recursive literary Tao

You are about to begin reading Italo Calvino's new novel, If on a winter's night a traveler. Relax. Concentrate. Dispel every other thought. Let the world around you fade. Best to close the door; the TV is always on in the next room. Tell the others right away, "No, I don't want to watch TV!" Raise your voice--they won't hear you otherwise--"I'm reading! I don't want to be disturbed!" Maybe they haven't heard you, with all that racket; speak louder, yell: "I'm beginning to read Italo Calvino's new novel!" Or if you prefer, don't say anything; just hope they'll leave you alone.

change and stability of Tao

"STABILITY" AND "CHANGE" DESCRIBE PARTS OF OUR DESCRIPTIONS

In other parts of this book, the word stable and also, necessarily, the word change will become very important. It is therefore wise to examine these words now in the introductory phase of our task. What traps do these words contain or conceal?
Stable is commonly used as an adjective applied to a thing. A chemical compound, house, ecosystem, or government is described as stable. If we pursue this matter further, we shall be told that the stable object is unchanging under the impact or stress of some particular external or internal variable or, perhaps, that it resists the passage of time.
If we start to investigate what lies behind this use of stability, we shall find a wide range of mechanisms. At the simplest level, we have simple physical hardness or viscosity, qualities descriptive of relations of impact between the stable object and some other. At more complex levels, the whole mass of interlocking processes called life may be involved in keeping our object in a state of change that can maintain some necessary constants, such as body temperature, blood circulation, blood sugar or even life itself.
The acrobat on the high wire maintains his stability by continual correction of his imbalance.
These more complex examples suggest that when we use stability in talking about living things or self-corrective circuits, we should follow the example of the entities about which we are talking. For the acrobat on the high wire, his or her so-called "balance" is important; so, for the mammalian body, is its "temperature". The changing state of these important variables from moment to moment is reported in the communication networks of the body. To follow the example of the entity, we should define "stability" always by reference to the ongoing truth of some descriptive proposition. The statement "The acrobat is on the high wire" continues to be true under impact of small breezes and vibrations of the wire. This "stability" is the result of continual changes in descriptions of the acrobat's posture and the position of his or her balancing pole.
It follows that when we talk about living entities, statements about "stability" should always be labeled by reference to some descriptive proposition so that the typing of the word, stable, may be clear. We shall see later, especially in Chapter ..., that every descriptive proposition is to be characterized according to logical typing of subject, predicate, and context.
Similarly, all statements about change require the same sort of precision. Such profound saws as the French "plus ça change, plus c'est la même chose" owe their wiseacre wisdom to a muddling of logical types. What "changes" and what "stays the same" are both of them descriptive propositions, but of different order.
Some comment on the list of presuppositions examined in this chapter is called for. First of all, the list is in no sense complete, and there is no suggestion that such a thing as a complete list of verities or generalities could be prepared. Is it even a characteristic of the world in which we live that such a list should be finite?
In the preparation of this chapter, roughly another dozen candidates for inclusion were dropped, and a number of others were removed from this chapter to become integrated parts of Chapters ... However, even with its incompleteness, there are a number of possible exercises that the reader might perform with the list.
First, when we have a list, the natural impulse of the scientist is to start classifying or ordering its members. This I have partly done, breaking the list into four groups in which the members are linked together in various ways. It would be a nontrivial exercise to list the ways in which such verities or presuppositions may be connected. The grouping I have imposed is as follows:
A first cluster includes numbers 1 to 5, which seem to be related aspects of the necessary phenomenon of coding. There, for example, the proposition that "science never proves anything" is rather easily recognized as a synonym for the distinction between map and territory; both follow from the Ames experiments and the generalization of natural history that "there is no objective experience."
It is interesting to note that on the abstract and philosophical side, this group of generalizations has to depend very closely on something like Occam's razor or the rule of parsimony. Without some such ultimate criterion, there is no ultimate way of choosing between one hypothesis and another. The criterion found necessary is of simplicity versus complexity. But along with these generalizations stands their connection with neurophysiology, Ames experiments, and the like. One wonders immediately whether the material on perception does not go along with the more philosophical material because the process of perception contains something like an Occam's razor or a criterion of parsimony. The discussion of wholes and parts in number 5 is a spelling out of a common form of transformation that occurs in those processes we call description.
Numbers 6, 7 and 8 form a second cluster, dealing with questions of the random and the ordered. The reader will observe that the notion that the new can be plucked only out of the random is in almost total contradiction to the inevitability of entropy. The whole matter of entropy and negentropy and the contrasts between the set of generalities associated with these words and those associated with energy will be dealt with in Chapter 6... in the discussion of the economics of flexibility. Here it is only necessary to note the interesting formal analogy between the apparent contradiction in this cluster and the discrimination drawn in the third cluster, in which number 9 contrasts number with quantity. The sort of thinking that deals with quantity resembles in many ways the thinking that surrounds the concept of energy; whereas the concept of number is much more closely related to the concepts of pattern and negentropy.
The central mystery of evolution lies, of course, in the contrast between statements of the second law of thermodynamics and the observation that the new can only be plucked from the random. It was this contrast that Darwin partly resolved by his theory of natural selection.
The other two clusters in the list as given are 9 to 12 and 13 to 16. I will leave it to the reader to construct his or her phrasings of how these clusters are internally related and to create other clusters according to his/her own ways of thought.
In Chapter ... I shall continue to sketch in the background of my thesis with a listing of generalities or presuppositions. I shall, however, come closer to the central problems of thought and evolution, trying to give answers to the question: In what ways can two or more items of information or command work together or in opposition? This question with its multiple answers seems to me to be central to any theory of thought or evolution.

