Natural Science and Quantum Physics
By Jutta Schmitt
In earlier expositions of our philosophy, we stated, that Natural Science falls in the realm of intellect, as intellect is directed towards Cosmos, and designs "thinking about natural acts", about acting nature. Reason, we stated, is directed towards Einai, and designs "thinking about social thought, about thinking society. Within the further elaboration of our philosophy, the limits of intellect in establishing a relation towards Cosmos became clear, as intellect is limited towards identification, which is equivalent to "non-relation", and thus remains within our Unilogics. It is only in our Trialogics, where a different relation towards Cosmos can be established, where a differentiation AND triversification of Cosmos itself can be performed, and where its multifacetical spectrum can be grasped by transcending the dialogical domain of Einai, of thinking.
One of the realms of Natural Science, that displays the difficulties of trying to approach a multifacetical, diverse spectrum with inadequate, unilateral-logical parameters, is Quantum Physics, which deals with microcosmic realities. In Quantum Physics, the scientists have been literally forced to transcend their unilateral parameters of thought, that is, the limits of intellect. In the following lecture we will try to illustrate, how Quantum Physics, epistemologically spoken, "lies in the neighbourhood" of our Trialogics, that we are currently elaborating in detail.
Thus, in today's introduction, we will deal with the topic mainly in an epistemological, more precisely, trans-philosophical way, although, at some moment, we will have to go into the most important details from a physical-scientific point of view. Please do note however, that we don't claim to be experts in Quantum Physics, but simply try to approximate the topic in what concerns the epistemological problems Quantum Physics deals with, and which are part and parcel of our Trialogics.
Classical Physics and Quantum Physics - A Brief Overview
In order to approximate what distinguishes Quantum Physics from Classical Physics, we will have to say a few words about the physics of Isaac Newton, who completed the transition, begun by Galileo Galilei,from medieval-scholastic, Aristotle-based physics towards a physical system, that has come to be known as "Classical Physics". An epistemological summary of Classical or Newtonian Physics can only draw one conclusion from it, which is, that Newton's world is a closed system of complete determinism. Every thing, every appearance, every process is strictly determined and basically follows the same set of everlasting rules, which are the laws of mechanics. Continuous, rectilinear-homogeneous motion reigns, "absolute" motion, isolated and enshrined within a closed inertial system, that tends to stay at rest internally and has no external relation to any other system.
The above described motion, as it is being cut off from any relation, both towards itself and towards rest, turns out to be motion-at-rest, in the final analysis, rest itself. Thus, Newton did not formulate the laws of motion, but the laws of motion-at-rest, of rest itself; and it was Albert Einstein in his general theory of relativity, who established the laws of motion, relating motion to rest and comprehending it as rest a n d motion, because what makes motion motion is precisely its being related to rest. Only by relating motion to rest can the "laws of motion" be explored, which firstly have to identify rest - what Newton did -, then to identify motion - what the Dutch physicist Hendrik Lorentz did in his famous transformation equation, which identifies the relation that exists between a system-at-rest and a system-in-motion with regard to the same temporal-spatial "event" to be measured -, and finally to differentiate motion as rest a n d motion - what Einstein did in his general theory of relativity, relying among other premises precisely on Lorentz' transformation equation.
We stated above, that the one conclusion to be drawn from Newton's Physics is determinism. Thus, all things, appearances or "events" stand in a causal chain of correlation and intercorrelation, which operates within the unilinear "cause-effect" parameters. Everything, all events, are necessarily locked into this causal connection chain; accident does not figure in this system. The performance of every thing, appearance and event is due to objective laws, more precisely, to the mechanical forces of pressure, push, and mass attraction. All effects are being reduced to mechanical causes, all motion to mechanical motion and all laws to mechanical laws. In mechanical determinism, the behaviour of any given inertial system is being determined in a unilinear way by its initial status, and so the necessary behaviour of the system as well as of its components can be predicted according to the laws of mechanics.
Determinacy and predictability are identical within this cosmovision, they fully coincide. As can be seen in the works of Kepler, Galilei and especially Newton, a system had been elaborated by these physicists, that not only correctly described the mechanical motion and intercorrelation of physical bodies in general, but that even allowed to exactly calculate and predict the motion of the macrocosmic bodies, that is, the orbits of the planets. No "supra natural hypothesis" were necessary anymore to explain the secrets of the universe. This is how classical mechanics came to be sort of a "prototype method" of the so called "exact" natural sciences, and its principles were assumed to be valid for the whole cosmovision of nature, which was seen as one, continuous, uninterrupted chain of causes and effects, necessarily and inevitably interlinked and related to each other.
This kind of universal, mechanical determinism found its utmost expression in the conception of Laplace's "Demon". The French mathematician and astronomer Pierre Simon Marquis de Laplace assumed an "intelligent being", that is conceived as being capable to know and analyze all forces that are acting in nature, as well as all the co-ordinates of all bodies at a determined time. Thus, the "Demon" could grasp the motion of the biggest body of the universe as well as that of the smallest atom in one sole formula. From any given status of the universe, the "Demon" could calculate each past and future status of the universe and its components in detail, due to the laws of mechanics.
Amongst other critics of mechanical determinism, the German philosopher Immanuel Kant, who, in 1755 in his astonishing "General History of Nature and Celestial Theory", where he explained the origin of the universe with the help of his nebular hypothesis and the forces of attraction and repulsion, emphatically denied in his attack against mechanical determinism, that causality could simply be reduced to a purely mechanical relation-chain of cause and effect. Kant demonstrated the narrow limits of mechanical determinism by stating, that the "Newton of the Blade of Grass" had not yet appeared, in other words, that the mechanical laws of cause and effect were not sufficient to explain more complex forms of motion, such as organic life:
"One should not be displeasured when I dare to say: that rather is the origin of all celestial bodies, the
cause of their motions, in short, the origin of the whole current shape of the universe to be clearly and
completely understood in a mechanical way, than the coming into being of a single herb or worm."
