex. Often this top/bottom axis will express the fact of being more or less adapted to the intended purpose, by mean of the non-duality of the opposites: in bottom, nothing can moderate the destroying aspects (which generally both lead to the same result; popular wisdom says that there «the extremes meet»); in the medium they neutralise each other, but the positive aspects also: the laters cannot express their full power in this compromise; in top, the whole positive force of both non-dual terms can express and built in a perfect harmony. For that, according to the nature of the problem, it is often legitimate to say that we have the good in top and the evil in bottom, or at least the realisation in high and the failure in bottom.
(Permalink) A summarized view of the Quadripolar Logic is the notion of the Three Pillars, known since the 11th Century.
We find the use of these three pillars for example in the court (plaintiff, judge, defendant), and it is probably not at random if they are in the same order as in the Hebrew Cabal. The Masonic temple also uses the symbolism of the «two pillars», which meaning is identical and the origin very likely similar.
(Permalink) It is also interesting to introduce the simplified notion of the Three Levels, which has the clear advantage of clarifying many notion which are usually confused, such as freedom and democracy, or non-duality (the true resolution of a conflict) with compromise (removing the destructive aspect of a conflict, but without solving it). (Even if compromises and democracy are progress compared to dictatorship or open war.)
The confusion between the three levels had several times terrible social consequences. Especially, the criticism of capitalism, democracy or law is relevant only if it allows to move toward the top level of non-duality, otherwise it necessarily falls to the lower level of duality and dictatorship. Several important movements either committed this error, or their thinking was reinterpreted: the Greek Cynics (Diogenes), Libertines (the founders of the modern world), Hippies, etc. were all used to promote materialistic and egocentric attitudes, against the ideals of freedom of their founders.
Of course we shall often simplistically say that a given situation is on one pillar, or on one level, but we must always keep in mind all the possible gradations of actual situations.
(Added on August 22, 2018:)
(Permalink) The definition of the quadripolar diagram implies that a given situation occupies a precise point on the diagram. However, situations are often fuzzy, or they involve many persons. They then occupy some (fuzzy) surface on the diagram.
The horizontal extent, or in summary the extent, indicates how far we go toward the Yin side or toward the Yang side, whether by the variety of the participants or by the intrinsic fuzziness of a situation. But only a situation including the central pillar is likely to evolve: the others are blocked or locked. This is the situation of extremists of all kinds, and why these people remain stuck in their opinions.
The vertical depth, or in summary the depth, similarly indicates how far we go towards the good or the evil, whether by the variety of participants or by the intrinsic fuzziness of a situation. There are no situations which locks the evolution, but it should be noted on the contrary that a group of great vertical depth is fundamentally unstable: the participants can not keep together along, even if their neuroses of opinion (chapter V -12) maintain an illusion of an agreement. Only groups with a spiritual authority and psychoeducation methods (ashrams) can remain in this state.
If we perform fuzzy logic calculations, I shall recommend using a Gaussian-like membership function, rather than the usual linear functions. Indeed, for these functions, the probability of the situation reifying itself at a given point is never zero, even very far from the extent or depth. This phenomenon is analogous to the tunnel effect in quantum mechanics, with the evanescent values of an orbital. In a quadripolar logic situation, we indeed observe such «tunnel effects». They have a low probability, but they often are decisive, whether a small number of people make the jump, or that a given person has a small probability of doing so. This translates either by inversions of alliance in the horizontal direction, or by evolutive leaps in the vertical direction. Spiritual enlightenment is in the latter case. Sociology must account with these phenomena, which can bring major changes in a society.
(Permalink) If seems not possible to create a mathematics or even relationship between statements within quadripolar logic. We just study one proposition (in the meaning of the Aristotelian logic), but the whole set of possible values for this proposition makes it rich enough for whole books of studies. Quadripolar Logic is even «fuzzy» like the logic with the same name, and we can even not define measurements: we shall then say that it is it is transcendent, like the Yin-Yang dialectics.
But Quadripolar logic is however exact, in the meaning that we can build diagrams matching with some social, psychological or spiritual realities, allowing to understand them and thus to solve problems arising in such domains, and to save an enormous amount of human suffering, while some other diagram, false or deviate, on the contrary will have for result to harden the situations without allowing for any efficient solution.
