The Overall Form &
Digression on Goethe’s Metamorphosis of Plants

Harmonia Plantarum – Harmony of Plants

Two Excerpts from Part I – The Form of the Plant

by Hans Kayser

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Here we arrive at the problem of the plant’s overall form, its stratification, planning, the idea of the plant.

Neither the idea of Goethe’s “primal plant,” nor the harmonic sound-images of the plant prototype, nor even the concept of the “plant” itself would make sense or be possible if we did not provide all real plants with a model, a “prototype” on the basis of which we can evaluate and look over the entire unfathomable domain of vegetable forms.

If, in the following, we assume that this “idea” of the plant must be at least equal, if not superior, to the surrounding requirements, then these requirements-with their individual ecological factors such as selective breeding, natural selection in the battle for existence, developmental necessities arising from the landscape, climate, or biological factors (relationship to insects, etc.)-are absolutely not to be neglected as unimportant. Otherwise this would be impossible; for since the rise of evolutionary thought, vast factual material on the dependency of plants on their environment has been produced, and one would have to be blind to ignore this material. On the other hand, the “idea” of the plant, or rather the plant’s “planning,” has been sorely neglected by modern science, or else been lost in a fruitless debate over the meaning and value of the plant system. Only very recently has a definite “metaphysics of plants” become noticeable, and this among specialists (H. Andre etc.) -a horrible expression to the ears of an old-school botanist,. but nonetheless a domain that deserves to be reconsidered on the basis of the vast amount of factual material that has been collected to date.

We will therefore assume evolutionary ideas to be correct and known, and then see to what extent emanationist thoughts arise from the previous factual material, i.e. results that necessarily lead to the conclusion that in evolution there is an emanation from bottom to top
and a planning from top to bottom, both side by side or overlapping.

When an embryo is divided, then according to the old materialistic-evolutionary viewpoint, a “half” must develop which is at least a rudimentary larva. The sensational experiments by Driesch and others, in which halved embryos grew into whole (although smaller) larvae, gave rise to “holistic research,” and indeed to a new branch of philosophy (gestalt theory), the central point of which is the fact, established via such observations, that the gestalt factor, the form potential, is more important in organisms up to a certain point than the field of material realization. When the egg or sperm cells of mosses are multiplied, the result is not doubled or tripled embryos, but simply larger plants with larger cells. But this preponderance of the gestalt, the form, and with it the “idea,” emerges even in the simplest life forms without human intervention, as one can see if the correct conclusions are drawn from the relevant phenomena. In my Horende Mensch, I used the example of the “volvox,” a new entity (spherical alga) emerging from originally independent green protoplasts, which behaves entirely like a separate individual, rolling here and there to find the best light and nourishment. As I watched, completely fascinated by the fine performance taking place under the microscope, there was a sudden jolt in the miniature green planet— probably caused by the overly bright light of the condenser-and it flew apart into its individual pieces: the many small protoplasts that had formed the sphere of the volvox swam
merrily away!

This is the phenomenon of “cell union,” which can be observed in many modifications in these same elementary life forms. Such union exist in the shape of strings of beads, threads, and above all, nets, with pronounced senary (and therefore harmonic) structure-shortly we will see an important example (the water net). Overall, the primary form potential here is in a hierarchal direction, i.e. the progression from simple to more complicated, higher levels of wholeness, whereas the field of material realization must submit to this will to form, often to the point of giving up the individual, original parts. This drive toward form becomes even more noticeable when one examines those primitive life forms in which the living substance (protoplasm) apparently shows no differentiation. The example of an amoeba is known; although a blob of slime with hardly any differentiation outside its nucleus, it still exhibits teleological behaviors (taking in of nourishment, protection from light, etc.). A lesser known and consequently more striking example is that of the slime mold, from whose almost uniform protoplasm mass there emerge various sporocarps (fruiting bodies) at certain times-only through this can they be distinguished at all.

“A species growing most readily on the bark of fallen pine twigs, Leocarpus fragilis, when fully grown forms an oily yellow mass, deceptively resembling the spilled yolk of a bird’s egg. The mass spreads over the dead twigs of the aforesaid conifer lying on the ground in a thin coat, in which no specific features are to be seen. Throughout an evening, Leocarpus can be seen in the aforesaid form as a so-called plasmodium. But in the course of the night, at certain places, bumps and warts emerge, and the whole mass then looks rough and grainy. By morning these protrusions have become egg- or pear-shaped bodies on thin stalks, no longer greasy but having a tl1in, dry skin, and inside, many hairlike threads with spores in between them resembling black dust. It takes Leocarpus about twelve hours to form these, and if one is patient enough to watch the masses forming all through the night, then one can actually see them rising up from the surface, becoming round, growing a skin, and taking on a pear shape. The protoplasm of Dictydium forms in quite a different way, and so do Didymium, Clatroptychium, etc. In fact, the forms of all slime molds would have to be described were we to cover all the multiplicity of forms taken on by the protoplasms of this group.” A. Kerner, from whose Pflanzenleben (I, p. 534 ff.) this description comes, then continues: “To establish the fact that whole similar protoplasms form visibly in a short amount of time and in a different way for each species, the above examples will be sufficient. It only remains to note that the form taken on by each specific protoplasm is independent from external conditions, and that in the same night, with the same humidity and air temperature, under the same glass cover, the pear-shaped Leocarpus and the cylindrical strands of Stemonitis can form right next to each other.”

But the classic example for scarcely believable form potential is the thousands of diatoms and radiolarian formations. Here as well, protoplasm droplets that are neither mechanically nor chemically distinguishable build a vast world of forms, which are also of
striking beauty (see my views of diatoms in Horende Mensch and Grundrifl). This preponderance of the formal, the gestalt, can now be followed from these “lowest” examples up through the entire plant kingdom, as far as its most complex formations.

