CHAPTER VI – The Staff of Mercury

PLANT BETWEEN EARTH & SUN 

by Olive Whicher & George Adams


Chapter 1: The Languge of Plants

Chapter 2 : Science of the Future

Chapter 3: The Polar Forms of Space

Chapter 4: Physical & Ethereal Spaces

Chapter 5:  Ethereal Space of the Plant Shoot

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42 Root and Shoot- Radial, and Peripheral Formations

Having gained a certain insight into the type of form belonging to the more ethereal, leaf-bearing regions of the plant, we come now to the polarity of root and shoot. In the root too, in its finer organs, the plant lives and grows by virtue of ethereal, suctional forces, but the whole orientation of the latter is different. Adapting themselves to the earthly-physical domain, roots bring about predominantly radial, densely filled forms, adapted to physical space. Radial forms are the natural expression of the material and physically spatial world, where both the forces and the movements go along lines from point to point. We see the same in human works of engineering, which, being well-adapted to purely physical ends, represent Nature’s physical aspect as it were in quintessence. Tube and pipeline – crank, girder and chain, “strut and tie” – these works abound in radial forms, mechanical and kinematical.

So too the living body produces radial organs where it enters into strong relationship with earthly forces. From the most rudimentary pseudopod of the amoeba to the highly organized limbs of the vertebrates and man, organs are formed to push and pull, to produce and to withstand the mechanical forces of the inorganic world. In the plant the radial quality reaches upward from the roots into the higher organs, both to sustain their weight and to transmit the fluids to and fro . Stem and branch, petiole and veins of leaves are wisely adapted to their mechanical function , where the sheer weight and leverage of spreading forms have to be borne and transmitted to the central stem. Indeed the pure line and structure of the mechanical forces are often more evident in the shoot than in the massive, gnarled or tangled root, but this is so in human architecture too, the farther upward we lift heavy matter from its normal home. A cantilever bridge, an arch, a girdered roof make manifest the play of forces precisely because the structure has to be reared into light and air with a minimum of material – into a realm where such material of its own accord would not rest.

Such then is the polarity of root and shoot. Below, the living form adapts itself to the character of physical space and earthly forces. Above, while even the most delicate leaves and petals still have to be borne aloft by radial and earthly organs, yet they immediately adapt themselves to another form of space, ethereal and peripheral. It is an interlocked polarity such as Goethe recognized for light and darkness in the realm of colour, each of the polar opposites diving into the realm of the other and manifesting from within it, as well as in its own domain. 

The living interplay of radial and peripheral formative processes, related as they are to the character of physical and ethereal spaces respectively, will obviously be of prime importance, and we shall therefore need to study this on a more simple and elementary level before proceeding to the essentially bipolar morphology of the higher plant. We will therefore begin with a more concentric form of life – a single living sphere, such as we find among the radiolaria in the animal kingdom (Figs. 56 and 57 ). (Or we might also think of a two dimensional, circular, leaf- like form.)

In the purely geometrical aspect, such a sphere, as we have seen, is formed in a dual way – pointwise and radially from the centre outward, planewise and plastically from the periphery of space inward. We will suppose now that the two components – radial, and peripheral or tangential – are not only dynamically active but are made visible in material organs or tissues differentiated from the rest of the body. The hardened and supporting organs of a living body may very fruitfully be regarded as containing the two morphological components which we will name: radial and spherical, or radial and peripheral. Some, like the long-bones in man, lay more emphasis upo n the former; others, like the skull – bones, upon the latter. We have already mentioned the significance of the peripheral formations – skin or carapace or exoskeleton – in relation to the ethereal.

The peripheral will always be in evidence, for the living body is differentiated from its surroundings by some kind of skin or at least surface– ayer of biological importance, the plastic form of which will be related to the ethereal forces . The radial will not always be materially manifest – least of all in the delicate beginnings of life – but it will tend to become so when in the course of development the living body comes into closer relation with the conditions of the physical and mechanical world. Nay, this will often happen without apparent purpose, as if by sympathetic mimicry of these conditions. We will suppose henceforth that our ideal living sphere does contain radial formations emanating from or at least oriented towards an internal centre. The radiolaria are good examples.

To give a rest to the rather overworked words, centre and focus, we may here borrow an astronomical term and describe this radiating centre as the “radiant“. Two alternatives present themselves. The physical radiant m ay or may not coincide with the ethereal point-at-infinity. If the  concentric, spherical or circular picture in its simplest form is to apply at all, we must assume, however, that it does. For the radiant is not likely to be a mere passive junction; hence with the other alternative we should come back again to a bipolar body and to the morphological type of the higher plant- this we shall follow up a few paragraphs further on.

We will imagine therefore that the centre of the sphere is both the point-at-infinity of the ethereal space of the living organism and the “radiant” from which some kind of physically differentiated forms ray out. In their ethereal aspect, these radii will now be lines-at-infinity, in the sense of paragraph 20. If they are physically hardened, whether as vessel or more_ solid fibre, we have the paradox that the infinitude – as it were, the ideal void – of the ethereal space coincides with a region of physical fulness and condensation. If they are hollow vessels, it is true, the ethereal lines-at-infinity only run along their axes, not in the actual substance. We are reminded of one of the main polarities of root and shoot- the cylindrical nature of the stem, the central core in the root (paragraph 6). But in either case, whether the matter be within or close around it – the innermost radial line is now an axis of physical strength and condensation. The stem too, after all, is not only a “spiritual staff” of life; it is a physical staff also.

Geometry alone will not tell us what is the real interplay of physical-material and ethereal activities. It can at most interpret and enlighten what we must read, in the last resort, from Nature. Reading from Nature, we declare that the paradox we have just voiced is also among the constantly recurring Urphenomena of living form. It is by no means always so; but Nature very often condenses her physically radial organs in or about the lines-at-infinity ether ethereal spaces.

(We may observe in passing that endo- and exoskeleton – concepts that apply of course more to the human and animal kingdoms than to the plant- now have this dual aspect: In our ideal living sphere they would be formed, geometrically speaking, by the lines-at-infinity of the two kinds of space: the former radially, pointwise, along the lines-at-infinity of the ethereal space; the latter spherically or peripherally, planewise, as from the infinitely distant lines of the physical Universe in which the creature lives. If the lines in question are of finite number and configuration the outcome will be, for the exoskeleton, some kind of polyhedral form. It would be interesting to study some of the radiolaria, pictured by Haeckel with such care and skill, from this point of view (Figs. 56, 57). For the rest, even the rounded forms of skull and carapace often show traces of an underlying polyhedral pattern.)

Many diversities will arise through the different kinds of interplay of radial structure from within and ethereal formative forces from without. We may imagine these, beginning again with the simple picture of the sphere. These are the obvious variations: The radial structures may extend to the main surface of the living body, or they may penetrate beyond it; or they may be restrained short of the surface, the fibres fading away or bending round until they run more tangentially and even undergo mutual anastomosis. The surface region will in this case be more continuous and smooth, as though the ethereal and plastic forces would here predominate. If the radii reach out more strongly, various forms of indentation will be produced, revealing different kinds of interplay of radial and peripheral components. In the extreme case there will be prickly and spiny forms; the plastic continuity may even seem to vanish altogether: Yet it will still be there, in that the radii do not extend at random. If we imagine a continuous surface drawn through their terminations, a plastic form, characteristic of the living species, will appear, and this indeed we nearly always see. We shall return to this thought shortly, when we contemplate the forms of leaves in the two-dimensionality of the plane (§48). 

Returning now to the ideal picture of a living sphere, let us look at the second of the two alternatives, namely, when the physical radiant does not coincide with the ethereal point-at-infinity. If the main ethereal focus does not coincide with the radiant from which the radial organs proceed, a bipolar body is the outcome. The radiant, being the source from which the radial organs have grown or upon which they converge, will be a focus of life in its own kind.

The bipolar body will thus contain two kinds of centre or focus. One of them will be predominantly ethereal and for this very reason will be of greater importance for the forming of the body as a whole; or as we have seen, the ethereal forces work the more powerfully, the less the focus of their space is physically formed, – the more there is of “chaos” in this region. The other focus is the radiating centre; it too is ethereal in nature, for without this the radiating organs would have no origin for their life and growth. Yet in this region, the physical is more in evidence, though we must remember that in a living body the polarity is always interlaced: the more physical realm has its ethereal and the
more ethereal its physical component.

Place the seed – the little point-like entity, seemingly composed only of material substance – into moist earth; give it over to the creative powers of the water, and presently the living forms will reveal the interweaving polarity of physical and ethereal spaces. Water as such tends to form a sphere; the spherical drop is like a microcosmic picture of the great water-sphere of the Earth, and as we have seen, the sphere is among the primary forms revealing and evoking the all-prevailing polarity of point and plane. We shall therefore not wonder that this polarity is made manifest in living form when in the moisture of the Earth the seed is brought to germination.

