Monday, November 8, 2010

History of western Tao

«A few words of apology and explanation are called for if this book is to escape even more severe censure than it doubtless deserves.
Apology is due to the specialists on various schools and individual philosophers. With the possible exception of Leibniz, every philosopher of whom I treat is better known to some others than to me. If, however, books covering a wide field are to be written at all, it is inevitable, since we are not immortal, that those who write such books should spend less time on any one part than can be spent by a man who concentrates on a single author or a brief period. Some, whose scholarly austerity is unbending, will conclude that books covering a wide field should not be written at all, or, if written, should consist of monographs by a multitude of authors. There is, however, something lost when many authors co-operate. If there is any unity in the movement of history, if there is any intimate relation between what goes before and what comes later, it is necessary, for setting this forth, that earlier and later periods should be synthesized in a single mind. The student of Rousseau may have difficulty in doing justice to his connection with the Sparta of Plato and Plutarch; the historian of Sparta may not be prophetically conscious of Hobbes and Fichte and Lenin. To bring out such relations is one of the purposes of this book, and it is a purpose which only a wide survey can fulfil.
There are many histories of philosophy, but none of them, so far as I know, has quite the purpose that I have set myself. Philosophers are both effects and causes: effects of their social circumstances and of the politics and institutions of their time; causes (if they are fortunate) of beliefs which mould the politics and institutions of later ages. In most histories of philosophy, each philosopher appears as in a vacuum; his opinions are set forth unrelated except, at most, to those of earlier philosophers. I have tried, on the contrary,  to exhibit each philosopher, as far as truth permits, as an outcome of his milieu, a man in whom were crystallized and concentrated thoughts and feelings which, in a vague and diffused form, were common to the community of which he was a part.
This has required the insertion of certain chapters of purely social history. No one can understand the Stoics and Epicureans without some knowledge of the Hellenistic age, or the scholastics without a modicum of understanding of the growth of the Church from the fifth to the thirteenth centuries. I have therefore set forth briefly those parts of the main historical outlines that seemed to me to have had most influence on philosophical thought, and I have done this with most fullness where the history may be expected to be unfamiliar to some readers-for example, in regard to the early Middle Ages. But in these historical chapters I have rigidly excluded whatever seemed to have little or no bearing on contemporary or subsequent philosophy.
The problem of selection, in such a book as the present, is very difficult. Without detail, a book becomes jejune and uninteresting; with detail, it is in danger of becoming intolerably lengthy. I have sought a compromise, by treating only those philosophers who seem to me to have considerable importance, and mentioning, in connection with them, such details as, even if not of fundamental importance, have value on account of some illustrative or vivifying quality.
Philosophy, from the earliest times, has been not merely an affair of the schools, or of disputation between a handful of learned men. It has been an integral part of the life of the community, and as such I have tried to consider it. If there is any merit in this book, it is from this point of view that it is derived.»

The Nobel Prize in Literature 1950 was awarded to Bertrand Russell "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".


The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.

Thursday, November 4, 2010

Participation (4 of Wands)


Each figure in this mandala holds the left hand up, in an attitude of receiving, and the right hand down, in an attitude of giving. The whole circle creates a tremendous energy field that takes on the shape of the double dorje, the Tibetan symbol for the thunderbolt.

The mandala has a quality like that of the energy field that forms around a buddha, where all the individuals taking part in the circle make a unique contribution to create a unified and vital whole. It is like a flower, whose wholeness is even more beautiful than the sum of its parts, at the same time enhancing the beauty of each individual petal.

You have an opportunity to participate with others now to make your contribution to creating something greater and more beautiful than each of you could manage alone. Your participation will not only nourish you, but will also contribute something precious to the whole.



Have you ever seen night going? Very few people even become aware of things which are happening every day. Have you ever seen the evening coming? The midnight and its song? The sunrise and its beauty?