If we begin with the latter, then we must first mention orchid flowers, whose pollination mechanism-regardless of the saprotrophism of most plants in this species and their fantastic flower formations-is so complicated that they often drive themselves ad absurdum toward certain extinction (this being from the “evolutionary” viewpoint), such as in the case of Ophrys muscifera. H. Andre (Urbild und Ursache in der Biologie, p. 150) writes on this:

“The formation of orchid flowers appears to be an excess required purely by formal laws, within which highly complicated and not always very functional pollination mechanisms emerge, while the common weed Senecio vulgaris produces a massive amount of seeds in an
entirely simple way.”

These two outermost poles of the plant kingdom-the thousands of diatoms and radiolarians, formed by a mysterious geometry of protoplasm cells, and the thousands of orchids with their eccentric flower formations almost transcending plant form -must strike dumb even the most rigid utilitarian skeptic, and leave .him contemplating what strange powers there must be which strive only for formal expression here-or may we say, with the courage of our convictions: for the expression of beauty? But there are so many other examples of the preponderance of plant forms that once one’s view is attuned to them, it is difficult to sort them out and choose a particular one. Let us consider the flower for a moment more, and set aside the question of the reasons behind the bizarre diversity of forms-some of which, certainly, can be explained in terms of utility and adaptation. Here, for example, there is the family Asteraceae, or Compositae, considered the most “developed” flowers. Their beauty is well known, and no one would consider these “illusory” flowers. And yet this is the case. The actual flowers of these
composites grow close together, often in their hundreds, in the center of the flower, and the wreath of petals around them, such as the white petals of the daisy or chamomile, is a trimming, so to speak, a superordinate overall form, which gives an entirely new face to the
multitude of real “flowers.” Here all utilitarian criteria break down, and we should speak not of an “illusory flower” but of an exponentiated flower of a higher nature, a phenomenon in which the pure, non-utilitarian drive toward form is openly expressed, striving only for beauty and harmony. The fact that the harmonics of plants appears at its purest in the flower will be shown later more extensively; here the reader should concentrate more generally on the value of the form-based element in itself. A typical example, not only for the objective existence of certain “form-ideas” regardless of their realization in any given plant species, but also for a separate causal foundation, is “mimicry.” In the animal kingdom, these “emulations” are considered without exception to be defensive measures against predators. In botany, however, there are other reasons. Why should seaweeds, in themselves very primitive and bizarre growths, almost all imitate land plant forms (France I, p. 473)? Seaweeds growing in cold northern seas have similar forms, sometimes even identical forms, to certain tropical land plants! Was there a “paleontological” common ancestor? The domain of algae is full of puzzling masquerades. “The classic case is the single-celled (!) sea alga Caulerpa, which imitates mosses, lycopodia, and ferns very closely, or rather is imitated by them, since it was first on earth. Not without
reason do we also call a great many plants after others, such as Acer pseudoplatanus, Iris pseudacorus, Robinia pseudacacia, etc. – they imitate the respective plants either as a whole or in their leaves.”

France, from whose Leben der Pflanze (I, p. 245) the above passage is quoted, and who was one of the first to question this “utilitarian mimicry,” also discusses the “leaf mimicry” of insects that lived in the paleontological plant world-before there were leaves and twigs of
the type imitated! (op. cit., p. 244.)

This is in no way intended to refute those cases in which protective mimicry apparatuses have been actually observed. But how can we know, in all cases, whether the protective apparatus was primary and the predator secondary in the stages of evolution-as the above example shows?

The only way out of the dilemma is to allow the form itself a certain autonomy, a value in and of itself, realized under various conditions of being. Just as a given tone-value can manifest on the basis of various tone-numbers-e.g. the note ab (where 1/1 = c) on the material
vibration basis of

2/ 5,     8/ 10,     11 20,     32/ 40, etc. –

so the value idea of a given form can find its realization through some given material basis of being.

A rather grotesque example of “form play” in nature, relating to a relatively humble type of plant, should be mentioned here-it is an uncanny example of that “will for form”whose absoluteness we all too often trivialize in every day examples, if indeed we do not overlook it entirely. This is the “egg of the white-veiled lady,” a Brazilian stinkhorn mushroom (Dictyophora phalloidea Desv., see Figure 24).

“This mushroom does indeed emerge from an egg, a white body 2-21/2 cm wide, which, soon after it has formed, grows rapidly, tapers, and bursts, whereupon a greenish cap appears atop a stalk that grows in length with remarkable swiftness. Moller found that the stalk grew 5 mm in 5 minutes; one can see it grow. The growth occurs so intensively that it is accompanied by a crackling noise. Thus it is also a case in which one can hear the growth. Once the veiled lady is about 10 cm high, her rather old-fashioned hat becomes sticky and slimy. Along with this, an insufferable smell is emitted, like a rotting corpse; this disrupts any dealings with this great lady of the woods to such an extent that our informant, upon an initial face-to-face meeting with her in the laboratory, almost passed out from the stink and had to leave as quickly as possible. This situation interfered somewhat with the enjoyment of observing the subsequent development of the veil. Suddenly, with a few thrusts, a magnificent net of white, shimmering mesh erupts beneath the cap, the whole mushroom shivers as if with joy at its own beauty, its cap trembles and quivers, the veil reaches down on all sides like a crinoline, and the resplendent mushroom is complete, a strange mixture of the ugly and the fair, blooming before the surprised observer of this process. Our picture (Figure 24, from Hackel) shows it in this mature condition. The time of blooming is calculated precisely. The development begins in the afternoon, becoming increasingly rapid; by twilight,
the veiled lady has completed her grooming and awaits her throngs of admirers. Two hours are usually enough for a mushroom to bloom out of an “egg.” Then the abominable smell, spreading over a radius of 100 meters, lures nocturnal carrion beetles which come to feast on the viscous juice, become smeared all over during their delicious meal, and thus spread the spores far and wide. This purpose achieved, the life of the strange fruit-which glows in the night like phosphor-is exhausted. By morning the whole fungus shrivels, the cap becomes wrinkly, the tasty juice dribbles down and stains the white veil, the cap droops to the side, and the first rays of dawn fall only on a pile of discolored slime. As in medieval legends, the night’s marvel becomes a pile of filth” (France, p. 221, cited in Alfred Moller’s book on mushrooms).

