Thursday, September 2, 2010
metaTao: the Tao of Tao
In common speaking a usual situation is the one when a descriptive/application term (called subject term) is applied to another term (object) within its scope of definition/application to form a predicate.
For example, the subject term "production" may be applied after the object "apple" getting the term "apple production", a well-formed predicate with meaning.
A special case is when the subject term and the object term coincide, or where the subject term is applied to himself.
In the example we get "production of productions", a term that has still meaning and could refer generally to the study of the production techniques.
When a term is applied to subject itself is of use described by the prefix meta (from the greek: μετά = "after", "beyond", "with", "self"): metaterm.
In the shown example a production of productions is called metaproduction.
Not all the words with the prefix meta naturally have this meaning, for example a metaphor is not exactly a "phor of phor" while Metaphysics is not properly physics applied to physics.
In metadescriptions it is crucial to distinguish between the two levels of discourse, the level of the object elements and that relative to the metaelements which describe them. Born here a further distinction between levels, the logical one in addition to the hierarchical.
The logic levels can be organized hierarchically, and hierarchical levels can also be logical levels.
The fundamental distinction between logical and hierarchical levels is that the classes that represent the first are one another self-contained but are always on the same logical plane: each class is an extension of the previous but still at the same logical level, such as biology contains the chemistry, chemistry include physics, etc. while the classes corresponding to logic levels are not on the same plane, between the there is a logical gap and not just an extension of new elements: a metaclass is not simply an extension of the classes that compose it but a new class with characteristics and logical/functional properties entirely new and different from those of the classes that compose it.
For example, the subject term "production" may be applied after the object "apple" getting the term "apple production", a well-formed predicate with meaning.
A special case is when the subject term and the object term coincide, or where the subject term is applied to himself.
In the example we get "production of productions", a term that has still meaning and could refer generally to the study of the production techniques.
When a term is applied to subject itself is of use described by the prefix meta (from the greek: μετά = "after", "beyond", "with", "self"): metaterm.
In the shown example a production of productions is called metaproduction.
Not all the words with the prefix meta naturally have this meaning, for example a metaphor is not exactly a "phor of phor" while Metaphysics is not properly physics applied to physics.
In metadescriptions it is crucial to distinguish between the two levels of discourse, the level of the object elements and that relative to the metaelements which describe them. Born here a further distinction between levels, the logical one in addition to the hierarchical.
The logic levels can be organized hierarchically, and hierarchical levels can also be logical levels.
The fundamental distinction between logical and hierarchical levels is that the classes that represent the first are one another self-contained but are always on the same logical plane: each class is an extension of the previous but still at the same logical level, such as biology contains the chemistry, chemistry include physics, etc. while the classes corresponding to logic levels are not on the same plane, between the there is a logical gap and not just an extension of new elements: a metaclass is not simply an extension of the classes that compose it but a new class with characteristics and logical/functional properties entirely new and different from those of the classes that compose it.
In the figure we have a class C2 with C1 elements, mapped to a metaclass C4 that contains as elements some class C3, of which C2 is an element,; this is further mapped to a meta-meta-upper class etc.. At each class corresponds a logic level 1, 2 etc.
Some examples of metaterms are metadata, data that organize data, metatheories, a theory on another theory, as metamathematics, where one can define metatheorems - for example on the proof theory of theorems in mathematics, or metalogic, a metatheory study of logic, especially mathematical logic.
One description area where the distinction between logical levels is essential is in the field of linguistics, the study of natural languages (such English, Italian, et.) and artificial languages, such programming languages (C, LISP, HTML, etc.). In fact, if a book on C is written in english there is no possibility of confusion between the natural language narrative subject (english) and the described object language (C), but when an english book speaks about english, such as a book of english linguistics , several problems of confusion may arise when an english word is used as a metaterm of the metalanguage subject and when instead is a term of the object language described. In this case the use of metaterms between language and metalanguage and the distinction between logical levels of discourse is essential.
In system theory a system is commonly composed of elements, but more generally may include other systems, and in this case is a metasystem, as well as a system process may be composed of other processes, and in this case is a metaprocess. The distinction between logic levels which operates the description of system/process is essential in order not to create confusion or paradoxes.
Some examples of metaterms are metadata, data that organize data, metatheories, a theory on another theory, as metamathematics, where one can define metatheorems - for example on the proof theory of theorems in mathematics, or metalogic, a metatheory study of logic, especially mathematical logic.
