Monday, July 16, 2012

the complexity from KaliYuga to Tao - I

*Presented at the Colloquium “Intelligence de la complexité: épistémologie et pragmatique”, Cerisy-La-Salle, France, June 26th, 2005

Why has the problematic of complexity appeared so late? And why would it be justified?

1. The three principles of the rejection of complexity by ‘classical science’

Classical science rejected complexity in virtue of three fundamental explanatory principles:
  1. The principle of universal determinism, illustrated by Laplace’s Daemon, capable, thanks to his intelligence and extremely developed senses, of not only knowing all past events, but also of predicting all events in the future. 
  2. The principle of reduction, that consists in knowing any composite from only the knowledge of its basic constituting elements. 
  3. The principle of disjunction, that consists in isolating and separating cognitive difficulties from one another, leading to the separation between disciplines, which have become hermetic from each other.
These principles led to extremely brilliant, important, and positive developments of scientific knowledge up to the point where the limits of intelligibility which they constituted became more important than their elucidations.
In this scientific conception, the notion of “complexity” is absolutely rejected. On the one hand, it usually means confusion and uncertainty; the expression “it is complex” in fact expresses the difficulty of giving a definition or explanation. On the other hand, since the truth criterion of classical science is expressed by simple laws and concepts, complexity relates only to appearances that are superficial or illusory. Apparently, phenomena arise in a confused and dubious manner, but the mission of science is to search, behind those appearances, the hidden order that is the authentic reality of the universe.
Certainly, western science is not alone in the search of the “true” reality behind appearances; for Hinduism, the world of appearances, the māyā is illusory; and for Buddhism the saṃsāra, the world of phenomena, is not the ultimate reality. But the true reality, in the Hindu or Buddhist worlds, is inexpressible and in extreme cases unknowable. Whereas, in classical science, behind appearances, there is the impeccable and implacable order of nature.
Finally, complexity is invisible in the disciplinary division of the real. In fact, the first meaning of the word comes from the Latin complexus, which means what is woven together. The peculiarity, not of the discipline in itself, but of the discipline as it is conceived, non-communicating with the other disciplines, closed to itself, naturally disintegrates complexity. 
For all these reasons, it is understood why complexity was invisible or illusory, and why the term was rejected deliberately.

2. Complexity: A first breach: irreversibility
However, a first breach is made within the scientific universe during the nineteenth century; complexity would appear from it de facto before starting to be recognized de jure.
Complexity would make its appearance de facto with the second law of thermodynamics, which indicates that energy degrades into caloric form: this principle lies within the scope of the irreversibility of time, while until then physical laws were in principle reversible and that even in the conceptionof life, the fixism of species did not need time.
The important point here is not only the irruption of irreversibility, thus time, but it is also the apparition of a disorder since heat is conceived as the agitation of molecules; the disordered movement of each molecule is unpredictable, except at a statistical scale where distribution laws can bedetermined effectively.
The law of the irreversible growth of entropy has given place to multiple speculations, and beyond the study of closed systems, a first reflection about the universe, where the second law leads toward dispersion, uniformity, and thus towards death. This conception of the death of the universe, long ago rejected, has appeared recently in cosmology, with the discovery of black energy. This will lead to the dispersion of galaxies and would seem to announce us that the universe tends to a generalized dispersion. As the poet Eliot said: “the universe will die in a whisper” ...
Thus, the arrival of disorder, dispersion, disintegration, constituted a fatal attack to the perfect, ordered, and determinist vision.
And many efforts will be needed-we are not there precisely because it is against the reigning paradigm-to understand that the principle of dispersion, which appears since the birth of the universe with this incredible deflagration improperly named big bang, is combined with a contrary principle of bonding and organization which is manifested in the creation of nuclei, atoms, galaxies, stars, molecules, and life.

