Tao somma dei due precedenti: Tao aureo

Statua di Leonardo Fibonacci nel Camposanto di Pisa.

Successione di Fibonacci e approssimazione alla sezione aurea

Un foglio del manoscritto su pergamena del Liber abbaci conservato nella Biblioteca Nazionale Centrale di Firenze (Codice magliabechiano Conv. Soppr. C 1, 2616, fol. 124r), contenente nel riquadro a destra le prime tredici cifre, in numeri arabi, della cosiddetta "successione di Fibonacci".

Il volo dei numeri di Mario Merz, un'installazione luminosa sulla Mole Antonelliana, rappresenta la successione di Fibonacci

Mathematician Alan Newell of the University of Arizona in Tucson and graduate student Patrick Shipman studied cacti to determine why this pattern is so ubiquitous. The researchers analyzed the plant’s shape, the thickness of its skin, and a host of other biomechanical constraints that steer its growth. When they plugged the data into a computer they discovered, to their surprise, that the most stable configurations inherently follow a Fibonacci-like form. “We show that energy is minimized by this relation”
Courtesy of Patrick Shipman

Girasole - Sunflower

Aeonium tabuliforme

Conchiglia di nautilo

Immagine al microscopio di un'ovaia di Anglerfish (Rana pescatrice)

Cancer cell division. This composite confocal micrograph uses time-lapse microscopy to show a cancer cell (HeLa) undergoing cell division (mitosis). The DNA is shown in red, and the cell membrane is shown in cyan. The round cell in the centre has a diameter of 20 microns.
Credit Kuan-Chung Su, LRI

Jean-Claude Perez discovered a DNA supracode controlling the self-organization of the nucleobases Thymine, Cytosine, Adenine and Guanine (T,C,A,G), which make up the steps in the double helix ladder of DNA. He discovered if you consider 144 contiguous nucleobases it results from 55 T bases and 89 C A G bases, all Fibonacci numbers. These resonances extend to the ratios of the Atomic Weights of the Bio-Atoms of Carbon, Oxygen, Nitrogen and Hydrogen that create the nucleobases of T C A G, such that the ratios of atomic weights in strands considered to be ‘junk DNA’, that is DNA which could not be translated into genetic information or related to known protein synthesis, were equal to Phi, the Golden Ration of 1.618.

gradienti meta-Tao

La successiva metastruttura discussa da Tyler Volk e Jeff Bloom sono i gradienti, intesi come variazioni continue di variabili - scalari o vettoriali - contrapposte a distinte variabili binarie "vere" o "false":

Background

Gradients refer to continuums and shades of gray rather than rigid binaries of black and white. Both hierarchies and holarchies can be described as clearly defined and fuzzy demarcations along a continuum. Size, color, light, temperature, speed, quantity, amounts, elevations, distances, etc. refer to continuums. Most choices for humans and other animals do not manifest as a clear binary, but as a multiplicity along a continuum with no clear “right” or “wrong.”

Gradient of the 2-d function f(x,y) = xe^-x2-y2 is plotted as blue arrows over the pseudocolor plot of the function.

Examples

• In science: speed; acceleration; temperature gradients; slopes; density; solubility; salinity; statistical degrees of freedom; levels of hurricanes, tornado, earthquakes; etc.

• In architecture and design: walkway design; handicap ramps; elevators; lighting of spaces; plumbing design; landscape drainage; golf course design; etc.

• In the arts: use of color, light, and shading; pace of action in dance and drama; curvatures in sculpture; tempo in music; etc.

• In social sciences: population densities, public opinion, intelligence (whatever it is), economic trends, from traditional to modern allegiances in tribal and cultural groups, intensity of emotions, etc.

• In other senses: “mixed emotions,” degrees of friendship, “closeness” of families, types of lies, etc.

Metapatterns

The Pattern Underground

apprendista del Tao

Tao Paradoxico-Philosophicus 14-16

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    Un dieu donne le feu     
     Pour faire l'enfer;      
      Un diable, le miel     
       Pour faire le ciel.      