One description area where the distinction between logical levels is essential is in the field of linguistics, the study of natural languages (such English, Italian, et.) and artificial languages, such programming languages (C, LISP, HTML, etc.). In fact, if a book on C is written in english there is no possibility of confusion between the natural language narrative subject (english) and the described object language (C), but when an english book speaks about english, such as a book of english linguistics , several problems of confusion may arise when an english word is used as a metaterm of the metalanguage subject and when instead is a term of the object language described. In this case the use of metaterms between language and metalanguage and the distinction between logical levels of discourse is essential.
In system theory a system is commonly composed of elements, but more generally may include other systems, and in this case is a metasystem, as well as a system process may be composed of other processes, and in this case is a metaprocess. The distinction between logic levels which operates the description of system/process is essential in order not to create confusion or paradoxes.
Tuesday, August 31, 2010
Monday, August 30, 2010
Tao level 0: relativity of Tao and Tao relative
In 1905, in what can be described with the same words Einstein himself used for the Newton's Principia as the "largest single contribution produced by a single individual in all the history of physics", Einstein introduced a revolutionary new paradigm, laying the foundations of Special Relativity.
ON THE ELECTRODYNAMICS OF MOVING BODIES
By A. EINSTEIN
June 30, 1905
It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the reciprocal
electrodynamic action of a magnet and a conductor. The observable phenomenon
here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbourhood
of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electromotive
force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to electric
currents of the same path and intensity as those produced by the electric
forces in the former case.
By A. EINSTEIN
June 30, 1905
It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the reciprocal
electrodynamic action of a magnet and a conductor. The observable phenomenon
here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbourhood
of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electromotive
force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to electric
currents of the same path and intensity as those produced by the electric
forces in the former case.
Einstein started from the consideration that the classical Newtonian mechanics transformations that bind space and time between inertial reference frames, who have between them a relatively constant speed, without acceleration, were the Galilean transformation, where time and space are absolute. In other words, the laws of Newtonian mechanics are invariant under Galilean transformations, that is co-variate with them, while this is not the case with the laws of classical electromagnetism.
Einstein showed that the correct transformations for electromagnetism that make invariant the Maxwell's field equations, are the Lorentz transformation where, unlike those of Galileo, time and space are no absolute but relative: both depend on the relationship between the relative velocity in relation to that of light between the two systems of reference .
When the Lorentz transformations are applied to the Newtonian mechanics to create relativistic mechanics, a new series of phenomena occurs against the common sense, which is based on the experience of objects which are large (compared to the atomic nucleus) and slow (compared to the speed of light), typical of classical physics, such as length contraction and time dilation measured between two reference systems that travel together to relative velocities close to that of light.
A typical apparent paradox due to the relativity of time is the twin paradox, a typical thought experiment (Gedankenexperiment), an experiment that is considered impossible to perform experimentally, or for its intrinsic structure or due to inadequate technologies, but the result, even conceptually, is significant: of two twins on earth one starts with a spaceship and reach speeds close to that of light. When he returns to earth he finds the other twin has aged, or he is younger. This is a direct consequence of special relativity largely confirmed experimentally. The paradox is that the twin on the ship could be argued that the other twin has left with the earth at the speed of light, so both should be rejuvenated to return. The paradox is only apparent and assumes that the situation of the twins is symmetrical why it is not: only the twin on earth has remained in an inertial frame, while the one on the ship in at least two times, acceleration and deceleration, is was in a non-inertial reference frame.
Einstein showed that the correct transformations for electromagnetism that make invariant the Maxwell's field equations, are the Lorentz transformation where, unlike those of Galileo, time and space are no absolute but relative: both depend on the relationship between the relative velocity in relation to that of light between the two systems of reference .
When the Lorentz transformations are applied to the Newtonian mechanics to create relativistic mechanics, a new series of phenomena occurs against the common sense, which is based on the experience of objects which are large (compared to the atomic nucleus) and slow (compared to the speed of light), typical of classical physics, such as length contraction and time dilation measured between two reference systems that travel together to relative velocities close to that of light.
A typical apparent paradox due to the relativity of time is the twin paradox, a typical thought experiment (Gedankenexperiment), an experiment that is considered impossible to perform experimentally, or for its intrinsic structure or due to inadequate technologies, but the result, even conceptually, is significant: of two twins on earth one starts with a spaceship and reach speeds close to that of light. When he returns to earth he finds the other twin has aged, or he is younger. This is a direct consequence of special relativity largely confirmed experimentally. The paradox is that the twin on the ship could be argued that the other twin has left with the earth at the speed of light, so both should be rejuvenated to return. The paradox is only apparent and assumes that the situation of the twins is symmetrical why it is not: only the twin on earth has remained in an inertial frame, while the one on the ship in at least two times, acceleration and deceleration, is was in a non-inertial reference frame.