the Teh of Tao

- 14 -

Look, and it can't be seen.
Listen, and it can't be heard.
Reach, and it can't be grasped.

Above, it isn't bright.
Below, it isn't dark.
Seamless, unnamable,
it returns to the realm of nothing.
Form that includes all forms,
image without an image,
subtle, beyond all conception.

Approach it and there is no beginning;
follow it and there is no end.
You can't know it, but you can be it,
at ease in your own life.
Just realize where you come from:
this is the essence of wisdom.

circular western and eastern Tao

The Seven Deadly Sins and the Four Last Things
Hieronymus Bosch or imitator
ab. 1500-1525
Oil on wood 120×150 cm
Museo del Prado, Madrid

Kalachakra Mandala

 International Kalachakra Network

Complex Tao level 2 and 0-5: Closure of Tao

The situation of the visual system of the brain, namely that the system is organized in a reticular pattern, and there is a convergence or coherence among  all the parts concerned, is not specific of this issue but is generalizable to all the brain areas and in general to all the nervous system: the flow of process/information occurs in a global network with multiple interconnections which works at any time generating an internal coherence state according to a cooperative process. 
The focus for the description of such set of processes is no longer to establish the information flow, which is practically impossible and also useless, but the specific modalities where the internal coherence states occur in the area of this network which defines itself.

This requires a change of the paradigmatic general principle to describe the systems by stimulus/reaction, input/output, and so on, characteristic of the heteronomous systems.

Such a scheme is valid when dealing with computers or control circuits or cybernetic system, but no longer when dealing with complex systems such the nervous system.
Maturana and Varela have defined a key concept (just apparently tautological) for the latter as Operational Closure: 

 the consequences of the operations of the system
are the operations of the system

where closure is not closeness. The Operational Closure defines some eigenbehaviors where the operations of a complex system, made by interconnected elemets, have as result an operation which falls again into the system domain itself and in its internal dynamics.

Closure is refers to the fact that the result of an operation is still inside the system itself this does not mean thta the system has not interactions with the external, since that - as any living system - it is an open system: the system is organizationally closed but open for what energy and environment exchange are concerned. The Operational Closure defines the stability and autonomy points, namely where the relations and interactions which defines the overall system are determined only by the sustem itself, and finally defines the system homeostasis, a condition of complementary interaction  stability/change which has a consequence the persistence of the system following changes: to be always itself the system must continuously change, and at the same time to change it must remain itself.