There is much variety in the structure of seeds and so there are differences in their mode of germination, but basic to them all is the form of the young plant within the ripe seed: it consists of a shoot (the plumule) a root (the radicle) and either one or two seed-leaves or cotyledons. In all cases, the same conditions must be fulfilled before germination will take place: there must be moisture, a certain range of temperature, varying with different plants, and there must be free oxygen for breathing. In other words, the seemingly dead little physical form, the seed, must be given over to the totality of the other three elements – water, air and fire – before any living forms may be conjured from it. What then happens will, however, always be the same, though the manner of achieving these same ends will show many differences. After the seed has been well soaked for a time, the radicle will appear first and grow down to become a well-developed root, which will later give off side- roots: then, secondly, the plumule will grow up to form the first shoot (Fig. 63).

A detailed study of the different forms of germination reveals in many fascinating ways the development of the bipolar form of the embryo, in which the consolidated form of the root may be seen in contrast to the little plumule, formed of planar organs, which – sometimes even already within the seed _ reveal the hollow-space gesture containing the ethereal focus. Typical on the one hand is the naked, densely filled, radial form of the root, growing downward into the soil, and on the other the sheathed form of the shoot, protected as it is in varying ways by bracts or enveloping seed-leaves (cotyledons) or by true leaves. From the very start, the ethereal space containing the focus of life is often to be seen in one of its most ideal manifestations. The germination of a seed is in fact like the coming-to-birth of the bi-polar form – a sundering of earthly and sun -like centres. It is then followed by a quick expansion into the developing green shoo t (Fig. 64). 

This first stage of development results in what is called the ” hypocotyl” , the first and primary node. Unlike the Plantain and the Dandelion, for instance, most plants do not simply raise a flower-bearing stem from a rosette of leaves on the ground, nor are the leaves, as in the Plantain, crowded together at ground level, each with a flower-bud in the axil. Frequent as these forms are, most plant develop node after node with lengthened internodes all up the leaf-bearing stem (Plates VIII and XIII) , and only then come to the crowning glory of the blossom. Often a far-reaching variation of the leaf-form accompanies the upward sequence of the nodes (as for instance in Figs. 84 and 85), and we must now begin to ask: What is the significance of the node as such in the bipolar morphology of the plant ?

Not only is the form and gesture of the whole plant, with its organs above and below the level of the soil at the hypocotyl, a clear indication of the fundamental polarity at this archetypal node, but a vertical section, for example, through a young seedling, will reveal the same polarity in the detail of the contrasting inner structure of root and shoot (Fig. 65).

Where the shoot is concerned we bear in mind what has been said about the cone-space. The gesture of the entire shoot may sometimes be more conical, sometimes more spherical, the stem may be cylindrical, but the structure is always peripheral and the organs predominantly planar. The leaves and branches spring from the cambium which is an outer layer of the stem; the stem itself may even be hollow.

The sections of Brussels Sprout (Brassica oleracea gemmifera) in the right-hand corner of Plate III – the horizontal section of a stem at the point where the leaf leaves it and the vertical section of a sprout which has begun to shoot- show the manner of branching of leaves from the outer layers of the stem. In the Dandelion (centre) and Hogweed (top-left) is shown the polarity of root and shoot, below and above the hypocotyl. The horizontal sections on the lower left of the picture show the contrasting structure of a stem and a root. The drawing of the stem is from a young Elderflower shoot, showing the cambium layer in the periphery, underneath the young green bark, from which any new organs would grow. In the later stages of development, when the stems of the Elderflower become woody, the material within them turns to pith and at last the wood becomes hollow, except at the nodes.

The structure of the root on the other hand is radial. The vascular system is internal, forming a central core from which the lateral roots grow out through the surrounding layers (Fig. 66). The root-tip burrows its way into the soil, its protective cap being constantly worn away and renewed. It is like a vital self regenerating little sword, piercing its way through the darkness. 

The point where the plant emerges from the soil into the light is in all respects a threshold and a crossing-point. In the vascular system there is a peculiar interchange of what is inner and outer; the whole plant is here drawn together into the primary node.

43 Rhythm of the Nodes – Levity in Upward Growth

The form and habit of plants arises from the interplay of the two poles – root and shoot, both of them imbued with the ethereal principle of life and growth, but the former entering into a more intimate relation to the earthy-material and gravitational sphere. Let us first try to picture the type of form that may be expected to arise within the predominantly ethereal region of the shoot, in the ethereal space determined by the sun-centre. The forms we here discern will then be modified by the interplay of the more earthly principle from below.

The young leaves that begin, reaching upward to envelop the sun-centre above the growing-point, tend out and away towards the horizontal. Although the shoot as a whole grows quickly upward, relative to the growing-point (or to the ideal “star” above it), the movement of the growing and expanding leaves is downward. The little leaves which today reach pertly up above the growing point from which they come, will soon, when fully grown, be far below it. It is necessary to understand this dual, upward-springing and at the same time downward-unfolding movement. Consider, for example, Silphium perfoliatum (Fig. 11 ).

The young leaves of Silphium perfoliatum (a plant related to the Sunflower, originally from North America) hollow out a plastic form, and surround a more or less spherical space which soon opens out and becomes shallower. The leaf primordia, microscopically small on the actual growing-point of the plant, are hidden deep within the young leaves, which grow out above them. In opposite pairs, like sheltering hands, they hold the innermost region from which the younger leaves spring. As the stem grows, the internodes lengthen and the growing-point is carried upward, the expanding leaves gradually leave the region of this inner space and open out towards the horizontal. They are succeeded by younger generations of leaves, so that the delicately formed hollow space at the tip of the shoot still remains, while the full- grown leaf actually reaches the horizontal plane. In some plants, this may be at the surface of the Earth itself, or it may be in the lower regions of the stem, where upward growth will as a rule have ceased. However this may be, we regard the leaf as an elementary planar organ of the ethereal Earth in the sense in which it was described in paragraph 32. From the aspect of our present study, near the Earth‘s surface there are many potential planes, one above the other. Every such plane can be a “median” plane or dynamic “plane of levity” for the ethereal space determined by the star-centre above the growing shoot. Think therefore of such a horizontal plane, towards which the growing and unfolding leaves are tending; it will be well below the ”star”, from which the vertical line of the stem reaches downward, as a rule passing through the plane at right-angles. We picture the star-centre, enfolded by the youngest leaves, the growing-point of the stem a little way below it, and beneath them all the plane towards which the leaves are tending.

Now we imagine this horizontal plane as the common “median plane” of a family of cones, as in Plate IV, or of a concentric family of ethereal spheres in the ethereal space determined by the star-centre, as in Plate IX. The two-dimensional curves in Plate IX serve to illustrate what we will call a family of concentric ethereal spheres. In the plate it is as though we are looking at them in cross section. As we have seen in Chapter III, there is no essential difference between a family of concentric spheres, whose “median plane” is the plane-at-infinity of Euclidean space and the projective transformation of such a family of concentric spheres, where the “median plane” is one of the planes of space. We have taken the top right-hand picture of Plate X as a picture of the former and the curves in Plate IX will serve to illustrate the latter.

As well as the cone space, we now have another geometrical thought form through which to perceive the ethereal nature of the process of unfolding leaves.

The ethereal concentric spheres will not look concentric, nor will they look like spheres, judged from the aspect of physical space. Yet they are truly concentric, and truly spherical, in the ethereal space determined by the “star” as point-at-infinity. Seen in cross-section, with the star- centre above and the horizontal plane appearing as a line below, they will look like a family of conics with a common focus and directrix. The “smallest” (that is, ethereally the largest) of them will be nearly circular in appearance, closely enfolding the “star”. Thence they enlarge into ellipses, followed by a parabola which opens upward and then a series of hyperbolae flattening into the horizontal line. In the ethereal aspect, the latter grow ever smaller; they vanish into “zero” when they reach the plane.

Just as we have compared the gesture of the cone forms in Plate IV, which open out from a vertical axis to a horizontal plane, with the unfolding gesture of the leaves of the Plantain, so now we gain another realistic picture for the understanding of the ethereal process of leaf- development at the growing point, if we imagine the unfolding leaves springing from the central stem between the growing-point and the plane, enveloping or at least touching successive spheroids. In some plants, as we have said, the gesture at the growing point is more spherical than conical, and this is often to be seen when the leaves at the top of the growing stem are related to a flowering process. In the Woodruff (Fig. 7), for example, it is interesting to see the more spherical gesture of the leaves which are creating the ethereal space for the flower, while the lower nodes take on the conical gesture more typical of foliage leaves up and down the stem of the plant (see also Plate XIII). In the forms sometimes to be seen at the top of the shoot, and very often in rosettes at the ground, each leaf, as it unfolds and grows, envelops ever flatter and more open spheroids, beginning near the star-centre and opening out towards the plane. 

Meanwhile the stem is growing upward; fresh leaf-buds are arising at the apex and m their early stage of growth enveloping the physically smaller spheres.

