§54. HARMONIC COSMOGONY
§54.1. Preliminary Note
The reader who has followed the investigations in this book closely up to this point, thought over their content, and above all experienced them, will wish to see in this closing chapter a certain summation of what has been achieved thus far. Admittedly, only an attempt can be made at this, in which both reader and author will do well to retain that kind of reserve that is inevitably necessary in such attempts: the general caveat of the insufficiency of human endeavors at understanding. The apparent apodictic quality of the following conclusions should therefore be understood only in the sense of a formulation appearing as correct to the author at the time.
As an interpretation concept, we choose “cosmogony” and use as its basis the systematic embodiment of akróasis, the “P”. “Cosmogony” means the study of the emergence of worlds; a significant, indeed enormous, frightening term, if we grasp it in its full breadth and depth. We will see whether and how we can treat it fairly. The accusation of inappropriately introducing and modifying the word and concept of cosmogony (and cosmology), used commonly in earlier times, can be dealt with simply by a reference to the Kosmogonie of Christian Von Ehrenfels (Jena, Diederichs, 1916), the modern founder of gestalt research. Here the concept of cosmology was awakened once again in its original meaning, under which we also have taken it up, whereas for example the cosmogony of Kant and Laplace was marked by a purely astronomical and natural-scientific attitude.
Regarding the “P” partial-tone coordinates, the reader will have been persuaded by studying §53 that it does not represent a simple intellectual scheme, but instead that both its entire form and its “selections” contain forms in themselves, which are expressively, constructively, and creatively active in nature and in our psyche. These akróatic forms thus have a reality character that is not regulative or analogizing, but instead constitutive, and as such they are indicators for us of realities in the highest sense. But the same goes for this as for all “realities”: they have their own voice, their own language, and each new language needs not only to be learned but also to be understood in its innermost nature, regardless of the individual character of those who speak the language. At this point there will always be a source of misunderstanding with regard to interpretation, and therefore one would do well to accept these “sources of error” as inevitable, not least as regards the harmonic diagram.
In what follows, we will proceed in each case by first indicating the harmonic phenomenon—which can be done very briefly since it has mostly already been discussed—then draw the cosmogonic conclusion, add a commentary to it, and finally examine what history has to say to us about our conclusions. As in all our “ektypic” examples, the following can give only a small limited selection.
Our
analyses will use the 1/4 PE in its familiar
modifications, and will use the polar depiction of the “P” in only one case,
where it is shown to be appropriate. First of all, we use as a basis the 1/4
PE9 in the location and “variation” shown in Fig. 471:
here, the tone d is set as the
generator-tone. This is firstly to show how it also “works” with other tones—the
logarithms naturally remain the same, i.e. 1/1 also has
the log 0.000 here, 3/1 has log 1.585, etc.—and also
because in this case the signs 
and 
are symmetrical to d on both sides, as we already see from the circle of fifths:
|
...
as es b
f c g |
d |
a
e h fis
cis gis ... |
|
└──────────────┘ └──────────────────┘
└───────────────────────┘ |
||
In addition, most of the scales derived from 1/1 d have a C-major character (analogous to 1/1 c = B-major), so that in the choice of this generator-tone, the “Dorian” background becomes especially conspicuous.
Figure 471
§54.2. The Deity
Expression: 0/0
Psymbol: 
Definition: Embodiment. Everything. Eternal rest. “Eidos.” Unmanifest deity.
Commentary: We did not arrive at this highest of all harmonic concepts of the 0/0 deductively, setting it at the beginning of the “P”, but instead inductively, following the generator-tone line and the equal-tone lines back beyond 1/1. This is exceptionally important for harmonic deduction, because it is precisely through this induction that we are forcibly led to this concept; so here we believed ourselves to be justified in speaking of a “harmonic proof of God,” i.e. the factual existence of an ultimate spiritual reference-point. Admittedly, our statements about this concept can only cling to words, such as totality, everything, groundlessness, eternal rest, etc., which attempt to express something for which there is no adequate term in any language, and for which 0/0 is simply the most accurate symbol. Mathematically, 0/0 can be every number, thus the totality of all numbers; therefore it meets with our definition, which indeed includes not only numbers but all being-values. Since the doubled zero is not arbitrary as a quotient (0/0), but instead is forced upon us in the mathematical-symbolic sense, we will henceforth pay special attention to precisely this expression, and draw our conclusions from it.
History
In §25, we already indicated those concepts of God, or better, Deity, that are to be identified with the 0/0. They are the “impersonal” concepts of God, concepts of a totality of all beings, all substances, the “Brahma” of the Indians, the “Nirvana” of Buddhism, the “Tao” of the Chinese, the “Ensoph” of the Kabbalah, the “groundlessness” of Jakob Böhme, the “absolute being” of Hegel, and finally the “unknown God” of modern Europe.
Opinions are divided regarding the ancient Judaic concept of God. In any case, the precise translation of the beginning of the Bible reads: “In the beginning, Elohim newly created heaven and earth.” The words “In the beginning” (bereshith) would be better translated “in principle”; bara means not only “to create,” but also “to create anew,” and—this is especially interesting—“Elohim” is known to be a plural, thus corresponding to our harmonic symbol 0/0, which then created, or created anew, “heaven and earth,” i.e. the polar principles 1/∞ and ∞/1. This “new” creation, however, assumes worldly conditions already gone by, and is not a creation from the Nothing, but at least a creation from existing possibilities. The metamorphosis of the “Elohim” into the later “Jehovah” or “Yahweh” then corresponds to the step from the 0/0 to the 1/1.
