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
Friday, March 11, 2011
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
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:
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
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:
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 fi and ai, 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 fi the result is still the function fi a unless a number ai, 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.
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: x0 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 x0 symbolized by Op. Op can be an operator, a functional, un algorithm and so such that applied to x0 transforms to x1:
subsequently applying the operation Op we have:
x1=Op(x0)
x2=Op(Op(x1))
......
xn=Op(n)(x0)
and repeating infinitly times the application of Op:
x∞=Op(∞)(x0)
that is
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 Ei=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 Ei, and is implied by these; operators and eigenvalues are complementary:
Op↔Ei
besides, since the Ei 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.
Wednesday, March 2, 2011
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).
"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).
Patience (7 of Pentacles)
There are times when the only thing to do is to wait. The seed has been planted, the child is growing in the womb, the oyster is coating the grain of sand and making it into a pearl. This card reminds us that now is a time when all that is required is to be simply alert, patient, waiting. The woman pictured here is in just such an attitude. Contented, with no trace of anxiety, she is simply waiting. Through all the phases of the moon passing overhead she remains patient, so in tune with the rhythms of the moon that she has almost become one with it. She knows it is a time to be passive, letting nature take its course. But she is neither sleepy nor indifferent; she knows it is time to be ready for something momentous. It is a time full of mystery, like the hours just before the dawn. It is a time when the only thing to do is to wait.
We have forgotten how to wait; it is almost an abandoned space. And it is our greatest treasure to be able to wait for the right moment. The whole existence waits for the right moment. Even trees know it--when it is time to bring the flowers and when it is time to let go of all the leaves and stand naked against the sky. They are still beautiful in that nakedness, waiting for the new foliage with a great trust that the old has gone, and the new will soon be coming, and the new leaves will start growing. We have forgotten to wait, we want everything in a hurry. It is a great loss to humanity.... In silence and waiting something inside you goes on growing--your authentic being. And one day it jumps and becomes a flame, and your whole personality is shattered; you are a new man. And this new man knows what ceremony is, this new man knows life's eternal juices.
We have forgotten how to wait; it is almost an abandoned space. And it is our greatest treasure to be able to wait for the right moment. The whole existence waits for the right moment. Even trees know it--when it is time to bring the flowers and when it is time to let go of all the leaves and stand naked against the sky. They are still beautiful in that nakedness, waiting for the new foliage with a great trust that the old has gone, and the new will soon be coming, and the new leaves will start growing. We have forgotten to wait, we want everything in a hurry. It is a great loss to humanity.... In silence and waiting something inside you goes on growing--your authentic being. And one day it jumps and becomes a flame, and your whole personality is shattered; you are a new man. And this new man knows what ceremony is, this new man knows life's eternal juices.
A western contemporary of Tao in Tao
Hendrick ter Brugghen (1588, Utrecht – 1629, idem)
Heraclitus - 1628
"INTO THE SAME RIVERS WE STEP AND DO NOT STEP.
YOU CANNOT STEP TWICE IN THE SAME RIVER.
EVERYTHING FLOWS AND NOTHING ABIDES.
EVERYTHING GIVES WAY AND NOTHING STAYS FIXED.
COOL THINGS BECOME WARM, THE WARM GROWS COOL.
THE MOIST DRIES, THE PARCHED BECOMES MOIST.
IT IS BY DISEASE THAT HEALTH IS PLEASANT;
BY EVIL THAT GOOD IS PLEASANT,
BY HUNGER, SATIETY; BY WEARINESS, REST.
IT IS ONE AND THE SAME THING TO BE LIVING OR DEAD,
AWAKE OR ASLEEP, YOUNG OR OLD.
THE FORMER ASPECT IN EACH CASE BECOMES THE LATTER,
AND THE LATTER AGAIN THE FORMER,
BY SUDDEN UNEXPECTED REVERSAL.
IT THROWS APART
AND THEN BRINGS TOGETHER AGAIN.
ALL THINGS COME IN THEIR DUE SEASONS.
INTO THE SAME RIVERS WE STEP AND DO NOT STEP...
... because the appearance, and remember, only the appearance, remains the same.
Otherwise, everything changes and flows."
"THE HIDDEN HARMONY
IS BETTER THAN THE OBVIOUS.
OPPOSITION BRINGS CONCORD.
OUT OF DISCORD
COMES THE FAIREST HARMONY.
IT IS IN CHANGING
THAT THINGS FIND REPOSE.
PEOPLE DO NOT UNDERSTAND
HOW THAT WHICH IS AT VARIANCE WITH ITSELF,
AGREES WITH ITSELF.