In the early stages of growth the internodes will not yet have lengthened out. The star-centre will be very near the horizontal plane; between the two the spheroids will be crowded very close together. We therefore begin with the same picture on a very small scale and, while expanding it without essential change of shape, simultaneously imagine the unfolding movement from the inmost forms to the larger and flattened ones. Combining the two transformations in this way, we have a picture of what happens as the shoot springs upward and the leaves unfold, down and away from the growing-point. For a beginning, we may imagine the horizontal plane fixed in position. In the resultant, till they have reached the horizontal, all the growing leaves are carried upward; the upward shooting of the growing-point more than makes up for their downward unfolding from sphere to sphere.

We here approach the kind of interplay between two opposite processes which was described in paragraph 5. This is indeed a characteristic of the life of plants to which our eyes will be opened ever more and more. It is the interplay between two activities – both of them physically and ethereally determined but in different ways – which both in quality and gesture and in their quantitative outcome partly tend to cancel one another out. It is so above all in the vertical dimension of unfolding growth.

Trying to think and feel in the qualities of ethereal space, let us now consider what the two components of this double process mean. The passing of the growing leaves from sphere to sphere, away from the “star of life” and flattening towards the plane, is for the ether-space, as we have seen, a spatial lessening. In the ethereal volume they contain, and in ethereal area, the hyperbolic spheroids grow ever smaller as they flatten; indeed they reduce to “nothing” when they melt into the plane. The more rounded spheroids (or the tiny cones) on the other hand, close to the point-at-infinity, grow ever greater and vaster as we go inward. Where there is physical increase, there is ethereal decrease. The leaves are born in the realm of the ethereal infinitude and thence grow out and downward, until they alight, so to speak, in the plane of Earth. It is as though the microcosmic Sun-space of the star were giving them to the Earth. As they grow larger physically, the ethereal space which they envelop grows ever less. This mathematical and quantitative aspect answers to what we see and feel: the young leaves with their tender yellow-green are replete with life; the fully opened ones with their darkening colour do indeed show the characteristic form of the plant more fully, but they have grown less vital – they are becoming ever more like finished, ultimately dying pictures of the archetypal form.

Thus, we reach the conclusion that whereas the upward growth of the stem, increasing the distance from the star-centre to the horizontal plane, appears in physical space like a pure expansion, what it means for the ethereal space determined by the star is none other than a primary phenomenon of levity or “Leichte”.

The relative Earth-plane to which the leaves are tending is an important plane of levity in the individual organism of the plant. The celestial sphere on the other hand functions as a universal plane of levity : for the levitational fields of force it is in polar analogy to what the Earth- centre is for the terrestrial phenomena of gravity. The plant’s individual plane is drawn out towards the cosmic plane. This finds expression in the upward movement of the star-centre. Ethereal, the upward growth brings the horizontal leaf-planes nearer to the heavens. The Earth- plane itself is in spring and summer breathing ethereally outward by virtue of the plants that grow upon it. Once we perceive the true idea, we see that it does so qualitatively even where it stays seemingly at rest.

For the spheroids – and their enveloping leaves – between the horizontal plane and the star-centre, this functional outward breathing of the Earth-plane involves an actual upward movement. Even by this rudimentary and no doubt over-simplified thought-picture we have interpreted the growth of plants with a quality of thought far more intimately related to the phenomena than any atomistic thought-form.

To sum up these thoughts concerning the upward growth of plants: raised from the region of convex growth where the plant is rooted in the earth, the physical forms of the leaves are so adapted as to envelop the ethereal spheres or cones in the region adjoining the main stem, between the star-centre and the horizontal plane below. The latter may be any horizontal plane above or at the surface of the soil. For the ethereal space of the star-centre, it is the plane of levity towards which the leaves are tending. But the plant with its ethereal spaces – convex and concave, root and shoot – is itself an organ in the larger cosmic organism of Earth and Sun, and as in any complex living body (cf. paragraph 33) the individual formative spaces, reaching the zenith of their activity from time to time, are so co-ordinated as to contribute to the larger whole, so the leaves, born in the region of the plant’s own sun-like space, are given over as they mature to the planet as a whole in its organic relation to the Sun and the surrounding heavens. They play their part as planar organs in the Earth’s levitational field (paragraph 31); the shoot as a whole is drawn up and outwards towards the cosmic plane of levity, the summer sky.

We take hold of a truly cosmic imagination of vital significance for the understanding of plant development if, while watching the visible upward development of the plant, as it grows taller in physical space, we realize that this is only one aspect of a twofold process. The leaves appearing at the top of the growing stem are, as it were, flowing downwards towards the Earth from an ethereal space; born out of the cosmos, they descend to Earth, there to grow larger, more filled with material substance and finally to die away again and disappear from earthly sight. It is a truth which applies to all life as it comes into being in the lap of Mother Earth, spends its allotted span of time there and passes away again. Scientists will always be at a loss to explain the appearance of life on the planet, until they take the long stride of thought  here involved – a stride which will, however, appear less long as scientific thought emerges from the comparatively short, but gigantically forceful period of nineteenth-century materialism in human history.

44 Goethe’s “Spiritual Staff” – ” Verticon” and Horizon 

Physically, then, the plant is centred in its roots below the surface of the soil; a firm physical structure, they hold it to the earth. Above, enveloped by the budding leaves, is the point-at-infinity of the ethereal space, imbuing the young organs with vital forces and drawing them forth to living unfoldment. It is as essential for the sprouting, developing activities of the plant as are the physical constituents of its body

The higher plant as it germinates reveals at once the polarity of root and shoot with the hypocotyl between. True leaves quickly follow the primitive seed-leaves or cotyledons (cf. paragraph 48) and each time this happens a node is formed. Sometimes the nodes remain close together as in Dandelion, Plantain and plants like the common wild Daisy (Bellis perennis); more often the nodes are at intervals up the stem. Biennial plants – Foxglove, for example (Digitalis purpurea) or Mullein (Verbascum thapsus)- have their nodes close together during the first year, the leaves making a wonderful hollow from which the flower-bearing stem springs with elongated internodes in the second year. The leaves may appear in alternate pairs, or they may spiral singly up the stem. Whatever the phyllotaxis, the principle is the same: the leaf as a more or less plane-like organ, with a bud or “eye” – dormant at first- hidden in the axil between leaf and stem.

In Plate XIII the Pepperwort (Lepidium campestre) and in Plate VIII the Dock (Rumex obtusifolius) reveal the upward striving of the plant, node after node. Every time the fresh young leaves appear they tend with their gentle cupping gesture the “star of life” which begets them. They do not hold it as their own; their time is allotted them, and they make way for the next generation. Opening out in succession towards  the horizontal plane, they become mature. Born of the ethereal source, receiving vital strength from thence, leaf after leaf gives of its life to the earth, remaining behind as the plant grows upward to bedeck the earth with plane upon plane of green.

As the plant grows, it is as though the quality and function of the hypocotyl were drawn higher and higher above the earth. Each time a new node appears, it springs from the one beneath it, and the polarity of root and shoot is in a sense renewed. Even the sprouting of actual roots at the node is a very frequent phenomenon, as for example in the labiates and in all plants from which cuttings will flourish. Goethe describes the upward growth as a gradual enhancement, the cruder substances giving way to finer ones. ⁵⁷ In rhythmic interplay between the “dark” pole and the “light” the plant grows, at each stage raising earth-matter to become more and more receptive of the light.

As Goethe sees it, the plant organs are ranged around a “spiritual staff”. How true this is! He speaks of the “law-giving power in the midst”. ⁵⁸ The central axis of the vegetative part of the plant – a region so often hollow or only containing pith – is the “infinitude within” of an ethereal space. This is not a physical or material staff. It is the line followed by the “star of life” as it draws the plant-forms forth; along it are the nodes with their potential powers of development. This is the “Staff of Mercury” – the “Caduceus”.⁵⁹ The old symbol stands for the forces of healing of the green leaves as they arise in rhythmic sequence, spiralling up the stem of the plant.

The Dock in Plate VIII revealing the staff of Mercury, shows also how the bud in each node, like a seed in the soil, may be called forth by its own “star of life” to develop staff upon staff of living forms.

In physical space, the two-dimensional analogue of concentric spheres will be concentric circles in a single plane, and as the former, growing infinitely large, tend to the plane-at-infinity, so do the latter tend to the line-at-infinity of the plane. In ethereal space, the two-dimensional analogue of concentric spheres will be concentric cones (Plate IV, Fig. 41 ). These will grow infinite inward instead of outward, tending in fact towards a focal line – the line-at-infinity of the point which contains them. It is the common line of the said point with the point-at-infinity of the ethereal space as a whole (cf. paragraph 34). The “line-at-infinity within” is the ideal axis of the stem – Goethe’s “spiritual staff”. It joins the node from which the leaves are springing to the star-centre, poised in the open space a little way above it

With respect to the physical and ethereal spaces of the Earth-planet, the plant itself, and the locality where it is growing, the vertical line of the stem is polar to the infinite horizon. The celestial plane, determining physical space, contains many lines-at-infinity, and among these some are of special import – for example the celestial equator, the ecliptic, the horizon. For a particular locality on Earth, the celestial horizon is all-important. Likewise in the ethereal space of the shoot, every line through the star-centre counts as a line-at-infinity, and among these one is of special import, namely the vertical line joining the star-centre to the focus of convex growth beneath it and to the centre of the Earth. Recognizing its ideal value in this sense, we can appreciate how deeply Goethe was impressed by the significance of this innermost line of the stem – the “spiritual staff”, the “vertical principle”, the “law-giving power in the midst” .