In the esoteric Indian teachings of the Upanishads, it is said, with an astonishing degree of philosophical wisdom for those ancient times, that the primal condition of things, the primal-being, i.e. the Brahman in the later sense, was “na a sad, na u sad” = “not being, but yet also being” (Deussen: Allgemeine Geschichte der Philosophie, vol. I, 1894, part 2, p. 117). A direct description of our harmonic symbol 0/0 can be found in a stanza of the later Upanishad: “Two things are latently contained in the eternal, endless highest Brahma: knowledge and ignorance. Ignorance is fleeting, knowledge is eternal, yet he who ordains them as Lord is the Other.” (Deussen, ibid., p .120)
“Knowledge” and “ignorance,” however, are both merely synonyms for things that are finally inexpressible, indefinable. “The Being that is Brahman should not be understood as the kind of being that we know through experience, and is, as we have seen, much more a non-being in the empirical sense. The depictions of the Brahman as the perceiving subject in us are accompanied, as a rule, by the assurance that this perceiving subject, the ‘perceiver of perception’ will remain eternally unknowable in itself, and merely indicate that the Brahman is devoid of any objective being” (Deussen, ibid., p. 133). Friedrich Schlegel (Über die Sprache und Weisheit der Inder, Heidelberg 1808, p. 247 ff.) translates the following passage from the very ancient Laws of Manu:
“It is said:
Once all this was darkness, unknown, and unspecified,
Unrevealed, unknowable, as if completely sunken in sleep,
It was the blessed self-subsistent, discoverer of the undiscovered,
The beginning of being, that steadily grows, that powerfully destroys the night,
That which is never to be grasped through sense, invisible, ever-inconceivable,
Which meditating, wanting to create many beings from its own body,
First created water, then the light of the sun was engendered.
The sun was like a shining gold egg.
In it lived Brahma, lord of the universe, through his own power.
In the egg this deity then sat idly for a year,
Then he himself divided the egg in two by his thought,
From the blessed pieces he then created Earth and Heaven…”
Regarding the above lines, and many other obviously number-harmonic passages in ancient Indian wisdom, an admonition in the Upanishads (Ramap. 84) is very noteworthy: “Do not give the diagram to the common people!” (Deussen, ibid., pp. 13 and 68). One may well conclude that even then, the initiates taught their students by means of symbolic geometrical figures, in a similar way to the Pythagoreans.
The
Buddhist concept of “Nirvana” is outlined in the following manner in the Udana,
section 8,
The concept of the “Tao,” for which there is no adequate expression in European languages, was not invented by Lao Tzu, who presents himself often enough as merely a preserver of ancient traditions. In the investigation of the relationship between the 0/0 and the 1/1, we will delve more deeply into the origins of the highest concepts of ancient Chinese wisdom. In the treatise Das Geheimnis der goldenen Blüte (Munich 1929, p. 11, tr. R. Wilhelm, introduction by C.G. Jung), which is based on earlier traditions of Taoism, the beginning reads: “The Master Lu Tzu said: That which exists through itself is the Tao. The Tao has neither name nor form. It is the One Being, the One primal spirit.” In complete opposition to the non-speculative tendencies of Confucianism, predominantly directed towards the practical, a metaphysically oriented movement appeared within it. “A unique speculative life was awakened in this school in the 12th century through the great sage Chu Hsi (1129-1200), who wrote about every course of life and assigned a place in the system to everyone, thereby solidifying the Chinese world of thought for many centuries. He went considerably further than Confucius with the natural-philosophical observations in his Sing-li (= natural law), in which, schematizing and developing the metaphysical views of the Ching, he arrived at an impersonal primal being, which reveals itself as eternal order” (Brockhaus).
The highest Egyptian deity is Atum-Re. “I am Atum, who was alone in Nun (chaos); I am Re with his shining, as he began to rule what he had created,” reads the Book of the Dead (F. Roeder: Urkunden zur Religion der alten Ägypter, Jena 1915, p. 239), corresponding perfectly to 0/0 → 1/1 in harmonic symbolism. “I am Re, the lord of the light-rays” (ibid. p. 266)—we need only remember our concept of the “equal-tone lines” radiating out from the 0/0 in order to obtain an even closer harmonic parallel.
The Babylonian poem of the creation of the world begins with these lines:
“When the sky above was not yet named,
The earth below did not yet have a name,
When Apsu, the primal beginning, creator of all,
Mummu, Tiamat, the mother of all,
Blended into one with their waters,
When there was neither dry land nor marshland,
When of all the gods not a single one lived,
Nothing was known, no fate defined,
Then the gods were created in their midst;
Lachmu and Lachamu were called into being.”
(A. Ungnad: Die Religion der Babylonier und Assyrer, Jena 1921, p. 27.)
Here, as in almost all
Babylonian legends of the creation of the world, a kind of chaos is assumed, a
primal condition (= 0/0) from which the two principles of male and female emerge. Diodorus Siculus
(II, 30) writes: “The Chaldaeans claim that the world is in its nature eternal,
it has never had a beginning and can also never end; but through a divine
authority all is arranged and cultivated, and also all changes in the heavens
are neither effects of coincidence, nor inner laws (!), but instead a definite
and unchangeably valid decision of the gods”—or, as we would say harmonically:
the norms.
Kabbalistic speculation,
as it is concentrated in the Zohar,
says the following about the absolute primal origin, the “En-soph”: “Before the
ancient of the ancients, the hidden of hiddens [revealed itself], there was
neither beginning nor end ... in the Book of Secrets it is imparted: the
ancient of ancients, the hidden of hiddens, has a certain form and thus far [up
to a certain point] can be known. But it is once again unknowable, because it cannot
be sufficiently grasped [by our thoughts]. Thus it has a certain form, but does
not let itself be known [in its most innate Being], because it is the ancient
of ancients [= the absolute primal origin]” (Zohar III, 128a, Idra Rabba. From Erich Bischoff: Die Elemente der Kabbalah, vol. I,
Jacob Böhme (Sex Puncta Theosophica, I, 7) sets the “groundlessness” as the highest principle: “Thus, the first
will is a groundlessness, to be regarded as an eternal Nothing, and so we
perceive it just like a mirror in which one sees one’s own image, just like a
life, and yet it is not a life, but instead a figure of life and of the image
of life.” Here, also, we need only imagine ourselves as a tone-point, i.e. as a
being-value, and look to the 0/0 along the “direction” of the equal-tone line
(“mirror”), and then we have a precise harmonic correspondence. In more recent
philosophy, Böhme’s concept of “will” has been equated with that of modern
philosophy (Schopenhauer etc.), and taken as anticipated by Böhme. But Böhme’s
“eternal will” is not merely to be grasped voluntarily. Böhme writes (I, 13):
“So the mirror of the eternal eye appears in the will, and generates another
eternal basis of itself in itself: this is its center or heart, from which the
sight of eternity always arises, and through this the will becomes astir and
active, namely of that which generates the center.” Harmonically, we interpret
this passage thus: only when the “mirror of the eternal eye” 0/0 “generates another eternal basis of itself in
itself,” i.e. looks at itself, becomes conscious, which we can express with the
term 0 ↔ 0, only then does the will become “astir,” i.e. becomes our
modern active concept of will, and appears in the 1/1, i.e. in the first conceivable “vibration,”
the actual Being, the creator-word “Let it be” (= Fiat).
