Tuesday, February 8, 2011

the Master - Major


The Master in Zen is not a master over others, but a master of himself - and this self-mastery is reflected in his every gesture and his every word. He is not a teacher with a doctrine to impart, nor a supernatural messenger with a direct line to God, but simply one who has become a living example of the highest potential that lies within each and every human being. In the eyes of the Master, a disciple finds his own truth reflected. In the silence of the Master's presence, the disciple can fall more easily into the silence of his own being. The community of seekers that arises around a Master becomes an energy field that supports each unique individual in finding his or her own inner light. Once that light is found, the disciple comes to understand that the outer Master was just a catalyst, a device to provoke the awakening of the inner.

Beyond mind, there is an awareness that is intrinsic, that is not given to you by the outside, and is not an idea -- and there is no experiment up to now that has found any center in the brain which corresponds to awareness. The whole work of meditation is to make you aware of all that is "mind" and disidentify yourself from it. That very separation is the greatest revolution that can happen to man.
Now you can do and act on only that which makes you more joyous, fulfills you, gives you contentment, makes your life a work of art, a beauty. But this is possible only if the master in you is awake. Right now the master is fast asleep. And the mind, the servant, is playing the role of master. And the servant is created by the outside world, it follows the outside world and its laws.
Once your awareness becomes a flame, it burns up the whole slavery that the mind has created. There is no blissfulness more precious than freedom, than being a master of your own destiny.

the Tao dilemma always actual


Tao without method

The impossibility to define a paradigm for complexity, and the consequent lack of general computing or description methodologies for the solution of complex problems in a certain field as a a consequence a great difficulty  fomulation, description and solution of problems involving complex systems.
A methodology è la scientific procedure that allows for the classic problem-solving process:

definition                            theory/model
                                                   ↕
problem →→→→→calculation/description→→→→→  solution
data

In classical science, in what Weaver definines as problems of simplicity and problems of disorganized complexity, the problem is always well defined, the theory or model provides the methodology of calculation/description, and with this one can find the solution, not known. So of the three terms problem-calcolous/description-solution two are known (problem, computing/description) and one does not know the solution, and for this it is estimated/described. The whole procedure takes place in the presence of a paradigm, which provides both the definition of the problem, and what data need to know to solve it, with the theory/model for the solution of the problem. If the problem is at the physical level the presence of a formal theory (ie mathematics) allows the solution in the form of a number or a function. For higher levels, such as chemistry, biology etc. The solution is an acceptable and complete description within the paradigm that contains the problem. It is worth noting - among others - that only the presence of a shared paradigm can, for example, allow the well-known assessment of school students or the validity or less of scientific and academic careers.

Take for example a simple problems of simplicity known to any elementary student:
in a cubic tank of L side come in IN liters of water any second from a  tap and come out OUT litters any second from an outlet: assumed that IN is greater than OUT after what time the water will reach the edge of the tub?
The theory that allows to do the simple calculation to find the solution is basic physics, and the calculation is made by a branch of mathematics called arithmetic, obtaining as a solution to the problem a number expressed in units of time.
Even in this elementary case is noteworthy that the involved assumptions are non-elementary, such the principle of conservation of energy (of the mass in this case) and the logical competence to perform arithmetic calculations, that is to know how to use the axioms (of Peano) e le rules of arithmetic.

For the problems of disorganized complexity applies the same methodology of solution, but passing from a paradigm, and then from a method, deterministic to a probabilistic one. For example, in the simple case of launching a coin if the question of the problem is placed in a deterministic way as "launching the coin will come out heads or tails?" the answer is impossible, while framed in terms of probability the problem is easily solved and the complete response is that the probability of output is exactly equal to 50% for both cases. In this case the solution is always expressed as a number or a function, as before, but expressed as a probability.
Whole sectors very complex of science and its applications are exactly solvable in this way, as the statistical mechanics, that is the application of the probability theory to the termodynamics behavior of systems composed of a large number of elements, providing a model to link the properties of individual atoms and molecules to the macroscopic properties of the system composed by them, or the information theory, developed by Shannon with contributions of the same Weaver, which is the theoretical basis of description and implementation of any telecommunication system.