An example of an operational closure for a complex system is the one between sensory-motor system and nervous system:

In the figure can be noted three levels of circular processes: that of the sensori-motor system with operational closure which defines the state of the brain and of the body, that of the nervous system ad closed dynamical system and finally the closed circular interaction between the two. The autonomous system so defined responds to the external perturbations adjusting itself and producing effects outwards.  

The same example is valid for a cell scheme:
 

 

 
The metabolic cell internal network produces a cell membrane such that allows at the metabolic network to produces the metabolites which form it, and so on. Through the cell membrane then there is the interchange of energy, molecules and so typical of the open systems. the system has clear characteristics of operational closure, stability, autonomy and homeostasis.
Generally the operational closure as recursive circular process in living systems links an automous system which generates a process network which produces some system components which in turn determine the closure/autonomy of the system, and so on:

Maturana and Varela have schematically symbolized the structure of any living system as:

 

where the operational closure part defines, and is in turn defined, by the organization of the living system which exchanges interaction with the environment as an open system.

The following table summarizes the characteristics of the heteronomous and autonomous systems:

                                                  heteronomous systems                      autonomous systems

operations logic                              correspondence                                              coherence

organizational type                        input/output                                           operational closure

interaction mode                  instructive-representational                         creating a world

---

The concept of operational closure, defined as the fact that a system has coherence states, - and one may say of existence - in the case where the operations made by the system fall within the system domain itself, is quite general.

At the level 0 and 1 physical-chemical, where a formal system is available  this is represented by a fundamendal class of equations called eigenvalues equations, in the form:

Hf=af

where H is a functional operator, f some functions defined in a functional space S(f) and a are generally real numbers.
If the equation, given a specific operator H, and specified the  boundary conditions, has solutions f_i and a_i, with i a discrete or continuos index depending from the boundary conditions, then these are called eigenfunctions and eigenvalues of the equation.
The equation entirely expresses the operational closure concept, since that made an operation H over a function f_i the result is still the function f_i a unless a number a_i, that is the operation lies always in the functional space S(f).
In physics some of the most important equations are of this kind, in particular (for the stationary sytates - i.e. time invariant) the Newton motion equations of classical mechanics, expresses in the hamiltonian form, and those of quantum mechanics in the two dual representations wavefunction/particle expresses in the first case by the Schrödinger equation and in latter by the Heisenberg equation, where H is a hamiltonian operator associated to the energy of the system.
The solutions in both representations give the system eigenfunctions and the energy eigenvalues, for example in the case of the simplest physical-chemical system, that of the hydrogen atom, the eigenfunctions are of the type:

while the energy eigenvalues give a set of possible discrete quantum levels for the electron:

In the same way the solution of the energy eigenvalue equation for higher elements, molecules and molecules chains by the atomic orbital model poses the basis for the chemical bond and therefore for the existence of any chemical compound.
Another fundamental class is the one whwre the operators H are linear, and therefore define a linear system; in this case any function f is an eigenfunction and, depending on wether the eigenvalues are greater or lesser then 1, there are characteristics of amplification or  attenuation.

At levels higher then the 2-3 biological/organism the operational closure concept continues to be meaningful as guideline to define or establish which are the stable states of a system.

There cab be cases of casi di meta-operational closure; a typical example by Von Foerster is the coupling between the nervous system and the endocrine system:

 

Both the nervous and the endocrine systems are operationally closed, represented by closed circles, and interact with each other, in particular the endocrine stabilize the nervous and  vice versa. The resulting system is representable in a three-dimensional way by a torus, where the longitudinal rings represent a system and the trasverse ones the other system. T'he overall effect is that of a meta-regulation, i.e. a regulation of a regulation.