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TRACTATUS PARADOXICO-PHILOSOPHICUS

14	Groups: consider observers interacting through their cognitive domains with other observers forming networks of observers and thereby creating organizations of different sizes and forms, such as open organizations, closed organizations or even organizationally closed unities, all made of observers.
14.01	These groups, originally undistinguished by their members, remain as such for most of their members.
14.1	Integration: members must follow the rules to define and maintain the group.
14.11	Disintegration: groups, whose members do not follow the rules, fall apart.
14.2	Logical observers adopt or reject the rules of the group through language, explanation and communication thus participating in trivial language-games and forms of life deprived of meaning and sense.
14.21	Paradoxical observers think and converse generating paradoxical contexts that lead to new meaningful and sensible language-games and forms of life.
14.22	Consequently, logical observers tend to make the group and its rules rigid and structured while paradoxical observers prefer to make them flexible and unstructured.
14.3	If the activities of the members surpass certain complexity, paradoxes may arise among the rules of their groups.

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15	Following rules: consider logical observers merely rejecting or adopting the few distinctions used as rules for their groups and those used to follow rules.
15.01	Since these observers only make distinctions as in following or not following rules, appropriate rewards or punishments can easily entice these and other observers into following rules and transform their groups into hierarchies.
15.02	These observers reinforce their following of rules through language, explanation and communication and with a hierarchical organization for their groups.
15.03	Paradoxical observers do not, and prefer to think and converse.
15.1	Since these rules constitute the essence of their hierarchies, logical observers often exaggerate their relevance and use them, for example, in “education”, with regrettable consequences.
15.2	Logical observers follow rules and pursue the goals of their hierarchies without regard for other observers, young observers included.
15.21	These observers develop a need to protect themselves from thinking, conversation, self-reference, paradoxes, uncertainty and unpredictability.
15.22	Therefore, they nourish a conspicuous ignorance about these “unconceivable” concepts.

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16	Pondering rules: consider paradoxical observers thinking and conversing about rules, thereby stimulating other observers to do the same.
16.01	These observers interact and make tentative distinctions as in following rules and not following rules.
16.02	These observers do not form hierarchies; they rather invent and participate in language-games with other rule-pondering observers.
16.1	Rule-following members protect their hierarchies from disintegration by maintaining the number of rule-pondering members as low as possible.
16.2	Rule-pondering observers, however, occasionally manage to join hierarchies of rule-following observers, attempting to make their members think and converse.
16.21	If partially successful, one or more members will leave the hierarchy and will contemplate thinking and conversing.
16.22	If successful beyond all expectations, the hierarchy will disintegrate.
16.23	If unsuccessful, the intruding observer risks an unpleasant expulsion such as would happen to a teacher caught educating his/her students.

Tractatus Paradoxico-Philosophicus

A Philosophical Approach to Education
Un Acercamiento Filosófico a la Educación
Une Approche Philosophique à l'Education
Eine Philosophische Annäherung an Bildung

Ricardo B. Uribe

Copyright © by a collaborating group of people including the author, editing consultants, translators, and printers. All rights reserved.

Tao Paradoxico-Philosophicus 11-13

Tao ricorsivo

M.C. Escher, Reptiles, 1943

M. C. Escher, Drawing Hands, (lithograph, 1948)

Abstract diagram of M. C. Escher's Drawing Hands. On top, a seeming paradox. Below, its resolution.
Douglas Hofstadter

Twelve self-engulfing TV screens. I would have included one more, had 13 not been prime.
Douglas Hofstadter

triangolo di Sierpinski

Alexandre Duret-Lutz, Recursive Blanket Flower

stati d'identità del Tao

Igor Morski

Dopo la descrizione dell'osservazione dei propri stati interni del sistema della coscienza, Charles T. Tart prosegue con la definizione e discussione dell'auto-osservazione degli stati d'identità, creati dal sottosistema della coscienza del senso d'identità:

Identity States

Self-observation, observation of others, and psychoanalytic data indicate that various stimuli can produce marked reorganizations of ego functioning very rapidly, even though these all remain within the consensus reality definitions of "normal" consciousness. These identity states are much like d-SoCs and can be studied in the systems approach framework. They are hard to observe in ordinary life because of the ease and rapidity of transition, their emotional charge, and other reasons. The isolation of knowledge and experience in various identity states is responsible for much of the psychopathology of everyday life.