We are behaving almost like blind people. In such a beautiful world we are living in small ponds of our own misery. It is familiar, so even if somebody wants to pull you out, you struggle. You don't want to be pulled out of your misery, of your suffering. Otherwise there is so much joy all around, you have just to be aware of it and to become a participant, not a spectator.

Philosophy is speculation, Zen is participation. Participate in the night leaving, participate in the evening coming, participate in the stars and participate in the clouds; make participation your lifestyle and the whole existence becomes such a joy, such an ecstasy. You could not have dreamed of a better universe.
 

the wind-up Tao chronicle


"Between the end of that strange summer and the approach of winter, my life went on without change. Each day would dawn without incident and end as it had begun. It rained a lot in September. October had several warm, sweaty days. Aside from the weather, there was hardly anything to distinguish one day from the next. I worked at concentrating my attention on the real and useful. I would go to the pool almost every day for a long swim, take walks, make myself three meals.
But even so, every now and then I would feel a violent stab of loneliness. The very water I drank, the very air I breathed, would feel like long, sharp needles. The pages of a book in my hands would take on the threatening metallic gleam of razor blades. I could hear the roots of loneliness creeping through me when the world was hushed at four o'clock in the morning."



I. point of view of Kasahara May

Tao Types


The formal treatment of hierarchical logical levels was carried out by Bertand Russell and Alfred N. Whitehead in the first decade of this century, and appeared in final form in 1910 in the monumental work of mathematical logic with the title of "Principia Mathematica".
A major aim of this work was to preserve classical logic from paradoxes and antinomies. The simplest example is the kind of paradox:
"This statement is false"
If the statement is true then it is false, if it is false then it is true.
By examining the logical structure of this statement is known as having two characteristics simultaneously valid:
  • The statement is self-reference, that is it refers to itself. For example the statement 'this apple is red"is not a paradox, since a statement is not an apple, while it may be true or false depending on whether the apple is red or not.
  • The statement has the logical structure of the type "assertion of a negation" or -equally- "negation of an assertion", and being self-referential denies himself. For example the statement "this statement is true" is not paradoxical, if it is true is true and if it is false is false.
In the classical Aristotelian logic such a situation is devastating, and is determined by the principle of contradiction, which asserts the falsity of every proposition implying that a certain proposition A and its negation, the proposition that non-A, are both true at the same time and in the same way. In the words of Aristotle (Metaphysics):


« it is not possible to say truly at the same time that the same thing is and is not»
In order to preserve classical logic from paradoxical and self-referential problems Russell and Whitehead was assigned to the hierarchical logical levels, which they called "logical types" special rules, establishing a hierarchy of logical types that can not be broken, especially the rule that objects (elements) of a class (together) are at logical level lower than the class and, to prevent the formation of paradoxes, a class may not have as an element itself or anything that presupposes all the elements of a collection should not be an element of the collection itself.
With this split-level logical types on two different planes, one for the class and the other for its members , along with the rule to prevent logical links between the two planes, Russell and Whitehead intended to prevent the formation of the paradoxes in logic. With this subdivision and rule logic
"self-swallowing" classes, in which an element of the class is the class itself,  become meaningless and without any logical validity.
A class of classes, ie, a metaclass, is not really a class, say for example that the set of all concepts is itself a concept is meaningless since it is a 'concept' of a higher logical type. The components of a Russellian hierarchy are among them as an element to a class, a class to a metaclass or one thing to their name.