As a conclusion to this
historical excursion, we share yet another definition of the “nature of God”
from the Catholic Kirchliches Handlexikon
by M. Buchberger (article: “Gott”):
“God
is really and substantially different from the world and inexpressibly elevated
above all that is outside of Him and that can be thought (Vatic.). As the
self-existent and necessary Being, God stands so far above the world of created
and contingent being that He does not connect with it, even in the highest
sense. Through this, in contrast to pantheism and monism, every possibility of
mixing and combining with the substance of the world is excluded, as is every
relationship of substance to the worldly manifestation as though to modi and
accidents of the one Divinity. God cannot be ‘seen’ (1. Timothy 6:16), but only
perceived through the ‘intellect’ (Romans 1:20), he is ‘spirit’ (John 4:24), ‘one singular, completely simple and
unchanging spiritual substance’ (Vatic.), thus a personality above the world.”
How a “personality” should suddenly spring from this absolute transcendence
of the divine—that is precisely the problem that the “intellect” wishes to
investigate, and that is the path of our following steps in harmonic cosmology.
The reader interested in
the history of religion will easily find a far greater number of related
examples in ancient myths, religions, and scholarship; but merely from the few
things imparted here, he will share the author’s deep wonder and inner awe at
the remarkable convergences, all meeting together as if at a focal point in the
harmonic symbol 0/0.
§54.3. The Act of Creation
Expression: 1/1
Psymbol: 
Definition: The
unity. “Let it be!” (= Fiat). Origo. Revealed God. Demiurge. Birth of space and
time (wavelength and frequency). Uppermost being-value.
Commentary: We
obtained the symbol for the deity 0/0 a
posteriori, since the 0/0 concept gives us no possibility of hearing,
measuring, and building a system from things such as frequencies or string
lengths. It is different with the unity 1/1. Here we must always begin with a phenomenal
investigation, and initially a systematization. The question immediately
arises: what concrete relationship does 0/0 have to 1/1?
Here we must traverse
the two ways, the ̔οδόν κάτω
and the ̔οδόν ̔άνω (upwards and downwards). “Upwards” (i.e. retrospective), as we saw, necessarily
yields 0/0
from the results of the main “intentions” of the “P”, e.g. the generator-tone
line:
0/0
↑
1/1
2/2
3/3
:
n/n
:
∞/∞
In a certain sense, the
progress from 1/1 to 0/0
is psychophysically demanded and required. The case is completely different,
however, for the “downwards,” i.e. when we think cosmologically. Here 0/0 signifies the primal beginning, the highest
peak of the system of the world, and how should we imagine 1/1 emerging from this imaginary “groundlessness”?
It is indubitable that a monstrous chasm exists between these two symbols; if
it is bridged, then everything else follows legitimately and arises of itself.
Harmonically, we have two
possibilities of bridging this metaphysical hiatus. First we observe once again
that this double zero is necessarily yielded as a quotient from the
interpolation of the “P”. We can now imagine that the symbol 0/0 becomes conscious of itself, perceives a
“will” in itself, looks at itself, and this we can notate as above, thus:
0 ↔ 0
In this instant, the
“all,” i.e. the fundamentally inexpressible, transmutes into a metaphysical
polarity of two entities, and thereby pushes the unity 0/0 → 1/1 out of itself. This is the great act of the
deity becoming conscious of itself, and simultaneously the emergence of the
first “number,” i.e. vibration or wavelength (time or space), and of the first
“tone,” i.e. psychical value. But we can also imagine that the 0/0 symbol potentiates itself, likewise grasping a
will to become conscious of itself, to reveal itself, and we notate it as:
0°
Here, one zero-value is set
as a power of the other, and thus it thrusts the 1/1 out from itself, from its endless abundance (indeed,
speaking mathematically, 0/0 can also mean “all,” every number, just like
0°). Here there is doubtless a discrepancy between the mathematical and
harmonic interpretation.
0/0, just like 0°, has no definite meaning
mathematically, i.e. it can mean everything.
One can think of 0/0 as appearing from 01–1 = 0°, or
vice versa, but both symbols can mean every number according to the
mathematical interpretation. It is different in harmonics. In the symbol 0° we
see, at the least, a self-aspectation (0 ↔ 0) or self-potentiation of the
zero, and at this moment the quotient 0/0 becomes an entity of a different type, namely
something perceiving itself unitarily: i.e. as the unity itself. Harmonically,
the passage or emanation of the 1/1 from the 0/0 signifies a transformation in the sense of
becoming conscious of the self, a direction of the will, an expression out of
the unity of the actual, the real. We will see in the following that harmonics,
in contrast to mathematics, has definitions that are not possible in pure
mathematical terms, or that no longer make sense in mathematics, especially
regarding the symbols of zero and infinity (0 ∞). In the unity 1/1 we see the highest instance of all that is
factual and real, and thus the realization of the first being-value itself.
Through the birth of this first “generator-tone,” the unity-tone is also
attached to the unity 1/1, i.e. the material (number) is placed next to the psychical (tone), or joined
with it a priori, like body and soul.
Since this first being-value (1/1 + generator-tone) stems directly from the 0/0—as every being-value does in later evolution via
equal-tone lines—and is aspected and pervaded by the being of this ultimate
spiritual court of appeal, body, soul, and spirit are unified here in every
harmonic “field,” and typified in 1/1. The following section will explain why we use
the ancient Chinese inverse symbol as a Psymbol for the unity (and
later in Table 472 for the entire “world-axis”).
Since every being-value
“is” and “tones,” and this can only occur on the basis of the temporal-spatial
reciprocity of frequency and wavelength, time and space are also born with the
unity 1/1,
and therefore the framework for the factual existence of all being-values.