3. Interaction Order/Disorder/Organization

How is it that both phenomena are related?
This is what I tried to show in the first volume of La Methode (The Method). We will need to associate the antagonist principles of order and disorder, and associate them making another principle emerge that is the one of organization.
Here is in fact a complex vision, which one has refused to consider during  a very long time, for one cannot conceive that disorder can be compatible with order, and that organization can be related to disorder at all, beingantagonist to it.
At the same time than that of the universe, the implacable order of life is altered. Lamarck introduces the idea of evolution, Darwin introduces variation and competition as motors of evolution. Post-darwinism, if it has, in certain cases, attenuated the radical character of the conflict, has brought this other antinomy of order: chance, I would say even a vice of chance. Within the neodarwinian conception, to avoid calling “creation” or “invention” the new forms of living organization such as wings, eyes - one is very afraid of the word "invention" and of the word "creation” - one has put chance at the prow. One can understand the rest of the fear of creation because science rejects creationism, i.e. the idea that God is a creator of living forms. But the reject of creationism finished in masking the creativity that manifests itself in the history of life and in the history of humanity. And, from the philosophical point of view, it is rather recently that Bergson, and then in another way, Castoriadis, put at the centre of their conception the idea of creation.
In addition, in the beginning of the twentieth century, microphysics introduced a fundamental uncertainty in the universe of particles that ceases to obey the conceptions of space and time characteristic of our universe called macro-physic. How thus these two universes, that are the same, but at a different scale, are compatible? One begins today to conceive that one can pass, from the micro-physical universe to ours, since between them a certain number of quantum elements are connected, in virtue of a process called decoherence. But there remains this formidable logical and conceptual hiatus between the two physics.
Finally, at a very large scale - mega-physical - Einstein’s theory discovers that space and time are related to one another, with the result that our lived and perceived reality becomes only meso-physical, situated between micro-physic reality and mega-physical reality

4. Chaos

All this made that the dogmas of classical science are reached, but de facto: although increasingly mummified, they remain.
Yet a certain number of strange terms would appear. For example, the term “catastrophe”, suggested by René Thom to try to make intelligible the discontinuous changes of form; then the fractalism of Mandelbrot; then the physical theories of chaos, which distinguishes itself from the rest, since today it is thought that the solar system, which seems to obey an absolutely impeccable and measurable order with the most extreme precision, considering its evolution in millions of years, is a chaotic system comprising a dynamic instability modifying for example Earth’s rotation around itself or around the Sun. A chaotic process may obey to deterministic initial states, but these cannot be know exhaustively, and the interactions developed within this process alter any prevision. Negligible variations have considerable consequences over large time scales. The word chaos, in these physics, has a very limited meaning: that of apparent disorder and unpredictability. Determinism is saved in principle, but it is inoperative since one cannot know exhaustively the initial states. We are in fact, since the original deflagration and forever, plunged in a chaotic universe.

Bruce Torrence, Lisbon Oriente Station, Panoramic Photograph, 2011

5. The emergence of the notion of complexity
However, complexity remained always unknown in physics, in biology, in social sciences. Admittedly, after more than half a century, the word complexity irrupted, but in a domain that also remained impermeable to the human and social sciences, as well as to the natural sciences themselves. It is at the bosom of a sort of nebulous spiral of mathematicians and engineers where it emerged at about the same time, and became connected at once, in the forties and fifties, with Information Theory, Cybernetics, and General Systems Theory. Within this nebula, complexity will appear with Ashby to define the degree of variety in a given system. The word appears, but does not contaminate, since the new thinking remains pretty confined: the contributions of Von Neumann, of Von Foerster will remain completely ignored, and still remain in the disciplinary sciences closed on themselves. One can also say that Chaitin’s definition of randomness as algorithmic incompressibility becomes applicable to complexity. Consequently, the terms chance, disorder, complexity tend to overlap one another and sometimes to be confused.
There were breaches, but still not an opening.
This would come from the Santa Fe Institute (1984) where the word will be essential to define dynamical systems with a very large number of interactions and feedbacks, inside of which processes very difficult to predict and control take place, as “complex systems”, where the classical conception was unable to be considered.
Thus, the dogmas or paradigms of classical science began to be disputed.
The notion of emergence appeared. In “Chance and Necessity”, Jacques Monod makes a great state of emergence, i.e. qualities and properties that appear once the organization of a living system is constituted, qualities that evidently do not exist when they are presented in isolation. This notion is taken, here and there, more and more, but as a simple constatation without being really questioned (whereas it is a conceptual bomb).
It is like this that it was arrived to the complexity I call “restricted”: the word complexity is introduced in “complex systems theory”; in addition, here and there the idea of “sciences of complexity” was introduced, encompassing the fractalist conception and chaos theory.
Restricted complexity spread rather recently, and after a decade in France, many barriers have been jumped. Why? Because more and more a theoretical vacuum was faced, because the ideas of chaos, fractals, disorder, and uncertainty appeared, and it was necessary at this moment that the word complexity would encompass them all. Only that this complexity is restricted to systems which can be considered complex because empirically they are presented in a multiplicity of interrelated processes, interdependent and retroactively associated. In fact, complexity is never questioned nor thought epistemologically.
Here the epistemological cut between restricted and generalized complexities appears because I think that any system, whatever it might be, is complex by its own nature.
Restricted complexity made it possible important advances in formalization, in the possibilities of modeling, which themselves favor interdisciplinary potentialities. But one still remains within the epistemology of classical science. When one searches for the “laws of complexity”, one still attaches complexity as a kind of wagon behind the truth locomotive, that which produces laws. A hybrid was formed between the principles of traditional science and the advances towards its hereafter. Actually, one avoids the fundamental problem of complexity which is epistemological, cognitive, paradigmatic. To some extent, one recognizes complexity, but by decomplexifying it. In this way, the breach is opened, then one tries to clog it: the paradigm of classical science remains, only fissured.