France remarks on this: “Who can deny that the Dictyophora’s elegant veil is merely a luxury and not a necessity? The strong smell of the plant is enough to lure insects; a proof for this is our local Phallus, which can stand without a veil.” Here the word “luxury” is only a
last resort, an epitheton ornans, exposing the lack of purpose and usefulness in such formations but not their own being, not the value-emphasized, predominant aspect of the will to form in itself.

But the value, the idea of the plant, shows itself not only in the predominance of the form but also often in other functions, serving the preponderance of form, of form constancy, along the way. And form constancy, i.e. the preservation of a form model through various
geological epochs, is nothing other than the will for sound intensity, the will to remain on the individual step reached.

Thus, for example, one can explain the puzzle of sexual reproduction-the multiplication of living beings could just as well take place via simple division, and for many species this is the case-with the fact that especially for higher life forms, chromosome mixing and the resulting “Mendelization” leads to a static equilibrium, an especially favorable situation for form constancy. The result, once again, is the dominance of the form model in question, and therefore the preservation of the “idea” that has been realized.

An example of the often almost unfathomable achievement and perseverance of an individuality is the behavior of plants toward the medium in which they grow. It is absolutely not the case that all plants, in terms of their chemical content, grow or thrive only in those types of soil which contain large amounts of the nutrients found in those plants.

“None of the circumstances observed in the choice of nutrients are anywhere near so striking as the fact that plants have the ability to isolate, and to some extent concentrate, certain substances important to them out of the many others, even when the soil contains these substances in hardly any measurable quantity. We have seen that nearly a third of the stern of the white sea rose is composed of salt. One might then believe that the water in which the sea rose grows must contain a significant amount of salt. But nothing of the sort! The swamp water surrounding the leaves and stalk of the sea rose contains only 0.035 %, and the silt in which the roots grow only 0.010 % salt. No less surprising is the presence of diatoms, whose shells are strengthened with silica, in waters that contain hardly any trace of silica. Above the Arzler Alps in the Solstein range near Innsbruck, at the foot of a mighty limestone wall, there is a spring whose cold water falls in small cascades between blocks of stone into the deep. The water itself is hard, containing much lime, and at some distance from the source there are tuff deposits. Directly at the place where the spring bubbles out of the rock face, the runnel is completely filled with a dark brown flaky mass, remarkably consisting of millions of silica-shelled diatoms, the dainty Odontidium hiemale, which arrange themselves into long
bands, thriving here in such sizes and numbers as have hardly ever been seen elsewhere. But the flowing water of the spring contains so little silicon that after boiling away ten liters of it, no trace of the element could be found in what remained” (from Kerner, Pflanzenleben I, p. 65).

These examples also show an astonishing preservation of form constancy in the face of environmental influences, which is all the more remarkable considering that for many ages, the dependency of all life forms on nourishment, or on the “soil,” has been viewed as infallible dogma from which nothing could escape. It is clear that “normally” plants and animals live and thrive where it is easiest to obtain what they need. But this would not prevent the dominance of form either, since the form would be able to seek out the “environment” most appropriate for it from the outset.

Let us now see what we can learn from these examples and discoveries offered to us by science regarding the question of shape and form.

The usual three methods of observing the form of a plant (morphology) are: basic geometric shapes and numbers; connection to generalized models and establishment of causes; and teleological connections between needs and environment (ecology). (See Handworterbuch der Naturwissenschaften I. A. article “Botanik.) In these methods, the objective is not so much to track down the mystery of the plant’s form, and more to delimit this form as a specific model among other biological forms and to determine its ecological relationships. Delving into the deeper background has long been frowned upon as “metaphysics,” and this is still the case among most modern researchers. However, there are signs of “philosophical” attitudes emerging; the work of contemporary botanist Hans Andre (Urbild und Ursache in der Biologie, Munich and Berlin, 1931), which we will continue to cite, may serve as a prelude to a new, deeper view of all the morphological and functional processes in living things.