History
In §25a, we introduced
various examples from history regarding both the eidetic God-concept of the 0/0 and the Origo 1/1, and a few of the highest philosophical
system-concepts, which we broadened in the previous historical review with
regard to the Eidos. There we observed that between these two different
viewpoints, the Eidos (0/0) and the Origo (1/1), one can perform a certain classification of these highest concepts, and subsequently
of the various religions and wisdom-teachings, which can also be important for
the inner characteristics of the studies in question. Here we want to take the
reverse path and allow ourselves a possible overview, admittedly also very
limited, of whether religious studies and philosophical or cosmological systems
exist that combine the two elements, Eidos and Origo. As a result, we can say
here, without being able to prove it due to the restricted space, that although
there are doctrines which in their collective character outspokenly tend toward
one pole or another (0/0 or 1/1),
both elements are found in almost all of them, albeit in more or less strong
“potency.”
This time we shall begin
with the Christian concept of the “personal” God, whose origin is in the Judaic
concept of Yahweh, and who definitely exhibits a stark Origo (1/1) character: But even with such an explicitly
concrete and unity-affirming God-concept, we find some philosophizing over the
“nature of God” on the orthodox side (as we saw from the above quote from
Bucher’s Kirchliches Lexicon) that
has hardly anything to do with a “personal creator God.” On the other hand,
besides the almost materialistically emphasized concept of Yahweh in the Old Testament,
there is the En-Soph of Judaic mysticism and tradition, about which any
adequate statement is explicitly denied. Obviously there are eidetic elements
here.
If we understand the above
concept of God in terms of his inner nature in the sense of the harmonic 1/1, and less in terms of the actual genealogy in
the relevant pantheons (since these are by no means unified, much less complete,
especially in Babylon and Egypt, and even less so in India), then we can
introduce something like the following entities: Marduk (Babylon), Yahweh
(Bible), God the Father (New Testament), Zarathustra (Persia), Osiris (Egypt),
Mithras (Iran), Zeus (Hellas), Jupiter (Rome), Buddha (India), the Monas
(Gnostics, Neopythagoreans, and Neoplatonists), the “One” (Plato), the Demiurge
(Greek philosophy), the Monad (Leibniz), and indeed all “monistic” systems.
As one can already see in
the mythological and religious entities that have the character of the Origo,
the idea of the redeemer or mediator is bound up with most of them, for example
when Christ is different from God the Father, he is still “consubstantial” with
him. In our following cosmogonic steps, we will also see a precise harmonic
correspondence.
A. von Thimus, who gives
an exhaustive analysis of some inscriptions at the Temple of Karnak in the 15th
section of his Harmonikale Symbolik,
writes the following (II, 339), based upon Lepsius and other sources about the
Egyptian god Nubti: “Also in his earth-born form, he is one with the permeating
divine spirit that vivifies the material creation; the figure of this god
symbolizes both the creative artificer of the All, and also the world of
elementary created things, fertilized by the life-breath of the divine spirit.
But he is also symbolically the bearer of the secret thoughts that lead to a
future spiritualization and transfiguration of the ensouled human creature,
summoned to union with the divine nature and to unification with its creator.”
The inner identification of this Nubti with the 1/1 and his “mission” as concentration towards
progress (or regress) to the 0/0 should not be misunderstood. Thimus shares a
wonderful passage from the unfortunately much misunderstood Iamblichus (De mysteriis sections 8.1 and 2) on the
ancient Egyptian doctrine of the first cause (ibid. II, 453-355):
“‘Before
any true being, and before the beginnings of all things, is the One God,
predominant over the first God and King, staying immovable in the oneness of
his unified Being. For neither the intellectual nor anything else is mixed into
his Being. He is set up as the primal concept of the truly good God, who is
father and creator of himself and the sole father. He is greater and first,
and source of all things, and the primary form of the first archetypes of
Intellect and Being. From this One, the self-sufficient God has created
himself, radiating in his brilliance, thus both sufficient to himself and
father of himself. For this God of Gods is the beginning, and the Monas
proceeding from the One, and the pre-substantial = primary origin of all that
is. From him proceeds Existence and likewise Being, due to which he is also
called the Father of Being; because he himself is the Being above all being,
the beginning of intellectual things, and for this reason he is also called the
beginner of the Intellectual.’”
Thus Thimus quotes
Iamblichus. The words “and the Monas proceeding from the One” show clearly that
this entire passage is about the attempt to build the demiurgic Origo concept
of God together with that of the eidetic deity (0/0), or through words and concepts (where the
sign of the “One” is obviously used for the 0/0 concept!) to somehow clarify the relationship
between Eidos and Origo.
F. Cumont (Die Mysterien des Mithra, Leipzig 1911,
p. 125) writes: “Mithra the creator is, to use the philosophical language of
that time, the Logos emanating from God, who partakes in God’s omnipotence, and
after he, as demiurge, has formed the world, he watches over it. The initial
overthrow of Ahriman, however, has not condemned him to impotence. The struggle
between good and evil continues on earth between the envoys of the Olympian
ruler and those of the prince of demons; he reveals himself in the heavenly
spheres in the opposition of the propitious and unpropitious stars, and
reflects himself in the heart of man, the microcosm.”
Here, then, as with the
Logos concept of St. John, the Logos is considered as emanating from God (0/0), i.e. as the Origo (1/1).
Proclus (in Timaeus 155) mentions a beautiful
legend: According to Pherecydes, the teacher of Pythagoras, Zeus (1/1) changed himself into Eros after he had decided to create the world from opposites, and
to bring things into friendly symmetry and to agreeable unity with themselves.
The speculations of Plato and the Neoplatonists (Plotinus, Proclus) about the
“One” are so well known that here we can be satisfied with this simple
reference. Through harmonic analysis, Plato’s Parmenides (The Ideas and the One) in particular, and his supposedly
last dialog, the Philebus, might
receive a whole new illumination, just as all of the Platonic “dieresis” of ideas and concepts can be
derived straight from the “law of harmonic quantization” as our “P” embodies it.
(For background, Stenzel’s Zahl und
Gestalt bei Plato und Aristoteles, Leipzig 1924, is best.)