6. Generalized complexity
But then, what is “generalized” complexity? It requires, I repeat, an epistemological rethinking, that is to say, bearing on the organization of knowledge itself.
And it is a paradigmatic problem in the sense that I have defined “paradigm”. Since a paradigm of simplification controls classical science, by imposing a principle of reduction and a principle of disjunction to any knowledge, there should be a paradigm of complexity that would impose a principle of distinction and a principle of conjunction.
In opposition to reduction, complexity requires that one tries to comprehend the relations between the whole and the parts. The knowledge of the parts is not enough, the knowledge of the whole as a whole is not enough, if one ignores its parts; one is thus brought to make a come and go in loop to gather the knowledge of the whole and its parts. Thus, the principle of reduction is substituted by a principle that conceives the relation of whole-part mutual implication.
The principle of disjunction, of separation (between objects, between disciplines, between notions, between subject and object of knowledge), should be substituted by a principle that maintains the distinction, but that tries to establish the relation.
The principle of generalized determinism should be substituted by a principle that conceives a relation between order, disorder, and organization. Being of course that order does not mean only laws, but also stabilities, regularities, organizing cycles, and that disorder is not only dispersion, disintegration, it can also be blockage, collisions, irregularities.
Let us now take again the word of Weaver, from a text of 1948, to which we often referred, who said: the XIXth century was the century of disorganized complexity and the XXth century must be that of organized complexity.
When he said “disorganized complexity”, he thought of the irruption of the second law of thermodynamics and its consequences. Organized complexity means to our eyes that systems are themselves complex because their organization supposes, comprises, or produces complexity.
Consequently, a major problem is the relation, inseparable (shown in La Methode 1) , between disorganized complexity and organized complexity.
Let us speak now about the three notions that are present, but to my opinion not really thought of, in restricted complexity: the notions of system, emergence, and organization.

7. System: It should be conceived that “any system is complex”
What is a system? It is a relation between parts that can be very different from one another and that constitute a whole at the same time organized, organizing, and organizer.
Concerning this, the old formula is known that the whole is more than the sum of its parts, because the addition of qualities or properties of the parts is not enough to know those of the whole: new qualities or properties appear, due to the organization of these parts in a whole, they are emergent.
But there is also a substractivity which I want to highlight, noticing that the whole is not only more than the sum of its parts, but it is also less that the sum of it parts.
Because a certain number of qualities and properties present in the parts can be inhibited by the organization of the whole. Thus, even when each of our cells contains the totality of our genetic inheritance, only a small part of it is active, the rest being inhibited. In the human relation individual society, the possibilities of liberties (delinquent or criminal in the extreme) inherent to each individual, will be inhibited by the organization of the police, the laws, and the social order.
Consequently, as Pascal said, we should conceive the circular relation:‘one cannot know the parts if the whole is not known, but one cannot know the whole if the parts are not known’.
Thus, the notion of organization becomes capital, since it is through organization of the parts in a whole that emergent qualities appear and inhibited qualities disappear.