Even in the case of problems of disorganized complexity, exactly solvable in a statistical sense, there are examples of the emergency of collective complex properties not immediately related to the properties of individual elements.
The most significant example is the following: there is a game where a ball bouncing along a plane falls on small cylinders arranged at random, which prevent the most direct route and at the end of this jungle of obstacles slips in a row boxes placed at the bottom of the hill. Guess where the ball will end up is a difficult task: the system is not integratble and there is chaos, unpredictability.


Yet there is a bet that one can do with a good chance of victory: that launching one thousand balls below the middle box will fill most of those at the edges. We are setting off from the world of determinism, but tring one would see that actually, as the number of launches increases, the profile of the heights of the columns of balls are getting closer to a Gaussian.


This result is based on one of the most important theorems of probability theory, the Central Limit Theoremwhich states that the sum of a very large number of indipendent random variables  tends to standard normal distribution, that is a gaussian, and this is more true as larger is the number of balls.
One can read the result in so many ways, attributing the cause to the different number of paths that lead to the individual boxes, or the "fraying" of the initial conditions along the paths. But in fact, we are facing a new phenomenon. We can not help but recognize that this is something different from the motion of a single ball; it is a collective effect, found only on repeated many launches, which requires the introduction of collective variables regulated by new laws of nature different from the deterministic laws of motion. They are the statistical laws, which by their nature apply only to systems composed of many elements. Laws in part linked to those of the motion of individual elements, but largely new and indipendent. Laws that allow no more sure forecasts, but probable. 

(freely adapted from a  presentation of  Prof. Mario Rasetti "Theory of Complexity", 2008)


In the Science of Complexity, that is for the problems of organized complexity, things are radically different: in this case the problem is almost always well defined, the theory/model can be known - although it may correspond to the union of many theories/models of different disciplines - the solution, in many cases - but not all - is already known, what is lacking is the calculation procedure/description, since there is not a general methodology for the solution of the problem.
In the Weaver classical example "What makes an evening primrose open when it does?" the problem is very well defined, the necessary data (climate, temperature variation, soil composition, structure - morphology - the stage of plant growth, etc.) can all be known with great precision, the solution is known to anyone who walks through meadow in spring: in continental Europe at a given latitude at a given altitude in a certain place  that in the previous years has hosted primroses and that has not undergone major ecological changes, the probability that some primroses bloom from late February to the beginning of May is 100%, however one can not define the solution even in a probabilistic/statistical  way  because no theory/model is able to provide a probability function in time, and still less it is possible to answer to what does or not blooming primroses, although a number of topics in physics, biophysics, chemistry, geochemistry, biochemistry and biology is capable of describing many of the processes involved, but the total process - complex - it is indescribable in complete form.

Monday, February 7, 2011

Immortal Dialogues of Tao: red Tao or blue Tao?




Have you ever had a dream, Neo, that you were so sure was real. What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world?

What is real? How do you define real? If you're talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain.

"I know why you're here, Neo. I know what you've been doing. I know why you hardly sleep, why you live alone, and why, night after night, you sit at your computer. You're looking for him. I know, because I was once looking for the same thing. And when he found me, he told me I wasn't really looking for him. I was looking for an answer. It's the question that drives us, Neo. It's the question that brought you here. You know the question, just as I did."

Neo: "What is the Matrix?"

Trinity: "The answer is out there, Neo. It's looking for you. And it will find you, if you want it to."