The deterministic cosmovision defines nature as a closed, inertial system, existing objectively and independently of human recognition, and being at rest in its totality. The Euclidean, three-dimensional concept of space and a correspondingly linear-homogeneous concept of time are not only the conditio sine qua non for "rest" and "motion" to make formal-logical sense, but also form the mayor underlying premises, both of determinism and of the vision of nature as a continuum, where necessity, causality and predictability reign. Thus, recapitulating: space, time, rest, motion, continuum, necessity and causality form the premises of determinism.
With the transition of Classical Physics towards Modern Physics at the turn of the 19th to the 20th century rose the suspicion, that the deterministic world outlook, as performed by Newtonian Physics and as exposed before, was most probably "wrong". The famous wave-particle-duality in Quantum Theory, described by Niels Bohr in his "complementarity principle" and specified by Werner Heisenberg in his "uncertainty principle", showed, that mechanical-deterministic explanations totally failed in the sub-atomic realm of reality, and had no validity where randomness reigns. From this particular problem was drawn the conclusion, that determinism as a whole had to be discarded and replaced with indeterminism - at least in sub-atomic reality.
The philosophical-epistemological origin of the indeterministic interpretation of sub-atomic reality by modern physics basically lies in identifying "determinacy" with "predictability". Indeterminism, as exposed by Quantum Physics, considers the predictability of events as the main criteria of their determinacy and thus concludes, that determinacy cannot be valid in a realm, where it is impossible to make unequivocal ("ein-deutig"), that is, definite predictions, as is the case in Quantum Physics, where randomness reigns and the "Demon" of Laplace has converted itself into Einstein's notorious "Dice-Player".
The indeterministic cosmovision defines nature in microcosmic dimensions as an open, dynamic "non-system", being its existence influenced by and thus dependent upon human recognition and measurement. Microcosmic events cannot be determined in space and time parameters, as the open system in its totality is in motion. Microcosm is a discontinuum, where randomness, qualitative "jumps" and unpredictability reign. Summing up: space (as non-space), time (as non-time), rest (as non-rest), motion (as non-motion), discontinuum and randomness form the premises of indeterminism.
Apparently, there is a decisive difference between determinism and indeterminism, being the one precisely what the other one is not, and vice versa. Yet, taking a closer look and speaking qualitatively, as none of the two establishes a relation towards the other, we are confronted with the very same thing, that is, with identity, with rest. The "relation" established between determinism and indeterminism is exclusive: it is determinism versus indeterminism, the formal-logical, exclusive non-relation: either the one, or the other. It is precisely this formal-logical non-relation that has come to be the mayor stumbling block in Quantum Physics and within the indeterministic world outlook. However, within Quantum Physics itself, we will see, that inevitably an effort had to be made to relate things in an "unusual" way, beyond the limits of Formal Logical either-or-relations, in order to interpret the events that occur in sub-atomic reality.
The Transition from Classical Physics to Quantum Physics
The Atomist Structure of Matter
At the turn of the 19th towards the 20th century, experimental physics became confronted with the atomist structure of matter and its characteristics of randomness, showing the atomist units of matter an accidental, indeterminable behaviour, that is, not definable within space and time parameters, which thus fell outside the range of the Newtonian laws of motion. Explanation efforts of this randomness behaviour led to the formation of Quantum Theory in the years between 1900 and 1926. But it was only after 1926, that a total rupture with Newtonian or Classical Physics was inevitable.
Quantum Theory departs from the assumption, that radiation energy is not being emitted or absorbed continuously, but in a discontinuous way as "minimum amounts" of energy, that are frequency-dependent and discrete. The assumption of the discrete character of events in sub-atomic nature has not been the exclusive discovery of the German physicist Max Planck; already in the late 19th century, the English physicist Sir Joseph John Thomson had discovered the discrete character of electrical charges. It was Planck, however, who, in 1900, explicitly formulated a "quantum hypothesis" as the result of his experiments on the distribution of energy concerning the spectrum of the black body radiation.
The main statement of Max Planck's quantum hypothesis is, that nature is not to be understood as a continuum, but in a discrete, fragmented, interrupted, unstable, accidental way. The matter-constituting, discrete "units" are the "quanta", the particles. Objects, that appear continuous to the eye, are being "quantized", that is, understood as being composed of particles, just like a photography, which is composed of uncountable colour spots, and appears as a continuum in its totality, but being quantized, however, it turns out to be composed of discrete particles. Planck himself did not yet try to relate the two moments, "continuum" and "discontinuance", like it sort of forcibly had been undertaken at a later point by the physicists Werner Heisenberg and Niels Bohr, in order to "make sense" of the events as they occur in sub-atomic reality. The insight in nature as being both continuous a n d discrete as well as neither continuous nor discrete "all at the same time", would certainly not occur to the quantum physicists of the first generation.
As we do not have access to "classified knowledge", and do not know the actual status quo of Quantum Physics at the turn of the millennium, we only can deduce from relating various important data, that formerly inconceivable kinds of establishing relations have long been "discovered" and are being (ab-)used in form of mind control and "classified technology". - In any case, in spite of Planck's experiments and formulation of the quantum hypothesis, theoretical physics long remained dominated by the classical, Newtonian conception of nature as being a continuum. Also, the scientific conception of the atomist structure of nature would still take years to be generally accepted.