Definition of Identity States

The concept of d-SoCs comes to us in commonsense form, as well as in terms of my initial research interests, from people's experiences of radically altered states of consciousness—states like drunkenness, dreaming, marijuana intoxication, certain meditative states. These represent such radical shifts in the patterning, the system properties of consciousness, that most people experiencing them are forced to notice that the state of their consciousness is quite different, even if they are poor observers. A person need not have developed an Observer in order to notice such a change in his state of consciousness: so many things are so clearly different that the observation is forced on him.
Although this is the origin and the main focus of the concept of d-SoCs, the systems approach is applicable to important variations occurring within the overall pattern we call the ordinary d-SoC, variations that can be termed identity states. My own self-observation and much scattered psychological data, particularly data gathered in the course of psychoanalytic investigations, indicate that as different situations impinge on a person and activate different emotional drives, distinct changes in the organization of his ego can take place. Certain drives become inhibited or activated, and the whole constellation of psychological functioning alters its configuration around them.
The most cogent formulation of these data into a comprehensive picture is that of the Armenian philosopher and spiritual teacher, George Gurdjieff. The following selection from Ouspensky's report of Gurdjieff's early lectures expresses Gurdjieff's idea that we have many "I's," many little egos:

"One of man's important mistakes," he said, "one which must be remembered, is his illusion in regard to his I."
"Man such as we know him, the 'man machine,' the man who cannot 'do,' and with whom and through whom everything 'happens,' cannot have a permanent and single I. His I changes as quickly as his thoughts, feelings, and moods, and he makes a profound mistake in considering himself always one and the same person; in reality he is always a different person, not the one he was a moment ago. "Man has no permanent and unchangeable I. Every thought, every mood, every desire, every sensation, says 'I.' And in each case it seems to be taken for granted that this I belongs o the Whole, to the whole man, and that a thought, a desire, or an aversion is expressed by this Whole. In actual fact there is no foundation whatever for this assumption. Man's every thought and desire appears and lives quite separately and independently of the Whole. And the Whole never expresses itself, for the simple reason that it exists, as such, only physically as a thing, and in the abstract as a concept. Man has no individual I. But there are, instead, hundreds and thousands of separate small I's, very often entirely unknown to one another, never coming into contact, or, on the contrary, hostile to each other, mutually exclusive and incompatible. Each minute, each moment, man is saying or thinking 'I.' And each time his I is different. Just now it was a thought, now it is a desire, now a sensation, now another thought, and so on, endlessly. Man is a plurality. Man's name is legion."
"The alternation of I's, their continual obvious struggle for supremacy, is controlled by accidental external influences. Warmth, sunshine, fine weather, immediately call up a whole group of I's. Cold, fog, rain, call up another group of I's, other associations, other feelings, other actions. There is nothing in man able to control this change of I's, chiefly because man does not notice, or know of it; he lives always in the last I. Some I's, of course, are stronger than others. But it is not their own conscious strength; they have been created by the strength of accidents or mechanical external stimuli. Education, imitation, reading, the hypnotism of religion, caste, and traditions, or the glamour of new slogans, create very strong I's in man's personality, which dominate whole series of other, weaker, I's. But their strength is the strength of the 'rolls' in the centers. "And all I's making up a man's personality have the same origin as these 'rolls'; they are the results of external influences; and both are set in motion and controlled by fresh external influences."
"Man has no individuality. He has no single, big I. Man is divided into a multiplicity of small I's."
"And each separate small I is able to call itself by the name of the Whole, to act in the name of the Whole, to agree or disagree, to give promises, to make decisions, with which another I or the Whole will have to deal. This explains why people so often make decisions and so seldom carry them out. A man decides to get up early beginning from the following day. One I, or a group of I's, decide this. but getting up is the business of another I who entirely disagrees with the decision and may even know absolutely nothing about it. Of course the man will again go on sleeping in the morning and in the evening he will again decide to get up early. In some cases this may assume very unpleasant consequences for a man. A small accidental I may promise something, not to itself, but to someone else at a certain moment simply out of vanity or for amusement. Then it disappears, but the man, that is, the whole combination of other I's who are quite innocent of this, may have to pay for it all his life. It is the tragedy of the human being that any small I has the right to sign checks and promissory notes and the man, that is, the Whole, has to meet them.
People's whole lives often consist in paying off the promissory notes of small accidental I's."