Ancient Chinese speculation places the
Tai-ki (1/1)
under the Tao (0/0) as a demiurgic principle; Windischmann writes on this in his excellent Philosophie im Fortgang der Weltgeschichte
(vol. I on China, Bonn 1827, p. 142 ff.), a book which has hardly been equaled even
today, though some of his understanding of details has been superseded
(especially regarding music and the study of numbers, for which he refers to
the French Abbé Roussier, Amiot, and others):
“The
ancients knew well that over this natural principle (Tai-ki) another ruled, ...
and Shi-tsen, an ancient writer from the Chou dynasty, says expressly that Tai-ki
has a lord over it ... further it reads: The Tao goes before the beginning of
things. Tai-ki is thus, in the sense of the ancients, simply the terminus a quo of all creatural
existence. But since this terminus is
simultaneously regarded as a beginning that proceeds from eternal wisdom or, as
we would say, as the basis for the world, as its firm coherence, thus it is
also the axis around which everything moves, including the main girder that
unites the whole building, as the sensory image of the spiritual Tai-ki, which
is the same as Tai-i (the unity). It is also called axle-tree, root, and peak
of the tree, foundation, axis, column. It is taught that it is not to be
confused with the doctrines of the disciples of Fo (the Buddhists) or with the
Nothing of the Tao-sse. It is the (positive) beginning that has been before all
things, but in reality is difficult to differentiate from them; because all
things are Tai-ki according to their type. In this sense it is also called the
axis of the world, that reaches from one pole to another and around which
everything changeable moves. Human understanding is incapable of grasping this
beginning, an unapproachable power, spiritual and inexpressible. The elements
came forth from it, and from them both the heavenly and the earthly. Obviously
the Tai-ki, since it starts from Tao, also translates as supremum principium, as far as it makes itself the foundation of
the world!”
If one uses as a basis the harmonic
assumption:
0/0 →
1/1 →
2/2 3/3 4/4 5/5 ... (generator-tone axis)
Tao Tai-ki “axis,” “girders,” etc.
then everything is immediately clear; but one also sees how hard it is for
speculation, with simple words and concepts, to bring into our waking
consciousness that which lies in us unconsciously as a psychical form.
Moreover, it appears not impossible to me that ancient Chinese number harmonics
arrived very early at a system analogous to our “P”. The material that
Windischmann gives based on French scholars such as Roussier etc. (whom I have
not yet been able to study) and which, after over a hundred years, still
remains completely untapped, especially in the Mémoires concernant les Chinois, must be newly approached from
harmonic viewpoints. The volume Chinesische
Musik, published by R. Wilhelm at the China-Institut (Frankfurt a. M. 1927)
is very beautiful with regard to the general attitude of the Chinese
philosophers, but is more than lacking with regard to fundamental
number-harmonic problems.
The reader might be
satisfied with these few examples, which offer historical ektypics about the
relationship of the Eidos to the Origo; it will be easy for him to complete the
material.
§54.4. The Creation Triad
Expression:
0/0
1/1 d
1/2 d, 2/1
d¢
Psymbol:
Δ
Definition: In the beginning of the creation process,
three entities form themselves, equal in value and different in nature. In and
through this ternary, the entire form of further evolution is given.
Commentary: Just as we no longer indicate the Eidos with a single 0
but instead with a doubled 0/0, we indicate the Origo not with a single 1,
but with a doubled 1/1. The duplicate form of these terms is, as we saw, not arbitrary, but is yielded
through strict induction from the structure of the “P” itself. Mathematically,
the two series are naturally identical:
|
mathematic: |
... 1/3 1/2 |
|
2
3 ... |
|
|
harmonic: |
... 1/3 1/2 |
|
2/1 3/1 ... |
|
|
|
g,, d, d d′ a′ |
|||
Harmonically, not at all; because here another element of symmetry of the
intervals is expressed, which is missing from the mathematical series; besides,
through the double-signature 1/1 we first obtain the possibility of clarifying
evolution from the Monas.
This twofold setting of
the One as the simplest proportion 1 : 1 or 1/1 involves the Two a priori, since two unities are placed in relation to one another.
With this, therefore, the two is born, namely in doubled form: two units as plain
2 (two), and each individual unit as 1/2 (the half) of
the whole signature 1/1—where naturally it is not the sum or the half of 1 that is understood, but
simply the possibility of arriving at the forms of the 2 and the 1/2
from the double-concept of the 1/1. This purely spiritual deduction of 2 and 1/2
from 1/1 now
allows us, however, to set it out factually, and thereupon the ternary 1/2
1/1 2/1
is obtained as the first stage of development. Now we also understand why we
use the ancient Chinese sign for Tai-ki for the unit 1/1 above as the Psymbol. It expresses
precisely the inversion (reversion) that takes place in 1/1 as the intersection point of the two
reciprocal series—1/3 1/2 1/1 and 1/1 2/1 3/1—namely the (mathematically expressed)
conversion of numerators into denominators:
... 1/3 1/2
1/1 2/1
3/1 ...
The fact that one half of
the sign is shaded is connected with the “earthly” character of the series 0 = 1/∞ 1/3 1/2
← 1/1
and the “heavenly” character of the series 1/1 → 2/1 3/1 ∞/1 = ∞, which we will discuss later. We see
on this occasion that the Tai-ki symbol emerges as a very precise designation
of one of the highest harmonic conditions, and thus as an archetypal form
anchored deeply in our psyche.
As for the triad:
appearing right at the beginning of the creation process, here we have
harmonically three different (here = d-)
values, which are inwardly equal and yet different in nature (in their location
and pitch). Since we can not only judge the three octave-tones d, d d¢ intellectually and physically (number-measure)
but also evaluate them psychically, and since they are at the pinnacle of the “P”,
this is probably the single instance, in the history of ideas, of a
psychophysical explanation for the “mystery” of the Trinity. Compare to this our
statements in §30 of this text.
History
There is so much
literature on the trinity problem in mythology, the history of religion, and
the history of philosophy (three-step dialectics), that we cannot discuss it
further here, and must refer the reader to the few bits of information about it
given in §30a and §50.5. Anyone who seeks to obtain any degree of historic
insight can only conclude that ever since humans have thought, they must have held
the form of this ternary as one of the most important psychic prototypes in the
subconscious, a form of entirely characteristic quality which strives again and
again in the most varied domains, above all those of religion and mythology,
toward some symbolic realization. And the phenomenon of the dialectic, with its
logical triad of thesis, antithesis, and synthesis, shows that the ternary
rules the form of our thought itself. Harmonics, however, simultaneously shows
that the ternary (as a cadence : crystal surfaces!) also inhabits nature as a
form-potency; through this it is raised above its merely “anthropomorphic”
meaning and obtains a universal character—which once again explains and makes
comprehensible such a far-reaching significance in the most varied human
spiritual domains.