Just as, for our human experience, there is in physical space one line-at-infinity of supreme importance, the infinite horizon where the Earth-plane upon which we live meets the celestial plane-at-infinity, so for the plant there is one line-at-infinity of supreme importance- the  line that joins the star or point-at-infinity to the Earth’s centre, or to the point at the Earth’s surface where the plant is rooted and whence it germinated. Such is the vertical line of the stem, – Goethe’s “spiritual staff”. It is the plant’s “infinitude within” in its line-wise aspect – ethereally one dimension lower though physically one dimension higher than the seed or star. Even as the “infinitude without”, determining our own spatial life and consciousness, has the two aspects – two-dimensional, spherical or planar when we look up and out into the star-strewn heavens; one dimensional and linear when with our consciousness turned to more earthly ends we scan the wide horizon – so for the plant there are these two infinitudes : the star and the spiritual staff, the point and the line, of which the former is primary and contains the latter, just as the heavens contain the infinite horizon. 

For the ethereal space that forms the plant, the spiritual staff- the central line of the stem – is therefore an “infinite line within”, in polar analogy to the horizon. This helps us understand the vast importance of an axis which is materially often hollow, or in a region of comparatively unimportant pith. “Pith” is a synonym of concentrated essence, the vital nerve of the thing in question; in many languages the words for pith and marrow are the same. Materially, pith does not seem to deserve this reputation. Ideally, we now perceive the significance of this inmost region. It is a formative infinitude, fulfilling a like function in the ethereal space of the plant as is fulfilled in the forming of physical and earthly space by the great circle of the celestial horizon. Goethe divines this when he writes of the roundness of the stem, which, he declares, if not outwardly round, is at least potentially round from within; in it he sees “the law-giving power of the midst”

Even as the geometry of a circle is largely determined by the line-at-infinity of the plane in which it lies, so is each cone or whorl of leaves, arising at a nodal point along the spiritual staff, well-centred and well-formed in relation to this innermost and now vertical infinitude. The  youngest leaves, those at the highest nodes, by their enveloping gesture indicate a cone of steeper angle, near to the spiritual staff; as they grow older the leaf-cones open and Hatten towards a plane. The cones that are nearest the infinitude within and that look narrowest to physical imagination, are in fact ethereally the largest; the downward unfolding growth is an ethereal reduction.

Geometrically, as we have seen (Plate IV and paragraph 20 ) such a family of cones, if carried by a single point, is polar to a concentric family of circles in a plane, which we may take to be horizontal. The vertical “infinitude within” is polar to the line-at-infinity of the plane; the horizontal plane towards which the cones will tend as they widen out is polar to the common centre of the circles.

Once more, as in paragraph 40, it is helpful to relate the ethereal process to the physical by mentally reversing the Row of time. In the physical world we get a movement of concentric circles when we throw a stone into a pond and watch the waves expanding- towards what would ideally be the infinite horizon. Reversing this, we should have the picture of circles tending inward concentrically from the infinite horizon-detaching themselves from thence, as it were, one by one. They lose themselves into the central point. This is analogous to the ethereal process shown by expanding leaves. They come from the realm of the infinite line within, and, with ethereal lessening of the cone-form they envelop as they grow older, will merge at last into the horizontal plane.

Also for the more spherical unfolding forms described in paragraph 43 we can apply the same thought-process. The “infinitude within” is then a point, namely the star-centre. Again and again, the growth of living forms from their seeds, or from the focal regions of unfolding life, is like an inversion – both in space and time – of what takes place in the physical world when entities disperse into the distance. Often when we look down upon the growing-point of a symmetrically growing shoot, it is as though we were gazing into the vanishing-point of some far perspective. We see what Goethe would have called an “open secret” . For the ethereal realm which we are here beholding, this is no vanishing-point; it is a point of origin, of creation. So too the “spiritual staff”. The “vanishing line” of physical perspective drawings most often represents the infinite horizon; the plant’s “infinitude within” is a creating line. 

This qualitative concept of the stem, or of the innermost vertical line at its centre, is so important both in itself and in its polar relation to the horizon as to deserve a specific name, conveying its geometrical character and at the same time sharply differentiating it from the concentrating and supporting function of a physical-material staff or axis. We shall therefore describe the innermost vertical line, seen in the aspect of ethereal space, as the “verticon”, although the form of word may be open to criticism from a scholarly point of view. The formative space of the archetypal plant- compare what was said of this in paragraph 11 – is spanned between the verticon and the horizon. The living plant is an entity both physical and ethereal, placed in the spatial universe in such a way that the Earth-plane from which it grows, the plane-at-infinity, the centre of the Earth and its own growing-point – or the star-centre hovering above this- are of prime importance: a pair of planes and a pair of points, with one of either cosmically given and one of either given locally or individually. The common line of the two points is the “verticon”, the common line of the two planes the horizon. Each of the lines functions as a line-of-points and as a line-of-planes, the points of the one bearing the planes of the other and vice versa.

Both the vertical and the spiral tendency, in Goethe’s sense, have to do with both these axes. In uniform circling-measure the points of the horizon determine the circling sequence of spiral phyllotaxis; the same circling-measure belongs to the planes of the verticon, for the controlling character of which the ideal “roundness” of the stem seemed so important to Goethe. The upward striving growth on the other hand, the rhythmic sequence of the nodes – for the physical aspect of the plant so obviously belonging to the vertical axis of the stem – in its ethereal aspects is related to the successive planes of the horizon. It is the horizon which bears the planar, levitational movement which we have just been considering. In other words the celestial horizon is for each Earth-locality the main ethereal “line of force”, relating the horizontal, potentially leaf-bearing planes of the ethereal spaces of the plants to the celestial plane, and thus determining the field of “levity” which draws the plants up and outward.

A threefold possibility of movement belongs to the physical-and-ethereal space which is thus spanned between the “verticon and horizon”. First is the upward-and-downward dimension – in its physical and pointwise aspect belonging to the vertical line in the midst, in its ethereal and planar aspect to the celestial horizon. Second is the circling dimension, determining the rhythmic regularity of phyllotaxis, and in some instances (e.g. the climbing plants, compare paragraph 11) involving the actual growth-movements of the plant.

Third is the radial, inward and outward dimension, revealed in the lateral expansion of leaf and branch and in the conical or spherical unfolding of the leaves from the near-vertical to the horizontal. This dimension too, which we may see imaginatively as one of in- and outward breathing between the innermost and outermost infinitudes, has its ethereal as well as physical aspect. Physically, the spreading leaves and branches carry the sap out from the region of the central line towards the horizon. Ethereally, every time a young unfolding leaf begins in close proximity to the “star” or to the “verticon” and opens down and outward, an ideal plane is leaving the region of the plant’s innermost infinitude and tending to alight in the horizon. The rhythm of contraction and expansion appears again in its dual aspect (paragraph 21 ).

Our descriptions so far have not included the specific phenomena of phyllotaxis – that is, the angular and numerical relations revealed in the spiral sequence of the leaves and in another form in the floral pattern. We do, however, believe that the dual, physical-and-ethereal space-formation – above all, the mutual and polar relation of “verticon and horizon” -provides the framework, as it were, within which these phenomena may receive their true interpretation. The plant – seemingly small as it is in spatial magnitude – reveals the Earth ‘s partaking in a far wider community of rhythms, forces and movements of the great universe, which are not only physical in character. What was described in paragraph 11 as the “spatial matrix” of plant life appears in its true light when the ethereal as well as the physical aspect of space-formation is perceived.

The plant is indeed only seemingly small! There are worlds beyond measure not only in the outer periphery towards which the plant expands visibly, but also in the innermost infinitudes of its living form . The plant, as we begin to perceive, when we contemplate it with open eyes and an inner perceptive judgement, comes into being in the interplay of spatial-counterspatial, macro- and microcosmic infinitudes. Far from being limited only to the outer study, however detailed, of the developing form, we are led to perceive in clear thought a cosmic process taking place before our very eyes.

There is another projective process whereby modern geometry paves the way to a clear understanding of the interplay between the two lines at infinity (within and without) which we have called the “verticon” and the “horizon” – the “spiritual staff” in the plant’s microcosmic ether-space and the cosmically given celestial horizon.

When considering the polarity between concentric circles in a plane and cones in a point (Plate IV and paragraph 20), we saw how in the the limit the infinitely expanded circle in the plane is polar to the innermost axis of the cone-space. The sphere, as well as calling forth the polarity of point and plane, calls forth also what we call the Line-Line Polarity of archetypal space. In Fig. 67 it is shown how a line passing through a sphere has a polar line at right angles to it outside the sphere. Move the inner line to pass through the centre of the sphere, and it will be seen that its polar line moves to the infinite. These are the two limits, and it is in this way that verticon and horizon are related projectively; as lines of free projective space, they return into themselves somewhat like great circles. Although of infinite extent, they are interlaced with one another in the same sort of way as the interlocked, finite rings in Fig. 68. 