8. Emergence of the notion of emergence
What is important in emergence is the fact that it is indeductible from the qualities of the parts, and thus irreducible; it appears only parting from the organization of the whole. This complexity is present in any system, starting with H2O, the water molecule which has a certain number of qualities or properties that the hydrogen or oxygen separated do not have, which have qualities that the water molecule does not have.
There is a recent number of the Science et Avenir journal devoted to emergence; to relate emergence and organization, one wonders wether it is a hidden force in nature, an intrinsic virtue.
From the discovery of the structure of the genetic inheritance in DNA, where it appeared that life was constituted from physicochemical ingredients present in the material world, therefore from the moment that it is clear that there is not a specifically living matter, a specifically living substance, that there is no élan vital in Bergson’s sense, but only the physicochemical matter that with a certain degree of organizing complexity produces qualities of the living - of which self-reproduction, self-reparation, as well as a certain number of cognitive or informational aptitudes, as from this moment, the vitalism is rejected, the reductionism should be rejected, and it is the notion of emergence that takes a cardinal importance, since a certain type of organizing complexity produces qualities specific of selforganization.
The spirit (mens, mente) is an emergence. It is the relation brain-culture that produces as emergent psychic, mental qualities, with all that involves language, consciousness, etc.
Reductionists are unable to conceive the reality of the spirit and want to explain everything starting from the neurons. The spiritualists, incapable of conceiving the emergence of the spirit starting from the relation brainculture, make from the brain at most a kind of television.

9. The complexity of organization
The notion of emergence is a capital notion, but it redirects to the problem of organization, and it is organization which gives consistence to our universe. Why is there organization in the universe? We cannot answer this question, but we can examine the nature of organization.
If we think already that there are problems of irreducibility, of indeductibility, of complex relations between parts and whole, and if we think moreover that a system is a unit composed of different parts, one is obliged to unite the notion of unity and that of plurality or at least diversity. Then we realize that it is necessary to arrive at a logical complexity, because we should link concepts which normally repel each other logically, like unity and diversity. And even chance and necessity, disorder and order, need to be combined to conceive the genesis of physical organizations, as on the plausible assumption where the carbon atom necessary to the creation of life was constituted in a star former to our sun, by the meeting exactly at the same time - absolute coincident - of three helium nuclei. Thus, in stars where there are billions of interactions and meetings, chance made these nuclei to meet, but when this chance occurs, it is necessary that a carbon atom will be constituted.
You are obliged to connect all these disjoined notions in the understanding that was inculcated to us, unfortunately, since childhood, order, disorder, organization.
We then manage to conceive what I have called the self-eco-organization, i.e. the living organization.

10. The self-eco-organization
The word self-organization had emerged and had been used as of the end of the 50’s by mathematicians, engineers, cyberneticians, neurologists.
Three important conferences had been held on the topic of “self-organizing systems”, but a paradoxical thing, the word had not bored in biology, and was a marginal biologist, Henri Atlan, who retook this idea, in a great intellectual isolation within his corporation, in the 70’s. Finally the word emerged in the 8O’s-9O’s in Santa Fe as a new idea, whereas it existed already for nearly half a century. But it is still not imposed in biology.
I call self-eco-organization to the living organization, according to the idea that self-organization depends on its environment to draw energy and information: indeed, as it constitutes an organization that works to maintain itself, it degrades energy by its work, therefore it must draw energy from its environment. Moreover, it must seek its food and defend against threats, thus it must comprise a minimum of cognitive capacities.
One arrives to what I call logically the complex of autonomydependence. For a living being to be autonomous, it is necessary that it depends on its environment on matter and energy, and also in knowledge and information. The more autonomy will develop, the more multiple dependencies will develop. The more my computer will allow me to have an autonomous thought, the more it will depend on electricity, networks, sociological and material constraints. One arrives then to a new complexity to conceive living organization: the autonomy cannot be conceived without its ecology. Moreover, it is necessary for us to see a self-generating and self-producing process, that is to say, the idea of a recursive loop which obliges us to break our classical ideas of product producer, and of cause effect.
In a self-generating or self-producing or self-poetic or self-organizing process, the products are necessary for their own production. We are the products of a process of reproduction, but this process can continue only if we, individuals, couple to continue the process. Society is the product of interactions between human individuals, but society is constituted with its emergencies, its culture, its language, which retroacts to the individuals and thus produces them as individuals supplying them with language and culture. We are products and producers. Causes produce effects that are necessary for their own causation.
Already the loop idea had been released by Norbert Wiener in the idea of feedback, negative as well as positive, finally mainly negative; then it was generalized without really reflecting on the epistemological consequences which it comprised. Even in the most banal example which is that of a thermal system supplied with a boiler which provides the heating of a building, we have this idea of inseparability of the cause and effect: thanks to the thermostat, when 20” is reached, the heating stops; when the temperature is too low, the heating is started. It is a circular system, where the effect itself intervenes in the cause which allows the thermal autonomy of the whole compared to a cold environment. That is to say that the feedback is a process which complexifies causality. But the consequences of this had not been drawn to the epistemological level.
Thus feedback is already a complex concept, even in non-living systems. Negative feedback is what makes it possible to cancel the deviations that unceasingly tend to be formed like the fall in temperature compared to the standard. Positive feedback develops when a regulation system is not able anymore to cancel the deviations; those can then be amplified and go towards a runaway, kind of generalized disintegration, which is often the case in our physical world. But we could see, following an idea advanced more than fifty years ago by Magoroh Maruyama, that the positive feedback, i.e. increasing deviation, is an element that allows transformation in human history. All the great transformation processes started with deviations, such as the monotheist deviation in a polytheist world, the religious deviation of the message of Jesus within the Jewish world, then, deviation in the deviation, its transformation by Paul within the Roman empire; deviation, the message of Mohammed driven out of Mecca, taking refuge in Medina. The birth of capitalism is itself deviating in a feudal world. The birth of modern science is a deviating process from the XVIIth century. Socialism is a deviating idea in the XIXth century. In other words, all the processes  start by deviations that, when they are not suffocated, exterminated, are then able to make chain transformations.