When Goethe, in his essay on spiral tendencies, recognized the explanation of the form of the plant as the highest task in plant physiology, and when that old champion of botany, Goebel (see his magnificent work Organographie der Pflanzen, 3rd ed., 1928) came upon the
insight, based on numerous observations, that the organization (form) of a plant was much more complex than life’s necessities required, this would lead one to expect an autonomous morphology, i.e. a type of grammar, a syntax of morphological laws, to emerge at long last from these findings. But this has not been the case. Researchers such as Cams and Steffens, inclined toward philosophical romanticism, came closest to this. But when the latter declaims: “Who can see into the inner depths of the manifold formation of plants, and survey the abyss
of peculiarity that remains enclosed in every form and is expressed in hidden ways? For, just as in the inner depths of the genius mind all is peculiarly formed, all thoughts ripen into ideas and any given observation can become alive: so a peculiar, i.e. inwardly unending, combination of elements and times grows into idea, becoming manifest in a vegetative form” (Steffens, Anthropologie, 1822, II, pp. 61-62)-these are very fine thoughts, but entirely noncommittal, and today’s researcher, accustomed to exactitude, can gain nothing from them.
Today Anthroposophy falls back on such half-faded methods. But as far as these endeavors are to be observed, especially in pedagogical terms, they revolve-as with Cams and Steffens -around a multitude of unconnected symbolic images, which can be very stimulating but never attain a solid basis for form laws in themselves, which latter we can both substantiate intellectually and understand psychically. Nees v. Esenbeck’s Formenlehre der Natur (1852) represents a single lonely block which unfortunately has neither been “chipped away” or
examined in terms of its material; and the following digression will go further into Goethe’s service toward the establishment of exact morphology.

Modern morphology mostly gets bogged down in concepts and leaves the puzzle of form laws unsolved-admittedly with a few exceptions, to be discussed later. Kerner, in a chapter on the “structure of plants” (I, p. 529 ff.), writes of “formation laws” and of a “building plan entirely independent from external influences” in plants; and the philosophically adept France (II, pp. 56-58) points specifically to the predominance of plant stratification, planning, and even the idea of plants and their psychical basis. But what are we to think when, for example, Kerner (I, p. 531 ff.) presents various theories of the “micelles” (molecule groups) as the actual vectors of plant building plans, but leaves us completely in the dark regarding the forms of these molecule groups?

H. Andre appears to have gotten closest to the problem in Urbild und Ursache in der Biologie. Central to this work is the idea, supported by certain elevated scholastic theses, that every biological entity is the realization of a “form actuality” in a “material field.” The material, passive in itself, is pervaded by powers of form, and living things especially are the ultimate manifestations of ideas or “archetypes.” Here the concept of the form receives an overall character that is not only more logical but also metaphysical. How Andre variegates this basic theme down to the “most factual” details, with the aid of an incomparable wealth of material, one can see for oneself in his book-here one will note that Andre touches here and there upon our harmonic question, namely exact psychical tectonics, and yet goes no further than certain (albeit very interesting) analogies. The value of his work for a “metaphysics of life,” for a deeper view into biology and its relationship to spiritual and even religious things, remains untouched by these “tangents.” It will be a task for harmonic research to return the tangents to the center of the circle, to that center from which, from a harmonic point of view, knowledge and belief spring forth as certainty!

From all these and the previous examples, except for morphological constancy, the significance of the character of the form as a whole follows of itself. Just like every natural and artificial form, every plant-regardless of its belonging in the system, its relationship to its surroundings, etc.-is an individual whole, or as one says today, a whole with “complex-causal gestalt character,” which cannot be identified merely from the sum of its parts.

The classic example for the clarification and interpretation of the wholeness concept, in contrast with a mere “sum” (which, externally delimited, can also be viewed as something “round,” i.e. whole in itself), is the chord. Each of the three notes c – e – g has its own value,
observed by itself, and exists in itself as something complete and whole. But if I play the three notes together on the piano, I no longer hear them individually but as something new and whole, namely a chord. The three note individualities retreat and are obliterated, melted
together into a new form, into a chord.

There are analogies to this example in almost all areas of nature and the humanities, and it is characteristic for harmonics (and various other domains) that modern gestalt research-perhaps one of the most important pioneering domains, albeit rather silent compared to the ever-sensational realm of modern physics-should continually use primitive musical examples for support, in order to elucidate its theorems most clearly. Uexkull’s Theoretische Biologie is full of analogies to the tectonics of music, and Andre uses the same comparison forms when he explains (op. cit., pp. 292-293): “If one considers that tones emerge via successive vibrations in time, and that organic forms, from the lowest process of protomer division to the progressive subdivision of enclosing circles into ever more enclosing circles (organs, tissues, cells, and cell organs), are realized in space, then we can take the analogy between time-form and space-form even further. The organism is ‘a unit distinct in itself,’ and becomes so all the more in its individual realization, the more it becomes a unit in its inner distinction. In the musical time-form, a form can also become ever increasingly distinct in itself. The lowest level of playing together is playing in unison. The form becomes more distinct in itself when the different instruments form a harmony with every note, and the highest level of the unit distinct in itself is reached when every instrument plays its own melody, yet all individual melodies are in polyphonic harmony.”

Earlier, we asked what science has to say to a kind of “prototypics” of plants, such as we initially developed in our various sound-images; and from the available, admittedly very incomplete material, we were able to form at least an approximate verdict . The scientific aspiration to grasp the problem of plants “from above,” i.e. in terms of its emanative source, is mainly concentrated the eliciting of a preponderance of the form, as well as in an emphasis on the gestalt factor as a value existing in and of itself.

How these two factors are connected, whether there is a prototypical tectonics (form development) working not only in concepts but also in visible, precise ideas, explained and interpreted for the first time by this preponderance of the formal, or how one should understand the laws of construction of this tectonics-this we have not yet been able to determine. In the following digression on Goethe, we will discuss the individual efforts made in this direction, in terms of the emergence of plants as a whole; and in the subsequent chapters we will discuss individual phenomena such as flowers and leaves.

The voice of one “preacher in the desert” shall be heard in closing because it is typical for a large number of researchers, relegating a problem no longer solvable in a purely scientific manner to the “aesthetic.” In principle this is correct, but neither the scientist nor the “aesthete” can do anything given such a task, because the problem has only been pushed around, and not in the least clarified.

