Abstract

The term pattern has recently gained prominence as key term in understanding mankind's quest to make the universe intelligible, to fashion a Cosmos from the pure Chaos of the undiscriminate swarm of photons, electrons, air pressure changes, chemical and physical stimulants, that organisms are exposed to every instant of their living existence. On pattern are based not only the sciences, but also human society, and in the wider sense, life, and the lawfulness of the universe. The present contribution connects Gregory Bateson's work as a recent trailblazer in the recognition of the role of pattern with Goethe's earlier work on Morphology and Metamorphosis. It links this to current scientific understanding of the working of the brain, as neuronal activation patterns, consisting of oscillation fields and logical relation structures of neuronal assemblies, treated formally as coupled dynamic systems and neuronal attractors, which are characterized by their space-time-dynamics. These are called neuronal resonance patterns, and patterns of patterns: metapatterns. Thus, pattern is the "infrastructure" of neuronal processing happening in our brains, below, and a few miliseconds before our working consciousness experiences the "phainomena" and "noumena", of our discernible impressions and thoughts. This spatio-temporal neuronal infrastructure is then re-interpreted in a Neo-Pythagorean way, as the "inner music of the brain", which supports a new validation for the old Pythagorean world views.

Der Begriff "Pattern" (Muster) hat in der letzten Zeit an Bedeutung gewonnen, als Schlüsselbegriff des Verständnisses des Universums, der Weise, in der das Verstehen einen Kosmos schafft, aus dem reinen Chaos der unterschiedslos auf alle Lebewesen hereinströmenden Photonen, Elektronen, Luftdruck-Schwankungen, chemischen und physischen Stimulantien, in jeder Sekunde des Lebens auf diesem Planeten. "Pattern" ist der Grundbegriff, auf dem nicht nur die Wissenschaften, sondern auch die menschliche Gesellschaft, und im weiteren Sinne, das Leben und die Ordnung des Universums beruhen. Der vorliegende Beitrag verbindet die Arbeit Gregory Batesons mit Goethes früherer Arbeit zur Morphologie und der Metamorphose. Dies wird mit der heutigen wissenschaftlichen Erkenntnis der Arbeitsweise des Gehirns verbunden, als Neuronale Aktivationsmuster, bestehend aus Oszillationsfeldern und logischen Relations-Strukturen von Neuronalen Assemblies, die formal als gekoppelte dynamische Systeme und Neuronale Attraktoren behandelt werden, und deren Funktion durch ihre Raum-Zeit-Dynamik bestimmt ist. Diese werden Neuronale Resonanz-Muster genannt, und Muster von Mustern: Metapatterns. Damit ist Pattern auch die "Infrastruktur" der neuronalen Prozesse in unseren Gehirnen, unterhalb, und einige Millisekunden bevor sie in unserem Normalbewußtsein als Phänomene und Noumena (Denk-Dinge) erscheinen. Diese spatio-temporale neuronale Infrastruktur wird in einem Neo-Pythagoräischen Sinn interpretiert, als die "Innere Musik des Gehirns", die damit auf eine neue Bestätigung der alten Pythagoräischen Denkweisen hinweist.

"The Definition of a Net: Anything made with interstitial vacuities."

Dr. Samuel Johnson

The term pattern has recently gained prominence as key term in understanding mankind's quest to make the universe intelligible, to fashion a Cosmos from the pure Chaos of the undiscriminate swarm of photons, electrons, air pressure changes, chemical and physical stimulants, that organisms are exposed to every instant of their living existence. On this facility are based not only the sciences, but also human society, and in the wider sense, life, and the lawfulness of the universe. (Goppold (1999d); Schunk (1996); Spengler: Morphologie der Wissenschaften (1980: 548-553)). Gregory Bateson's work (1972-1986) is to be considered as trailblazer in this development, even though he is not often acknowledged for his accomplishment, still being considered as some kind of a maverick in the more fashionable positivist, realist, reductionist, and materialist, scientific circles.

When introducing his famous paradigmatic statement: "a pattern that connects", Bateson refers to Goethe as source of inspiration (1979: 17, 18). In Goethe's terms, his quest for "the patterns that connect" is called Morphology and Metamorphosis. Widely known workers who have employed (some version or derivation of) Goethe's concept in the cultural area were Frobenius (Haberland 1973), and Spengler (1980), and through a detour over Franz Boas, the American Anthropologist Ruth Benedict, in her famous work: "patterns of culture" (1934). Her work had in turn influenced Bateson, via the other famous woman disciple of Boas: Margret Mead, who was Bateson's wife at that time. (Bateson 1979: 211-212). The Goethean type of morphology (there are slightly different versions in many sciences) might be called the Gestalt tradition of morphology. Its earlier traces go back to Herder and Vico. (Straube 1990: 168), (Herder 1975: XVI-XVII), Berg (1990: 61). Severi's (1993: 309, 311-315) description sums up the essentially holistic and dynamic character of Goethe's conception of morphology.

