Plant Between Earth & Sun – Chapter IV: Physical & Ethereal Spaces

PLANT BETWEEN EARTH & SUN 

CHAPTER IV – PHYSICAL & ETHERIC SPACES


Chapter 1: The Languge of Plants

Chapter 2 : Science of the Future

Chapter 3: The Polar Forms of Space

Chapter 5:  Ethereal Space of the Plant Shoot

Chapter 6: Staff of Mercury

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27 – Space & Counterspace

From the deeper concepts of space to which projective geometry has led, we derive a theory concerning the type of formative field which the specific phenomena of life reveal. The theory will obviously bear on all living forms – plant, animal and man. We introduce it in connection with the higher plants (the cormophytes and above all the flowering plants), since it is here that the type of form and’ unfolding growth which the geometrical ideas suggest is most directly evident.

In the foregoing chapters we have stated it descriptively, bringing in the geometrical ideas with the help of simple illustrations and in imaginative language. We shall now characterize more precisely the scientific notions employed and draw attention to the problems they involve, addressing ourselves at this point to scientific readers. The reader untrained in mathematics need never lose heart, for just as one grasps for practical purposes many a realm of modern technical science, without necessarily following in detail all the underlying mathematics, so, too, in this realm of the ethereal forms and forces.

The path along which we are led is as follows. Projective geometry as we have seen treats, as equivalent, forms which are capable of mutual transformation by perspective or by a sequence of perspectives. It studies, therefore, mobile types of form, rather than rigid forms. Moreover the laws differentiating one type from another spring from those interweaving relationships among the planes, lines and points of space which are made use of in all perspective constructions. This has a twofold outcome, which proves of great importance when we begin to see
the real universe of Nature in this aspect. It makes us far more aware of the totality, and above all, the infinite distances of space. In the constructions of perspective the latter are not left as a vague and inconceivable infinitude as in the ancient geometry of Euclid. They are transformed into quite tangible “vanishing points”, “vanishing lines” and so on, thus making manifest the real part they play in the spatial structure of the most material and finite forms- the crystals, for example.

The second outcome is that projective geometry overcomes the one-sidedly pointwise idea of three d1mensioinal space which prevails in the old geometry and, to a great extent, m our instinctive feeling. It reveals the interplay of two mutually polar and complementary principles-pointwise and planar, or centric and peripheral. The Principle of Duality or Polarity, consistently applied, shows that the plane plays a no less primary and fundamental part than the point in the formation of space. ¹⁷ Weaving between the two, with a perfectly balanced relation either way, is the third fundamental entity, the straight line. All this is of untold significance for an imaginative and at the same time reasoned scientific understanding of the world of Nature.

Attention has been drawn to the evident relation of plane and point to Goethe’s ideal conception of expansion and contraction. The plane is what the simplest of spatial forms, the sphere for example, becomes when expanded without limit; the point, what it becomes when contracted . It may well prove that Goethe, both as botanist and physicist, divined a truth, the full and clear expression of which belongs to the science of the next hundred years from now. Projective geometry has also led to a clear understanding of how and why it is that the perfect polarity of space as regards point and plane is not immediately manifest in the more rigid space of Euclid, and was therefore unknown until a little more than a century ago. It is due to the decisive part played in the space of Euclid – the space in which rigid bodies, for example, preserve their shape and size as they move – by the infinite periphery, which has the character of an unique, infinitely distant plane, the “plane-at-infinity” of space. This cosmically given plane determines the laws of parallelism which play so great a part in the translational and sliding movements of rigid matter; it determines the space of created things.

Within the infinitely distant plane there is also the invariant imaginary circle, to which the basic forms of right angle and of rotational, circular movement are due, ²⁵ even as the laws of parallelism and of translational movement are due to the infinitely distant plane as such.
Euclidean space is a three-dimensional projective space in which the plane-at-infinity, bearing the imaginary circle, is kept fixed. The  presence of an unique plane, with no unique point to balance it, upsets the all-prevailing polarity of point and plane, which is only restored when by projective transformations one, as it were, unfreezes the “Absolute” and lets it move.

A most revealing paradox emerges, of which the philosophical implications are far-reaching. The polarities of spatial structure are so interwoven that the very realm in which point-centred entities (atoms, material bodies with their centres of gravity, electric and magnetic poles and so on) are at home is a realm determined by an unique, cosmically given plane, which in the nature of the case is inaccessible to any material body – and, no doubt some would say, inconceivable to any mind inhabiting such a body! An unique entity of the expansive kind holds the field for the relationships, both geometrical and dynamical, of multitudes of contracted, pointlike entities. Such is the space of
Euclid, which we may call physical space, since the typical laws governing the behaviour of inert matter – the laws of elementary physics and mechanics – are very intimately related to the structure of this space. (The relationship is brought out in the parallelogram of forces, the law of moments, in vector analysis and other geometrical devices by which one estimates the interaction of physical forces .)