Gurdjieff's concept of these rapidly alternating I's is similar to the systems approach concept of d-SoCs. If we call each I an identity state, then each (1) has an overall pattern of functioning, a gestalt, which gives it a system identity and distinguishes it from other identity states; (2) is composed of structures/subsystems, psychological functions, skills, memories; (3) possesses unique properties not present in other identity states; (4) presumably has some stabilizing processes, although apparently fewer than the ordinary d-SoC as a whole, since identity states can change so rapidly; (5) functions as a tool for coping with the world, with varying degrees of effectiveness; and (6) requires an induction process to transit from one identity state to another, a requisite stimulus to bring on a new identity state.
These alterations in functioning that I call identity states can thus be usefully studied with the systems approach to consciousness. Yet they are almost never identified as d-SoCs in ordinary people, for several reasons.
First, each person has a large repertoire of these identity states and transits between one and another of them extremely readily, practically instantly. Thus, no obvious lapses or transitional phenomena occur that would make him likely to notice the transitions.
Second, all these identity states share much psychological functioning in common, such as speaking English, responding to the same proper name, wearing the same sets of clothes. These many common properties make differences difficult to notice.
Third, all a person's ordinarily used identity states share in his culturally defined consensus reality. Although certain aspects of reality are emphasized by particular identity states, the culture as a whole implicitly allows a wide variety of identity states in its definitions of "normal" consciousness and consensus reality. Within the cultural consensus reality, for example, there are well-understood concepts, perceptions, and allowed behaviors associated with being angry, being sad, feeling sexual desire, being afraid.
Fourth, a person's identification is ordinarily very high, complete, with each of these identity states. He projects the feeling of "I" onto it (the Sense of Identity subsystem function discussed in Chapter 8). This, coupled with the culturally instilled need to believe that he is a single personality, causes him to gloss over distinctions. Thus he says, "I am angry," "I am sad," rather than, "A state of sadness has organized mental functioning differently from a state of anger." The culture also reinforces a person for behaving as if he were a unity.
Fifth, identity states are driven by needs, fears, attachments, defensive, maneuvers, coping mechanisms, and this highly charged quality of an identity state makes it unlikely that the person involved will be engaged in self-observation.
Sixth, many identity states have, as a central focus, emotional needs and drives that are socially unacceptable or only partially acceptable. Given the fact that people need to feel accepted, an individual may have many important reasons for not noticing that he has discrete identity states. Thus, when he is in a socially "normal" identity state, being a good person, he may be unable to be aware of a different identity state that sometimes occurs in which he hates his best friend. The two states are incompatible, so automatized defense mechanisms (Gurdjieff calls them buffers) prevent him from being aware of the one identity state while in the other. This is, in systems approach terminology, state-specific knowledge. Ordinarily, special psychotherapists techniques are required to make a person aware of these contradictory feelings and identity states within himself. Meditative practices designed to create the Observer also facilitate this sort of knowledge.
The development of an Observer can allow a person considerable access to observing different identity states. An outside observer can often clearly infer different identity states, but a person who has not developed the Observer function well may never notice his many transitions from one identity state to another. Thus ordinary consciousness, or what society values as "normal" consciousness, may actually consist of a large number of d-SoCs, identity states. But the overall similarities between these identity states and the difficulty of observing them, for the reasons discussed above, lead us to think of ordinary consciousness as relatively unitary state.
Gurdjieff sees the rapid, unnoticed transitions between identity states, and their relative isolation from one another, as the major cause of the psychopathology of everyday life. I agree with him, and believe this topic deserves intensive psychological research.