Goethe's emphasis on the permanent change of all forms, the metamorphosis, has given occasion for the subtitle of this paper, a slight paraphrasis of Nietzsche's central tenet: "The Infinite Return of the Eternally Unequal" (originally: "the infinite return of the eternally-equal"). In a more down-to-earth tone, Riedl (1995, 1996c) describes the obligation of modern biology to Goethe's work:

Stafford Beer describes the essentially observer-dependent character of pattern:

In his work "Impossibility", John Barrow points out the universal importance of pattern perception and generation as the foundation of mathematics, which he describes as the base of the modern exact sciences. (Barrow 1998: 5-6, 57-58, 89, 190-193):

A definition of mathematics is quoted by (Allot (www)):

More support for the general principle of pattern (or paradigm, according to Kuhn 1962) can be found in present neuronal research of cognition, also called Neuro-Aesthetics, and Neuro-Semiotics. (Brock (1994), Breidbach (1993-1997)). According to this recent work, cognitive orientation and action of innervated organisms is effected by neuronal activation patterns, consisting of oscillation fields and logical relation structures of neuronal assemblies, treated formally as coupled dynamic systems and neuronal attractors. These are specifically characterized by their space-time-dynamics. In the present context, these phenomena are also called neuronal resonance patterns, and as higher-order hierarchical aggregates, patterns of patterns: metapatterns. (Volk 1995). Thus, pattern is the "infrastructure" of neuronal processing happening in our brains, below, and a few miliseconds before our working consciousness experiences the "phainomena" and "noumena", the Gestalten of discernible impressions and thoughts. (Goppold (1999d); Klages (1981, I: 57-60)).

While the recent excitement over this new scientific approach to a truly universal theory of everything (consisting of patterns) may sound very impressive, for music theorists, it sounds like "nothing new under the sun" and reminds rather of the prototypical nouveau-riche parvenu "bourgeois gentilhomme" of Molierè's comedy, who is over-excited when discovering that he constantly speaks prose (patterns). For the pattern approach as a theory of everything has been known to the music community for at least 3000 years, and most probably much longer. In the ancient cultures of the Western oikumene, it was known by the name of Pythagoreanism. The deep history connected with Pythagoreanism is described by Hertha v. Dechend in "Hamlet's Mill" and her other works (1977-xxxx). According to her, this history reaches back into the farthest and remotest antiquity of humanity, at least 10,000 years. Typical for the attitude of the (populistic writers of) modern natural sciences, Barrow's statements about Pythagoreanism are derogatory: There is only a passing remark under "crank science", where he writes off "the ancient Pythagorean sect who mingled mathematics with mysticism... Thus, musical harmony was linked to the motions of the heavenly bodies." (1998: p. 3).

To Barrow's excuse, it needs to be noted that there is so much nonsense that has been written about Pythagoreanism by people who had no idea about what it meant, that under all this fog, it is easy to confuse the fakes, with what might have been the core of this archaic knowledge system. The fog probably started rising quickly and thickly right at the beginning, with the very first records, or rather fables, around the alleged life and work of Pythagoras, which are related to us by Iamblichos (Bloom www). The WWW is a rich ressource for materials on Pythagoreanism, the usual "nugget of gold" intermingled with tons of dross, modern mythologies, which are busily fabricated today as much as in antiquity (Pyta-www). Obviously, those traces, remnants, and rumors, called "Pythagorean", must appear as mystical and crank compared with the immense exactness, elaboration, sophistication, and social entrenchment of mathematics, and so Barrow may be excused to want to keep his popular science work clear of such uncertain material. The present paper cannot make any better claim to "true authority" over Pythagoreanism than maybe hundreds of other more or less scholarly works, of which a few shall be listed: (Behrendt (1992); Bloom (www); Godwin (1989); Haase (1998); James (1993); Kayser (1930-1950); Kepler (1982); McClain (1978); Platon , Timaios (1988); Rouget (1985: 187-226); Rudhyar (1988); Schneider (1951-1990); Stege (1925); Thimus (1868-1876); Timaios Locris (1779)).