The same versatility and detachment of modern thought which enabled projective geometry first to liberate itself from the rigid laws of Euclidean space and then, returning to it, to understand this space in a deeper aspect, gave rise to the idea of other forms of space, subject like that of Euclid to the more general projective laws and yet of different spatial structure. Among these are the “non-Euclidean geometries” , which have been partly applied in the Theory of Relativity. Discovered in the early nineteenth century by Lobachevsky, Bolyai, Riemann and others, their inclusion in the wider framework of projective geometry was only afterwards made clear through the work of Arthur Cayley
and Felix Klein. Now it is also possible within this wider framework to conceive a type of space – the precise’ ‘dual” or polar opposite of that of Euclid-which, we shall try to show, belongs essentially to the phenomena of the living world. ^{14 15}

Euclidean space being a projective space governed by the invariance of an unique, infinitely distant plane, the polar opposite type of space will be a space determined by an unique point. The latter too will have the functions of an infinitude, but this need not mean “infinitely far away” in the ordinary sense, since to apply such a criterion would be to think again in terms of physical space. On the contrary, whereas the infinite periphery of the latter is in the nature of the case an infinitude without, the unique point of the polar opposite type of space will
have the character of an infinitude within. We shall be likely to find it by looking not outward but inward, into the innermost heart and core of the spatial field in question. To use the very suggestive terms coined by Dr. E. Lehrs in his book Man or Matter, whereas the space of Euclid is governed by an all embracing plane, this other space is governed, as it were from the very innermost by an all-relating point.

The space determined by an ”all-relating point” being polar to that of Euclid in all respects, its elementary entities (of no dimension and of zero volume) will be planes and not points. Its finite forms will tend to envelop the point-at-infinity within, and volumes-or substantial content, if such there be-will be calculated from without inward. The top right-hand drawing in Plate X for example, pictures a family of spheres in this other space, growing in volume from without inward. The finite ”planar volume” of each sphere is the entire space outside the surface; the remaining hollow, towards the point-at-infinity at the centre, though physically finite, is infinite in the measures of this other space. The latter is indeed the true negative of Euclidean space – related to it, in a qualitative sense, as the mould is to the cast and we may therefore call it “negative-Euclidean space”, or even negative space pure and simple.

For the full determination of a negative-Euclidean polar space, the pomt-at-infinity must be imagined as bearing an absolute imaginary cone, polar to the absolute imaginary circle in the plane-at-infinity. To begin with, we take this cone to be “spherical” ²⁰  – in direct perspective with the absolute imaginary circle. This assumption is however not not essential; the absolute cone may be elongated or flattened ellips0idally m one direction or another.

28 – Relation to the Non-Euclidean Spaces

The significance of our hypothesis – namely that this other kind of space plays its part of the structure of the real universe – is brought out very clearly if we take our start not only from Euclidean space but from the two kinds of non-Euclidean space, all of which emerge from the more universal form of projective space as shown by the Cayley-Klein theory. It is well known that Euclidean or “parabolic” space is a degenerate transition-stage between the two non-Euclidean types, known respectively as hyperbolic and elliptic. ³² These spaces are obtained if the “Absolute” is supposed to be a “finite” sphere or quadric surface, of real or imaginary radius, say a ,which is transformed into the (doubly covered) plane-at-infinity when a grows infinite.

So long as a is infinite, the principle of duality is preserved, though in different ways m the hyperbolic and elliptic cases. For in the former instance the absolute sphere, being real, separates off the interior from the space outside. The interior will naturally be regarded as a pointwise space, and it was this alone which geo

metricians had in mind when these ideas were first developed . Within this space, it is true, the perfect polarity of point and plane breaks down, but the remaining space outside, regarded as a planar space, is polar to it with respect to the Absolute, and the two spaces, taken together in their mutual relation do full justice to the principle of duality. (A. N. Whitehead, in his early work Universal Algebra, calls the space outside the Absolute the “anti-space”, corresponding to the “space” within.)