M. Mobius, emeritus professor of botany in Frankfurt a/M., who tends to write like a “dry,” systematic scientist, writes in his essay “Uber nutzlose Eigenschaften an Pflanzen und das Prinzip der Schonheit” (in Berichte der deutschen botanischen Gesellschaft, vol. 24, 1906, p. 5
ff.):

” … But of the reason for the formation of the leaf in its specific idiosyncrasy, why it is egg-, heart-, needle-, or arrow-shaped, single or combined, smooth, toothed, or indented, of this in most cases we have no idea. . . . It is even harder to believe in the possibility of an
explanation for the diverse formations of Desmidiaceae, algae, and diatoms . … all are minute water plants, for which the slight differences in their ways of life have absolutely no relationship to the diversity of their shapes. The existence of some 3,700 species of Desmidiaceae and some 6,000 species of diatoms, all so variously formed, is enough to persuade me that in the emergence of these species, the utilitarian principle has not played the decisive role ascribed to it by the Darwinian theory of natural selection, and that for these reasons, this theory is already invalid.” Mobius gives further examples: mushrooms (Corda’s Prachtflora europiiischer Schimmelbildungen); flowers, for which “symmetry is the highest law”; orchid flowers, whose form can be explained neither by pollination nor by symmetry; ditto fruits and seeds. Furthermore, many flower colors, such as the red cones of pine, larch, and yew trees, pollinated by air and not visited by any insects; the yellow color of hazelnut blossoms; the colors of peaches, apples, red radishes, and so on ad infinitum. “If one could explain the meaning of the ornamental beauty, then a great number of those peculiarities which we must presently still describe as useless would be explained.”

 

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Having concluded these examples and ideas-very instructive and appreciative of the significance of the ” a priori” form from the scientific viewpoint, but telling us nothing about the actual tectonics of plant morphology-we will now return to our harmonic investigation, and attempt to find some keys in the diagrams we developed initially. For the time being it can be a matter of the plant form in itself, without any specific observation of leaves, flowers, etc.-the harmonics of the details and functions will speak of these later.

Our diagrams were developed on the basis of the so-called “partial-tone coordinates,” i.e. a psychophysical configuration that strives for realization both within us and outside us. It is very important to continually emphasize this “dual citizenship” of the harmonic diagram in
the world of the soul on the one hand and in the natural world on the other hand. Because the first and most important conclusion to be drawn from this-that there exists a precisely graspable psychophysical and therefore psychically and materially provable tectonics-is
what legitimizes harmonics in all its investigations, and characterizes it as a “science” of an entirely particular type.

First, let us examine the diagrams developed in this book more closely and try to summarize, in a few theories, the results of the knowledge gained from them in terms of the plant’s overall form under the aspect of the examples science has given us. We arrive at the following formulations:

1. The plant is a psychophysical (psychical-natural) creation, whose external prototype (primary form model) corresponds to an internal value emphasis.

2. This “value emphasis” corresponds in tum to determined forms in our psyche, forms which we in fact only “understand” psychically. Consequently, we can view the plant as a realization of certain prototypes of our inner life-as a projection of our psychical
structure.

3. The habitual growth of the plant form is centered around a midpoint (generator-tone) from which, upwards and downwards, either one harmonic system splits or two harmonic systems “grow out”: in this polarity, harmonics simply sees the origin of life, a polarity that begins with the division of the cell’s nucleus.

4. Since this polarity manifests in every individual harmonic system as major-minor reciprocity, various possibilities for harmonic plant prototypes emerge ass a result of the group-theory variability of harmonic system formations. These possibilities provide a concept
for an exact morphology of plant archetypes.

5. Due to the “telluric adaptation” of the minor chord, we gain our first psychical view into the internal relationship of root and stem, and thus the possibility of understanding the puzzle of “geotropism,” the cardinal relationship between root and stem.

6. The external form of the two systems and the internal major-minor reciprocity copy, in their most important elements, the external image of plant prototypes: generator-tone center as nucleus; vertical axis as stem or trunk and root; bifurcation into above-ground and below-ground parts. The characteristic organs of the plant hereby emerge from the harmonic prototype (archetype, idea).

7. We come closer to this external form with the logarithmic illustration (Figure 15 ff.), since in general the nature of the logarithmic corresponds most closely to the growth process, in terms of its quantitative measurement. This “abating” of the plant form on all sides, made
obvious by logarithmic illustration, is the greatest proof for its psychical background: according to this, the plant does not grow by tone-numbers, i.e. not by material impulses, but by tone-values, the way we hear, i.e. by psychical impulses. As we shall see later, string
division offers enlightening prototypics for bifurcation, wherein the element of the limit, the abating, is expressed in the spatial measures, which are inseparably connected to the tone-values.

8. Likewise, we come closer to the actual plant forms, and to their mode of growth, when we set the generating center (1/1 ) equal to the corresponding index of the logarithmic system (10/10), as was the case in Figures 17 and 18 with their indexes. From here we come
upon one of the great mysteries of plants, almost never touched upon in botanic literature, namely the limitation of the plant form. The answer to the question “Why do trees not grow all the way to heaven?” therefore lies, from the harmonic perspective, in an a priori “indexing”
present even in the plant’s seed. Even the seedling (1/1) grows according to an index number already present in it and identical with it in terms of value C/1c=10/10 c!), which determines its final growth, i.e. its index limit, from the start. Figures 17 and 18 show this very clearly with the indexes, and from this it is obvious that the final index 10, i.e. the fully grown plant, does not represent simply a summation of preceding forms, but rather organic growth, up and out, of the above- and below-ground parts of the plant, whose equilibrium (i.e. harmony) is reached once the hierarchy of index 10 resounds both above and below. When choosing corresponding logarithmic systems, one can naturally set any number as the “index.”