11. The relationship between local and global
In logical complexity, you have the relation between the local and the global.
One believed to be able to assume the two truths of the global and of the local with axioms of the style: “think globally and act locally”. In reality, one is, I believe, constrained in our global age to think jointly locally and globally and to try to act at the same time locally and globally. Also, which is also complex, local truths can become global errors. For example, when our immune system rejects with the greatest energy the heart that one grafts to him, like a nasty foreigner, this local truth becomes a global error, because the organism dies. But one can also say that global truths can lead to local errors. The truth of the need to fight against terrorism can lead to interventions, which will favor even more the development of terrorism, just look at Irak.

why a Tao?

Metalogue: Why a Swan?

Daughter: Why a swan?
Father: Yes—and why a puppet in Petroushka?
D: No—that's different. After all a puppet is sort of hu­man—and that particular puppet is very human.
F: More human than the people?
D: Yes.
F:  But still only sort of human? And after all the swan is also sort of human.
D: Yes.
* * *

D: But what about the dancer? Is she human? Of course she really is, but, on the stage, she seems inhuman or impersonal—perhaps superhuman. I don't know.
F: You mean—that while the swan is only a sort of swan and has no webbing between her toes, the dancer seems only sort of human.
D: I don't know—perhaps it's something like that.

* * *
F: No—I get confused when I speak of the "swan" and the dancer as two different things. I would rather say that the thing I see on the stage—the swan figure—is both "sort of" human and "sort of" swan.
D: But then you would be using the word "sort of" in two senses.
F: Yes, that's so. But anyhow, when I say that the swan figure is "sort of" human, I don't mean that it (or she) is a member of that species or sort which we call human.
D: No, of course not.
F: Rather that she (or it) is a member of another subdivi­sion of a larger group which would include Petroushka puppets and ballet swans and people.
D: No, it's not like genera and species. Does your larger group include geese?
F: All right. Then I evidently do not know what the word "sort of" means. But I do know that the whole of fantasy, poetry, ballet, and art in general owes its meaning and importance to the relationship which I refer to when I say that the swan figure is a "sort of" swan—or a "pretend" swan.
D: Then we shall never know why the dancer is a swan or a puppet or whatever, and shall never be able to say what art or poetry is until someone says what is really meant by "sort of."
F:  Yes.
D:  But we don't have to avoid puns. In French the phrase espece de (literally "sort of") carries a special sort of punch. If one man calls another "a camel" the insult may be a friendly one. But if he calls him an espece de chameau—a sort of camel—that's bad. It's still worse to call a man an espece d'espece—a sort of a sort.
D: A sort of a sort of what?
F: No—just a sort of a sort. On the other hand, if you say of a man that he is a true camel, the insult carries a flavor of grudging admiration.
D: But when a Frenchman calls a man a sort of camel, is he using the phrase sort of in anything like the same way as I, when I say the swan is sort of human?