If the Absolute is imaginary (elliptic space), there is no real surface to sunder the predominantly pointwise from the predominantly planewise realm. Space remains one and undivided, and to this single space the principle of polarity applies m its full scope. The nineteenth century mathematician and philosopher W. K. Clifford, ³³ lamenting the fact that the balanced harmony of the Principle of Duality no longer applies in the seemingly Euclidean geometry of the real world, suggested that universal space was perhaps after all elliptic, but with a
finite value of a so large as to have escaped detection. “Upon this supposition”, he writes, “the whole of geometry is far more complete and interesting; the principle of duality, instead of half breaking down over metrical relations applies to all propositions with out exception.”

We may now picture the continuous transitions between these different forms letting vary throughout the range of real numbers. Taking our start from the hyperbolic form, with a real absolute surface dividing space from anti-space, if we increase the value of a towards infinity the surface expands; the planar antispace outside is reduced and when is reduced and when at last the Absolute expands into a plane, the anti-space is flattened into nothing. Meanwhile the pointwise space inside, from being hyperbolic, becomes parabolic, in other words Euclidean. It becomes “physical space” as we know it.

If on the other hand, beginning again with hyperbolic space and anti-space, we decrease a (or, on the planar side, increase a^-1), the absolute sphere will draw in towards the centre. This time the pointwise space inside will be reduced, whereas the planar space outside grows inward. When at long last a becomes zero, it is the former space which is reduced to nothing; only the planewise space outside is left. This in its turn becomes negatively parabolic – inside-out Euclidian, one might also call it – oriented towards and Absolute which is now the point-at-infinity within, bearing an imaginary cone.

There are in fact two possible transitions from real to imaginary finite values of a, namely through ± oo and o. The former leads to the plane-at-infinity and so to Euclidean space with its pointwise bias. This one alone was given serious attention hitherto. The other leads to the negative or polar counterpart, – to a parabolic space of which the primary elements are planar, determined by a point-at-infinity in the innermost. This would suggest that the polar symmetry of which Clifford felt the lack is to be looked for, not man universal space given
once for all, but in another way; namely that the Euclidean space of the physical universe, single and relatively everlasting – co-extensive in time with this universe itself in its present form – is pervaded by a myriad relatively transient negative space-formations. These, in their spatial character, represent the missing counterpart of the space of Euclid. This is the space referred to in so many ways by Rudolf Steiner; the idea of a kind of space so essential for the understanding of the laws of the living kingdoms. He called this space by many names,
– “Negative Space”, “Ethereal Space”, “Sun-space”, and “Gegenraum”.

29 – The Essence of the Seed

Wherever in the realm of living things there is a seed or germinating centre of fresh life, there is the “inward infinitude” of such a space. The ideal relation to ordinary space is a true polarity; only with respect to time, and with respect to unity and multiplicity, the two kinds of space play quite different parts, thus making possible the side-by-side and transitory existence of multitudes of living creatures.

Physical space is there for all time – at least as long as Earth-evolution lasts, and in this space, time is measured spatially. The hands of the clock or the shadow on the sundial mark off equal distances or equal angles during the passage of the hours. Even this, as the leap-year tells, is a compromise, for the Universe itself is alive, and not bound and limited to a rigid geometry!

The ethereal spaces, on the other hand, could really be called “Time-spaces”; they come and go in the interplay of the cosmic and earthly rhythms. The seeds lie dormant in Earth-space, until such time as the cosmic processes of the space of which each one is the inward infinitude begin to be active, m harmony with the cosmic rhythms of the seasons around the Earth. Then the plant begins to unfold: rootlet (radicle) down into the soil; shootlet (plumule) growing upward according to the laws of this other space, revealing planar organs, rather than radial or materially filled forms.

As well as being a little centre in Earth-space, the seed is the focus of an ethereal space, and gives birth, as the plant develops, to countless other foci of ethereal spaces, as the further buds and growing-points – seed-like organs – appear one after the other. They come into being, becoming visible in Earthspace, unfold and die away or become transformed as their purpose is achieved; and all in the manifold interplay of the cosmic rhythms with Mother Earth. It is an unending, rhythmic interplay between expansion and contraction considered extensively and contraction and expansion considered intensively. This deeper approach to the idea of “expansion and contraction” is very valuable; tiny forms, like seeds or pollen-grains, are ethereally vast, while large and fully developed forms are often nearing their end.

30 – Ethereal ( Peripheral or Planar) Forces

United with all developing life in organic Nature are the forces of the universe called by Rudolf Steiner, and also by an ancient and never quite obliterated traditional knowledge, the etheric or ethereal forces. These are the peripheral cosmic forces, a conception concerning which we can now form precisely, for with the ideas of modern geometry, we have transcended the one-sidedly centric approach to form, and are capable of becoming spiritually perceptive toward the signature of the peripheral forces and the planar space-formation of natural
phenomena.