The extension of relativity to non-inertial systems and the integration of the last part of classical physics, the theory of gravity, was made by Einstein in 1916 as a theory of General_relativity, central to any cosmological model of the Universe.
As speed becomes smaller than the light, Lorentz transformations are reduced to those of Galileo, and Relativistic mechanics reduces to the Newtonian, in which case the Theory of Relativity is considered as an extension of classical physics.
Tao level 0: Observing the Tao and the Tao which observes
In defining a system is central the role performed by the Observer.
It is in fact the observer which determines how and many are the system elements, which are the relations/processes to be observed and defines the system boundary. Furthermore, to discover and define the system - to measure it at level 0 - the observer must interact with it, and therefore modified it, so the original system is never known but only the detected one can be described. More, also the system under observation may interact with the observer. It is therefore necessary to consider a broader vision at a higher-level system which consists of observer-observed system.
This apparently lapalissade view is not so obvious since still today persists the myth that the reality of scientific description, particularly for the "hard sciences" such physics - described in the formal language of mathematics - is "objective" therefore not dependent from the observing subject. In this myth the observer never modify the observed system by observing it, and can always know the "original" physical reality
This gross confusion of one of the foundations of Galilean scientific method
that is the result of an experiment to be considered valid must be independent and agreed by all parties that carry out it, is the result of seventeenth-century Descartes'dualism between res extensa and res cogitans, mind and body, subject and object at physical level 0.
The myth of objectivity, at least at level 0, is also a consequence of the enormous success until 1900 of the newtonian classical physics (classical mechanics and gravitation) and Maxwellian (classical electromagnetism) to explain virtually all the physical phenomena observed, from the motion of the planets to the propagation of light. Even today almost all the technologies developed in 800s and 900s, from mechanics to electronics, have their foundation based on these two classical theories, which are the basis of our experience of "subjective" reality of the physical level 0.
In classical physics, the observer does not exist, or rather has no influence, if not for the fact that all laws/equations are to be defined in a given coordinate system, specifying the location and the time reference from which one points. All the laws of classical physics are invariant to any reference system in space and time, that is are valid for any observer at any place and at any time. Space and time are therefore considered absolute.
The conceptual paradigm of classical physics was radically revolutionized at the beginning of 900s when "places" of physics not yet studied previously where examined theoretically and experimentally, particularly those of high speed/energy (comparable to that of light) and picodimensions such as the inside of the atomic nucleus and of its constituents.
In the two theories developed during the 900s for these areas of phenomena, the theory of Special Relativity and of Quantum Mechanics, the observer's role is central, and denies any possibility of beliefs as "objective reality" and of commonsense already at the level 0.
The figure shows the scope for the various theories. Horizontally is shown the size of objects d, vertically their velocity v. As the upper limit of speed is shows the speed of light c and as the upper limit of size below which quantum phenomena are involved is given as the length (diameter) of an atomic nucleus Lp. For dimensions larger than Lp and speed lower to about half that of light c/2, that is in the world of our experience, classical physics CF is valid; for dimensions smaller than Lp and speed lower than c/2 quantum physics QF applies; for dimensions larger than Lp and speed higher than c/2 is the relativistic physics RF that applies; finally for dimensions smaller than Lp and speed faster than c/2 are valid both quantum theory and relativity, or the quantum-relativistic physics Q-R F, is to be used .
The integration between Quantum Mechanics and Theory of Relativity was initiated by the work of Paul Dirac in 1928 and followed with the development of Quantum Field Theories.
Some relevant experiments that demonstrate the key central role of the Observer and rule out the commonsense of the everyday experience described by classical physics are:
Syntropy
This gross confusion of one of the foundations of Galilean scientific method
that is the result of an experiment to be considered valid must be independent and agreed by all parties that carry out it, is the result of seventeenth-century Descartes'dualism between res extensa and res cogitans, mind and body, subject and object at physical level 0."No amount of testing can prove I'm right, a single experiment can prove that I was wrong."
Albert Einstein, letter to Max Born, 1926 december 4
The myth of objectivity, at least at level 0, is also a consequence of the enormous success until 1900 of the newtonian classical physics (classical mechanics and gravitation) and Maxwellian (classical electromagnetism) to explain virtually all the physical phenomena observed, from the motion of the planets to the propagation of light. Even today almost all the technologies developed in 800s and 900s, from mechanics to electronics, have their foundation based on these two classical theories, which are the basis of our experience of "subjective" reality of the physical level 0.