Verticon and horizon express the most extreme form of what are called “skew” lines in projective space – lines which have no point and no plane in common (cf. the Axioms of Community of Point, Line and Plane in paragraph 18).

Any such pair of lines, however skew and however far apart, will be related projectively, if considered both pointwise and planewise. As a plane of one of the lines turns about it, it will engender a point which runs along the other line, through the infinite and back in either direction. Add to the two skew lines a third, skew to both, and the plane of the first line will meet this third line also, begetting yet a fourth line, namely, the line common to the two points – one on each of the other two lines – which are engendered by the moving plane.

As the plane continues to turn, the fourth line thus engendered will move round, sliding, as it were on the three given skew lines (Fig. 69). The movement of this fourth line depicts an infinite manifold of line, moving right round and leading back at last to the starting-place. This line will plasticize a line-woven hyperboloid surface, opening upward and downward and returning into itself through the infinite. Such a linewise hyperboloid is spanned between two axes, an inner and an outer – those lines to which we have given the name “verticon” and “horizon”. In Fig. 70 we have set a family of hyperboloids one within the other, which accords well with their nature. It is revealed that the closer to the vertical axis the form approaches, the less inclined from the vertical are its lines (generators) and the slimmer is the form. Moving out from surface to surface, the generators become more and more inclined, until, if we were able to follow them right out to the infinite, we should see them all merge into the infinitely distant line at right-angles to the inner axis. It is easy to see how the slim hyperboloids around the vertical axis degenerate into it when they reach their inner infinitude; not so easy to imagine how the outer surfaces fold in upon the outer “celestial” axis, degenerating at last into this other infinitude. In Fig. 71, we see the same process, with emphasis on the spiralling surfaces. This world of line-woven manifolds or reguli, as they are called, is a matrix for all manner of spiralling forms and movements; Goethe was indeed approaching one of the deepest secrets of plant life, when he recognized what he called the vertical and the spiralling tendencies in plant growth”. It is in this realm that thought-forms are given towards the understanding of the cosmic significance of phyllotaxis.⁶⁰ 

To understand Rudolf Steiner’s idea of plant morphology, the counterspatial nature of the vertical line of the stem- the “line-at-infinity within” of an ethereal space – is essential. In its deeper nature, the unfolding plant, with its green leaves appearing in the sequence of nodes, is not three-dimensional at all; it is so only inasmuch as it is on the way to becoming a material form m Earth space. Just as the celestial horizon perceived at any point on the Earth’s surface has an outer, spatial significance for an organism growing at that point, for it determines the two-dimensional positive-space plane at a point of which the organism is situated at a given moment, so, for the sun-like space of the growing plant, the line joining its sun-focus with the centre of the Earth is a significant line, for it gives the plant its negative- dimensional character in ethereal space. The sequence of unfolding cones at the nodes is a negative-dimensional process in ethereal space. The living manifestation of the Mercury staff involves a continual breathing process of expansion and contraction, taking into account positive and also negative space-forms.

We have seen that the essential geometrical thought-processes upon which modern geometry depends are akin to the rhythmic expansions and contractions seen by Goethe in the life of plants. In perspective transformations we alternately expand a form into a plane, where it has visibly outspread before us, and gather it into a point or eye, where it becomes, in the way we have described it, intensive – a form of lines and planes within the point – invisible to outer perception, but still perceptible to the activity of thinking.

So too, the plant alternately shows forth its forms and gathers them potentially into the seed or eye; it lives extensively in summer, intensively in winter-time. Moreover in the life and unfoldment of a single plant, the underlying archetypal form is alternately revealed, expanded in the leaf, and gathered up into the potentiality of node and eye. The leaf qua plane is physically two-dimensional, ethereally of no dimensions; the seed or eye, qua point, vice versa. We are reminded again of the ideal expansi0n that goes hand in hand with physical contraction. The stem, bearing leaves and eyes, is the one-dimensional entity both physically and ethereally, joining the two interlacing aspects.

A plastic form, within the physical or Euclidean two-dimensionality of a plane, will be what we call a plane curve – a circle for example or a plane spiral. Likewise a plastic form in the ethereal two-dimensionality of a point, as we have seen, will be some form of cone. For example, we have shown in Plate VI a very beautiful spiral cone by perspective from the logarithmic spiral, and have been led to the ethereal significance of the cone-forms which are so characteristic a feature in many plants. The points that bear the successive cones, shown by the upward-opening of leaf and branch, are the nodes along the upright stem. Like a plane curve, a cone is, strictly speaking, a one-dimensional form within a two-dimensional space, whereas a sphere or spheroid is two-dimensional within a space of three dimensions. 

In the enveloping gesture of young leaves – from among countless examples we mention Woodruff, Lilac, Rhododendron, Dog’s Mercury – the plant is using the dual potentialities of space at a less plastic level, just as a plane curve or a cone is less plastic than a true surface. We have also to understand this conical, two- and one-dimensional aspect in relation to the whole ethereal space of the plant with its star-centre above the growth-point. The star itself, as we have seen, is a kind of spiritual seed-point; for the ethereal space which it determines, it is, like the plane-at-infinity. of physical space, a two-dimensional form – only intensive instead of extensive. As in physical space every line within the plane-at-infinity is infinitely distant, so in ethereal space every line that passes through the “star” is so (cf. paragraph 34).

This subtle play with the 0- and 1- and 2-dimensional organs of space, both positive and negative, is most characteristic of the higher plant. Precisely this organic dissolution of the plump three-dimensionality of space is rendered possible by the projective interplay of the two polar-opposite types of space. This makes the beauty of the plant, and the many ways in which the plants achieve it contribute to their infinite variety and their effect upon our life of feeling.

The plants reveal this dynamic of the Mercury staff in very different ways. The living, rhythmical process, in which the bi-polar space is continually being renewed at a higher level, where there are very definite nodes, separated by internodes is especially evident in the dicotyledonous plants, such as those we have evidenced as examples. In the monocotyledons, the Mercury staff is revealed in a different way (cf. paragraph 48). The interplay between the forces of light of the star-centre and the physical material of Earth does not reveal itself with such contrast in the -Lily as in the Rose. While showing the sequence from node to node far less definitely, the monocotyledons express the interweaving of the two poles in gradual transition from roots to bulb, from bulb to leaves, and then to the flower within the leaves. Sudden contrasts are rare; the poles are far more closely bound together. The succulent, tenacious life of the bulb often gives birth to the rudimentary flower deep down in the earth, long before it appears and becomes fully developed in the light and air. Not the principle of the nodes is pronounced; rather the vertical axis. The monocotyledon bears itself erect and the plant organs are arranged around the axis often with very little differentiation between rootlike organ, leaf, stem and petal. The whole of the very central region of the plant- the ”spiritual staff” – seems concerned with the flowering and fruiting process. In Colchicum for example the flower extends right down into the bulb, while in Garlic (Allium vineale) bulblets are formed high up among the flowers. 

Of the two great classes of higher plants it would be true to say that changes of form through metamorphosis are greater in the dicotyledons than in the monocotyledons. In the dicotyledons the two poles-the “light” and the “dark” – are more sundered, with greater opportunity of living interplay between them; in the monocotyledons they are more united.

45 The Lemniscatory Process – Radial and Peripheral Formation

We have now come to the point at which it will be valuable to introduce the idea of yet another geometrical process – one which has, as it were, been at hand all along and which can give wings to our further thoughts concerning the interplay of the two active poles, physical and ethereal, in the bi-polar nature of the plant. We shall be led from the idea of mere variation of form to the deeper concept of metamorphosis, as approached by Goethe and developed much further by Steiner.

Let us consider the drawings in Plate X. The first two of these have figured very often in our deliberations so far. We will describe them yet again.

The first drawing shows a family of concentric circles, the length of their radii changing in geometrical progression between the centre and the infinite periphery; emphasis is laid on their radial properties. In the second drawing the same circles are shown, but in the polar-opposite way; for every point in the first drawing there is a tangent line in the second. Here the emphasis is on the peripheral aspect.

Picture these drawings three-dimensionally; the circles would then be spheres, pointwise and radial in the one, planewise and peripheral in the other. They illustrate two opposite worlds. In the one the points shoot outward, becoming lost in the infinite distance; or else they concentrate as though attracted for ever inward by a central point, like a centre of gravity. This is the picture characteristic of physical forces; it is typical of physical space.

The second picture illustrates the opposite process. Planes move inward from the infinite distance, spending themselves like waves on a shore as they reach towards an infinitude within; or they withdraw out and away to the periphery. Planes do not move in a manner characteristic of a projectile as points may do. They hover or float inward or outward in relation to the centre. As they come inward they envelop and mould a hollow space from outside, quite opposite in character to the point-filled radial sphere which grows from the centre of the other picture. The outward movement of the planes would have a suctional effect rather than an explosive one. If we think of the points in the first picture as being drawn to the central point as to a centre of gravity, so we conceive a force  f “levity” which would draw the planes of the second picture outward towards the periphery (paragraph 31).