The criteria for something to "make sense" is a parameter setting, within which we arrive at the conclusion, that something does or does not "make sense". Mathematics and Formal Logics talk about their logic as of a two-value-logic, simply because it operates with two values: "true" and "false". In reality, however, it is a one-value-logic, precisely because only one of two or any given number of values can be "true" - never both or all of them, and so we arrive at the famous, exclusive non-relation that affirms the one, true principle: either true or false.
The problem starts, whenever something is obviously not explainable within the formal logical Either-Or-Parameter Setting, and we still try to force it into this strait-jacket, although it completely falls outside its range. In this case, only if the parameter settings as suggested by Formal Logics are being left behind, can a different kind of relations be established between any two or three or "x" given values, which was exactly the case in Quantum Physics, where a different kind of parameter setting had to replace the formal-logical one, and where explanations of a complicated nature demanded a different kind of logical relation than the one and only "either-or-relation", that is allowed to be established in Formal Logics, and that no longer "makes sense" in a multi-mensional environment. Specifically, this problem can be traced in the steps that had to be taken beyond Formal Logics, as they manifest themselves in the wave-particle duality and the inevitably adopted "complementarity principle".
The conception of the "complementarity principle" is a methodological and epistemological, non-formal-logical tool for the interpretation of quantum mechanics, specifically the wave-particle-duality, and was introduced into Quantum Physics in 1928 by the Danish physicist and head of the famous Copenhagen School, Niels Bohr. The complementarity principle states, that, epistemologically spoken, both aspects, the particle a n d the wave aspect, equally apply to elementary particles, but that the aspects themselves radically exclude each other. It so denotes a specific relation between two concepts, that both determine a n d exclude each other, concerning sub-atomic, elementary particles.
In sub-atomic reality, the properties that are displayed by the particles depend on the nature of the experiment; in one case, the particles act like such, in another case, the same particles act like waves; but they never act as both, particle and wave, at the same time and in the same respect. Thus, wave- and particle properties are complementary, that is, elementary particles have both particle and wave properties, but never display these properties simultaneously. From the fact, that the respectively displayed aspect depends on the choice of the measurement apparatus and thus from the scientist who conducts the experiment, has been drawn the conclusion, that the respective properties do not actually "belong" to the elementary particle itself, but are being created in the experiment, in the scientific process of observation. In spite of the complementarity principle and still stuck to Formal Logics, the wave-particle duality turned into a real dilemma for the quantum physicists.
Interestingly, this dilemma had found an early expression in the 17th century dispute between the followers of Newton's and the Dutch physicist Christiaan Huygen's respective theories of light. Newton developed a particle-based theory, whereas Huygen's theory of light was wave-based. Both theories were equally adequate to explain the phenomena of light. In the course of the 19th century, Huygen's wave-based theory seemed to have finally won the battle, as it was the only one that was capable of explaining the phenomenon of diffraction of light.
However, with the discovery of the light-electrical effect by the German physicists, Heinrich Hertz and Wilhelm Hallwachs, a phenomenon became known, that principally could not be explained with the wave-based theory. It was Einstein in 1905, who, with his photon-theory and having fallen back upon the particle theory of light, gave the first plausible explanation for the light-electrical effect as discovered by Hertz and explained by Hallwachs. An experiment conducted by the American physicist Arthur Holly Compton in 1923 and which came to be known as the "Compton-Effect", provided the experimental proof for the adequacy of the particle-theory of light.
From that point on, there were two specifically different, scientific ways of explanation for determined properties of light. The insight into the particle-properties of light-waves led the French physicist Louis-Victor De Broglie in 1925 to an investigation of the reverse problem: If waves possess particle properties, do particles also possess wave properties? De Broglie's hypothesis was confirmed by the observation of particles in different experiments, in which the particles revealed typical wave properties like interference and diffraction, frequency and amplitude. This meant, that both, electromagnetic wave and particle, had to be assigned both particle a n d wave-properties. It was the German physicist Werner Heisenberg, who, in 1927, with the help of his uncertainty principle, gave an insight into this mutual dependence of properties that yet exclude each other.
Perhaps it is interesting to note here, that due to the persistence of formal logical thinking, even in a realm the explication of which demanded a much more advanced logics than unilateral either-or parameters, many efforts had been made to ultimately eliminate one of the two intrinsical components of the theory of the wave-particle duality and to reduce it to the "standard" formal-logical, unilateral scheme of deterministic mechanics. Efforts were made in order to re-establish and universalize the "classical" particle theory and diminish the wave character of particles by only admitting "probability waves"; and also in reverse, to eliminate the particle aspect and only admit waves, by reducing the particle phenomenon to the assumed existence of "wave packages", like the Austrian physicist Erwin Schrödinger did. Yet, "probability-waves" and "wave-packages" still operate with both of the two principles, that is, particles a n d waves. So, none of these efforts was convincing and it became more than evident, that not only did the conception of the closed system of classical mechanics fail in explaining the structure and properties of the so called "smallest particles of matter", but that the very assumption of the existence of ultimate, "smallest" matter-units itself had to be reviewed, if not discarded.
The simple fact, that the complementarity principle does not allow to draw the classical, "unequivocal", that is, formal-logical "either-or-conclusion", has led many a physicist to assume, that the wave-particle-duality forms a logical contradiction, and thus has to be interpreted as an argument for agnosticism, which has often been underlined with Heisenberg's uncertainty principle, which we will illustrate just now. They argue, that complementarity, as it impedes an unequivocal conclusion to be drawn from the observed experiment with regard to it's underlying reality, demonstrates the ultimate limit of human recognition of nature.