---

The general treatment of the operational closure as limit of recursive operations which lie in the same domain has been developed by Heinz Von Foerster in the following way:

let a variable x₀:  x_{0 is quite general, it can be a function, a numerical value, an arrangement (number lists, vectors, geometrical configurations), behaviors described by functions,} behaviors described by _{propositions and so on. We define an operation over} x_{0 symbolized by Op. Op can be an operator, a functional, un algorithm and so such that applied to} x_{0 transforms to} x_1:

x_1=Op(x₀₎

subsequently applying the operation Op we have:

x_1=Op(x₀₎

x_2=Op(Op(x₁₎₎

_......

x_n=Op⁽ⁿ⁾₍x₀₎ 

and repeating infinitly times the application of Op:

x_∞=Op^(∞)₍x₀₎

that is

x_∞=Op(Op(Op(Op(Op(Op( ...

in the last expression we note that the initial variable x₀ is disappeared, and that any infinite sequence of Op can be substituted by Op^(∞):

x_∞=Op(x_∞)
x_∞=Op(Op(x_∞))
 x_∞=Op(Op(Op(x_∞)))
... 

if this system of equation has solutions of the form E_i=x_∞i then they are called eigenvalues, eigenoperators, eigenalgorithms, eigenbehaviors and so.

The operational closure is expressed as the limit of a recursive process of applications of Op:

lim (n→∞) Op⁽ⁿ⁾ =  OP →

                         ↑←↓

and in particular the operator Op implies its own eigenvalues  E_i, and is implied by these; operators and eigenvalues are complementary:

Op↔E_i

besides, since the E_i self produce themself, through the Op⁽ⁿ⁾ complementary to them, they are self-reflexive.

Some examples given by Von Foerster are the operator H=SQRT, the square root of a number; starting from any real positive number x₀ and applying infinite times the operation SQRT the eigenvalue is x_∞=1 and SQRT(1)=1 is an eigenvalue.
Another example is the phrase (in english):

THIS PHRASE HAS ... LETTERS

where instead of ... should be substituted a number by letters which make true the phrase; In an ontological sense the phrase exists, namely becomes logically true, only for its eigenvalues, otherwise is false.

In the case of levels 2-3 studied by Maturana and Varela lthe operational closure of the operations Op of the systems becomes:

                                                         ORG →

                                                          ↑ ←  ↓

that is the operational closure defines the organization of the system and vice versa the organization defines its closure.

the Pearl of Tao

speaking of Tao

Gregory Bateson, photographer. Margaret Mead and Gregory Bateson working among the Iatmul,
Tambunam, 1938.
Gelatin silver print.

LANGUAGE COMMONLY STRESSES ONLY ONE SIDE OF ANY INTERACTION

We commonly speak as though a single "thing" could "have" some characteristic. A stone, we say, is "hard," "small," "heavy," "yellow," "dense," "fragile," "hot," "moving," "stationary," "visible," "edible," "inedible" and so on.

That is how our language is made: "The stone is hard." And so on. And that way of talking is good enough for the marketplace: "That is a new brand." "The potatoes are rotten." "The eggs are fresh." "The container is damaged." "The diamond is flawed." "A pound of apples is enough." And so on. But this way of talking is not good enough in science or epistemology. To think straight, it is advisable to expect all qualities and attributes, adjectives, and so on to refer to at least two sets of interactions in time.
"The stone is hard" means a) that when poked it resisted penetration and b) that certain continual interactions among the molecular parts of the stone in some way bond the parts together. 
"The stone is stationary" comments on the location of the stone relative to the location of the speaker and other possible moving things. It also comments on matters internal to the stone: its inertia, lack of internal distortion, lack of friction at the surface, and so on. Language continually asserts by the syntax of subject and predicate that "things" somehow "have" qualities and attributes. A more precise way of talking bout insist that the "things" are produced, are seen as separate from other "things," and are made "real" by their internal relations and by their behavior in relationship with other things and with the speaker.
It is necessary to be quite clear about the universal truth that whatever "things" may be in their pleromatic and thingish world, they can only enter the world of communication and meaning by their names, their qualities and their attributes (i.e., by reports of their internal and external relations and interactions).