9. We saw the first possibility for differentiation of this as yet purely schematic harmonic plant model in the discussion of Figures 3-13, as a different arrangement and inner value emphasis, i.e. through a selective choice of preferred ratios (such as fifths, thirds) within a given index. We called this value-emphasized element the “generator” and made the observation that on the basis of such a viewpoint, the solution for a further puzzle could at least be attempted in an understandable context: namely, the puzzle of how we should explain the emergence of various categories of plant forms from one archetype. Here, purely visual and psychical elements, a specific grouping and selection of tones and intervals, characterized the individual categories of plant forms morphologically.

10. We also begin to trace the reasons behind the varied external appearances within a single species of plant when we assume that within a given index, not only are identical ratios preferred (such as fourths, fifths, thirds, etc.), but also in free creative formation, just as in a
musical composition, certain motifs and themes are chosen. Since this is possible only in higher indexes, an interpretation is given for the relative similarity of seedlings, and for the later diversity of the same plants.

Were we to summarize these ten points in a universal statement, we could say:

The plant, in its complete form, is the image of a certain psychical structure in us, whose form we can detect in a harmonic manner, in a way that is understandable both to our intellect and to our feelings. This “sound-image of the archetypal plant” is in the process of growth (indexing) in a polar tension between a bright domain of light and a dark domain of earth. Only when this tension has reached its equilibrium (index limit) is its harmony achieved, the limit of its growth reached. Just as every composition plays around a main key,
so there are determined group arrangements of the harmonic sound-image which correspond to the various plant form categories. Just as for the construction of motifs and melodies only a few of the twelve possible tones, including their audible octaves, are chosen and rhythmized,
so the creative force chooses certain values from the primordial idea of the plant form, in order to make the infinite diversity of plants. Stem, root, and bifurcation are the universal “classic forms,” the framework within which this formation is expressed.

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Digression on Goethe’s Metamorphosis of Plants

In a letter to Knebel from July 18, 1787, three years before the publication of his Metamorphosis, Goethe wrote of his original intent to entitle the work Harmonia Plantarum.  Admittedly, the word harmonia was not meant in the sense of an exact harmonic discipline; but Goethe’s reasons for considering this title at all, and then deciding against, are cause for much contemplation.

The word Harmonia was used commonly in pre-classical times to describe a summary, fundamental discipline. Kepler’s Harmonice Mundi refers to a climax very much beholden to harmonics in the modern sense; but in the Middle Ages there were harmonies of the most diverse domains, even a harmonia evangelica, reaching up to the beginnings of modern research. In their best form, works of this kind were oriented toward what was so close Goethe, as a scholar, for all his life: a synthetic understanding of the mysteries of forms in themselves. In place of the harmony concept, the concept of the “signature” was often applied (Bohme: De Signatura rerum or On the Birth and Description of All Beings), as well as the concept of “physiognomy” (e.g. Giambattista della Porta: Physiognomia coelestis and De humana physiognoma, ca. 1600). As is well known, the physiognomy concept was revived by Goethe and others (e.g. Lavater), nurtured by the Romantics, and has become very current in recent times in the “gestalt theoretic” directions of almost all branches of science. Varied though these devices such as “harmony,” “signature,” “physiognomy,” and “gestalt” may be as concepts in themselves, they point just as strongly to a common center: to
the mystery of form.

Here I would like to attempt to illustrate the important elements in Goethe’s Metamorphosis of Plants sub specie formae, i.e. in broad terms. Then the relationship of harmonics to plants, or to specific harmonic value-forms, will emerge entirely of itself. Goethe imagines the form and growth of the plant as a six-step process of metamorphosis of one main organ (namely the “leaf”), rhythmized in expansions and
contractions.

From the seed, the cotyledons or seed leaves develop first as the lowest substance, “still crammed almost full with the raw material.” Then the leaves form as the second step. “They are on a higher level of construction and refinement, due to the light and the air.” Further up, as the third development step, the sepal appears, the actual flower petal as the fourth step, and the stamens and carpels as the fifth and sixth steps.

Generally, in Goethe’s view, the plant therefore grows in a “senary” manner with the following steps: 1. cotyledon, 2. leaf, 3. sepal, 4. petal, 5. stamen, 6. carpel. In these leaf metamorphoses, contractions (wave troughs: cotyledon, sepal, stamen) change places three times with expansions (wave peaks: leaf, petal, carpel). Physiologically, Goethe imagines this process as a kind of filtering of the juices from the lower regions up to the top: a finer juice requires a finer filter.

In §§73 and 115 of his Metamorphosis, Goethe gave a brief summary of his study, reproduced here for the sake of completeness and thoroughness:

§73: “From the seed to the highest development of the carpel, we first noticed an expansion, thereupon we saw the calyx emerge through a contraction, the petals through an expansion, but the sexual parts through a contraction, and we will now soon see the greatest expansion in the fruit and the greatest contraction in the seed. In these six steps, nature inexorably completes the eternal work of the reproduction of vegetables through two sexes.”

§115: “If the plant is to sprout, bloom, or bear fruit, then it is always the same organs which, in manifold functions and often in modified forms, fulfill the commands of nature. The same organ that expands as a leaf on the carpel and has taken on a highly diverse form
now pulls together into a calyx, expands again into a petal, contracts into the sexual instruments, in order finally to expand into a fruit.”