The work of formal systematization and logical foundation of the Principia Mathematica posed the possibility of creating a unique logical-formal system and organize all of mathematics and then physics. The vision was that romantic due to the success of classical physics, namely that the universe was extremely complicated but fully describable if the logic and the math behind the physics were a complete formal system of description of the physical layer.
Thus arose the question of
completeness and consistency of such system; it is complete if all true statements of mathematics are derivable "demonstrable" at its inside, it is coherent-consistent  if no internal contradictory statements can be derived, namely a proposition and its negation. A question of this sort comes in metamathematics, because it is a math survey on mathematics.For this purpose D.Hilbert launched the so-called "Hilbert's program" in the 20s: to demonstrate the completeness and consistency of the PM, or the attempt to axiomatization of mathematics. The main points were: 
  • Formalization of all mathematics: all mathematical propositions should be written in a precisely formal language , and handled according to well-defined rules.
  • Completeness: proof that all the statements that are true can be proved mathematically in the formalism.
  • Consistency: a proof that no contradiction can be obtained in the formalism of mathematics. This test of consistency should preferably use only methods "finitistic" about finite mathematical objects.
  • Conservation: proof that all the results of "real objects" obtained using the argument about "ideal objects" (as uncountable sets) can be tested without the use of ideal objects.
  • Decidability: there should be an algorithm to decide the truth or falsity of any mathematical proposition.


The Russell and Whitehead's monumental effort to save the classical logic and the Hilbertian program that followed were literally swept away forever by the work of Kurt Gödel in1931, in particular the two incompleteness theorems, not by chance entitled "On formally undecidable propositions of Principia Mathematica and related systems", that demonstrate how a axiomatic theoretical building can not simultaneously satisfy the properties of consistency and completeness, and that no consistent system can be used to demonstrate its own consistency.
During those same years, the development of quantum physics and relativity poses a definitive end to the idea that complete formalization of the physical Universe, together with its logical foundations, was possible.


The work of Russell and Whitehead has today an historical significance, however paradoxes and paradoxical situations exist, as well as in logic, also in life. Its use was, unexpectedly, in the description of the interaction and communication with animals and humans by Gregory Bateson. In his words:

"What Russell and Whitehead had faced was a very abstract problem: logic, which they believed, had to be rescued from the tangles that arise when the "logical types", as Russell called them, are mistreated in their mathematical representation.
I do not know if, while working within the "Principia," Whitehead and Russell had any idea that the object of their interest is essential for the life of humans and other organisms.
Whitehead certainly knew that playing with the types you can have fun and you can make the humor emerge. But I doubt that he ever passed the stage of fun and has come to realize that the game was not insignificant and that would throw light on the entire biology.
While not having to contemplate the nature of the human dilemmas that would have been revealed they avoided - perhaps unconsciously - to arrive at a more general understanding."




Wednesday, November 3, 2010

fractalised Tao



«Never-ending wonders pop out from simple rules, if these are repeated ad infinitum.»

Benoît Mandelbrot

the (not) certainty of Tao



Hieronymus Bosch
The Crowning with Thorns 
about 1485, oil on oak, National Gallery - London

In medieval iconography the four characters who surround Jesus symbolize the four human representations considered in the Middle Ages. In particular, the character in the bottom right, is still holding Jesus for the mantle and the ground freezes, represents the slavery of certainty in relation to the transcendental: "If I know, I already know"

from H. Maturana, F. Varela, "Tree of Knowledge", 1984

Tuesday, November 2, 2010

Tao types


A possible cataloging , not exhaustive, of the various types of systems based on the structure, function, internal properties or of input/output can be:
  • Absurd-Meaningless - Impossible, by constrast: Ingenious
These are systems for which the selection and composition of elements and/or the types of relationships/connections that are chosen do not have any sense or are inconsistent with fundamental laws.
It's worth noting that many fundamental discoveries were born to find meaning or links in natural or conceptual systems, where before it was thought there were not.
  • Trivial
These are systems whose description/analysis/knowledge does not add any information.
  • Simple
These are systems whose structure/functionality is easy to analyze/describe/implement.
  • Elementary
These are systems that have basic features but whose structure/description is not necessarily simple.
  • Deterministic / Random-Stochastic
This terms generally refer to the internal state of the system (defined by the set of internal state observable variables or to the characteristic of input/output. If a defined state of the system is a precise and unique state of the process or if a set value input produces always a defined output value then the system is deterministic - once determined these values are valid forever. If the values are descrivable by a probabilistic random variable the system is random, also known as dynamic random or stochastic, governed by a certain probability distribution on the values. Typically this means that some parts of the system/subsystem/processes are of random/probabilistic nature.
  • with/ without Memory
In systems with memory the system status and/or the value of the input/output function depend on the state or the input of the past.
This term refers to the in/out function of the system, whether linear or not.
Typically a system is only linear in the range of values over a certain dynamic of values, the input / output becomes non-linear, such as saturation. A typical example of linear system are the amplifiers.