In the present context, this term will be used not as historical identifier for an alleged musico-mystic school located in the ancient oikumene, founded by one individual named "Pythagoras" in Kroton in Greek Italy, but as a generic name for a certain way of pattern perception and organization that concentrates on the cognitive aspects of music as "structure in time", as opposed to its purely aesthetic and psychological effects. In the Kuhnian (1962) sense, the term "Pythagorean" stands for a paradigm of understanding ourselves and our place in the cosmos. This is of course a very different outlook (actually not an out-look at all), than the currently dominating positivistic, objectivistic, natural scientific one. By this the name "Pythagorean" can be used as a loosely-fitting envelope for a thought system that has probably quite independently been pursued on all continents, among most ancient peoples, like Africa, Asia, Australia, China, Egypt, India, Mesopotamia, and Meso-America. (Dechend (1977-xxxx); Granet (1994); McClain (1978); Rudhyar (1988); Schneider (1951-1990); Strehlow (1947-1996)). Thus we are relived of the burden to ascertain whether any such person by the name of Pythagoras had ever lived, and what he teached. One source for example derives the name Pythagoras from the Indian Pitar Guru (Father Guru).

See: http://www.aros.net/~eriugena/essyht~1 (URL)

There is a certain boisterous tendency of ancient Greek "his"-story-telling to take into ccount, in that they tended to "re-christen" (christos: well oiled, greased) material from ancient traditions of other civilizations that they came in contact with, under a name of their own people, and declare that this was the one who discovered or invented it. The historical fallacy is nowhere as apparent as with Pythagoras himself since the famous theorem that is attributed to him was known to the Egyptians probably since millennia, before some Greek mercenary or merchant venturer (probably of the Naukratis colony) stumbled upon it and made it known to his (still somewhat unsophisticated) fellow country-people. We are the unsuspecting heirs to a lot more of such Greek fables. (Not only the Kretans, but likely most of those wheeling and dealing, peddling and battling, Greeks, of antiquity, were prolific yarn-spinners).

Music can be understood in generic manner as an art form consisting of the generation and reception of temporal audible and dynamic patterns. In our Western cultures, music is primarily cultivated for its aesthetic and psychological effects. "Music is essentially a play upon feeling with feeling." (Seashore 1967: 9). But there are also important cognitive aspects of music since its patterns form systems of "structures in time". Music is geared like no other elaborated system in wide usage towards generation and representation of dynamic patterns, a task that the conceptual modes of speaking and writing are particularly bad at. (Radwan 1999). Although mathematics has developed elaborate formalisms for dealing with motion (the calculus) and gravitational fields (tensor math), it is a static notation system depending on a kind of writing, and its usage is clumsy for describing any dynamics of comparable complexity as appears in music. For these reasons, a few considerations will be given to the possibility of a re-appraisal of music in a Neo-Pythagorean scheme, trying to recover, or to reconstruct, the modes of thinking of the old Pythagorean schools, without falling into their traps.

Another cogent reason to revive the Neo-Pythagorean legacy comes from our understanding of the working of the neuronal system (above). Since by the present scientific tenets, all our mental perceptions, actions, and creations can and must be mapped to neuronal action in the brain, this is becoming a paradigm that all of science will be forced to reckon with. Barrow's (1998: 96) characterization gives the evidence : "a three-pound mass of matter that ... can conceive of a universe a hundred billion light years across." Everything we perceive through our senses (the afferent system), gets translated into neuronal pulse patterns in the immensely complicated webwork of synaptic connections in the brain. The working of the brain is an immensely complicated system of frequencies and connections onto which all the phenomena of the perceived world are mapped and processed. This might give a start to some Neo-Pythagorean considerations. Music is a system of patterns in time, and as Barrow above points out, the ability to perceive and produce patterns is fundamental to our understanding of the world and ourselves. The frequency pattern distributions of neuronal action in the brain are a kind of "music" going on in each of our heads, and this "neuron-spike music", is what forms all our conceptions of the universe. In this, we can rightly speak of a "cosmic music" in the Neo-Pythagorean sense, quite different from what the old Pythagoreans thought, but still, based on the same principles: harmonics, resonances, and rhythms as the base stuff out of which the (phenomenal) universe is woven. The ancient Pythagoreans could not conceive of a neuronal system that performs this "music" and so it appeared as a projection onto the material cosmos, while it has been going on in our brains all the time. We do not need to worry very much about the seemingly mystical flavor of the old views: Pythagoreanism is a paradigm based on form (or pattern) and not on content, (Bateson 1972: 449), and whoever lets himself get trapped by the content of any version, just hasn't understood Pythagoreanism.