This argument makes perfect sense within the limited horizon of unilinear Formal Logics and its one and only, exclusive either-or parameter precisely of not-relating things, where "contradiction" is the forbidden fruit, and where it is imperative to derive all different aspects from the one, single principle, "A". From the point of view of any other logic, beginning with dialectics, this argument is equivalent to sheer unilaterality and misses the multi-mensional boat, where contradiction is a conditio sine qua non for valid statements, and where the assertion, that properties, that exclude each other, are being displayed in different sides of the same, physical event, is a valid assertion and actually meets with sub-atomic reality.
With unilateral logics, unilateral problems can be solved. With multimensional logics, multimensional problems can be solved. There is no problem whatsoever to make the multimensional statement, that the elementary particles are neither particles nor waves, or that they are both, particles a n d waves, and even, that they are both: [particles and waves] AND [neither particles nor waves].
At an earlier stage of Quantum Physics, it was only the discredited dialectical materialists, who were able to approximate the wave-particle duality without any problems, and who thought of the necessity to apply at least a three-value-logic in order to adequately express the phenomenon, and where, as they expressed it, besides the two values "absolute truth" and "absolute falseness", a third one should be added, that is, "relative truth". (And we, in this case, would add the "missing link" they forgot: "relative falseness".)
From all what we have been elaborating so far, we can state: Particles and waves are the two sides of the same phenomenon. We can call the phenomenon "wavicle" or "particlave", and, according to our trialogics, understand it as: 1., being particle, 2., being wave, 3., being particle a n d wave, 4., being neither particle nor wave, that is, being particle a n d wave AND "wavicle".
Towards Heisenberg's Uncertainty Principle
From 1925 on, departing from Planck's quantum hypothesis, quantum mechanics began to be elaborated. (Note the inadequacy of the concept "mechanics" here, which belongs to the classical, Newtonian, deterministic closed-system conception of unilateral cause and effect.) Basically and according to the duality-problem, there were two simultaneous and independent formulae: Werner Heisenberg's matrix mechanics, which departed from classical particle-mechanics, and Erwin Schrödinger's wave mechanics, which departed from the description of the wave-phenomenon. Both formulae dealt with the very same scientific-physical phenomenon, and their conclusions were equivalent; this means that the illustration of the phenomenon is essentially the same, however each formula constitutes and expresses a different, mathematical method.
Keeping in mind, that the physical object of quantum mechanics is the structure of atoms, from the above explained results, that this structure cannot be described either trough the classical wave-, or the classical particle concept, but precisely through the two of them. Quantum mechanics thus denotes and reflects the wave-particle duality in it's method of explaining it by both, wave a n d particle mechanics. The scientific-physical problems, that had formerly risen when applying only one of the two concepts, turned out to be fake problems caused by a limited, formal-logical conception of exclusive either-or non-relations, and thus not to be related to the real physical problems as such.
Werner Heisenberg's Uncertainty Principle
In 1927, Werner Heisenberg discovered a problem with regard to improving measurement conditions in order to achieve greater accuracy. He sustained, that due to a basic, objective limit, the precision of measurement procedures in order to eliminate disturbances caused by the same measurement procedure, cannot be improved, let alone optimized. The simultaneous determination of the variables energy (E) and time (t), respectively impulse (p) and range (stretch, span) (q), the product of which is the physical equivalent of an "effect", is impossible to realize in an accurate, definite way. If the exact location in space of an electron was to be measured as precisely as possible, the electron had to be exposed to extremely short-waved light or "hard gamma radiation". This, however, caused a significant change in the electron's impulse. Was the electron being exposed to less energy containing, long-waved light, the impulse suffered less influence, but the location could not be determined with exactitude, it became "unsharp" (uncertain).
As, in the sense of classical mechanics, the unequivocal determination or definition of a particle's status requires the simultaneous knowledge of its place and impulse, which is the equivalence to its "departure conditions" or "origin", the representatives of the Copenhagen School (Bohr, Heisenberg, Schrödinger, Jordan) draw from the above illustrated problem the conclusion, that events in the sub-atomic realm are basically subdue to indeterminacy. The determinacy of Classical Physics, understood as predictability and "personalized" in Laplace's "Demon", had found it's counterpart in the indeterminacy of Quantum Physics, understood as unpredictability, and the "Demon" suddenly turned into Einstein's dice-playing "God".
Before we continue with our exposition, we will take a short look at the definitions given to "quantum", "particle" and "wave". The concept "quantum" is being defined as "smallest, indivisible energy amount", and often used synonymously with "particle". The concept "particle" is being defined as "material body of smallest expansion" and is being counterpoised to the concept of "wave", that denotes an "infinitely extended, periodically spreading, oscillating change of a physical quantity".
Particle, being conceived as "body", in other words as being physically delimited, denotes the ancient Greek´s notion of peras, the "limited", whereas wave, being conceived as infinitely extended, that is, without limits, denotes the ancient Greek´s notion of apeiron, the "unlimited". We only can indicate here, that peras and apeiron, in early Greek Philosophy, determine each other and are linked to the philosophical problem of the relation of "part" and "totality".
Being the elementary particles or "wavicles" both, particles a n d waves, as well as neither particles nor waves, they cannot be interpreted within a formal-logical theory like the classical, mechanical model introduced in our description of determinism. An electron, for example, simply does not have a defined location in the sense of Classical Physics, precisely because it is no sharply limited, rigid particle or "body". It is itself a limited-unlimited, oscillating wavicle. Thus, to demand a "clear", "unequivocal" definition and location in the sense of Newtonian mechanics does not make sense in Quantum Physics.
The indeterministic conclusions, as drawn from Heisenberg's Uncertainty Principle, are based on the simple fact, that two determined, complementary variables cannot be measured simultaneously with the expected exactitude, that is, their "origin" or departure conditions cannot be determined, and also not any other past, present or future status. The behaviour of the elementary particles is "probable" according to probability calculus applied in Quantum Physics, but unpredictable in a formal-logical, deterministic-mechanical sense. Although Max Planck himself had noted, that Heisenberg's uncertainty principle does not necessarily exclude determinism, none of the quantum physicists ever came to establish a similar relation between determinism and indeterminism as had been established between particle and wave properties, or even to go further and understand indeterminism as [determinism a n d indeterminism].