Functions of Identity States
 
An identity state, like a d-SoC, has coping functions. The culture a person is born into actively inhibits some of his human potentials, as well as developing some. Thus, even in the most smoothly functioning cultures, there is bound to be some disharmony, some conflict between a person's emerging and potential self and he demands placed on him to which he must conform in one way or another if he is to survive in that social environment. The psychopathology of everyday life is abundantly obvious and has been amply documented by psychological studies.
At the fringes of consciousness, then, there is a vast unknown, not simply of relatively neutral potentials that never developed, but of emotionally and cognitively frightening things, conflicts that were never resolved, experiences that did not fit consensus reality, feelings that were never expressed, problems that were never faced. Immersion is consensus reality in the ordinary d-SoC is a protection from this potentially frightening and overwhelming unknown; it is the safe, cultivated clearing in the dark, unexplored forest of the mind.
An identity state is a specialized version of the ordinary d-SoC, a structure acceptable to consensus reality (ignoring obviously pathological identity states). The extrainformational "This is me" quality from the Sense of Identity subsystem added to certain contents/structures constellates the energies of consciousness around them and produces an identity, a role that a person partially or completely identified with for the time. The identity "eats energy."
A particular identity state thus acts as loading stabilization for the ordinary d-SoC; it absorbs much available energy that might otherwise activate unknown and perhaps implicitly feared contents that are not acceptable. When you "know" who are, when you take on an identity state, then you immediately have criteria for dealing with various situations. If I am a "father" in this moment I know that certain things are expected and desired of me and I can cope well within that framework with situations involving my children. If the situation changes and I now become a "professor," then I have a new set of rules on how to cope with situations involving people who have identified with the roles of "students."
Some of a person's most important problems arise when his is in an identity state that is not really suited to the situation: my children are unhappy when I am a professor when they want a father, and I am not comfortable when my students want me to be like a father when I think the role of professor is more appropriate.
Being caught in a situation in which one has no ready role to use and identify with is unusual. For most people such situations can be lightly confusing or frightening, since they do not know how to think or act. They can become susceptible to any authority who offers ready-made roles/solutions in such situations. If the country is "going to hell" and nobody seems to have any answer, it may feel much better to be a "patriot" and blame "traitors" than to live with your confusion.
On the other hand, lack of an immediately available role can offer a unique opportunity to temporarily escape from the tyranny of roles.
Once a person has identified with a role, the resulting identity state stabilizes his d-SoC not only through loading stabilization, but through the other three stabilization processes discussed... When he is coping successfully and thus feeling good in a particular identity state, this constitutes positive feedback stabilization; he tends to engage in more thoughts and actions that expand and strengthen the identity state. If the fear of having no identity is strong and/or the rewards from a particular identity state are high, this can hinder escape from that identity state. Consider how many successful businessmen work themselves to death, not knowing how to stop being businessmen for even short periods, or how many men die within a few years of retiring, not having their work identity to sustain them.
Success from being in a particular identity state encourages a person to avoid or suppress thoughts and actions that tends to disrupt that state: this is negative feedback stabilization. A "good soldier" is obtaining valuable information about enemy troop movements—information that may save the lives of his buddies—by torturing a native child: he actively suppresses his own identity state of a "father" is order to function effectively in his "soldier' identity.
Being in a particular identity state also functions as limiting stabilization. The identity leads to selective perception to make perceptions congruent with the reigning identity state. Certain kinds of perceptions that might activate other identity states are repressed. The tortured child is perceived as an "enemy agent," not as a "child." This keeps emotional and attention/awareness energy out of empathic processes that, if activated, would undermine and disrupt the "soldier" identity.
Identity states, then, are both tools for coping with the environment and ways of avoiding the unknown. The degree to which they serve mainly one or the other function probably varies tremendously form individual to individual and identity to identity. Some people are terribly afraid of anything outside the few narrow identities they always function in: by staying in one of the other of those identity states constantly, they never feel the fear of the unknown. Others have less fear of the unknown, but find the rewards from functioning in a few identity states are so high that they have no real need or interest to go outside them. The latter type probably characterizes a stable, well-integrated society, with most citizens quite content in a socially accepted identity states.
For discussion of radically altered discrete states like hypnosis or drunkenness, the concept of the ordinary d-SoC as relatively unitary is useful. As the systems approach becomes more articulated, however, we shall have to deal with these identity states that exist within the boundaries of the ordinary d-SoC and that probably also function within the boundaries of various d-ASCs.
In this book, I continue to use the terms discrete state of consciousness and discrete altered state of consciousness to refer to the rather radical alterations like hypnosis or drunkenness that gave rise to the concept in the first place. I use the phrase identity state to indicate the more subtle division.

who knows where the Tao goes?

Across the evening sky all the birds are leaving
But how can they know it's time for them to go?
Before the winter fire, I will still be dreaming
I have no thought of time

For who knows where the time goes?
Who knows where the time goes?

Sad deserted shore, your fickle friends are leaving
Ah, but then you know it's time for them to go
But I will still be here, I have no thought of leaving
I do not count the time

For who knows where the time goes?
Who knows where the time goes?

And I am not alone while my love is near me
I know it will be so until it's time to go
So come the storms of winter and then the birds in spring again
I have no fear of time

For who knows how my love grows?
And who knows where the time goes?

Putney Vale Cemetery and Crematorium, Wimbledon, Greater London, England