- I imagine that right now you're feeling a bit like Alice. Tumbling down the rabbit hole.
- You could say that.
- I can see it in your eyes. You have the look of a man who accepts what he sees because he's expecting to wake up. Ironically, this is not far from the truth. Do you believe in fate, Neo?
- No.
- Why not?
- 'Cause I don't like the idea that I'm not in control of my life.
- I know exactly what you mean. Let me tell you why you're here. You're here because you know something. What you know, you can't explain. But you feel it. You felt it your entire life. That there's something wrong with the world. You don't know what it is, but it's there. Like a splinter in your mind -- driving you mad. It is this feeling that has brought you to me. Do you know what I'm talking about?
- The Matrix.
- Do you want to know what it is? The Matrix is everywhere, it is all around us. Even now, in this very room. You can see it when you look out your window, or when you turn on your television. You can feel it when you go to work, or when go to church or when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.
- What truth?
- That you are a slave, Neo. Like everyone else, you were born into bondage, born inside a prison that you cannot smell, taste, or touch. A prison for your mind. Unfortunately, no one can be told what the Matrix is. You have to see it for yourself. This is your last chance. After this, there is no turning back.

blue pill: You take the blue pill and the story ends. You wake in your bed and believe whatever you want to believe.
red Pill : You take the red pill and you stay in Wonderland and I show you how deep the rabbit-hole goes.

Remember -- all I am offering is the truth, nothing more.
 
I can only show you the door. You're the one that has to walk through it.

Sooner or later you're going to realize just as I did that there's a difference between knowing the path and walking the path.

nothing from Tao


"NOTHING WILL COME OF NOTHING"