In the last analysis and as long indicated by dialectical materialists, Heisenberg's Uncertainty Principle expresses the limits, within which the exclusive particle- or the exclusive wave-theory are applicable. It sort of provides an evaluation of the mistakes one commits, when unilaterally applying either the particle or the wave theory.
As Quantum Physics in its totality remained within Formal Logics, despite the efforts undertaken in the form of the complementarity principle and the wave-particle duality, indeterminism has been equaled and associated with formal logical contradiction and thus with epistemological agnosticism.
According to the conclusions drawn by the Copenhagen School of physicists from the problems as they manifest themselves in Quantum Physics, cosmic, sub-atomic objectivity - we would say, identity - , is denied; the epistemological object does not exist as such, as part of objective, cosmic reality, but is perceived as being created in the process of measurement and observation. The complementary properties, wave and particle, are perceived as being produced by the subject, who influences the object in the experiment. Thus, this is why it is not possible to recognize the "object-in-itself", its essence.
Accordingly, the Copenhagen School gave an agnosticistic interpretation of the wave-particle-duality and the uncertainty principle, being this agnosticism an intrinsical part of what has become known as the Copenhagen Interpretation of Quantum Physics. We must mention, however, that at a later point, the agnosticistic unity of the Copenhagen School fell apart, and a differentiation set in, with Niels Bohr and Max Born turning towards materialism, Werner Heisenberg turning from subjective to objective, platonic idealism, and with only Pascual Jordan remaining on the original, subjectivistic-idealistic position.
We conclude, that one of the reasons if not the main reason for the subjective-idealistic interpretation of Quantum Physics by the Copenhagen School, is their remaining stuck in Formal Logics from their heads to their toes, and operating with the respective, limited, epistemological parameters. The unastonishing fact, that the mechanistical conception of causality failed in Quantum Physics, necessarily had to lead to the interpretation of indeterminacy in the sense of agnosticism by the physicists of the Copenhagen School.
Thus, the kind of indeterminism arrived at by the Copenhagen quantum physicists is nothing but another version of classical determinism itself, not being able to transcend the formal logical limits of unilaterality.
------------oOo-----------THE CONCEPT OF SPACE
REFLECTIONS ON THE CONCEPT OF SPACE
(This series of articles is dedicated to the
unconventional Scientist and Philosopher, Don
By Jutta Schmitt
Introduction: Our Philosophical Context
Before we commence with the investigation on the concept of Space, we firstly
will have to make a few general observations concerning our philosophical context,
within which, of course, we will elaborate these reflections on Space. As we will be
dealing with a concept, that forms one of the two primordial conditio sine qua non
of the classical Natural Sciences (the other one is Time), we will start our short
determination point of departure, our "Standortbestimmung", with a brief
explanation of our postulate, Cosmos.
As is well known, our postulate is Cosmos. It is our starting point, our natural,
physical basis, our identity. In the course of our own acting a n d thinking AND
transcending, however, we have seen, that we can establish a clear distinction
between different "aspects" of Cosmos, as they unfold themselves in our further
logical operations like counterpoising [Cosmos a n d Einai] and juxtapoising
[Cosmos and Einai AND Nothing].
One aspect is what we call "Cosmos-as-such", Cosmos itself, the Thing Cosmos,
or Cosmos-At-Rest, of which we are part and parcel by the very fact, that we are
concrete, cosmic, physical beings. In this respect, and as often stated before, we
ARE Cosmos, which expresses itself by our physical-natural, cosmic acts. Another
aspect is, what we call "Cosmos as reflected by Intellect", Cosmos as perceived by
us, the Thought-Thing (Gedankending) Cosmos, or Cosmos-In-Motion, as it is
expressed by our abstract, intellectual-social, ontic thoughts. Thus, our cosmic acts
we simply express as being Cosmos ourselves, and our ontic-cosmic thoughts
about Cosmos, our percepts and concepts, we express in our Unilogic as part of
Dialogic, as existing Einai, that is, within Einai, within Thought itself, via the
Intellect, whereas Reason, we said, as another aspect of Einai, deals with "thinking
about thought itself.
Yet another aspect of Cosmos is what we call "K", Kosmos or "Relational
Kosmos", being Kosmos both - At-Rest and In-Motion, as well as neither At-Rest
nor In- Motion; that is, Kosmos known as neither Thought-Thing nor thoughts
about the Thought-Thing. With the help of our logical and methodological
triagories we illustrate our cognition, recognition and knowledge of our main
epistemological Triagory: Kosmos-Einai-Nothing.
On other occasions we have explained, that we can establish a kind of analogy
between concepts, categories and relations as they apply in "Patrian" Formal
Logics and Dialectics, and our own percepts, concepts, unigories and diagories as
developed by our method and philosophy, being the Patrian analogy however
clearly marked off as "/and" or "/a n d".
What concerns us here, is, that within the context of our interlinking Triagories, we
can identify and establish the analogy to what connotation Space and Time have in
the Patria (properties of matter or concepts of intellect, for example), and in our
philosophy, where Space and Time equal percepts, that is, levels of thought within
Einai, that refer to Cosmos as a thought-thing).