§54.5. The Creation-Polarity
Expression:
Psymbol: 
Definition: The creation triad requires creation-polarity. Infinity
(∞) and Nothing (0) emerge, as well as the median line (1/1 2/2 3/3
...) = Origo-axis.
Commentary: In the progression from the Eidos 0/0 to the Origo 1/1 we see, harmonically, the actual process of
the world’s becoming. We can easily go on to describe the further evolution
from the 1/1, indeed we must follow a “before” and “after” here, or some kind of
progression. But this is only required by our method of expression; because
fundamentally, with the birth of the Origo 1/1 the immediate emergence of the entire cosmos
is given in its ideal form. Its temporal developments are only evolutions of
the system of the “P”. We could thus just as well have put the polarity before
the triad and discussed the subsequent creation steps in any order, since they
spontaneously emerged, as great cosmological prototypes, with the creation of
the Origo, comparable with the sudden crystallization of a substance, the
completion of a chemical process, the “brainwave” of a thought, an idea—these
examples taken admittedly only as completely insufficient comparisons. The
reader should turn his attention more to the types in themselves than to the
series-progression.
The creation-polarity, and
the Origo-axis (generator-tone line) which it necessitates, bring into the
world the concept of the Infinite (∞),the concept of the Nothing (0), and
the concept of constancy, perseverance (1/1 2/2 up to ∞/∞).
All three of these
concepts have vectorial, direction-giving, “intentional” character. Whereas the
vectors 0 and ∞ go out from, or back to, the origin 1/1, the vector ∞/∞ (origo-line) takes its origin from the highest
harmonic value 0/0. Cosmologically, these expressions and definitions are of great
significance.
From this, we see firstly that
the Infinite requires the concept, indeed the actuality, of the Nothing, and
vice versa. Both concepts, and not only the one “or” the other, are
intentionally posited for the reality of the creation. These two are primal
principles of the limitless (̔άπειρον) and of the limiting (περαίνοντα) of the Pythagorean-Platonic philosophy, and
furthermore the prototypes of all dualistic systems, be it in mythology,
religion, or science. But we see further that these two principles have no
direct participation in the deity 0/0 as vectors or intentions, but are instead
“origo-nally” required, i.e. are a direct emission of the Monas 1/1, the concrete act of creation. Thus in
harmonics, the two directions that embrace the Monas 1/1, the Nothing (0 = physically the “empty”
universe, philosophically the absolute privation, ethically the complete want)
and the Infinite ∞ = of the unending universe, the concept of
endlessness, (the infinite plenitude), stand in opposition to the symbol of
eternal rest, the deity (0/0), or simply eternity. We will soon speak in
more detail of the inner psychophysical content of these vectors.
These two principles are
now brought into a sensible relationship through the Origo-axis (1/1 2/2 3/3
...), which we can also call the unity-line of the world; indeed without this
they are entirely unthinkable. This unity-line, however, goes as a vector back
to the 0/0
and thus symbolizes its direct origination from the deity. Precisely this fact
allows deep speculations (Plato, Plotinus, etc.) to conceptualize about the
“unity,” while the epistemological deliberations and analyses of the concept of
the “Nothing” and the “Infinite”—if I may express myself in the mode of the
ancients—never participate in “the gods” and remain as they have remained, more
or less domiciled in purely logical spheres.
History
An ektypic evaluation of
the two vectors 0 ← 1/1 → ∞ was already attempted in §19a
ad 1 and §50.5, especially with regard to the Pythagorean concepts of the unlimited
(∞) and the limiting (0). We will add a few more examples here. If one
sees in the Origo-axis 1/1 2/2 3/3 ... the single,
cohesive element of the 0 ← 1/1 and 1/1 → ∞ vector, then one can
understand the dark declaration of Heraclitus’s riddle: “The way up and down is
one and the same” (Diels: Fragmente der
Vorsokratiker, Heraclitus fragment, 60).
Robert Eisler writes, in
his Weltenmantel und Himmelszelt (Munich
1910, pp. 558-559):
“When
Pherecydes was the first to teach that souls were “eternal,” i.e. not merely
immortal, as Homer said they were, but instead beginningless and endless, and
that birth and death mean only a changing of place in the universe, this agrees
very well with the striving for reunification with the two eternal and
beginningless principles ̕Aιθήρ
(ether) and Γη̃
(earth). But of course, it can just as well be said that body and soul, spirit
and matter are imperishable and without origin. There can be no doubt that this
dualistic anthropology under Pherecydes had an ethical goal, if one remembers
that the primal origin of one element of man, Zeus-Ether, is called the
‘perfect good,’ whereas Chthonie Ge appears throughout as mother of the riotous
... foes of the gods ..., the source of everything evil and of that in man
which opposes the will of gods.”
Harmonically, we
understand souls as “eternal” when we assume the reference-direction of all
being-values as being toward 0/0. If it is true that Pherecydes explained souls
as “eternal” and “not immortal,” then this expresses that wonderful impression
that the Pythagorean-harmonic symbol of the Eidos (0/0) allegorizes so beautifully—and realizes. The
idea of immortality, to which something more or less material always clings, is
stripped of all materiality through transformation into the “eternal,” and
transposed to the highest reality of the Eidos (0/0).
The equating of the 1/1 → ∞ pole with “good” and the other
0 ← 1/1 with “evil” once again reveals the replacement of outline and possibility
with fact and reality, typical of the ancients; compare this to the following step.
The Orphic expressions ΑΙΩΝ
ΑΠΕΙΡΟΣ (unending duration = 1/1 → ∞) and NYΞ ΑΠΕΙΡΟΣ (unending night
= 0 ← 1/1) are very remarkable; they doubtless correspond to the inner psychical
configuration of our two harmonic series-pairs. If one applies the ancient
procedure of “psephoi” (gematria), as mentioned with similar examples in §17b,
substituting the corresponding number of the alphabet for every letter, then
for both double names one obtains the sum 128 = 27, the seventh
octave-power!
The two polarities Yin and
Yang (– – and —) which proceed from the Tai-ki of ancient Chinese wisdom, on
which not only the I-Ching but all of
Chinese philosophy is based, are the exact counterparts of our harmonic series-pairs
0 ← 1/1 → ∞, and their definitions as darkness and light, no and yes,
female and male, etc., show just how purely Chinese thought grasped and
manipulated a prototypical psychic form—remember what was said in §50.8 regarding
the I-Ching diagram.