This quotation of King Lear telescopes into a single utterance a whole series of medieval and more modern wise saws. These include:
a. The law of the conversation of matter and its converse, that no new matter can be expected to make an appearance in the new laboratory. (Lucretius said "Nothing can ever be created out of nothing by divine power.")
b. The law of the conservation of energy and its converse, that no new energy can be expected in the laboratory.
c. The principle demonstrated by Pasteur, that no new living matter can be expected to appear in the laboratory.
d. The principle that no new order or pattern can be created without information.
Of all these and other similar negative statements, it may be said that they are rules for expectation rather than laws of nature. They are so nearly true that all exceptions are of extreme interest.
What is especially interesting is hidden in the relations between these profound negations. For example, we know today that between the conservation of energy and the conservation of matter, there is a bridge whereby each of these negations is itself negated by an interchange of matter into energy and, presumably, of energy into matter.
In the present connection, however, it is the last of the series that is of chief interest, the proposition that in the realms of communication, organization, thought, learning, and evolution, "nothing will come of nothing" without information.
This law differs from the conservative laws of energy and mass in that it contains no clause to deny the destruction and loss of information, pattern, or negative entropy. Alas - but also be glad of it - pattern, and/or information is all too easily eaten up by the random. The messages and guidelines for order exist only, as it were, in sand or are written on the surface of waters. Almost any disturbance, even mere Brownian movement, will destroy them. Information can be forgotten or blurred. The code books can be lost.
The messages cease to be messages when nobody can read them. Without a Rosetta stone, we would know nothing of all that was written in Egyptian hieroglyphs. They would be only elegant ornaments on papyrus or rock. To be meaningful - even to be recognized as pattern - every regularity must meet with complementary regularities, perhaps skills, and these skills are as evanescent as the patterns themselves. They, too, are written on sand or the surface of waters.
The genesis of the skill to respond to the message is the obverse, the other side of the process of evolution. It is coevolution (Stochastic system of evolutionary change in which two or more species interact in such a way that changes in the species A prepare the ground for natural selection of changes in species B. Subsequent changes in species B, in turn, pave the way for the selection of the most similar changes in the species A.)).
Paradoxically, the deep partial truth that "nothing will come of nothing" in the world of information and organization encounters an interesting contradiction in the circumstance that zero, the complete absence of any indicative event, can be a message. The larval tick climbs a tree and waits on some outer twig. If he smells sweat, he falls, perhaps landing on a mammal. But if he smells no sweat after some weeks, he falls and goes to climb another tree.
The letter that you do not write, the apology you do not offer, the food that you do not put out for the cat - all these can be sufficient and effective messages because zero, in context, can be meaningful; and it is the recipient of the message who creates the context. This power to create context is the recipient's skill; to acquire which is his half of the coevolution mentioned above. He or she must acquire that skill by learning or by lucky mutation, that is, by a successful raid on the random. The recipient must be, in some sense, ready for the appropriate discovery when it comes.
Thus, the converse of the proposition that "nothing will come of nothing" without information is conceivably possible with stochastic process. Readiness can serve to select components of the random which thereby become new information. But always a supply of random appearances must be available from which new information can be made.
This circumstance splits the entire field of organization, evolution, maturation and learning, into two separate realms, of which one is the realm of epigenesis, or embryology, and the other the realm of evolution and learning.
Epigenesis is the word preferred by C.H. Waddington for his central field of interest, whose old name was embryology. It stresses the fact that every embryological step is an act of becoming (Greek genesis) which must be built upon (Greek epi) the immediate status quo ante. Characteristically, Waddinton was contemptuous of conventional information theory, which allowed nothing, as he saw it, for the "new" information he felt was generated at each stage of epigenesis. Indeed, according to conventional theory, there is no new information in this case.
Ideally, epigenesis should resemble the development of a complex tautology (Set of propositions related to the validity of the "links" can not be doubted. The truth of propositions but is not required. Example: Euclidean geometry.) in which nothing is added after the axioms and definitions have been laid down. The Pythagorean theorem is implicit (i.e., already folded into) Euclid's axioms, definitions, and postulates. All that is required is its unfolding and, for human beings, some knowledge of the order of steps to be taken. This latter species of information will become necessary only when Euclid's tautology is modeled in words and symbols sequentially arranged on paper or in time. In the ideal tautology, there is no time, no unfolding, and no argument. What is implicit is there, but, of course, not located in space.
In contrast with epigenesis and tautology, which constitute the worlds of replication, there is the whole realm of creativity, art, learning, and evolution, in which the ongoing processes of change feed on the random. The essence of epigenesis is predictable repetition; the essence of learning and evolution is exploration and change.
In the transmission of human culture, people always attempt to replicate, to pass on to the next generation the skills and values of the parents; but the attempt always and inevitably fails because cultural transmission is geared to learning, not to DNA. The process of transmission of culture is a sort of hybrid or mix-up of the two realms. It must attempt to use the phenomena of learning of the purpose of replication because what the parents have was learned by them. If the offspring miraculously had the DNA that would give them the parental skills, those skills would be different and perhaps nonviable.
It is interesting that between the two worlds is the cultural phenomenon of explanation - the mapping onto (I use the phrase, to map onto, for the following reasons: All description, explanation, or representation is necessarily in some sense a mapping of derivatives from the phenomena to be described onto some surface of matrix or system or coordinates. In the case of an actual map, the receiving matrix is commonly a flat sheet of paper of finite extent, and difficulties occur when that which is to be mapped is too big or, for example, spherical. Other difficulties would be generate if the receiving matrix were the surface of a torus (doughnut) or if it were a discontinuous lineal sequence of points. Every receiving matrix, even a language or a tautological network of propositions, will have its formal characteristics which will in principle be distortive of the phenomena to be mapped ontoit. The universe was, perhaps, designed by Procrustes, that sinister character of Greek mythology in whose inn every traveler had to fit the bed on pain of amputation or elongation of the legs.) tautology of unfamiliar sequences of events.
Finally, it will be noted that the realms of epigenesis and of evolution are, at a deeper level, typified in the twin paradigms of the second law of thermodynamics. (1) that the random workings of probability will always eat up order, pattern, and negative entropy but (2) that for the creation of new order, the workings of the random, the plethora of uncommitted alternatives (entropy) is necessary. It is out of the random that organisms collect new mutations, and it is there that stochastic learning gathers its solutions. Evolution leads to climax: ecological saturation of all the possibilities of differentiation. Learning leads to the overpacked mind. By return to the unlearned and mass-produced egg, the ongoing species again and again clears its memory banks to be ready for the new.