By means of an exact scientific method, we achieve an ideal basis upon which to build up an understanding of the polarity between the physical and the ethereal cosmic forces.

Negative-Euclidean space leads naturally to the concept of a type of dynamic forces, polar opposite or “dual” to those of classical physics and mechanics. These will be forces acting from plane to plane about the common line of the two planes, even as physical, point-centred forces act from point to point along the line which joins them. ³⁴ This is consistent with the idea that the primary entities in such a space are planar. Since every plane in space – transformable as it is, projectively, as “vanishing plane” into or from the infinite- shares something of the quality of infinite expanse pertaining to the all-embracing plane, the planar type of force may also be described as peripheral, by contrast to the centric forces predominating in the material, inorganic world. This, then, is the essential theory we are advancing:

The processes of the spatial Universe involve not only the centric forces of which the prototype is gravity, but also the peripheral or planar type of force. “Negative spaces”, interpenetrating the ordinary space of Euclid, provide the field of action for these peripheral forces, even as the latter space – its parallel and orthogonal structure determining the composition and resolution of material movements and physical force – – is the domain of gravitational, electromagnetic and other centric forces. The two kinds of space and force constitute a true, qualitative polarity – the primary polarity of the spatial world, more fundamental probably than the point-to-point polarities of physics. To this polarity the projective Principle of Duality (Polarity)¹⁷ provides the ideal key . The phenomena we see around us are an expression of the interplay of the two opposite kinds of activity. In tendency, however, matter that falls out of the living process is predominantly subject to the centric type of forces, whereas in a living body, notably in regions of germination and vital growth, the peripheral type of force will be in evidence, in addition to and to a greater or lesser degree   transcending the other.

Just as the space of Euclid and the corresponding forces are naturally described as physical space and physical forces, so too the negative or polar counterpart of these deserves a more concrete and descriptive name: We choose the name ethereal, thereby restoring to this word a meaning more akin to what it undoubtedly conveyed to our forebears – a meaning which still echoes on in literature and poetic diction. In this sense we speak of “ethereal spaces”, meaning in the first place negative-Euclidean spaces as above defined and of “ethereal forces”, meaning the peripheral or planar forces. We here approach a wider question which is increasingly felt at the present time. Science as represented by its best exponents has grown more historically conscious, less categorical in its claims, more interested in its own cultural antecedents in prescientific times, and above all more alive to the problem. How does our scientific thinking, with all its technical results, affect the social and psychological stability of human life and even the cosmic balance of the Earth-planet as a whole? Now the idea of ethereal forces and activities belongs to the spiritual and philosophic heritage of mankind, both in the East and in the West. Needless to say, the ancient cosmologies did not express it in the scientific form which must be sought for if the conception is to be useful in the present age. But if one follows up in thought the geometrical paths here suggested negative-Euclidean space and the idea of forces polar to those of classical mechanics – one enters in imagination a realm of spaciousness and buoyancy which is “ethereal” in the original connotation of the word.

Yet it will not only be a question of the re-discovery of something known in more instinctive ways to men of olden times. The opening of scientific knowledge in this new direction must also be a real spiritual achievement in the cultural development of modern man, and this will also call for a change of method, not to say a change of heart. In the science of living things, the separation between man the knower and the object of his knowledge is not and cannot be so great as in the science of the inorganic world. For man himself is born of living Nature. In mode if not in content, his thinking and imagination are a function of his own life as one of Nature’s children. If the ethereal formative forces, of which the theory is here propounded, are a reality, they will be there not only in the growing plant or animal, the outer object of our
researches, but in our own thinking activity, inasmuch as our own forces of life and growth have gifted us with power of imagination. If then our knowledge of the organic world, transcending the merely empirical and descriptive stage, is to penetrate to the idea, the underlying force and essential “law” of what is living, we are in a different situation than when examining the laws and forces of the inorganic world. We are a stage nearer to the primal fount, not only of the outer world but of our own thinking about this world. In saying this, the authors once
again acknowledge their indebtedness to Rudolf Steiner, ¹³ who was the first to indicate that the “ethereal” be conceived and investigated in the present sense, and who outlined the methods to be followed. For he not only understood the essence of Goethe’s method of research into the living world, but carried it a stage further.