We have been concerned to understand the quality of this hollow space; we regard it as picturing an ethereal realm in contrast to a purely physical one. It is a receptive region of a planewise nature; the planes move in unendingly towards an infinitude within, just as in the other drawing the points move out into the infinite expanse. The “infinitude within” is also like a springing source of planar movement as the planes open out and away from it. This centre too is a point, but it is quite different from the matter-filled points of physical space.⁶¹ In terms of physical space there is less than nothing in it. The contrast between the two centres is as darkness to light; if the physical centre is “dark”, this one is “light” (paragraph 37).

The interplay between these two active poles, physical and ethereal in the double sense just explained, leads to a fresh archetypal form between them, so that the organism as a whole becomes of threefold, not only twofold nature. It is a purely geometrical form to begin with, but we soon learn to see in it the archetype of an exceedingly manifold and versatile principle of space-formation, perhaps of scarcely less importance in the life of Nature than the sphere- and circle-forms from which we took our start. It is the outcome when spherically formed spaces, ethereal and physical, are interpenetrating between two distinct poles. If radiant and ethereal focus are one and the same point, the formative ether-spheres and the outward-radiating activity are in polar relation to one another, the one tending inward in the same geometrical progression as the other outward. We now preserve this relation when the two poles are distinct, as they are in a bipolar organism. We look for the places of interpenetration of two distinct families of concentrically growing spheres (or circles, in the plane picture ). From the physical radiant we let a sphere grow outward – in simple “growth-measure” or geometrical progression. Towards the ethereal focus we let a corresponding sphere grow inward in the same growth measure; the one is a radial, the other a peripheral process.

In the third drawing (returning to the two-dimensional aspect) the two families of circles are made to interrelate with one another. Bring the two families into movement in imagination. From the “dark” centre the red circles grow outward, expanding into the infinite periphery; from the infinite expanse the blue circles “grow inward” until they lose themselves in the “light” centre. As they do this the circles interpenetrate and give birth to the forms in the fourth drawing.

To follow this in detail, imagine to begin with a very small red circle growing outward and a very large blue one coming inward. At first they have no real point in common. Soon, however, they will touch in one point at the lower end, nearer in or farther out according to how the outward and inward movements have been timed. From this moment they interpenetrate, crossing in points on either side of the central line, which as they move upward describe one or other of the curves of the fourth drawing. The upper end of each curve represents the moment when the circles again lose touch, the red circle growing outward and away and the blue one disappearing into the “light” centre.

While the red circle is increasing and the blue decreasing a moment is bound to come when they are of equal size. If at this moment they still interpenetrate, they will quite obviously be forming one or other of the oval or indented curves. If they just touch in the middle in a single point, they will be forming the looped or figure-of-eight curve. If the equal-sized circles fail to meet, a double egg-shaped curve inside the loop will be the outcome.

The curves thus formed are the “Curves of Cassini”, one among them, the looped curve, being the “Lemniscate of Bernoulli”. They are all continuous curves, weaving in the most harmonious way between the two centres, which are their foci. ⁶²

The Cassini curves are here regarded as expressing the dynamic interplay of two contrasting processes, radial and peripheral. The mathematical law of their formation suggests this interpretation, as the pictures show. There is a figure eight curve placed vertically. The upper and lower loops are equal and at the crossing-point in the middle the curve cuts through ,itself at right angles. There is a focal point within each loop. Within and around this figure eight curve and, to begin with, following it closely, the curves of Cassini are drawn – in an unlimited number, one within the other. The curves close outside will be in one continuous sweep, indented in the middle. As we go farther out the indentation gradually disappears; at last we get pure ovals, which, going farther out to the periphery, become more and more circular in form. The curves within the lemniscate are divided into egg-shaped ovals. As we go farther in towards the foci, the twin ovals not only become smaller; they too become more and ignore nearly circular in outline. We now consider the complete picture – lemniscate and curves of Cassini all together – filling the entire plane. (If we rotate it about the vertical axis we get the corresponding spatial forms; the surfaces close inside the lemniscate will be egg-shaped and the indented ones close outside it like an hour-glass.)

It is important not to remain bound in imagination to the rigid forms but to see each curve, once it is created, as a stage in a process of metamorphosis. Not only do the forms arise as the result of dynamic movement, but they are themselves in movement. Each curve represents a single moment in the change of forms one into another. The curves flow into one another in a sequence of metamorphoses. Unmoving, however, like two stern guardians in the whole process are the two points, the “dark” centre and the “light”, the influence from each pervading the whole in varying measure. Below, the curves are more in the realm of the radial activity; above, in the peripheral. Constant also is the infinite circle of the plane, for as the curves move outward they become more and more nearly circular, until they echo away into the infinite periphery of space.

A word must be said about the double egg-shaped curves inside the loops of the lemniscate. Each pair, one in one loop and one in the other, form a single curve which is in reality just as continuous as the lemniscate itself or the curves around it. To follow round the curve just inside the lemniscate would be to pass at first round the red part, then to cross the intervening space and follow round the blue. The underlying mathematical process reveals that this is possible: in
the realm of idea the seemingly divided curve is continuous,⁶³ though in its most external aspect it manifests in two distinct parts, the one oriented more towards the “dark” pole, the other towards the “light”. 

We began by picturing the first two drawings of this plate three-dimensionally and it is necessary also to do this for the third and fourth drawings. We then come to the idea of a Cassini space, expressing the interplay of pointwise and planar, radial and peripheral activities. Seen in this aspect, the Cassini form is indeed an emblem of one of the most essential polarities in Nature. The forms pervade the whole of space, flowing through it like waves, anchored in the two centres and dying away into the infinite sphere around – the infinitely distant plane of space. We learn to create this geometrical picture accurately in imagination. It must not remain static. In bringing the forms into movement we learn to see them as gesture. It is not the mere form but this gesture of form along with the underlying mathematical idea of its creation which we shall apply to our further contemplation of the higher plants.

This conception may be varied in many ways. For example we can make the potencies or “common ratios” of outward and inward growth unequal instead of equal. A metamorphosed family of curves results; the lemniscate is changed into a figure-eight curve with the one loop larger than the other, the crossing point being proportionately shifted towards the centre of faster movement, so that the smaller loop surrounds this point (Plate XI upper left). A great variety of lemmscatory spaces is thus obtained. We shall now use the names in this wider sense, speaking of “lemniscatory” or “Cassinian space-formations”. Needless to say, this refers not to the mere outer forms but to the dynamic process by which they come into being. The variety is still more increased if we allow one or both of the families of spheres to grow outward from or in towards an eccentric point (Plat: XI upper right). Moreover sundry projective transformations are possible, e.g. the spheres may first be elongated into elliptic forms. It is a realm of “lemniscatory space-formations” arising from the mutual interplay of physical and ethereal spaces – one of the fundamental though not the only type of form to which this interplay will lead.

All  that was said of the polarity of root and shoot and of the rhythmicized polarity from node to node will find expression in this form. We draw the lemniscate and its Cassini curves (representing, in a plane picture, the corresponding surfaces of rotation) in such a way as to recall the functional polarity of the two families of spheres. The lower spheres will be predominantly radial and physical; the upper ones peripheral, ethereal. We must allow this difference to be transmitted to the resulting Cassini forms, so that even if (as in the original form of these curves, discovered by the astronomer whose name they bear) the lower half of the picture is outwardly the mirror-image of the upper, the qualitative difference is preserved. The lower one of the two foci must be felt as radiating, filling the ovals in this region from the centre outward; the upper one as an “infinitude within”, surrounded by enveloping and planar form~. For they are functioning as “radiant” and “sun-centre” respectively. The lemniscatory form with its “Cassini space” will then appear as the natural emblem of the organic unity and polarity of root and shoot.

Let us now picture, in relation to this space, a plant in the early stages of growth, when the first few leaves after the cotyledons have developed but before the stem has shot upward making the internodes distinct. Take the Dandelion plant (Plate XII), or again the Greater Plantain or the Daisy- plants where the internodes are not lengthened between the foliage-leaves. Other examples will be found in most young plants : Lettuce seedlings, Marigolds, Stocks and Wild
Mullein come to mind.

The crossing-point of the lemniscate primarily represents the “hypocotyl”, where root and shoot meet and the plant normally passes from the dark earth into realms of light and air. Here is the natural interchange of inner and outer as revealed in the anatomical structure of root and stem and in the transition from radial to more enveloping forms (paragraph 42 ). The young Dandelion leaves are arrayed around the growing-point, their upper surfaces facing inward and often curved as though to mould the hollow sphere. In some plants the invisibly moulded form is more conical; Dandelion and Plantain show individual variations in this respect. In either case we are impressed with the contrast between the wiry, radial quality of the roots and the planewise enveloping gesture of the upper part of the plant, and ifwe call to mind how the lower half of the Cassini picture was contrasted, qualitatively, with the upper, we see how the whole plant-form – “radial below, enveloping above” – belongs to the ”lemniscatory” space-formation.