* * *
F:  It's like—there's a passage in Macbeth. Macbeth is talk­ing to the murderers whom he is sending out to kill Banquo. They claim to be men, and he tells them they are sort of men.
Ay—in the catalogue ye go for men.
as hounds and greyhounds, mongrels, spaniels, curs,
shoughs, water-rugs and demi-wolves are clept
all by the name of dogs.
(Macbeth, Act III, Scene 1)
D: No—that's what you said just now. What was it? "Another subdivision of a larger group?" I don't think that's it at all.
F: No, it's not only that. Macbeth, after all, uses dogs in his simile. And "dogs" means either noble hounds or scav­engers. It would not be the same if he had used the domestic varieties of cats—or the subspecies of wild roses.
D: All right, all right. But what is the answer to my question? When a Frenchman calls a man a "sort of" camel, and I say that the swan is "sort of" human, do we both mean the same thing by "sort of"?

* * *
F: All right, let's try to analyze what "sort of" means. Let's take a single sentence and examine it. If I say "the puppet Petroushka is sort of human," I state a relation-ship.
D: Between what and what?
F:  Between ideas, I think.
D: Not between a puppet and people?
F:  No. Between some ideas that I have about a puppet and some ideas that I have about people.
D: Oh.
* * *
D: Well then, what sort of a relationship?
F:  I don't know. A metaphoric relationship?
* * *
F: And then there is that other relationship which is emphatically not "sort of." Many men have gone to the stake for the proposition that the bread and wine are not "sort of" the body and blood.
D: But is that the same thing? I mean—is the swan ballet a sacrament?
F:  Yes—I think so—at least for some people. In Protestant language we might say that the swanlike costume and movements of the dancer are "outward and visible signs of some inward and spiritual grace" of woman. But in Catholic language that would make the ballet into a mere metaphor and not a sacrament.
D: But you said that for some people it is a sacrament. You mean for Protestants?
F: No, no. I mean that if for some people the bread and wine are only a metaphor, while for others—Catholics —the bread and wine are a sacrament; then, if there be some for whom the ballet is a metaphor, there may be others for whom it is emphatically more than a metaphor—but rather a sacrament.
D: In the Catholic sense?
F:  Yes.
* * *
F: I mean that if we could say clearly what is meant by the proposition "the bread and wine is not `sort of' the body and blood"; then we should know more about what we mean when we say either that the swan is "sort of" human or that the ballet is a sacrament.
D: Well—how do you tell the difference?
F:  Which difference?
D: Between a sacrament and a metaphor.
* * *
F: Wait a minute. We are, after all, talking about the per-former or the artist or the poet, or a given member of the audience. You ask me how I tell the difference between a sacrament and a metaphor. But my answer must deal with the person and not the message. You ask me how I would decide whether a certain dance on a certain day is or is not sacramental for the partic­ular dancer.
D: All right—but get on with it.
F: Well—I think it's a sort of a secret.
D: You mean you won't tell me?
F: No—it's not that sort of secret. It's not something that one must not tell. It's something that one cannot tell.
D: What do you mean? Why not?
F: Let us suppose I asked the dancer, "Miss X, tell me, that dance which you perform—is it for you a sacra­ment or a mere metaphor?" And let us imagine that I can make this question intelligible. She will perhaps put me off by saying, "You saw it—it is for you to de­cide, if you want to, whether or not it is sacramental for you." Or she might say, "Sometimes it is and sometimes it isn't." Or "How was I, last night?" But in any case she can have no direct control over the matter.

* * *
D: Do you mean that anybody who knew this secret would have it in their power to be a great dancer or a great poet?
F: No, no, no. It isn't like that at all. I mean first that great art and religion and all the rest of it is about this secret; but knowing the secret in an ordinary conscious way would not give the knower control.

* * *
D: Daddy, what has happened? We were trying to find out what "sort of" means when we say that the swan is "sort of" human. I said that there must be two senses of "sort of." One in the phrase "the swan figure is a `sort of' swan, and another in the phrase "the swan figure is `sort of' human." And now you are talking about mys­terious secrets and control.
F: All right. I'll start again. The swan figure is not a real swan but a pretend swan. It is also a pretend-not hu­man being. It is also "really" a young lady wearing a white dress. And a real swan would resemble a young lady in certain ways.
D: But which of these is sacramental?
F: Oh Lord, here we go again. I can only say this: that it is not one of these statements but their combination which constitutes a sacrament. The "pretend" and the "pretend-not" and the "really" somehow get fused to­gether into a single meaning.
D: But we ought to keep them separate.
F: Yes. That is what the logicians and the scientists try to do. But they do not create ballets that way—nor sacra­ments.

Metalogue: Why a Swan?; Impulse 1954.