A related symbol comes to
mind here, upon which Egyptological research has continually foundered, despite
its known content, namely the so-called “Ankh,” 
.
This hieroglyph, signifying the symbol of divine life, is known to appear even
in the earliest monuments and inscriptions, and not only in Egypt, but also on
Etruscan, Sicilian, Persian, Babylonian, and Chaldaean images, gems, coins,
etc. (Thimus II, 111 ff. with ill.). One should read Thimus on the contrast of
this hieroglyph with the sign of the cross and his deep speculations about it.
Unfortunately, Thimus, whom I so much admire, either completely missed the
simplest derivation of this Ankh, or else did not think about it at all, since
it seemed self-evident to him. Namely, if one draws the “P” with basal series
not bent at a right angle but lying along a line, with the 0/0 point as a circle above and the generator-tone
axis directly below, then the result is Fig. 471a.
Figure 471a
One must admit that for
the most important laws of the “P”—Eidos, Origo with its three “directions”—no
better graphic image-concept could be found. This same symbol, so widely used
in Egyptian hieroglyphics and on Egyptian reliefs, allows one to assume with the
highest probability that the system of the “P” established on the basis of the
monochord was known in the secret schools of
The ancient Babylonian
doctrine, still echoing in the cosmogony of Berossus, of the emergence of the
world of the senses from the unification of a creating male and receiving
female, birthing, primal force (corresponding to the Chinese Yin-Yang principle)
is recorded in the Origenian
Philosophumenis. This “Origenes of the Heathens and Neoplatonists”—not to
be confused with the church father of the same name!—next to Plotinus the most
significant scholar of Ammonius Saccas, declares (according to Friedrich
Münter: Religion der Babylonier,
Copenhagen 1827, p. 46): “Diodorus the Eritrean and the musician Aristoxenus
say that Charatas the Chaldaean taught Pythagoras this: two are the principles
of all things from the beginning; a paternal and a maternal. One is light, the
other dark. Qualities of the light are warmth, dryness, lightness, swiftness;
to the darkness belong the cold, damp, heavy, and sluggish. And from all these,
along with man and woman, emerges the world, and there is a musical harmony.”
The Neopythagorean
Numenius of Apamea (2nd century a.d.),
forerunner and influencer of Plotinus, “founder of the doctrine of the three
deities following one another in rank: the highest principle νου̃ς, the demiurge, and the world” (Überweg, Geschichte der Philosophie, vol. I, 1926, p. 514), assumes a
principle (0/0) that is timeless, eternal, always the same as itself, spatially
unmovable, unchanging, simply being. But since the world cannot be identical
with this absolute, a second principle must mediate: the demiurge (1/1).
“Numenius
differentiates first the world-maker (δημιουργός)
from the highest god as a second god. The first god is good in and through
himself; he is pure thought-activity (νου̃ς) and principle of being (ο̕υσίας ̕αρχή)
and as King (βασιλεύς),
free from all labor. The second god (demiurge) is good through participation in
the nature of the first; he looks at the supernatural primal images, works with
matter, and thus sculpts the world, in that he is the principle of becoming.
The world, the product of the demiurge, is the third god. The basis for this
doctrine was first supplied by the demiurge and the divine world of the Platonic
Timaeus. But the overseer (demiurge),
to whom the same original ideas apply, cannot be the highest court of appeal in
the longing for absolute divine transcendence. Thus a higher god prevailed over
him, to whose designation the Platonic ideal of the good and the Aristotelian
placement of the deity as the basis of the pure νου̃ς offered a footing, perhaps with a contribution
from the character of the βασιλικη
επιστήμη (royal knowledge) from Plato’s
Politicus, 305d. Also Plato’s Sixth
Letter comes into consideration.”
(Überweg, ibid. p. 521). Now, when Numenius, as Proclus tells us (in Timaeus III), “traced the soul back
to numeric relationships,” and, according to Eusebius XI, 22, commends
penetration of the numeric secrets as the way to knowledge—just as for the
Pythagoreans, the source of all Platonism (Eusebius IX, 7 and XIV, 5)—then the
presumption is allowed that Numenius probably used direct Pythagorean
traditions as a basis, and knew of the Pythagorean “P” system in some form.
When he designates his three deities (besides the titles Nous and Demiurge)
expressly with πατήρ (father), ποιητής (overseer,
demiurge) and ποίημα (the created, the world), the harmonic succession 0/0 → 1/1 → “P” is so obvious that no doubt can remain that he was a true and not merely “syncretistic”
Pythagorean.
Finally, I will give a few
more interesting related Kabbalistic passages from the strange work already
mentioned above. Anonymously published in his own time, Molitor’s Philosophie der Geschichte, oder über die Tradition
(Münster, 4 vols., 1834 ff.) treats “the tradition in the old covenant and
its relation to the church of the new covenant, with especial reference to the
Kabbalah” in a most thorough and profound manner, and should have been
republished long ago as one of the most important spiritual products of the
Schelling-Baader era. In the appendix to vol. II of his work, Molitor offers a
few passages from Kabbalistic writings (Zohar
etc.) in Hebrew and German, from which I choose the following:
Of the Ain-soph, it is
said: “Before the world was created, He, the [Most Blessed] and His name were one.”
“He created the tangible from the void and made its nothing into something.”
“Even in the minerals, like dust and stone, there is necessarily life and
spirit, and a star or watchman over it.” “Ain-soph is separate and removed from
all imaginable. It comes before all emanations and creations, and in it is no
time.” The Kabbalists distinguish the Being from the Light within the Ain-soph,
and say that the world was created from the light. Etz ha Chaiim tells us, in
the passage: From Ain-soph came out a straight, fine line in the manner of a
canal: “Only the illumination of Ain-soph, but not its Being. This is what the
doctrines say: it is the place of the world; but the world is not its place. For
its Being does not extend itself, but its light does.” Here think of the
equal-tone rays from the harmonic symbol 0/0!
§54.6. The Creation of
Expression: (Fig. 472)
Psymbol:
×
Definition: The first senary evolution cycle of the “P”
creates a world of pure major and minor chords, mutually pervading each other,
a pure “paradisiacal” world that ends in the seventh ratio-series as a closed
index, repeating itself again in several “senary” series-groups and
series-pairs, but these become ever rarer in the course of further
differentiation. Thus we can with good reason conceive of the closed complex PE6
(as well as PE8) as a world of pure chords reposing in
themselves, as a domain of pure harmonic conditions, which is unique in its
type and represents the first cycle of harmonic cosmogonic evolution.