Out of his spiritual researches, Rudolf Steiner described the ethereal formative forces, which sustain all life, as proceeding from the periphery inward towards a “relative central point”, rather than from a centre outward. He described them as forces “which have no centre, but a circumference”, meaning by circumference not just a horizon, but a whole sphere,-like the cosmic sphere of the heavens. In one lecture, he even used the words “surface-like” and “planar” to describe the forces working inward from the universe, and he described the “Gegenraum” as a “plastically formed space”. Insisting that it is not possible to learn to know the “etheric or formative-forces body, which streams through the human being” by studying it from the point of view of ordinary space, he said: “It is only possible to study it, if we think of it as being
formed from out of the whole cosmos; if we can understand that these planes of forces, approaching the Earth from all sides, come towards man and plastically mould his formative-forces body from outside.”³⁵

The “relative” central point, towards which the etheric forces “work from without inward” is the all-relating point or focus of the counterspace in question. It is not the source of the ethereal forces, but rather the innermost infinitude of the negative space – the infinitely receptive realm – such as is the outermost periphery of space for the outward radiating, centric, physical forces. The source of etheric forces is never a point-like centric realm, but a peripheral one; ideally It is a planar realm. What for positive space is most spread out and scattered, is for this other space the unified planar source from which the lifeforces spring.

Ether-spaces are formed and dissolve again in the life-cycles of organisms. Wherever from a  germ-cell – a seed, a germinating realm in an already created organism – new life unfolds, whether such a germ is in watery living substance or freely poised above it, we may discern the presence of an “all-relating point” – the inward infinitude of an ethereal space. This becomes evident where surfaces envelope and enclose the germinating point within, or through the gesture of leaf-like organs, which develop around an innermost point and open out from it.

31 – “Negative Gravity” or “Levity”

The most elementary kind of ethereal force – a force of mutual attraction from plane to plane, in polar analogy to the gravitational attraction of material particles for one-another – will naturally be described as “negative gravity” or levity. This term again is justified by the expansive forms and movements which arise if one imagines what will happen, say, to a sphere enveloped and permeated by planar entities between which such a force is working. To each planar entity, in such a case, a certain intensity must be attributed-analogous to the mass of a material particle. We call it levitational intensity. ⁵⁶ According to their intensities and geometrical distribution in the ethereal space to which they
belong, a number of planar entities will have a resultant plane of levity, analogous to the centre of gravity of a material system. ³⁷

The hypothesis, that negative-Euclidean spaces and planar forces play a real part in living Nature, implies that the vast reaches of the spatial cosmos will have quite another function in this respect than in the merely pointwise, mechanical aspect of the world. For the infinitude is now within and not without, and as a corollary the origin, the middle region or focus of activity (it will be a planar, not a pointwise focus) will often tend to be in realms which from a physical point of view appear as inaccessible infinitudes. We will deal first with the geometrical
and then with the cosmological aspect of this problem.

Geometrically, the study of an ethereal distribution will involve problems which do not occur in ordinary geometry or mechanics. For one is not pursuing the mere idea of negative space in the abstract, but observing how it is revealed in living forms, made manifest in physical effects. It will therefore in every instance be not only a question of the ethereal (negative-Euclidean) geometry as such, but of the way it is immersed in the physically spatial world. Often this will suggest the kind of form known as a plastic perspective – frequently recognizable in the plant kingdom – though with a dynamic significance which we are not accustomed to associate with a perspective. The simplest possible correlation will, however, lead to concentric forms, and precisely here the most important plane of the ethereal space will tend to be, physically speaking, infinitely far away.

For example, take a sphere or spheroid. ³⁸ Projectively, the Euclidean centre is defined as the pole of the unique, infinitely distant plane. In ethereal space it is the point-at-infinity which is unique; a sphere will therefore have, not a central point but a central plane, polar to the unique point of the space. Since the expression “centre” implies a point, we have decided to speak of the mid-plane or median plane of the sphere. Precisely this plane will often be in the vast distances of the physically spatial cosmos. In effect, if the point-at-infinity is at the
Euclidean centre of the sphere, the ethereal median plane will be the Euclidean plane-at-infinity itself – the uttermost periphery. In the simplest of living organisms – the spherical and polyhedral forms, for example among the protozoa- this concentric situation is clearly realized. Indeed it is most probably the primary situation, from which the more eccentric forms are evolved. The vast distances of the universe are therefore playing quite another part, in relation to life on Earth than. would seem possible if the real structure of the world were
only pointwise.