This notion of transcendence may shock some. «Transcendant» simply means that the reasoning cannot be reduced to a limited series of Aristotelian inferences. For instance, mathematicians say that the number pi is transcendent, because it cannot be calculated directly. Logics based on a non-duality are transcendent for the same reason. We can even find cases where gradated logics are not reducible to Aristotelian inferences, for instance for emotions, or when strange attractors come on the stage. However when we come to the domain of the mind, this is really spiritual transcendence, for the same reason. If the divine realm of the religions cannot be reduced to any material or mundane causality or purpose, we also note that it does not always obey to Aristotelian logic.
(Permalink) Added on November 7, 2017
Even if the Quadripolar Logic is not formalisable in the sense of Aristotelian mathematics, it still sends to accurate concept, even if accessible only to meditation. Hence the idea to use notations, similar to the ones used in mathematics. I propose some:
-Using dash to express a Yin-Yang dialectics: hot-cold, male-female...
-Using slash to express an Aristotelian good/bad opposition: discipline/dictatorship, freedom/disorder...
These choices are not at random, there already is some support in common litterature. However they are yet inconsistent, not established conventions.
-We can also use the Yin-Yang UTF8 symbol ☯ (☯ or ☯ or simply ☯) to express a dialectics: Male☯female... (To type an unicode character, type the value of the character, like 262f, using the numeric keypad for the numerals and the normal keys for the letters, then press and hold the left ALT key, press the X key, then release both keys.)
Unfortunately, since I created this page, some web browsers repress this symbol with an unsightly black square. There is no typographic solution to this problem at the moment, and sites like facebook or wikipedia who want to represent these symbols correctly use images (image emojis). So I am keeping an eye out for solutions.
Quadripolar logic also needs a symbol. There are none really matching it, so that the UTF8 committee will have to create one. Some existing ones may work, but it is not really their purpose: ∷ (mathematical sign ∷) ⛚ (Drive slow sign ⛚) ⌘ (Place of Interest ⌘) (Added August le 17, 2019:) We can also use two colons symbols, like this: :: Still there is a risk of confusion. Here I put it in bold, to minimise the said confusion.
Since this sub-chapter was a later addition, I did not attempted to harmonise the remainder of this book. This would take weeks of work.
(Permalink) We are now going to study many examples to see how it works, including false examples to dissipate many possible misunderstandings.
Another (Permalink) lesson of the previous diagram is for some people who were upset with the prohibition and obligation system related to marriage (3), and who proposed the free union (2) as more libertarian. Why these attempts often lead to so dreadful failures? It is that getting up in the diagram, way 8>, can be done only by achieving psychological qualities like gentleness and mutual respect. It is worth undertaking this, but it requires time, efforts and sincerity. If, with in mind to follow way 8> we only suppress the marriage contract, without having achieved sufficient respect of the other, then we in fact go to way 9>, towards the perverted free union (4), sharing of selfishness and problems. We went down while believing to go up. In fact, marriage and law, like a buoy, are a guarantee for ordinary people to be maintained within a certain level, without falling too low, while being sometimes an obstacle for those who are spontaneously able to express an authentic mutual respect in the white zone (1). For a person, a buoy can be an indispensable help, but for the flying bird, it is an useless burden.
The situations (2) and (4) are homonymous situations: they are apparently described by the same words and speech, but they lead to opposed results, because they apply to persons who do not have the same psychological, moral or spiritual level, persons who are in different heights in the diagram. (2) leads to happiness, and (4) to suffering.
The persons who confuse (2) and (4) make a vertical confusion within the diagram. This can lead to painful misunderstandings, which were very common in the evolution of modern societies:
An immoral sensualist will make you experience (4) while claiming about (2), and a puritan nutter will fight the divine (2) by confusing it with (4), and while doing this they will both create suffering. Another example of homonymous situations would be the beneficial sexual liberation in the 1960' years and the pornography which is now inflicted to all of us in its name (Porn Internet, naked advertising...)