THERE IS A HARMONY IN THE BENDING BACK,
AS IN THE CASE OF THE BOW AND LYRE.
THE NAME OF THE BOW IS LIFE,
BUT ITS WORK IS DEATH."
YOU CANNOT STEP TWICE IN THE SAME RIVER.
EVERYTHING FLOWS AND NOTHING ABIDES.
EVERYTHING GIVES WAY AND NOTHING STAYS FIXED.
COOL THINGS BECOME WARM, THE WARM GROWS COOL.
THE MOIST DRIES, THE PARCHED BECOMES MOIST.
IT IS BY DISEASE THAT HEALTH IS PLEASANT;
BY EVIL THAT GOOD IS PLEASANT,
BY HUNGER, SATIETY; BY WEARINESS, REST.
IT IS ONE AND THE SAME THING TO BE LIVING OR DEAD,
AWAKE OR ASLEEP, YOUNG OR OLD.
THE FORMER ASPECT IN EACH CASE BECOMES THE LATTER,
AND THE LATTER AGAIN THE FORMER,
BY SUDDEN UNEXPECTED REVERSAL.
IT THROWS APART
AND THEN BRINGS TOGETHER AGAIN.
ALL THINGS COME IN THEIR DUE SEASONS.
INTO THE SAME RIVERS WE STEP AND DO NOT STEP...
... because the appearance, and remember, only the appearance, remains the same.
Otherwise, everything changes and flows."
"THE HIDDEN HARMONY
IS BETTER THAN THE OBVIOUS.
OPPOSITION BRINGS CONCORD.
OUT OF DISCORD
COMES THE FAIREST HARMONY.
IT IS IN CHANGING
THAT THINGS FIND REPOSE.
PEOPLE DO NOT UNDERSTAND
HOW THAT WHICH IS AT VARIANCE WITH ITSELF,
AGREES WITH ITSELF.
THERE IS A HARMONY IN THE BENDING BACK,
AS IN THE CASE OF THE BOW AND LYRE.
THE NAME OF THE BOW IS LIFE,
BUT ITS WORK IS DEATH."
Heraclitus of Ephesus (535 - 475 BCE)
what we see of Tao?
One of the fields of complexity where most has been concentrated the research is the neurophysiology of the vision system, that is how and what we see.
Anatomically and physiologically the brain visual system is widely known:
The image formed on the eye retina and codified is transferred by the optic nerve in the lateral geniculate nucleus (NGL/LGN), situated in the thalamus, from where nerve pathways go toward the visual cortex (CV/VC), the brain area which specific elaborate the information coming from the optic nerve. In particuar images from the right eye are elaborated in the left visual cortex, and vice versa.
The visual information flow according to this anatomical-functional model is represented as:
Following this model some thousands (litteraly) of works and papers has been made. The direct consequence of a model of this kind is the representationalist approach to the brain, outlined by Maturana and Varela with the Caesar's figure looking at the Imperial Eagle:
In the Varela words:
"The Caesar's Eagle is represented in his brain through the activity flow (the film tape) cthat undergoes a "treatment" (by some small operator) and which later produces the behavioral proof of the recognition by the word "eagle" (through carefully selected organ pipes)"
A model of this type is also what normally assumed by common sense: an object outise ourselves is represented in some way inside our head; more technically an object in the visual field are associated specific neural activity patternsi, typically in the primary visual cortex. The ultimate consequence is when we imagine ourselves, where the imagined ourselves naturally imagines himself, and so on, as in the following illustration by Von Foester, an extreme solipsism case:
In reality, the model of the flow of visual information in the brain is radically different, closer to the following type (NPG: geniculate nucleus; Coll. Sup.: superior colliculus; Ipo.: isothalamus; FRM: midbrain):
where have been added those connections to the NGL which do not come only from the retina but also from other central areas of the brain, including the same visual cortex. The conclusion is that less then 20% of the information dell'informazione which get the geniculate body come from the retina. The situation, drom the point of view of a neuron in the geniculate body, is more similar to a cocktail party rather than to a linear element of an information chain forwarded from the retina to the visual cortex. In addition, the dashed arrows may be bidirectional for the information, for example the visual cortex receives information from the geniculate body but at the same time forwards other information to the geniculate body. The Varela conclusion is:
"... in the visual system ... does not exists an overall flux, the system is organized in a reticular pattern, and there is a simultaneous convergence or coherence among all the parts concerned."
Francisco J. Varela: Brain complexity and autonomy of the living
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