Linear systems are the only ones that can have a complete formal description of their features. A technique for dealing with nonlinear systems is to linearize them for a certain range of values, or simulate them by one or more linear systems.
  • stationary / non stationary
Systems are stationary (or time invariant) when the internal parameters do not depend on time but are constant.
Among all the linear systems are of particular interest those lwhich are linear and stationary, for which the output signal depends only on the instantaneous value of the input signal. Conversely, there are linear dynamic systems, which are those systems for which the response depends - as well as input from the actual value - even from its past history.
  •  open / closed / isolated / adiabatic
Open systems, first defined by von Bertalanffy, are systems that can thermodynamically interact with the external environment exchanging both energy (work or heat) and matter.
A closed system is a system that does not exchange mass with the external environment, while it may carry exchange of energy in all its forms (including heat) or work.An isolated system is a system that does not interact in any way with the environment, or which does not exchange neither mass, nor work and heat.
An adiabatic sistem is a closed system that can not exchange heat or matter with the external environment, but can exchange work.
  • concentrated / distributed constants
It is a terminology normally applied to systems circuit. If the minimum wavelength of the signals passing through a circuit is large compared to the components/elements of the circuit is said to be with constant-concentrated, conversely if it is comparable is called with distributed parameters. A typical example are microwave circuits, where the wavelength of the signals is the order of cm. or mm.
  • discrete time /continuous time
It is an alternative and more genera definition for the values/variables/processes of digital/analog types. If the variables or processes of the system are discrete in time, or only may take certain discrete values, the system is discrete-time, while if they have continuous values over time are continuous time.
  • discrete states-events / continuous states-events
Similar to the precedent for the system internal states.
  • synchronous / asynchronous / syncronicity
In the first two types we refer in general to the comparison between the internal processes of the system or of some internal processes and other external to the system boundary. If the two processes have a correlation, usually in time, of the one-to-one among them, such as the type of cause and effect, these processes are synchronized with each other,  while if they are temporally independent are called asynchronous.
The term syncronicity was introduced by Carl G. Jung in 1950 to describe a connection between events, psychological or objective, which occur synchronously, ie at the same time, but between which there is not a relation of cause and effect but a clear commonality of meaning. By extension, a system is synchronic when has relations between internal and/or external processes of synchronic type.
  • Paradoxical or Oscillators
The oscillatory systems are those where the internal states, processes or the system's output are of oscillation type , with a period, usually in time. The oscillation of the state or output can be generated by a system internal or internal/external paradox , for example of the type "if not then yes - if yes then not"; in this case the state or the system output becomes a continuous oscillation of yes and no.
The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter to describe a situation where by moving up or down through a hierarchical system one finds oneself back where one started. Strange loops may involve self-reference and paradox. By extension strange loop systems are those where internal processes are of this type.
  • Chaotic
A dynamical sistem is of  chaotic type if it has the following three main characteristics:
  1. Sensitivity to initial conditions, that is to infinitesimal variations of the boundary conditions (or, generally, of the inputs) match with finite variations in the output. As a trivial example: the smoke of burning matches under the most very similar  conditions (pressure, temperature, air currents) follows trajectories from time to time very different.
  2. Unpredictability, ie it is not possible to predict in advance the performance of the system on long times compared to the characteristic time of the system starting from assigned boundary conditions.
  3. The evolution the system is described, in the phase space, by many stochastic trajectories as seen by an external observer, which all remain confined within a defined space: the system that is not evolving toward infinity, for any variable; in this case we speak of 'attractors' or even 'deterministic-chaos'.