Ethereal concentric spheres and cones (Plates IX and IV), express the aspect of the shoot in the ethereal space of the star-centre pure and simple. If, as we are now doing, we contemplate the actual relationship of root and shoot, the polar opposite character of the two main components of plant growth – positive or convex from the root upward, negative or concave from the star-centre downward – will find expression in the lemniscatory formation (Plate X, etc.). This is of course a highly idealized conception applied to a very complex reality. Yet it contains a true ideal key. If a concentric, more or less spherical organic entity is formed by the perpetually living balance of spaces positive and negative, or centric and peripheral tendencies, the separation of two centres will by this same mutual activity give rise to a type of form of which the Cassini space is at least a functional indication; it is indeed often realized to a remarkable extent even in the outer form, as we shall see when we study flower-forms.

The dark and light centres – red and blue respectively in Plate X, green  and peach-blossom in Plates XI, XVII and XVIII – are each of them to be conceived in the polar aspect. The centre of convex growth – to begin with, in the root – is not exclusively physical, since in that case it would not be imbued with life, but here the physical is predominating; we therefore refer to it briefly as the physical or “dark” focus and picture it in terms of the radial circles. The “light” or star-centre – focus of concave growth- is to begin with purely ethereal; only at a later stage, through the flowering and fruiting process, does it become imbued with matter. Taking the one realm therefore to be predominantly physical and the other ethereal, the simultaneous process, outward in the one family of spheres and inward in the other, is the natural expression of their mutually polar relation. In both instances the process is determined by the relation of the infinite centre within to the infinite periphery of physical space. The form is therefore not self- polar, since there are two centres, both in relation to the one plane-at-infinity. Also the Lemniscate and Cassini forms arise by the pointwise interpretation of the respective spheres, although the spheres of the upper family are planar. 

The geometrical progression, being functionally a process taking place between two infinitudes – point within and plane without, in this instance – enables the outward and inward movements to be coordinated in the simplest and truest way. This remains so even when the common ratios are different as in Plate XI (top left) or when the one point is eccentric as in Plate XI (top right).

Morphologists have often noted – in connection with the logarithmic spiral, for example – that geometrical progression is natural to living growth. The concept of ethereal space helps us to understand the ideal reason. Concentric growth towards the infinite periphery is organically a process taking place between two infinitudes – that of the living entity’s ethereal space in the centre as well as the infinitude of physical space in the periphery. Therefore the true mathematical process is here the hyperbolic or multiplicative one with its two distinct functional infinitudes and not the parabolic or additive with only one.⁶⁴ If we combine the potentized growth-measure which is thus determined between centre and periphery with the circling-measure determined by the absolute circle (and by its counterpart, the absolute cone in the ethereal centre), the logarithmic spirals, seen in so many living forms (Figs. 52-55) are the outcome, nor need the growth have followed spiral lines to produce them. The logarithmic spirals of composite flower-heads or leaf-rosettes, though not concentric in all dimensions, are concentric in a plane which, to begin with, is ideally the horizontal plane. They are growth- measure forms between the Euclidean infinitude of the horizon and the ethereal in the innermost – the region of the “verticon” or “spiritual staff”.

Ifin the forming ofthe typical bipolar space as in Plate X the potentizing rates, or common ratios of geometrical progression for the inward and outward movements are the same, it is mathematically obvious that the Cassini forms, the “curves of constant product” must result. But the essential thing is the geometrical progression as such, and the co-ordination of inward and outward movement in the two families of spheres; hence if the ratios are different a transformation of the same “lemniscatory” type of space results (Plate Xl). ⁶²

The combination of physical outward with ethereal inward movement suggests that while the plant is physically growing it is being endowed, through its star-centre, with ethereal energies from the great Universe. This combination of physical outward growth with ethereal inpouring from cosmic sources seems to accord with the predominantly anabolic physiology of the green plant, which in its growth not only renews its own life but provides nutriment for other creatures. The interrelation of outward and inward processes need not, however, be thought of as taking place in external time; the time-parameter in the description, and in the mathematical deduction in Note 62 is but to indicate the functional correlation. What does take place in time in the ethereal region of the shoot is the unfolding and expansion of the leaves as described in paragraph 41. (It may be mentioned in passing that if in the process indicated by the bottom left-hand picture, Plate XI, the direction of the upper spheres is reversed and both families of spheres tend simultaneously outward, the resulting forms are reminiscent of the invaginations of animal embryology.) 

Let us turn once more to the rhythm of the nodes. For the development of the shoot, the hypocotyl is a first and primary node. Every node shares something of its nature, as a “nodal point” in the prevailing physical-and-ethereal polarity (Paradoxically, as often happens with the first member of a homologous series, the hypocotyl as the initial node is archetypal and yet in obvious respects atypical.) Consider how each node evolves in the growing plant. It begins its existence in an almost microscopic region where at the growing-point of the stem the primordia of the leaf-buds are born. It is at this moment beneath the sun-centre and above the more physical and radiating realms of root and lower stem which carry it and provide substance. Ideally it is poised radiant below and the sun-centre above, like the lemniscatory crossing-point in the bipolar space. But at a later stage the node becomes more physical; it becomes part of the supporting ground by which the younger nodes are sustained. From being poised as it were between Sun and Earth, it now condenses to a more earthly form and function; so it becomes a radiant in its turn and indeed appears as such, more or less markedly according to the form of plant. 

Now the radiant, as we have said before, is at once a focus of life- life in which the physical predominates. Therefore the plant has power to generate ever new centres of such life as it  proceeds from node to node. It derives this power from the relation of its earthly nature to its “sun” or “star”, which – for the single shoot- remains one and constant. Moreover, in the ideal bipolar space, it is at a lemniscate crossing-point that each new focus of earthly life is born. The crossing-point is in fact a new potential “point of chaos” which then becomes a centre of physically radiating forms – in other words, a living radiant. This now enables the lemniscatory space to be potentized, renewed again and again at a higher level – from node to node up the stem.

(The potentiality we here attribute to the lemniscatory crossing-point is suggested also by its mathematical properties. In the Cassini-space as a whole it is a singular point with a certain quality of chaos. A differential invariant becomes zero as we approach this point; the differential coefficient becomes indeterminate when sought by ordinary methods. The mathematical properties of this region are in harmony with its organic function. )

We gain a beautiful and very suggestive geometrical picture of these relations if, as in Fig. 72, we begin by drawing a large and simple lemniscate of Bernoulli, taking this curve to typify the whole Cassini-family of which it is a member; the same will presently apply to its successors. We indicate the radiant below, the sun-centre above, bringing out this qualitative difference in the way we depict the focal region within either loop. Now we recall that the crossing-point is to become a fresh radiant ; we therefore draw a second lemniscate, with the top focus  that is, the sun-centre – unchanged but with this crossing-point for its lower focus . The new lemniscate will of course be half as large; its upper loop will be entirely within that of the first.

Now we repeat the process, using the new crossing-point as a new lower focus. We obtain curve after curve, one within the other enveloping the same uncentre, and each one with its earthly radiant raised to the level of the previous curve‘s crossing-point. If in the quality of the picture we have expressed the underlying thought, it will tell its story. It is of course, like all geometrical emblems of this kind, too static, for (as in paragraph 43) we should have to imagine the whole picture, or at least the upper part of it, simultaneously growing and expanding as we pass up and inward from node to node.

Revolved about its central axis, this family of curves reveals a formative principle which is at work in many variations in the plant world. Seeing each lemniscate in the polar aspect we have explained – radial below, enveloping above- it shows the inner meaning of the ”cup within cup” formation described in paragraph 8. Moreover the whole picture, reminiscent as it is of the “Mercury staff” or “Caduceus” form traditionally associated with the leafy region of the plant, gives to this ancient symbol a very significant, functional meaning. If we now rotate the successive lemniscates about the vertical axis, each through a constant angle from the last, we shall be able to follow the various number-relations and types of phyllotaxis; the planes will indicate the main directions of the leaves – or rather of their petioles – growing in spiral sequence from the nodes. Fig. 73 represents the decussate form of phyllotaxis, to be found, for
instance, in the Stinging Nettle (Urtica dioica) in Fig. 74.