In a series of short essays we will try to investigate, how exactly the concept of
Space appears in the various cosmovisions of Patrian Philosophy, Mathematics
I. General Definition of Space
It is almost impossible to undertake a "general definition" of the concept of space,
as there are at least three major connotations to it, that is, philosophical,
mathematical and physical. In a vague (trialogical) approach, however, and
departing from the rigid-dualistical separation of what we have called the two
intrinsical parts of history, that is, nature a n d society, the concept of Space
applies mainly to the realm of Nature, philosophically, physically and
mathematically. Even in the arch-idealistic, philosophical system of the German
philosopher G. F. W. Hegel, where even Space is determined as a mode of being
of the "Spirit" or the "absolute Idea", it still applies to the realm of Nature, when
Hegel formulates, that Nature is "Exhibition of the Spirit in Space"("Auslegung des
Geistes im Raum").
The concept of Space constitutes a supra concept that subordinates concepts like
"matter", "universe" and "nature", where Space denotes a measurable quantity,
that forms the basic condition for the "existence" of matter, the universe and of
nature, in short, of the "objectively existent reality". Space also is considered to
form the basic condition for the general existence of extended, physical bodies and
their being next to each other in the universe and in nature. The concept of Space
is furthermore being associated with the perception of "emptiness", often pictured
like a kind of vessel, that is able to contain a vast variety and diversity of extended
bodies or things, which are apart from each other and yet right next to each other
at the same time, and which change their respective location, which move in
Space. Interestingly, the extended bodies themselves are being conceived as having
attributes of Space. The German concept "Raum" is probably the best example for
the association of "Space" with the perception of "emptiness". It stems from the
Old High German "rûm", and denotes "not filled", "free room".
If we think about how Space conceived as "totality" relates towards the spatial
extension of particular things, we start touching one of the physical aspects of a
philosophical problem, which is that of the relation between the variety and
diversity of the many "particular things" towards the unity or totality of matter on
particularitthe whole; we touch the philosophical problem of howy and totality are
related. Further physical aspects of the same philosophical problem are the relation
of "the limited" with regard to "the unlimited", of discontinuity towards continuity,
of divisibility towards indivisibility, and also the relation of rest towards motion.
Before we will go into the specific definitions of the concept of Space as they
apply to philosophy, physics and mathematics respectively, we will have to take a
glance at the mythological and philosophical origin of the very concept, always
keeping in mind, that historically, philosophy was the mother of all sciences, and
thus provides us with the original tracks of scientific concepts, like in our case,
"Space". -Philosophy here means Western, Ancient Greeek Philosophy, which, in
turn, has its roots in Greek, Mediterranean, African, Arabian and Asian Mythology.
1. The mythological-philosophical Origins of the Concept "Space"
The Greek term "chaos" stands for the conception of an empty, gaping, yawning
Space, and the very root of the word literally imitates the articulation of yawning.
Chaos so denotes the "original state of the world", which Hesiod (Theog. 116,
700) calls "the immeasurable Space, that was before all other things" and that, at
the same time, constitutes the Origin of all things. Only later, when the dualistic
conceptions of darkness and light, of matter and spirit, of good and evil, which
mortally oppose and exclude each other, began to arise in mythology and early
philosophy, did Chaos acquire negative connotations, as expressed by Anaxagoras
(Diels 46, B.1. 12), Plato (Tim. 30 A ff.) and Ovid (Metam. I 7).
The Greek term abýssos denotes the lowest depth, the abyss, that, what lies below
the Earth, below any still reachable ground, the bottomless, the unfathomable, the
immeasurableness, that, what has no bottom, also the infinite, the nothing. Abyssos
also reflects the greek chaos, býthos (gap, chasm, depth, the deep), and appears
related to the mythological conceptions of the Greek Underworld, of Hades (Hell).
In manicheism, a religion that combined elements of Buddhism and Christianism,
and which was based on the dualistic conceptions mentioned above, abyssos was
related with the greek term hýle, that is "matter", "substance", and became
associated to the world of darkness, denoting the material, the dark, the evil (in
contrast to the world of light, the spiritrual, the light, the good).
1.3. To kenón
The Greek term to kenón (in latin: "vacuum"), denotes "space without matter",
"empty space", the void. The Greek Atomists assumed the existence of empty
space in order to explain motion. Empty space, they argued, is the primary
condition for things to be able to move at all. The examples they gave ranged from
condensation to dilution, from growth and expansion to compression and
contraction. Aristotle decidedly rejected the assumption of the emptiness of space,
and as the science of physics long remained based on Aristotelian views, nature
was attributed a "horror" with regard to emptiness, which found it's expression in
the famous latin formula: "horror vacui". Only with the detection of atmospheric
pressure by Galilei's disciple Torricelli (1608-1647) did the conception of empty
Space gain validity and was the Aristotelian notion dethroned. Other phenomena,
however, like the propagation of light by waves, point to the non-emptiness of
space as conceived by Aristotle and led to the interpretation of space being filled
with an omni-present "ether". We will be dealing with these physical aspects of
space more extensively at a later point of our exposition.
Finally, the Greek term oudén (latin: nihil) denotes "no thing". Understood in an
absolute, logical sense, this term denotes the total negation of being. Oudén, "no
thing" or "nothing" equates "vacuum" in Parmenides' philosophy. According to
Parmenides, being "is", whereas not-being "is not". Being "is" and corresponds
with Pleón, the complete filling of space; whereas not-being "is not" and
corresponds with to kenón, vacuum, empty space. Oudén, not-being, which
equates vacuum, simply cannot "be". This is the reasoning of Parmenides with
regard to oudén, empty space. Later, we will get back to Parmenides and his
conception of filled Space, Pleón. Oudén for thinkers like Plato and Plotin simply
denotes matter, as not being "true".