A chaotic system is deterministic in general, that is regulated by a very precise law that requires  to assume a certain state (given its previous history and the law). The special feature of chaotic systems (a result of which are often confused with the random systems) is the fact that the upgrading law strongly depends on the initial conditions: a tiny change in initial conditions lead the system in a state far from what it could have achieved without this small variation.
  • Fractals
The term fractal was coined in 1975 by Benoît Mandelbrot, and derives from the Latin fractus fraction; in fact fractal images are considered by the mathematical objects with fractionary dimension. A fractal is a geometric object that is repeated in its structure the same on different scale, or that its aspect does not change at any magnification. This feature is often called self-similarityThe distinctive feature of fractals is that while the generation rules are relatively simple, their result produces meta-infinites.
By extension, fractal systems are those where processes or even the elements are of a fractal type.
  • Synergistic
The term synergetics was introduced by Hermann Haken within theframe of laser physics in the 70-80 years .Is commonly defined as a combined action of two or more elements, resulting in enhanced efficacy compared to their simple summation. It follows that a synergy is a simultaneous action of two phenomena, forces, or other entity, which strengthens the individual effects. A system is synergistic if one of its internal or external/internal processes have a synergy.
  • Undecidable
It is a characteristic that occurs in a particular set of dynamic systems called finite automata, in particular for the Turing machine (TM). A TM (similar in all effects to a computer) is a formal system which can be described as an ideal mechanism, but in principle feasible, which can be in well-defined states (state machine), operating on strings according to strict rules and is a computing model. In a system of this type one pose the halting problem, or if it always possible in a TM, which has unlimited evolution, described a program and a given finite input, decide whether this program will end or will recur indefinitely. It was shown that there can be no general algorithm that can solve this problem for all possible inputs.
  • Complicated/Complex
The term complicated derives from complicatus, ie "with folds", and can be explained by the socalled classic science, while complex (from complexus, ovvero "weaving") cannot be explained by classical science.
The definition of complexity is itself complex - many authors in different fields have proposed their own definition of complexity. Moreover, the distinction between complicated and complex is not clear, both systems have in general the following features:
  1. structure with many elements already in themselves complex
  2. non-linear interactions among the elements
  3. open system type
  4. structure very often of net-type
  5. necessity for the description of hierarchical and/or logical levels
Generally the characteristics of a complex system are that its elements are undergoing continuous changes individually predictable, but which is not possible or is very difficult to predict a future state.Moreover, complex systems can present a emergence behaviour, or a situation in which a system exhibits inexplicable properties on the basis of the laws governing its components. This fact arises from non-linear interactions among the system's comoponenets. Furthermore the system has adaptive characteristics, or modifies its parameters, elements and processes  according to different inside or outside situations.
In general all living systems are complex while artificial systems can be very complicated but not necessarily complex, or with a degree of complexity much lower than the living ones.

The best example of a complicated system is Internet, a set of transmission networks based on the same protocol, which at present interconnects some hundreds of millions of machines among clients, hosts, servers and networks equipments such as switchs and routers. Though Internet, as well as being very complicated, has indeed a certain degree of complexity - due to its network structure, the number of elements, the interactions between them and the hierarchy levels of the communication protocol used (IP) - still has a complexity much less than the smallest living organisms, such as those unicellular like  protozoa, or single cells.
Other examples of complex systems are cellular automaton, the earth's crust, considered as a dynamic system in the plate tectonics, all the ecosystems (even the simplest), the economical systems, the social systems, the nervous system , the climate systems,  local or global.
  • Hologramatic
by extension of the physical case, obtained with laser interference, they are complex systems in which any partial subset arbitrarily divided contains the structure of the entire system.