Node after node, the plant raises the dual potentiality of the hypocotyl higher above the surface of the Earth. Each new node gives the basis for further vegetative development; every side- shoot, growing in the axil of a leaf, springs from the node even as the main shoot springs from the hypocotyl (Plate VIII). The node does indeed contain germinating powers, as is well-known from the practical use we make of this in propagation by cuttings. Spanned in a rhythmical interplay between its own sun-centre and the earthly realm from which it grows, the plant thus rears its living form and substance from the ground. This is the process Goethe sees when he describes the upward growth as a gradual enhancement, the cruder substances giving way to finer ones until the greatest refinement is achieved in the flower

This “Caduceus” sequence of lemniscatory spaces from node to node is an interesting and natural further development of the basic idea. The lemniscatory node or double-point is a unique point of balance between the primary foci in the Cassini space as represented in Plate X or in the other pictures. This very point, we suggest, tends to become a fresh ethereal focus within the living body, in other words a fresh centre of “convex growth”. In such a centre, acting as the “infinitude within” of an ethereal space, there must be something of the quality of void and chaos (paragraph 40). Now in the mathematical form of the Cassini space the region of the lemniscatory node has special properties. The neighbouring curves, save for the one which goes exactly through the point, tend to avoid this region. Moreover if by differentiation one seeks to ascertain the slope of the two curve-branches passing through the node, one gets an indeterminate value, due to the fact that at this point a certain differential invariant becomes zero. All these things indicate that here may be a realm of new beginning. The mathematical and botanical conceptions of a “node” coincide; and experience confirms what the mathematical idea suggests – the germinating powerof the plant is renewed. The entire plant is, as it were, newly planted. The lemniscatory process, working originally between the star-centre and the root as indicated in Plate XII is thus repeated between the star-centre and each successive node. The star-centre as such is not repeated but remains as an inexhaustible fount until at last the flowering and fruiting process receives it into the body of the plant. 

It is in the very nature of the higher plant that in the rhythmic repetition from node to node or m some other way, the plant takes its time as it goes towards the culmination of its life in the flower and fruiting process. Herein lies the possibility of metamorphosis. There are lower forms of plant life, the fungi, for example, which do not do this, and hurry towards fruition. Fig. 75 shows a tiny fresh-water alga- the almost microscopic Botrydium granulatum, which grows on moist clay in drie-up pools or swamps. Within its single cell-wall it imitates the higher plant’s polarity: downward a branching system of root-like organs, upward a single, green, pear-shaped sphere, within which spores are formed. It is again a “lemniscatory” space-form – radial below, enveloping above. But the focus of the upper sphere is not left in open air; it is claimed at once, drowned as it were in the watery realm to which the plant belongs. The comparison of this with the typical form of the higher plant would be achieved by slicing off the upper portion of the sphere and re-forming the resulting chalice to a ring of leaves or to a kind of calyx. The “star of life” would be restored to realms of light; instead of teeming spores a flower would be formed to prepare fruit and seed in more stately measure.

Such transformation cannot be made in a single stage; rhythmic unfolding of the leaves and nodes precedes the flower, taking its course in realms of air and light during a certain period of time. This is the rhythmic process indicated in the “Caduceus” – the potentized lemniscate- formation – and we can well understand the traditional relation of this principle in the higher plant to the powers of healing, pictured in Mercury’s staff. The higher plant attains its virtues
by tarrying m the realms of light and air, taking a longer time to unfold and to mature through all the stages of metamorphosis.

46 The Hidden Vortex

There is much in the plant shoot which is reminiscent of spiral- and vortex- formation. If we follow the arrangement of leaves up the stem, we move upward in a spiral (even if, as in the decussate arrangement, we go round the stem at ninety degrees a time). But this actual movement as such is not present in the plant, nor even in the movement of the sap (except in microscopically small forms), for in the main the cells run vertically up and down the stem. At most, the movement of the sap in twining plants follows an outward, spiralling path. But twining plants are rather apart; they are only possible, because other plants in which the “law- giving power in the midst” does rule, provide them with vertical stems and trunks around which they may twine. 

There are times in which even the higher plant – and a free-standing one – loses its virtue, that is to say, loses its beautiful and healthy balance between the vertical and spiralling principles of its life. This becomes manifest in abnormal growths, and it is in the abnormal forms which may appear in plants that the plant flaunts her secrets abroad for those to see, who, like Goethe, have eyes to see. Forms of growth may arise, which reveal that even in the normal plant forces are latent- brought to rest by the “law-giving power” in normal circumstances. Fig. 76 shows a Valerian plant, discovered and pictured by Goethe. In this swollen stem, the sap surely does flow in a spiral. Such fasciated stems may be found particularly in wet seasons. It is often possible to find, for example, a Dandelion (Taraxacum oificinale) or a Common Hawkbit (Leontodon hispidus) or other plants in which several Rower-stems have grown together to form a thick spiral, at the top of which may be gathered a number of flowerheads. One may
often discern a spiralling twist in the great trunk of a tree, which would normally be straight. Fig. 7 7 shows what happened to a Garden Mint!

The spiralling or horizontal tendency has more to do with the forming of substance than the vertical tendency, which reveals the upward striving of the plant in the rhythm of the nodes to more rarefied forms and more advanced conditions of its life. In these fasciated stems it is as though the vertical principle – its mathematically musical, though silent spiral – has been overcome, and has been drawn down into crude material substance. For the plant the result is that there is no longer the power to create fertile flowers and seeds. The plant’s invisible, cosmic vortex, open to the starry worlds, has become cluttered with substance. It has become “blind”. In common parlance we even call a seedless Rower “blind”.

Ideally, a vortex unites and holds in balance the power of the vertical infinitude within, and that of the celestial horizon. In water and air, where there is a vortex, there is tremendous actual movement around the hollow space; in a tornado, there is what is called the “eye” of the storm. Rudolf Steiner has described the plants as sense-organs of the Earth; he has said the same of the Earth’s springs. We may regard a vortex as a sense-organ, receptive of cosmic influences (Fig. 78); so long as the inner space is clear and open to the universe, the sense-organ can perceive. ¹³ In the hidden vortices of plant life, planetary and starry forces are perceived by the Earth and received by Mother Nature for her children.

So far we have been thinking mostly ofa single point-at-infinity of the first main stern. In the development of most plants there will be many ether-spaces, as the intensive spaces of the buds in the axils of the leaves open up and form side-shoots. In many plants this development is held back, until the apical stern has reached a certain culmination, perhaps in a flower. Each side- shoot has its ether-space, with the infinitude within at the growing-point, and their formative influences are mutually balanced in an organic hierarchy of power. Every such bud or eye is the living focus for a formative activity from the periphery inward. Again, we must recognize the active interplay between radiant and ethereal focus, and since the ethereal foci are moulding the living forms round and about themselves, the radiant process, reaching up and outward, will tend to conform to their influence. The ramification of side-shoots in plants or of twigs and branches in the case of trees and shrubs will not take place in a haphazard way. Each plant has its own typical plastic outline, and this will not be a mere passive result of the centric forces only, but the outcome of an active interplay; the peripheral forces are always there to meet and “inform” the radial, outward growth. This is precisely the impression we receive from many leaf-forms, from the forms of trees and from the forms of many an inflorescence, such as the flowers of the Urnbellate family – the umbel of Archangelica (Archangelica oificinalis), for example – or of a Composite, such as the Milfoil (Achillea millefolium). Here we behold the almost magical continuity of delicately moulded surface made by the many florets, each of them borne by its own stalk to the very place where it needs to be. The polar, physical-and-ethereal interpretation, with the ethereal, peripheral forces directly related to the plastic, planar surface forms is from the outset far nearer to the phenomenon we see than any merely physical attempts at explanation.

Envisaging the plastic form of the whole plant, if in imagination for a moment we think of every sun-centre shining forth like a visible star, then the more complex plant-with its main outline, its strong branching forms, and its young shoots reaching up towards their “stars of life” – is like the picture of a tree with many candles, symbol of renewed life on Earth .

Most seedlings show the upward-opening hollow cone clearly in the first stages of their development. It is the typical picture of plant substance formed to receive the light-source of its life. In shrubs and trees, as growth continues, the upward-opening conical gesture of leaf and branch is repeated again and again; the forces of the light are received into the living, developing substance. Meanwhile, the tree as a whole gradually assumes its characteristic shape – a downward-opening cone, dark and opaque against the sky (Figs. 79 and 80). Diagrammatically expressed, this twofold process may be symbolized in the picture of two interlacing triangles (Fig. 13). Changed from a dead form into a functional, dynamic image, the ancient symbol of Solomon’s Seal relates to this aspect of plant growth. The downward-opening triangle pictures dark matter being formed and moulded by the light; the upward-opening triangle pictures the cup of light with the darkness rising to receive and enfold it. Change this straight-lined and angular form into forms of curved outline and the picture will be capable of a much wider application. 

In the centres of vital growth, which multiply as the plant matures, the gesture, as we have so often seen, is a hollow cone, or cup-a concave form. But as the living substance accumulates, the plant as a whole will form its own individual plastic outline and this will tend to be convex. Concave is the gesture of unfolding growth, convex the plastic outline of the resulting form. A beautiful example is the cushion of an Alpine Saxifrage.

The synthesis of concave and convex growth in the higher plant is typical and fundamental. At its young and vital, ethereally active centres, the plant makes concave forms; these hollow spaces it then gives away on all sides as it unfolds, but the living substance thus derived, as it assumes completed form, is moulded into convex shape and substantial form, which is more natural to the material world (Fig. 81 ). Not only do convex and concave relate essentially to root and shoot, but the entire plant is a synthesis ofthese polarities, which weave through and through it and into one another.

Gallery with All Plate Images from Beginning of the Book

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Chapter 1: The Languge of Plants

Chapter 2: Goethean Science and Geometry

Chapter 3: Polar Forms of Space

Chapter 5:  Ethereal Space of the Plant Shoot

Chapter 6: Staff of Mercury

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