The same will apply in the realm of forces. Mid-point and median plane are purely geometrical concepts. Now in the physical-material realm, if a distribution of point-centred masses is symmetrical and uniform, the geometrical centre will also be the centre of gravity. For instance, in Plate X, if equal masses are placed at the ends of the radii on any one of the circles or of the spherical surfaces they represent, the centre of gravity of the system will be at the centre. The system of particles will tend to contract towards this common centre, and the picture might well be taken as representing successive stages of this gravitational contraction. Analogously, in the top righthand picture, if the common centre is the point-at-infinity of an ethereal space and the tangent lines signify planar entities belonging to that space, we need but imagine them to be all of equal levitational intensity, and by their mutual attraction they will tend outward to their common “plane of levity”, which will now be the infinitely distant plane of the physically spatial world. (Nor is there any need to suppose that they would take an infinite time in getting there, since the ethereal distance ³⁹ which separates them from thence is by no means infinite! ) This indeed represents the simplest, in a way the archetypal picture of a positively buoyant and expansive, levitating field of force.

Ethereal concentric spheres will, however, not always appear in this simplest form. If in relation to physical space the point-at-infinity is eccentric, they will appear as in Plate IX which shows in cross-section a family of spheroids with, say, U as common focus and with a common polar plane of U, appearing in the picture as directrix. In effect, they must all touch the absolute imaginary cone in U. 25 If
this is spherical as we assume, a sphere in the ethereal space can only appear as a Euclidean sphere if U is at the Euclidean centre as in Plate X. The horizontal plane in Plate IX (considered spatially) is of course the common median plane; likewise it is the plane of levity if we imagine a uniform distribution of levitational intensities among the tangent planes of one or more of the spheres uniform, that is to say, with respect to the measures proper to the space in question. This picture of ethereal concentric spheres with horizontal median plane beneath the point-at-infinity is archetypally related to the gesture of unfolding leaves at the growing-point.

The idea which is shown in Plate X, with its particular relationship between “centre” and periphery, has, however, archetypal and cosmic
significance. We will state it in the following words:

An ethereal-concentric formation, with a common median plane, appears in physical space as concentric, when and only when the common median plane is the infinitely distant, all-embracing plane of physical space. Then, however, the central point of the physical spatial formation is at the same time the all-relating point of the ethereal formation. A form is concentric both in space and in counter space when and only when what for the one space is the all-embracing is for the other space the all-relating Absolute.

What is here formulated in pure thought corresponds to real relationships in Nature. All forms which have arisen out of a living process, and become visible and tangible in a physical body, have arrived, as it were, in physical space, and are things among things. They are to be found in a particular place on Earth and with a particular relationship to the Earth’s surface.

If such a created form has come into being out of a formative ether-space, then, in the gesture and quality of its form can be recognized its relation to this ether-space. But there belongs to this thought the question: What relationship to physical space has the ethereal median plane belonging to a particular form?

If the organic form reveals a concentric symmetry, as do many of the minute protozoa, studied so intensively and pictured by Ernst Haekel (Figs 56 and 5 7 ), it is in a special sense cosmic. These forms, with their wonderfully regular, polyhedral shapes sometimes have concentric shells, one within the other. The median plane of the ethereal space-formation is here at the same time the heavenly sphere itself- the all-embracing plane of earth-space.

This comes to expression mostly in organisms which float freely in water or which develop in a fluid medium, such as the germ-cell or morula in the early stages of development of a complicated organism.

In this more concentric growth, Nature reveals the meaning of what we have called growth-measure, namely, the result of a balanced interplay between an inner infinitude and an outer, cosmic periphery. The seed or germ-cell is an “infinity within”. Here we touch on the morphological secret which divides the inorganic from the organic. Its signature is revealed in the ” Spiral of Life”.

Many organisms reveal this physical-ethereal spatial concentricity, not so much in all three dimensions, but in a plane, or projected into a plane, for instance, those with axial symmetry. The plane in question will then lie at right angles to the axis of symmetry, and its infinitely distant line is polar to this axis or- to an “all-relating point” within the axis. These, for example, are “ethereal median-planes”, in which the symmetry may be revealed. The cyclic or regular spiral-formations of many leaf-rosettes and in the centre of many flowers is of this nature. It is also revealed in most sea-shells (see Figs. 52-55).

In the gesture of living forms, we learn to read the script of organic morphology and see the fundamental difference between those forms which lie inert in Earth-space and those into which there plays – or has played – the cosmic force of negative-gravity or “levity”, drawing the living substances upward towards the light and air and away from the earthly centres of gravity.