2. Excursion: Space, Light, Don Albert and "The Blank".
In a first approximation towards the cosmovision of Don Albert (there certainly is
much much more to it than the analogy we will establish within this context
towards Greek mythology and philosophy), and with regard to the investigation of
"what was before all other things", Don Albert, just like Hesiod, pictures an
"original state of the world". In his mind, Don Albert tries to "get rid of matter",
and so encounters "darkness". When trying to "get rid of darkness", he encounters
"the Blank" - the physical equivalence to what he has been elaborating in his
mathematics. Finally trying to "get rid of the Blank", Don Albert encounters
"Directions", the very constituent parts and components of a doublefold "entity":
Space and Light. "Directions" in this surprising cosmovision equally constitute the
components of Space as well as the constituent parts of Light Photons. So, in this
unconventional Science and Philosophy of Don Albert's we find, that, "in the
beginning" there were the components of Space and Light, which philosophically
coincides with many an original cosmovision of early(Greek) mythology and
Don Albert's "Blank", being conceived as the origin of the universe, gives birth to
two simultaneously different and yet complementary States of Origin: A positive
State of Origin, where energy is being formed, leading to the composition of the
Quasi-Stellar-Sources, and a negative State of Origin, where the negative Space of
the blackholes is being formed, which are, according to Don Albert, light
disassociating into it's basic forms!
So we find, that the positive State of Origin is one of composition, and the negative
State of Origin is one of decomposition or disassociation, being these two states of
origin complementary and unable to exist the one without the other. (We are
convinced, that, if the proof was to be made with the help of the observation of the
star fields near a black hole, Don Albert would be proven correct in his
assumption, that stars tend to drift away from the black hole, as it is not a
"gravitational collapse", but disassociating light, according to the very logic of his
theory of the origin of the universe.)
We have here a surprising analogy between Don Albert's scientific-philosophical,
astrophysical cosmovision, and early (Greek)mythology and philosophy, with the
decisive difference, however, that Don Albert's cosmovision does not deteriorate
into a dualistic, either-or state of Formal Logics, but constitutes a complementary
vision of simultaneous, different, equally valid states of a different kind of Logic.
Don Albert speaks: "The Ubiquitious Blank".
As to the origin of the universe, and the basic condition for something to be or to
come into existence, we will let Don Albert speak for himself.
The Blank within the range of Knowledge and Limitation:
"In 1960, I was thinking, and I got rid of all possible matter. I turned it into energy
- mentally, then I got rid of all energy - light -, and I had nothing but darkness!
Then, I got rid of darkness - I found I could, I could conceive of this - and then, I
had Blank. I tried to get rid of the Blank, and I couldn't, no matter what I did. And
years later,as I became more familiar with the subject, I recognized, that I am a
product of this creation, and as a product of it I cannot conceive of something
which is a priori to the existence of the Blank. In other words, there is a limitation
that man faces. � Our physical existence, our mental existence, our spiritual
existence seem to be limited to this existence, this creation, and not to something
before it. There are, in fact, limitations in this universe, in this existence, in this
creation. I don't care how you want to say it, but limitations do exist."
The Blank as the Bringing Forth of Directions and their many Appearances:
"So, I get back to the Blank. Now, I recognized from that, that the Blank is less
than darkness, is less than zero. � Now, I watched the Blank for a while � and
marvelled at it. � Suddenly I realized (that) what's being created here are
Directions. � So I recognized, that right angle or 90 degrees not only does .. exist
in almost everything in this universe,
I recognized, that it seems to constitute some basic principle in origin itself, in the
existence of this universe, it's construction."
Formed Directions constitute the Nature of Light:
"Now I've got a pyramid. � This little pyramid made of directions � you will
find, that this pyramid actually tumbles in such a manner, that it describes a
sinus-wave, in other words, this little crystal made of directions is what we call a
Photon of Light. And it's path is that, which we call a Wave of Light, in other
words: We have the particle- and the ondulatory nature of light, and this is it's
origin: Light is made of directions, organized, formed."
(All quotes are taken from the Video: "Don Albert's Brain Trust", Volume I;
Executive Producer: Vic Campbell)
In a preliminary conclusion, we find, that in Don Albert's cosmovision,
"Directions" constitute the basic components and therefore the conditio sine qua
non of Light and Space, of Energy and "Non-Energy" (which is not equivalent to
More on this at a later point of this series of articles. - In the second part to come
of our "Reflections on the Concept of Space", we will be dealing with the
philosophical concept of Space, as conceived by both the materialist and idealist
philosophers of Ancient Greece, and the implications of the philosophical
conception for the classical,physical and also mathematical notion of Space.
Five Epistemological Problems concerning the Philosophical Conception of Space.
By Jutta Schmitt
In the first part of our exposition "Reflections on the Concept of Space", we gave a short introduction into the Context of our own philosophy and some of it's methodological parameters, undertook an approximation towards a "general definition" of the concept of Space, took a glance at the Greek, mythological-philosophical origins of the concept and showed a surprising analogy between ancient Greek, mythological philosophic notions of Space and the concept of Space as conceived in Don Albert's modern, unconventional Science and Philosophy of the Third Millennium.
In this second part of our exposition, and before going into the specific philosophical definitions of Space as exposed by distinguished representatives of the materialistic and idealistic schools of thought in Ancient Greece, we will have to get acquainted with five epistemological problems concerning the philosophical conception of Space.
II. Specific Definitions
1. The Philosophical Concept of Space
1.1. Five epistemological problems with regard to the philosophical conception of Space.
Let us briefly indicate the basic epistemological, methodological and logical problems concerning the philosophical notion of Space, which, within the Western-European philosophical tradition, has been close to the physical-mathematical notion of Space. In the further course of our elaborations, we will take reference to these problems and to how they have been solved, respectively.