In Western scientific cultures, mathematics has taken the main place of a universal substructure system to systematically interrelate the phenomena of the perceived world. This is evidenced with the above quotation from John Barrow's work. Barrow's description might be taken as a typical example for many other works forming a system of apologetics of the present entrenchment of mathematics as the only general structural system that modern societies are dependent upon for better or worse. Such apologetics follow roughly the same pattern of implicit ethnocentrism as do the apologetics of alphabetical writing: that the western mathematical and writing systems necessarily form the apex of an evolutionary progression, and that there exist no equivalent alternative models, and that all prior attempts and alternatives are to be classed as mystical, primitive, retarded, half-way solutions, etc. This ethno dominance complex has been exposed by writers like Boone (1994), and Bednarik (1994) for the writing systems, and Dieter Straub (1990) has taken up the tack for a fundamental criticism of mathematics as a system of ethno-dominance. The crucial problem for giving counter-examples to the alleged necessity of societal domination of alphabetical writing, and Western mathematics is the immense weight and sophistication of those entrenched systems. With literally millions of person-years of cumulative work investment behind them, it might seem like a hopeless case to show that alternative systems might give better societal results than the presently used ones. Prime example for such uselessness are the hundreds of attempts to create new writing and language systems which all ended up in cultural cul-de-sacs. See: Eco (1993).

The only possible situation that would justify such an approach is if it can be shown that the entrenched systems form a cultural cul-de-sac themselves, and that the societal conditions have changed to a sufficient degree that other, hitherto non-available or non-practical alternatives had obtained a new significance. To show that this is indeed the case, or will be within the next 50 or 100 years, is the aim of this presentation. The case of writing is being treated in other works (Goppold 1999d). The reason why musical metaphors appear as a promising approach to new alternative general structure systems is the abovementioned increase in neurological knowledge. There is a direct correspondence between the outer music we can hear and the inner, inaudible music of our neurons. This correspondence consists in an immense neuronal computing facility that we unconsciously employ when we hear patterned sounds, especially music, and every trained musician has honed this facility to the utmost. Mathematics is, compared to this, an incredibly circuitous way of constructing a structural relation and transformation system that must go from the visual to the verbal, to the structural domain, and back. How nonsensical the mathematical system is, can be appreciated if we were to rename all the musical terms like second, quart, fitth, octave, etc. by the names of composers, and each novice musician were forced to learn the ropes of his profession in this way: Here we have a Beethoven scale, there is a Mozart transpose, this is a Bruckner beat, and you should play this piece in Lisztissimo, ma non Bacho. There are quite revealing anthropological observations to be made, of the "totems and taboos of the natives of the Western white races" (Popper 1962). This cognitive load of such nonsensical associations serves primarily as a European scientific version of the time honored ancestor cult of tribal legacy, since mathematics texts virtually read like mathematicians' graveyard registers, and the mathematics training must be considered as a particularly brutal initiation ritual designed to mercilessly weed out those people who can't cope with such nonsense. And so, only a few people in a thousand make it through the training necessary for quantum or relativity physics. By this, this knowledge has become as arcane and as restricted to "inner circles" as the higher initiation levels of earlier theocratic hierarchies and power structures, with similar results. As Straub shows, the inner circles of mathematics initiates of theoretical physics enjoys a totally unchecked and self-serving power influence over increasingly vital sectors of our societies. (Straub 1990: p. 7, 11, 12, 15, 16-18, 42-44, 46, 50-51, 52-56, 78-79, 209-211, 226-238).