32 – Cosmological Aspect

Returning now to the simplest picture, where the ethereal forms are not only concentric in their own right, so to speak, but are concentrically planted in the physical universe of space, we have to face the cosmic implications. At first sight the idea of a realm of form and of dynamic forces having their source or planar focus in the infinite periphery seems paradoxical. For one instinctively tries to relate it to the existing physical cosmology with its vast distances – parsecs and light-years – estimated, in the last resort, in terms of miles or kilometres. It is of
course a real question, what the relation of the ethereal formative spaces to the universe of stars will be. But it is probable, as has so often happened in the history of science, that we first have to learn how to put the question. We must go one step at a time. It is in the living world on Earth- the plant world above all – that we see those phenomena which find their natural interpretation in the idea of negative or planar space. There is no reason to abandon this because we do not yet see how it relates to the existing physical cosmology- subject as the latter
is today, in any case, to rapid and far-reaching changes-or for that matter to the existing theory of the sub-microscopic realm of molecules and atoms.

We are, however, attributing a fundamental role to the Principle of Polarity in the real nexus of the universe, and this in two respects can help us with the present problem. On the one hand the two polar-opposite aspects of truth which it reveals can each be studied in its own domain. Undoubtedly the interrelation of the two, when understood, raises one’s knowledge of the truth on to a higher level. But it does not invalidate or lessen what was known before, of the one or the other aspect. Over two thousand years of “Euclid” taught men the truths of pointwise space; these were in no way vitiated, only their understanding was deepened, when the polar aspect was revealed. To quote
Professor Turnbull, ⁴⁰ the two aspects are not against, but “‘in and through” each other – “contemporaneous and complementary … Nevertheless, each can be followed for its own sake without necessarily forcing attention on the other.” Therefore we may allow the phenomena of life to teach us concerning Nature’s planewise aspect without embarrassment due to the vast accumulation of “pointwise” knowledge, and above all, pointwise theoretical constructions.

On the other hand the Principle of Polarity shows that the different entities of space are not external to one-another but interwoven. For point- and planewise space, not only are the standards of large and small reciprocal to one-another; even the relationships of part and whole are interlaced. In Euclid’s pointwise aspect, for example, the point is the elementary entity “which hath no parts”; the plane is composite, a two-dimensional manifold of points. In negative space the roles are interchanged; the plane is now the fundamental element and the
point is composite – a two – dimensional manifold of planes. And this is only the beginning; taking the lines into account, the mutual relations as to part and whole are even more deeply interwoven.

Projective geometry thus teaches an organic world-conception, transcending the merely additive idea of size and structure and the crude eighteenth-century idea of spatial causation, where outward and impenetrable objects – real or imagined- do but push and pull each other. But the same lesson is to be learned from the phenomena of life, if we can look as Goethe did with fresh and open mind. Not only gravitation and inertia, by the Newtonian interpretation (or by its present-day modifications) ruling the cyclic movements, show the Earth planet’s community with Sun and stars. The life of plants reveals it no less directly. Through the green plant, all life on Earth is sustained by the Sun’s light – a gift from the universe of stars. Nor need we merely think of the solar energy as outward spatial causation, striking the green leaf after having made its way through the intervening mileage. What the phenomena reveal and what healthy feeling tells as we accompany the Earth’s life through the seasons,- is reinforced by the ideal lessons of the new geometry. The plants will now appear rather as organs which the Earth puts forth, expressing in a primary and direct way her organic relation to the Sun and through the Sun to the celestial universe. When we begin to look at the question in this light, the finding of planes of levity in the vast periphery of the cosmos no longer appears so paradoxical.

The concept of ethereal space enables the Earth-planet as a whole to be regarded as a living entity- not in a vaguely philosophic sense, but in a way that lends itself to detailed investigation. As a first working hypothesis, we imagine the ethereal space of the planet to have its point-at-infinity at the Earth’s centre. The tangent planes at the surface – in the concentric spheres at different levels (stratosphere, atmosphere, hydrosphere, biosphere, lithosphere, etc.) – are then no mere geometrical abstractions but represent, potentially at least, constituent
elements of the ethereal planet, just as the stones and grains of sand, each with its centre of gravity, are among the constituents of the material Earth. The mutual force of attraction between these planar entities will then constitute a field of levity, in polar relation to that of terrestrial gravity. Physical entities will under certain conditions be received into the sphere of action of these ethereal forces, resulting in phenomena which are not due to physical or pointwise (atomistic) forces only. A primary phenomenon of this type, according to the theory here advanced, is the upward and outward growth of plants (compare Chapter V).