One must admittedly beware of imagining this metamorphosis of the “leaf” as the common plant leaf in some kind of concrete form. §120 of his Metamorphosis describes his inner spiritual view of this “leaf” phenomenon, and reveals that Goethe was only envisioning
a prototype, a primal form, taking effect in a protean manner in the various parts of the plant: “It is self-evident here that we must have a universal word with which to describe this organ, metamorphosing into such diverse forms, and with which to compare all the appearances of its form; at present we must be satisfied by being used to viewing appearances forwards and backwards against each other. For we could just as well say that a pollination apparatus is a contracted petal as we could say of the petal that it is a stamen in a state of expansion; a sepal
could be a contracted carpel approaching a certain degree of refinement, just as we could say of a carpel leaf that it is a sepal expanded through the influx of rawer juices.”

To summarize the basic ideas of Goethe’s plant metamorphosis, we can reduce this to four great morphological forms:
1. Primal organ, “leaf”
2. Expansion – contraction
3. Six-step rhythm
4. Differentiation (refinement)

Summed up in one sentence: The plant emerges via a six-step contraction and expansion of the juices of one basic organ, the “leaf,” whose juices are more refined at higher levels.

In view of the numerous other morphological and physiological plant-related questions, one might view this “metamorphosis” as very primitive, and argue that such cheap generalizations do not do justice to the nature of the plant.

Goethe himself would have had no answer to this objection. His purpose was not to establish a new “botany,” but to seek out a few basic principles by which plant forms could be understood.

In many passages in his writings, he makes specific reference to the restrictive, limiting nature of his Metamorphosis: “I protest here once again that I bring forward this way of viewing plants only conditionally, and present it as incomplete in itself” (Weimar edn., vol. 7,
p. 18).

But precisely this synthetic element is what makes his ideas so great. He, the great seer and observer, looked for a few basic principles that were also understandable to his inner eye, and found them in a basic idea (“leaf”), in a morphological breathing process (expansion-contraction), and in a hierarchical stratification (six-step, upward refining rhythm).

It is no great feat to dissect some phenomenal domain further and further-be it that of plants or of something else-in order to find new things and set these things going on tracks that have been there for centuries. For this one only needs good powers of deduction, a behind to sit on, and the corresponding funds and institutions to provide sufficient materials.

But it is a great feat to identify, in the multitude of ever more accumulating material, the great universal lines and forms that arrange materials from within, and to connect them with a few significant ideas. Here, besides intellect, a behind to sit on, existence, and research
material, one also needs genius-an extremely rare phenomenon, as we all know.

The scientist Goethe had such a genius mind, and it is gratifying that Goethe, with his Metamorphosis (in total contrast to his color theory), achieved lasting success in the science of botany, with only a few adversaries. Adolf Hansen, former professor of botany at the University of Giessen, in what is probably his best and most thorough work, Goethes Metamorphose der Pflanzen (Giessen, 1907; text and plates volume), gives very precise proof of this, and writes (p. 102): “The proof that Goethe’s ideas are in agreement with modern theoretical views in plant physiology that are scientifically valid to the highest degree affirms indisputably that his work is of scientific significance, and on the basis of my studies I can say that it is of enormous value.”

We must now examine what correspondences exist between Goethe’s Metamorphosis of Plants and harmonics. They are astonishingly close, as we will show hereafter as we discuss them successively in the order of the aforementioned principal ideas.

1. “Primal organ (leaf).”

If such a concept is to be understandable and to have any meaning at all, its emergence must be placed within our psychical capability and grasped as an idea. Certain resonances from outside reach the antenna of ideas in us, causing it to resonate and thus to form the idea
into an expressible value, a concept. The “sound-image of the primal plant,” as we developed it in the previous diagrams, is also an idea, whose harmonious sound resonates as a synthesis of the impressions coming from outside, i.e. achieves concept and form in the direction of the collective “plant” model.

Here is the “leaf,” which metamorphoses into the model of the plant. Here there is a specific graphics of harmonic value-forms which form the primal plant image, and whose peculiarities (generator-tone axis, bifurcation as a series impulse, logarithms of tone-values as a limiting principle, etc.) allow a metamorphosis within both the collective model and the individual plant types. Strangely, via the conversion of all possible notes reduced by octaves (i.e. transposed into a single octave) into tone segments and tone angles, we arrive at a pronounced leaf form, after connecting the relevant intersection points graphically. Figure 50 shows the harmonic order of the tones of this “leaf” and thus, for the first time, supports Goethe’s viewpoint in a precise psychophysical manner.

Goethe’s Metamorphosis lacks this connection to a deeper universal psychical form, which harmonics provides with its primal phenomenon of tone-number and the laws and norms that follow from it. Here, a characteristic property is common to both ways of seeing: namely, the way from value to being and the control of being by value. Goethe was very well aware of this inversion of being and value!

“One can say that no one can ask a question of nature that he cannot answer; for in the question lies the answer, the emotion that causes one to think and suspect something about such a point.” (Naturwissenschaftliche Schriften, Insel-Auslage, I, p. 189.)

2. “Expansion -contraction.”

If we write out the primary partial-tone series (over- and undertone series):

then we have an illustration, as exact as it is obvious, of Goethe’s two concepts, which one might call inhalation and exhalation, and whose rhythm plays a substantial role in harmonics under the device of the perspective and the equidistant (see my Abhandlungen, p. 41 ff.). In
harmonics, however, we learn that this centripetal and centrifugal element is ultimately a psychical value-form, whose background rests upon the two psychical worlds of major and minor. One need only place together the following concepts (to which many others could be
added)

in order to see immediately that Goethe, with this pair of concepts, found a form of great inner and outer amplitude, making it fruitful for the perception of plant forms.

3. “Six-step rhythm.”