In classical physics, the observer does not exist, or rather has no influence, if not for the fact that all laws/equations are to be defined in a given coordinate system, specifying the location and the time reference from which one points. All the laws of classical physics are invariant to any reference system in space and time, that is are valid for any observer at any place and at any time. Space and time are therefore considered absolute.
The conceptual paradigm of classical physics was radically revolutionized at the beginning of 900s when "places" of physics not yet studied previously where examined theoretically and experimentally, particularly those of high speed/energy (comparable to that of light) and picodimensions such as the inside of the atomic nucleus and of its constituents.
In the two theories developed during the 900s for these areas of phenomena, the theory of Special Relativity and of Quantum Mechanics, the observer's role is central, and denies any possibility of beliefs as "objective reality" and of commonsense already at the level 0.
The figure shows the scope for the various theories. Horizontally is shown the size of objects d, vertically their velocity v. As the upper limit of speed is shows the speed of light c and as the upper limit of size below which quantum phenomena are involved is given as the length (diameter) of an atomic nucleus Lp. For dimensions larger than Lp and speed lower to about half that of light c/2, that is in the world of our experience, classical physics CF is valid; for dimensions smaller than Lp and speed lower than c/2 quantum physics QF applies; for dimensions larger than Lp and speed higher than c/2 is the relativistic physics RF that applies; finally for dimensions smaller than Lp and speed faster than c/2 are valid both quantum theory and relativity, or the quantum-relativistic physics Q-R F, is to be used .The integration between Quantum Mechanics and Theory of Relativity was initiated by the work of Paul Dirac in 1928 and followed with the development of Quantum Field Theories.
Some relevant experiments that demonstrate the key central role of the Observer and rule out the commonsense of the everyday experience described by classical physics are:
- relative Space and Time in Special and General Relativity
- Experiment of the double/single slit "normal" and "delayed" by Wheeler
- E-P-R Paradox and Quantum Entanglement
Syntropy
Wednesday, August 18, 2010
no Tao for old men
Sailing to Byzantium
I.
That is no country for old men.
The young In one another's arms, birds in the trees--
Those dying generations -- at their song,
The salmon-falls, the mackerel-crowded seas,
Fish, flesh, or fowl, commend all summer long
Whatever is begotten, born, and dies.
Caught in that sensual music all neglect
Monuments of unageing intellect.
II.
An aged man is but a paltry thing,
A tattered coat upon a stick, unless
Soul clap its hands and sing, and louder sing
For every tatter in its mortal dress,
Nor is there singing school but studying
Monuments of its own magnificence;
And therefore I have sailed the seas and come
To the holy city of Byzantium.
III.
O sages standing in God's holy fire
As in the gold mosaic of a wall,
Come from the holy fire, perne in a gyre,
And be the singing-masters of my soul.
Consume my heart away; sick with desire
And fastened to a dying animal
It knows not what it is; and gather me
Into the artifice of eternity.
IV.
Once out of nature I shall never take
My bodily form from any natural thing,
But such a form as Grecian goldsmiths make
Of hammered gold and gold enamelling
To keep a drowsy Emperor awake;
Or set upon a golden bough to sing
To lords and ladies of Byzantium
Of what is past, or passing, or to come.
I.
That is no country for old men.
The young In one another's arms, birds in the trees--
Those dying generations -- at their song,
The salmon-falls, the mackerel-crowded seas,
Fish, flesh, or fowl, commend all summer long
Whatever is begotten, born, and dies.
Caught in that sensual music all neglect
Monuments of unageing intellect.
II.
An aged man is but a paltry thing,
A tattered coat upon a stick, unless
Soul clap its hands and sing, and louder sing
For every tatter in its mortal dress,
Nor is there singing school but studying
Monuments of its own magnificence;
And therefore I have sailed the seas and come
To the holy city of Byzantium.
III.
O sages standing in God's holy fire
As in the gold mosaic of a wall,
Come from the holy fire, perne in a gyre,
And be the singing-masters of my soul.
Consume my heart away; sick with desire
And fastened to a dying animal
It knows not what it is; and gather me
Into the artifice of eternity.
IV.
Once out of nature I shall never take
My bodily form from any natural thing,
But such a form as Grecian goldsmiths make
Of hammered gold and gold enamelling
To keep a drowsy Emperor awake;
Or set upon a golden bough to sing
To lords and ladies of Byzantium
Of what is past, or passing, or to come.
W. B. Yeats (1865-1939)
Subscribe to:
Posts (Atom)
Posts