(Permalink) In the above example, (2) and (1) are horizontally reciprocal situations©, where the simple inversion of the ¥in or ¥ang character of the concerned object (here the type of behaviour) does not change anything to the degree of suffering or happiness of the protagonists, does not change anything to the situation itself. According to a simplistic analysis, the horizontally reciprocal situations appear as opposite, or are described by contrary speeches, whereas they are basically the same thing, the two ¥in or ¥ang faces of the same coin, and that they address to persons with the same moral, psychological or spiritual level, but of different temperaments.
The error of believing that two reciprocal situations are contrary, incompatible or opposite is an horizontal opposition©. If a person makes clan with one of the two reciprocal situations, while believing to fight the other, in fact he reinforces it. (French popular wisdom states that the extremes join up) While believing to be released from the other, he binds himself more to it, and while crediting his own with all qualities he runs straight on to disillusion.
In the example above, the grotty-punk movement (2) succeeded, by presenting its cynicism as being «a liberation», to smash down the idealism of the 1960-70's youth, with an effectiveness of which the traditional extreme right wing and even hitlerian youths would never have dared to dream. (A direct action of fascists on the contrary would have triggered a violent response from youth) There is even a feeling of an occult collusion between these two, for example when (2) acts in a way to be a «cause» for the racism dear to the (1), while (1) organises «police unfortunate mistakes» and other injustices to excite the (2)'s hatred of society. Maybe one day we shall find extreme-right shareholders of a rap editor, perhaps one day we shall be aware to have seen skinheads protecting a neo-nazi meeting.
But what is significant to understand here is that such a voluntary and organised complicity is absolutely not necessary to the effective working of the synergy between the two horizontally reciprocal situations, since they are basically the same thing and that progress of each one immediately benefits the other. When «mistaking» cops or extreme right «militia» brawl with young rapper rapscallions, they COLLABORATE. Do not disturb them!
(Permalink) We need to clearly understand the dynamic effect of passing from a reciprocal situation to another, very similar to that of a pendulum. The more we deviate from the middle way, the more we cause a force in return towards the other extreme. The more we react in a stupid, sectarian or dualistic way (in the bottom of the diagram), the more these forces are violent, and the more this swinging move goes far in misfortune. Thus the situation caused by the grotty-punk movement (malign excess of «freedom») at the moment when I write (1999), starts to produce the fruits that everyone may have logically expected: the come back of the moralists, immediately exploited by the puritan «moralists». This initially appears in a very positive way (fight against paedophilia) then more polemic (Clinton case in the USA, anti-PAC struggle in France. This PAC being mixing together very positive elements and others very negative, any position like «pro» or «anti» is unavoidably stupid). If this motion continues, we could soon assist to a return of the anti-happiness and anti-life «moralistic» ideologies... (This tendency is confirmed on 2010) If we want to get back to a safer middle way, it is necessary to slow down this swinging, or to push at the right time in order to stop it. And this right time, paradoxically, is often the opposite of what we should think obvious.
Let us see one example, about the right time to «push»: currently (France, 1999) to grasp on extreme «libertarian» positions, like this PAC which leads to «legitimate» «homosexual parenthood», is the most effective mean to cause the come back of anti-life ideologies (2017: prediction realized, with the come back of fascism. Who read this book?). For the true libertarians, if they really want to avoid this come back, it is on the contrary the very moment to fight besides the moralists against the grotty-punks and excesses of the «libertarians», in order to keep control on the force in return, and to avoid it to benefit only to the «moralists». The ideal moment for them to act would have been, but it is far too late, to fight the grotty-punk movement at the time of its birth, instead of stupidly identifying themselves with it. And for the true moralists, the moment already came for them to engage the struggle against the «moralists», who, if they are left without control, will be before a few years a real danger for the society (added in 2007: they are now, especially in the USA).