If one now builds a pure
spiritual world behind the 0/0, on the model of the imaginary basal series 0/∞
← 0/1 0/0 1/0 → ∞/0,
which can happen purely constructively and is shown in the upper sector of Fig.
472, then we see in this imaginary “P” domain to a certain extent the spiritual
prototype for the “real” “P” realized in the lower sector. The reader is asked to
inwardly grasp the illustration of Fig. 472, i.e. the “above,” “below,” as well
as the variation and combination of the “P” given there, in terms to its form; of
course, we can also lay it on its side, place one of the two imaginary basal
series upon the other, choose the hexagonal form of the illustration, etc. This
imaginary, purely spiritual world has a much simpler structure compared to the
real “P”. Its axis is the 0/0-axis, that of the Eidos. At the left we see
only vertical 0-series of identical spiritual values; to the right we see only
vertical series of the spiritual “whole numbers”; we can no longer logically or
material-mathematically grasp the terms of 0/3 and 3/0,
for example, as quantities, but instead as purely spiritual values. A spiritual
zero-world appears in this upper sector left of the 0/0 line: to the right, the metaphysical “birth”
of the whole numbers. We have not reached this arbitrarily, but through
retrograde interpolation of the “P” in a strictly legitimate way, similarly to
how we arrived at the elicitation of 0/0.
Commentary: The reader has been carefully instructed in previous
chapters regarding the “senarius” and its closed core in index 6 of the “P”, as
well as regarding the “ekmelic” character of the seventh-series, being the
first beyond the senary. In Fig. 472, we attempt to show the corresponding
difference between the “spiritual,” “emmelic” (senary), and “ekmelic” (outer
senary) central ratio-builders of the vertical middle axis by leaving the
ancient Chinese Yin-Yang symbol “empty” in the first case, half-shaded in the
second case, and filled out in black in the third case. Through this, we obtain
a clear optical image of the conditions in question.
Figure 472
It is now the time to
discuss summarily the problem of the transcendent signs, becoming especially
important in Fig. 472, 0, ∞, 0/∞, ∞/0,
∞/∞, etc. For the mathematician, 0 and ∞ are still unequivocally
ratio-based concepts: “zero” and “infinity.” The definition of 0/0, which can mean “all,” i.e. every number, is
more difficult for him, and the terms 0/∞, ∞/0,
∞/∞, ∞, ∞/n, have hardly any meaning for
him.
Let us look at what
harmonics says to this (see Fig. 472). Let us begin with the perpendicular
middle axis. In the upper domain, up to the middle field, which belongs to both
sectors, it has the value 0/0. The mathematical conclusion “everything”
agrees with the harmonic one here, even if this naturally also attains the
greater amplitude, since the harmonic concept of 0/0 designates the highest concept of the Eidos
reachable in us. In the lower domain we find the value 1/1, generally speaking n/n, which is mathematically equal to 1. Harmonically,
however, it is evident that besides the unity (Monas), the situs, the place, i.e. the location in the field, also plays a
role. Thus the 1/1 is different from 2/2, 3/3, etc.
in its position, since it must obviously be ascribed an exceptional rank in
contrast with the other units. The units 2/2 ... 6/6
are once again different from units such as 7/7, 11/11, 13/13 etc., since these units represent
intersection points of ekmelic series-pairs. Here, therefore, we have three
different characters of units, whose being-values are the same but whose
field-value within the “cosmological” succession is different. This difference
applies only in the topological sense, not in the ontological, and can be taken
into consideration only in judgments of location, not in terms of being. It is
interesting that the vector of all these units 1/1 2/2 3/3
... ∞/∞ leads to a doubled infinity ratio, which we must view harmonically as the
maximal Being, and cosmologically as the end of the development of the world.
If this point is reached, then ∞/∞ ignites itself upon 0/0 and the entire world-system is cleansed again
in an enormous melting process. As for the imaginary basal series that belong
to both sectors:
|
0 = 0/∞ ... 0/2
0/1 ← |
0/0 |
→ 1/0 2/0
... ∞/0 = ∞ |
with regard to the symbol ∞ = infinite, we are still in agreement
with mathematics, though harmonically we grasp the concept of infinity not only
in terms of size, but as the infinity of the being-values. The term 0 = zero,
on the other hand, can mean the mathematical Nothing or a limiting value (limes), while harmonically, we grasp it
more in the sense of an absolute lack (ethically), a thickest concentration
(materially), and simply a limit (in the sense of not being able to go any
farther). It is these two imaginary series, coupled in the 0/0 value, that represent the communication
between the “lower” real world and the “upper” spiritual world. Parallel to
them, in the lower (material) sector, run only series of the limited form 1/∞ 2/∞ 3/∞
... or ∞/1 ∞/2 ∞/3 ... which,
taken themselves again as vectors, tend in both cases toward the maximal
being-value ∞/∞. The corresponding parallel lines in the upper (spiritual) sector, on the
other hand, always collectively observed from the 0/0 line, have the limited form 0/∞
0/∞ 0/∞ ... or ∞/0
∞/0 ∞/0 ..., and do not
construct any recognizable vector tendency, whereas the not yet limited
parallel lines, for example 0/5 0/4
0/3 0/2 0/1 0/0 or 5/0 4/0
3/0 2/0 1/0 0/0, all turn themselves from the imaginary basal
series toward the highest 0/0 value. Whereas all concrete partial-tone
series of the lower sector still express, in their limiting values, what I
might call a “concrete” infinity (1/∞ 2/∞ 3/∞
... or ∞/1 ∞/2 ∞/3 ...), all
the analogous series of the spiritual sector, turning away from the 0/0 axis, point to the two completely transcendent
concepts, 0/∞ and ∞/0,
and, turning toward the middle axis, to the highest transcendent concept of 0/0.
The collective impression
of the spiritual sector is one of absolute repose, symbolized by the three
great harmonic-metaphysical principles of the 0, the ∞, and the 0/0, and characterized by the majesty of the
spiritual being-values1° 2° 3° ... and the connected transcendent emergence of
the whole numbers, adjoined to which we must imagine toning spiritual media,
for whose description every term fails us.