One of the most respected and accomplished workers pursuing the Pythagorean paradigm was Johannes Kepler . In his "Harmonice Mundi" (1619) he had proved a harmonic relationship of the planetary orbits. (Haase 1989: 111-130). Kepler cannot be lightly accused of having been a "crank scientist". As opposed to other, more mystical proponents, like Athanasius Kircher, and Robert Fludd, Kepler based his work on rigorous scientific discipline. His scientific work is rightly remembered as pioneering achievement. The correctness of his planetary calculations has been confirmed by Francis Warrain in 1942 (Haase 1989: 120-121). His breakthrough achievement is that he dared to think against a societal consensus that had held the conceptions of earlier scientists in firm thrall: that the orbits of the planets must, by reason of symmetry, be circular, a creed which Copernicus, and even Galileo, had still firmly adhered to. (Haase 1989: 119). He established that their orbits were elliptical, and he managed to incorporate this complication into his harmonic schema. This was a hidden agenda of much greater significance than the smoke-screen battle for which Galileo had been stylized as the scientific martyr-hero of that epoch: his alleged resistance against the Ptolemaic church dogma of geocentrism ("and yet she moves"). The issues that the church authorities were getting "uptight" about, lay elsewhere. (Redondi (1991); Lippe (1997)). In this context it might be well worth to remember the famous phrase of Archimedes: "Noli turbare circulos meos." This should be interpreted as expression of the fundamental tenet of all astronomy from 300 B.C. up to Kepler: That for (divine) symmetry reasons, the planetary orbits had better conform to circularity. This fundamental tenet of a deeply valued conviction for which one would even die a martyr's death would be a much more suitable explanation for his statement than the myth of protecting his circular drawings when he was put to death by an intruding Roman legionary. The dogma of symmetry was much more tenacious than that of religion. Kepler was the last Pythagorean worker who had an equally solid footing in all the relevant fields: Astronomy, Mathematics (Geometry), and Music. After him, a line of Harmonics workers attempted to pursue the work: Albert v. Thimus, Hans Kayser, and Rudolf Haase, but these could not merge the by now different sciences any more the way Kepler had done. After Kepler, the scientific world changed its focus, and Haase sums up the contrast between Kepler's approach and that of modern sciences: "Thus Kepler's harmonic worldview differs markedly from that of the natural sciences which is characterized above all by causal thinking, a quantitative perception of the world, and a functionalistic procedure with mathematics at its core. Perhaps this harmonic worldview can provide the much-needed complement to the scientific one, long recognized as one-sided." (Haase 1989: p. 125)

The rising feeling of discontent with certain side-effcts of the application of science, in its fundamental role in the global techno-capitalist complex, is one aspect why one might want to resuscitate the old Pythagorean legacy. But returning to old mythologies by itself is of no great use if the momentum of societal technological development goes in a different direction. It is therefore instructive to get an understanding of Kepler's work, but not what he did, but how he proceeded (form over content). He refused the path of the believer, who stuck to the (supposedly) ancient scriptures, and interpreted them to their heart's content, heaping only nonsense on misunderstanding, but he applied a very stringent style of reasoning, to the most recent and sophisticated technological and scientific material avaliable in his day. And being a renowned expert in all the relevant fields, he was able to unify this scientific knowledge in one point of perspective. For us today, the question is of minor interest, if the creator God had arranged the planets in such a way as to produce the most pleasant and elaborate harmonies, if they could be made audible. The current scientific mainstream rests on the paradigm of evolution which makes the question of the ideas of a creator God a moot one.

We return to the initial quote by Samuel Johnson, definition of a net: Anything made with interstitial vacuities. Nietzsche takes up the theme in: "Der Wanderer und sein Schatten", 11:

Klages (1981, III: 512) gives us the solution: The different meanings of the ancient Greek words metron and rhythmos express a dialectics of perception: It is as if we view the world through a fence: With the metron, we are fixated on the fence posts and bars, with rhythmos, we are more concerned with the interstices. Music is a pattern of interstitial silences. Thus, music gives us a way of perceiving the patterns of the world in an entirely different manner, than science forces us to: We are not bound to the substantiality of matter, but can focus our attention on the spaces between the fence posts. Come to where the freedom is.

Mahler

The great achievement of western music, the emulation of writing through musical notation and uniform tuning systems, is also its greatest problem, since notations are systems of constancy, uniformity, and metrics, and thus tend to freeze the essential dynamics, the prime raison d'etre, of music. (Celibidache 1992). Thus, the non-written traditions of music, like ethnomusic, Free Jazz, and Indian Raga, preserve best the dynamic core of the music tradition of humanity. A Raga forms a musical environment (context, con-tempus), that is carefully fit "in tune" with the cosmic rhythms (each Raga has its specific time), and "tuned in" with the moods of the audience in a very long procedure, before it proceeds into the formal part. And only through and after this careful tuning procedure, is then the sound and rhythm value of each single elementary piece played by the instruments, determined. We could also say that this unfolds a time structure, which is, in the Indian tradition, carefully integrated into the cosmic time panorama, in which each performance makes an essential contribution towards reinforcing and rejuvenating the cosmic pattern. (Rudhyar 1988). This is totally opposed to the metric tuning system of western music. Electronically reproduced music carries this even further, because it is totally de-contemporalized.

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Dr. Andreas Goppold

http://www.noologie.de/ (URL)

http://www.bib.uni-wuppertal.de/elpub/fb05/diss1999/goppold/ (URL)

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