Second example, illustrating the good moment to slow down: Michael Gorbachev, after having set in motion freedom reforms in the USSR, quickly found himself in a position to have to slow down the reforms which he however himself wanted to promote, in order not to go towards an excess of laxness. No many Russians understood, even if this situation is quite simple and completely comparable to pushing a car on a down slope: for a small starting effort, it is then necessary to slow down the movement that we however wish, in order to keep the control of the situation. This was not understood, and unfortunately Boris Eltsine's Russia went towards a foreseeable chaos, where it got bogged down even more deeply than under the dictatorship, after having passed in a few days beyond the middle way which would have enabled it to progress (Updated March 2012: Putin seemed for a time to bring back the necessary authority. But, with refusing to help Syria, he demonstrated his weakness.)
I wrote in 1999 that this situation could also happen in Iran. But in 2010 it is funny to note that the franctical grasp of Ahmadinejad is the fastest way to lead to a democratic and even secular Iran :D.
I also wrote in 1999 that a gigantic catastrophe was preparing in China... but it appeared since (2010) that even the extreme-right materialist chinese government has still enough memories of its Yin-Yang culture to release the pressure progressively, so that, after all, China may settle softly in democracy without starting a huge ecology crisis.
This comprehension of the non-duality of the two ways (10) (chapter I-3) is the Middle Way, which basically differs of a compromise between two objects experienced as opposite or enemy. Contrary to a generally accepted idea this comprehension does not necessarily imply to give up any of the two ways (8) or (9); the exact way that you will actually follow is indeed an affair of opportunities and of personal predilection, and it can be rather extreme.
Buddhist and Taoist philosophies also claim to promote the Middle Way. I think what we found here with quadripolar logic is really the same thing, as we can check with meditating according to one of these philosophies or according to the quadripolar logic, that is by using the correct intuitive mind faculties which allow to master this field of transcendent non-measurable logic. However the quadripolar logic has the advantage of making explicit distinctions between things which are often confused in the original Buddhist or Taoist doctrines.
Various examples in politics In this beginning of 21st century many Third World countries are still in (4). Europe is rather in (5), democracy, where a minimum of freedom is guaranteed by laws. (6) is a wise and good willed dictatorship (rare) and (7) a limp or corrupt democracy, which tolerates (2) and often shows to be the cause of a come back of (1). Indeed excesses of any on the two sides end up wearying people, producing an illusory revolution or a reaction, both simple horizontal inversions©. The History is filled with this style of coming and going forth which produces much noise and furor and appear very significant to those who experience them; but they remain quite futile as long as they do not really allow to go up in the diagram, by mastering necessary psychological qualities. In Western Europe neither revolution nor reaction brought anything durable; true democratisation (rise in the diagram) only came from a long lasting work with social education. This basic democracy still appears quite weak, but it was however able to effectively resist the nazism, and to turn this nasty experience into an European cohesion force, trough pardon to Germans, non-dual with an absolute rejection of nazism. Let us note that the words «reaction» and «revolution» cannot be simply looked at as left/right reflections into the diagram: a revolution is an idealistic or utopian attempt to go up in the diagram (French or Russian revolution, Hippie movement) whereas a reaction deliberately seeks to descend (monarchist reaction, nazism, grotty-punk movement). An horizontal inversion may arrogantly claim to be a revolution, it is indeed a reaction if the result is to go down (example: The invasion of Tibet by the Maoists, presented like a liberation and a progressist revolution whereas it was one of the greatest cultural losses of all times, brutally making this unhappy country pass from (6) to (1)). An authentic revolution can be recognised from the fact that it allows to get higher into the diagram, whatever left or right path it may use.
(Permalink) If we convene to note a force acting toward the left (toward more Yang) as being before the diagram, while a force which acts toward the right (toward more Yin) is noted behind the diagram, then the diagram takes a volume. In the case of a flip-flop movement of reciprocal situations, the situation moves following a loop, seen from above. When the situation betters, or worsens, we have an ascending or descending spiral. I also mention that, into the spiritual development, we often find ourselves into similar situations, but each time from a higher point of view, as if we were going up on an helical path.
The specialists will easily notice the relevant analogy with oscillating systems, described by the differential equation of the second order, with a calling back force and an inertial term. The damping term is generally too strong or too weak in the bottom, and optimal only at the top. When we deal with non-measurable fact, it is only an analogy. But if we introduce a measure, then the two cases become the same thing.
Also see the (note 8)
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