the sheltering Tao


paradigms - and not - of Tao


The philosopher and historian of science Thomas Kuhn proposed in 1962 the concept of paradigm of a, or all, the science. Paradigm comes from greek παράδειγμα paràdeigma and means pattern, example, sample.
Huhn defines a scientific paradigm as: "... what is shared by members of a scientific community, and conversely, a scientific community consists of those who share a certain paradigm."
Ironic cartoon on the different views on science between Karl Popper and Thomas Kuhn.
More generally, a paradigm can be described as a "constellation of beliefs shared by a group", or "a constellation of findings, concepts, values, techniques etc.. shared by a scientific community to define legitimate problems and solutions".
As such, a paradigm has a fundamental influence on the methodology in which design, construct and discusses the validity of any experiment or scientific description, and then defines what is significant and what is not, what is considered science and what is not:

"...paradigm ... is the systematic articulation of a set of practical tools and concepts, and an a priori definition of the object and its rules of experimental manipulation"
(I. Stengers)

Kuhn defines a scientific revolution as a paradigm shift. The transition from a science experienced as paradigmatic belief stems from a subsequent appearance of "anomalies " theoretical and/or experimental, leading to questioning of the paradigm and the development of a broader science. Periods like this have happened many times in the history of science, Kuhn makes several classic examples such as Copernican revolution, the revolution of modern chemistry by Lavoisier, the revolution of electrostatics by Franklin, the Darwin revolution or the Theory of Relativity by Einstein.





A paradigm can be changed by a subsequent paradigm, more general, such as the Copernican system, with the earth revolving around the sun, is valid if the reference system is placed in the center of the sun, if it is placed in the center of the earth continues to be valid the geocentric model, neither has absolute validity but still relative, it depends from where is more convenient to place the reference system, that is the system that makes the simplest possible the equations of motion. Actually, the most convenient point is neither on earth nor in the sun, but in center of mass of the Sun-Earth system, at about 450.000 Km from the sun center on the sun-earth line, where the two gravitational forces cancel each other, also called Lagrangian point. The heliocentric system is therefore no more "right" than the geocentric, simply is more convenient for the description and the calculation of the gravitational field equations.

 








  
The paradigm shift and the resulting scientific revolution are not just abstract theoretical concepts but they have profound impacts on the every day lives since they are the source of the subsequent development of technologies:


Isabelle Stengers points out that for the science of Complexity we can not define a paradigm. Defined a complex system as:

"According to Atlan a complicated system is a system we understand the structure and operating principles: in principle nothing prevent that with time and money one can come to have a full knowledge of it.
On the contrary, the complex system is the one where we have a general perception, in terms of which we can identify and qualify, even though we know we do not understand it in its details"

In a system of this kind:

"The separation between what is meaningful and what is noise can be no longer founder, made once and for all in the name of a general theory, it should be thought  as such for each single system.
Therefore what is questioned is the paradigmatic character of theories, namely their ability to drive a process from identifying similarities in themselves indicating a way of separating and handling"

In the distinction of simple/complicated/complex then only the first two are calculable,  exactly the first, the second potentially or statistically. In a complex system is hard to tell what is noise and what is significant, because the noise, or chaos, can generate those emergent properties peculiar of complexity. It follows the impossibility of a calculation and description methodology, valid for all systems - or, at least, within the same class - but only a specific one  for a specific system. This is one of the peculiar difficulties of Complexity: the uniqueness of each complex system.

Isabelle Stengers, "Why can not there be a paradigm of complexity", in G.Bocchi, M.Ceruti (edt.s)













 



Isabelle STENGERS