In this form, two value-forms are unified. First the senary, the rhythmical element. By “senarius,” in harmonics, we initially mean the ratios of 1-6 and 1-1/6, which produce the pure major and minor triad, and thereafter, in the special case of music, the amplification of these first six whole numbers through their multiples and submultiples, which produce musically usable tones among the infinite possible ones. In my works, I have referred in many places to the great morphological value of this selection principle-for this is obviously what it is-in the most varied domains. It is therefore nothing strange that Goethe has the plant completing itself in six steps; this is in agreement with the inner and outer conciseness of this number selection. For Goethe, however, this six-step process is not a stringing together, a summation, of something equal, such as the number progression 1 2 3 4 5 6, but instead the six-step deployment of a primal organ (“leaf”) in six different modifications. The number progression alone give no hint of this, but the insertion of the tone-values does:

 

Here we in fact have the deployment of one primal tone in 6 different partial-tones, in a closed major chord-the subsequent ratio 7 *b ♭, as we have seen, brings in the first dissonant” tone-value. The external picture becomes even clearer when we use the string lengths instead of the vibration numbers, drawing the size ratios of the individual string segments (Figure 25). Here, as in the logarithmic illustration, a kind of /1 diminution” emerges, an “abatement” which indeed occurs in some way in almost all plant forms.

4. “Differentiation= refinement of juices.”

In Figure 25, as noted, the perspective element becomes visible, which Goethe described as the “refinement of the juices” from bottom to top. Furthermore, in this and the previous illustration, we have obvious proof for the rhythmic nature of the various steps, or as Goethe expressed it, for the “nodes.” Oddly enough, the idea of the “node” and node construction, i.e. rhythmic growth stages, is common to plants and acoustic vibration phenomena; we will return to this later.

Goethe has been accused of neglecting the root in his metamorphosis. As we saw in our initial “sound-images,” this vital organ not only can but must be included in the morphological idea of the plant, if one is to come to a deeper understanding of the overall form. Despite this, the unsettling rumblings of Olympus must reply to this accusation in extenso: nothing can give a better view into the thought process of a great mind than the way in which that mind defends itself. Under the title “Unfair Claim,” Goethe wrote in June 1824:

“The accusation has been made that in my discussion of the metamorphosis of plants, I took no account of the root. I have as much respect for the root as for the foundations of the cathedrals of Strasbourg and Koln, and the way in which these were built has not remained
entirely unknown to me. But our actual observation of the building begins from the surface of the earth. The deeper things on which the higher, heaven-seeking things rest are left to the intellect, the beliefs, the conscience of the master; but we, from the admirable and consistent
nature of the construction, conclude cheaply upon the excellence of the substructure.

“So also with the root, which in fact did not concern me at all; for what care I for a formation which can only manifest itself in threads, ropes, knots, and tubers, and with such restrictions, can only exist in unpleasant change, wherein endless varieties are apparent, but never an improvement? It is this improvement alone that drew me to my path, my calling, held me fast to it, and swept me up in it. Let each one tranquilly follow his path and look back on what he has contributed in forty years, as .a good guardian spirit has allowed us to do.”

As a conclusion to this section, we will note the interesting fact that Goethe, in connection with the dynamic fundamental principle of his metamorphosis, may have evaluated expansion and contraction “in the progressive changing of the plant’s parts” (“a force that I can only call uninvited expansion and contraction” – Werke, Weimar edn., vol. 7, p. 12) in an “algebraic manner”:

“It would be better to give it an X or a Y, in the algebraic manner, since the words expansion and contraction do not express this effect in its entire scope. It pulls together, spreads out, draws out, draws in, joins, splits, becomes colored, loses color, widens, lengthens, softens, hardens, shares, revokes, and only when we see all various effects in one can we then know concretely what I have thought to explain and sort out with these many words” (ibid., see also Metamorphosis of Plants §102). Here Goethe made it clear that he felt that one must have a central, profound concept, subsuming the above word pairs-just as in harmonics we use the value-form of the polar partial-tone series, which is the prototype for all concept pairs of similar origin (on this, see the section “The Harmonic Inversions” in my Grundrifi, p. 212 ££.). It was not without a certain degree of humor-Goethe himself would have admitted this, with a friendly raised eyebrow-that he calculatedly took refuge in mathematics, the value of which he considered highly questionable for the evaluation of biological phenomena-indeed, often enough, he questioned the value of mathematics in itself.

But was this flight into mathematics not, rather, a flight into symbolism? Was this the wish of a great seer and observer to find a neutral sign, a “signature,” by means of which one could also operate “metamorphically”?

In an obscure passage from his Collected Works (Cotta, 1840, vol. 40, p .430), there is a highly revealing reference that is also illuminating for harmonics. Here, after Goethe calls the idea of metamorphosis “a highly dangerous gift from above,” a “vis centrifuga” whose impulse, leading “into the formless,” one must oppose with a “counterbalance,” a “vis centripeta, which in its deepest foundations cannot harm any superficiality,” he then says: “Perhaps we can save ourselves from this confusion via an artificial process: comparison with the naturally ever progressing notes and the equal tempering, confined to an octave, whence a decidedly drastically higher music, for the protection of nature, first becomes possible. We must allow an artificial balance to enter in. Symbolism must be devised! Who will provide it? Who will recognize what is provided?”

“After having risen to this insight, we are no longer in a position, in the handling of the natural sciences, to set the experience in opposition to the idea; we are much more accustomed to seek out the idea in the the experience, being persuaded that nature progresses according to ideas, and likewise that the human, in everything he undertakes, is pursuing an idea” (Goethe, Naturwissenschaftliche Schriften, Insel edn., I, pp. 328-329).