1. The first problem concerns the objectivity / the subjectivity of Space: Is space an objectively existent reality, independent from human recognition, as exposed by the respective materialist cosmovisions in philosophy? Or does Space exist as a subjective concept of the human intellect, a product of the human mind, as exposed by the idealist cosmovisions in philosophy? Can we go further than the traditional philosophical conceptions, and understand Space as both, an objectively existent reality and a subjective concept of the human intellect? If so, how do objectivity and subjectivity relate to each other? Can we even go beyond this, and conceive Space as "transcensive", that is, neither objective nor subjective? If so, how does "transcendence" relate to objectivity and subjectivity?
Problem number one expresses the ultimate, fundamental question of philosophy, if and how subjective thought is related to objective reality. The different philosophical answers that have been given to this question determine the respectively different philosophical schools, ranging from materialism to idealism to agnosticism. Yet, the validity of this question is not at all limited to philosophy in the narrow sense of the term, but directly touches the whole realm of physics and the way how to deal with physical reality in all it's aspects, as for example can be seen in quantum physics, where the Copenhagen School of quantum physics gave an agnosticistic interpretation of the wave-particle duality, which definitely is not the only valid interpretation of sub-atomic reality (see my article on quantum physics posted on this Forum - J.S.).
2. The second problem concerns the rest / the motion of Space: Is Space "Space-at-Rest"? What do we understand by Space-at-Rest? Or is Space "Space-in-Motion"? What do we understand by Space-in-Motion? Is Space both, at-rest and in-motion? If so, how are "at-rest" and "in-motion" related? Is Space relational", that is, neither at-rest nor in-motion? If so, how does "relation" relate to rest and motion?
3. The third problem concerns the vacuum / the plenum of Space: Is Space a vacuum? What do we understand by "empty" Space? Or is Space a plenum? What do we understand by "filled" Space? Is Space both, a vacuum and a plenum? If so, how do vacuum and plenum relate to each other? Is Space an "oscillatum", that is, neither vacuum nor plenum? If so, how does "oscillatum" relate to vacuum and plenum?
We have already seen within the context of the mythological-philosophical origins of the concept of Space, specifically with regard to the terms "tó kenón" and "oudén", that there are two philosophical streams of Greek thought concerning problems 2 and 3: One of them, the Atomists (Leucippus, Democritus, Epicurus), associated Space with vacuum and motion. They considered vacuum the conditio sine qua non for the smallest particles of matter, the atoms, to be able to move; whereas the other school of thought, the Eleatics (Xenophanes, Parmenides, Zenon), associated Space with plenum and rest, and denied any possible motion.
Interestingly, tó kenón, "Space without matter", that is, the Greek-Atomistic conception of Space as a vacuum, has found a theoretical enhancement in the discussion of modern physics, specifically in the field of electromagnetics, as proposed by Col. T.E. Bearden (http://www.cheniere.org).In his 1984 paper on Electromagnetic Theory, with regard to the clear distinction between charged mass and charge itself, Bearden points out, that what is presently referred to as "vacuum" in physics, is precisely the "absence of mass" (translated into Greek terms: tó kenón, space without matter), or "massless charge", also "anenergy" (we would say: the complementary counterpart of energy). Moreover he states, that "vacuum has no mass, but it has great massless charge and virtual particle charge flux", which implies, that "a charged vacuum is the seat of something in motion". Thus and according to the new electromagnetic theory as exposed by Bearden in his 1984 paper, Space, vacuum and motion are interrelated moments of the same "thing" (that is, anenergy), just like has stunningly been sort of anticipated and dealt with by the early Greek Atomist philosophers in 500 B.C.
Of course, we still will have to investigate though, in how far also the Eleatics' association of Space with plenum and rest, have found a theoretical enhancement in the discussion of modern physics.
4. The fourth problem concerns the finiteness / the infinity of Space: Is Space limited? What do we understand by "limited"? Or is Space unlimited? What do we understand by "unlimited"? Is Space both, limited and unlimited? If so, how do finiteness and infinity relate to each other? Is Space "transfinite", that is, neither finite nor infinite? If so, how does "transfinity" relate to finity and infinity? (- Related problems in the realm of physics are the discretion / the continuum of Space.)
Problem number four will have a heavy weight in all three, the philosophical, physical and mathematical notions of Space. The problem arises philosophically in the form of Anaximander's "apeiron" (the greek term "peras" denotes limit), that, what has no limit (a-peiron), also that, what has no shape. We also will see, that, interestingly, Pythagoras implicitly operates with the same conception of Anaximander's apeiron, so as to underline his concept of number, of "arithmos", which denotes that, what limits, what gives shape. In a way, Pythagoras' "arithmos" can be conceived as a discrete, discontinuous quantity, which limits the continuous unlimited. Here, we will see an early relation of "the unlimited", also "the continuous", towards the limited, the discrete; being the unlimited the basic condition for that, what limits, what gives shape, for "the discrete".
5. The fifth problem concerns the unity / the diversity of Space: is Space unified ("universe")? What do we understand by "unified" (universe)? Or is Space diverse? What do we understand by "diverse"? Is Space both, unified (universe) and diverse? If so, what is the relation between unified (universe) and diverse? Is Space "triverse", that is, neither unified (universe) nor diverse? If so, how does triversity relate to unity ("university") and diversity? (- Related problems in the realm of physics are the indivisibility / divisibility of Space.)
Once again, we will have to take a look at the Greek Atomists as well as the Eleatics as far as problem number five is concerned. Space as associated by the Atomists not only with vacuum and motion, but with divisibility and diversity, contrasts the Eleatics' association of Space with plenum, rest, indivisibility and unity. -
In the following part of our Reflections on the Concept of Space, we will deal in detail with the distinguished representatives of the afore-mentioned, ancient Greek philosophic tendencies, the Atomists and the Eleatics.
(TO BE CONTINUED)