If the distribution of levitational intensities is uniform, the Earth’s plane of levity will be the plane-at-infinity of physical space, just as the point-at-infinity of the ethereal space is at the same time the centre of gravity.

The question is at once suggested whether this simplest of relations – namely the mutual concentricity of the Earth’s gravitational and levitational fields, or of the physical and ethereal spaces to which the planet belongs – is subject to geographical modification and, above all, seasonal variation. The phenomena of plant life suggest a seasonal swing in levitational intensity between the northern and southern hemispheres. The plane of levity itself will then be undergoing some regular form of cosmic movement, for which the plane-at infinity may represent not the stationary but the average or equilibrium position.³⁷

Regarding the planet as a whole in this ethereal or planar light, phenomena which appear merely physical when studied in minute pointwise regions and with pointwise forms of thought, as for example within the confines of a laboratory, may reveal quite another aspect when the entire planet or even wide geographical areas are considered. We believe that this will prove so above all in the hydro-, aero- and thermodynamic realm, so that the concept of ethereal space and force will open up new prospects in meteorology.

If an ethereal field is to be attributed to the Earth itself, the same will apply a fortiori to the Sun, source of all life on this planet. (We leave aside, for the purpose of the present work, the question of the other planets, also the relation of the Earth’s ethereal field to lunar rhythms.) Here the well-established physical theories – theories of light and radiant energy generally – will at first occasion difficulties. From the phenomena it is quite evident that the ethereal will have to do above all with light and warmth and the chemically active rays, which play so
great a part in physiology and of which, for life on Earth, the Sun is the primal source.

33 – Organic Interplay of Surfaces

It becomes a methodic principle to look at all things from the polar aspect. Take once again the simplest instance, suppose the form to be spherical, with or without a sharply defined outer surface. Imagine the top left- and right-hand pictures of Plate X superimposed concentrically on one-another. This then would represent a spherical entity at once ethereal and physical in nature and indicates the form of question. To what extent does the one or the other predominate? Or is it- as a limiting case, so to speak-wholly belonging to the one realm?

If the sphere has a well-defined surface and therefore size, we shall not judge this from the mere physical aspect as though it might grow bigger and bigger into the surrounding void; we shall experience a certain balance between outward and inward, radial and peripheral magnitudes. In its ethereal aspect the sphere grows bigger when the surface recedes towards the infinite point within. The physical and ethereal aspects of magnitude are reciprocal. This applies, in particular, to the normal size of any living creature. Growth is an interplay
between °two infinitudes, both of which express degeneration or loss of form – the one by contraction into a point, the other by flattening into a plane. (This is most vividly portrayed in the picture of “ethereal concentric spheres”, Plate IX.) Each living entity according to its kind achieves “generous proportions” when in its own way poised between the two extremes. It is a balance between two active principles, physical and ethereal respectively.

The same polar aspect arises- at least as a question to be put to Nature with regard to the manifestations of radiant energy. Think of a radiating centre – a glowing flame for instance, or a space in which some chemical reaction is generating heat. May this phenomenon too be a manifestation of ethereal space as well as physical? If it be so, the surrounding periphery of space is no mere void into which physical energies are being spent, but is playing a more active part.

In its planar character and in its orientation towards an infinitude within, the concept of negative-Euclidean space provides, as was said, an essential key to the formative processes of life. This does not mean, however, that it can be applied as rigidly as can the laws of ordinary space and of the physical forces working upon inorganic matter in solving, say, the problems of mechanics. The living realm is more transient and mobile. In all but the simplest of living organisms there will be more than one ethereal centre or point-at-infinity within; in other words there will be a number of ethereal spaces interpenetrating one-another, according to the differentiation of organs and functions. Their formative
processes will be related organically and in a definite hierarchy of importance. Some will be subservient to others; some will be relatively transient, others more enduring.

Geometrically and dynamically, this involves problems; but our guiding thought is in the right direction. The underlying notion is that of projective space. This becomes differentiated according to the spatial character of the “absolute” which is presumed invariant. If the “absolute” is composite, or even subject to variation in time, the problems that arise will once again relate to the more general projective space. In thinking out the negative or “dual” of the space of Euclid, and in conceiving that this type of space is essential to the formative processes of life, it is therefore not a question of attributing to the latter all the rigidity and permanence of the former. One may let go of a fixed anchorage while still retaining the fundamental concepts of projective geometry – the interrelation of point, line and plane. This science as developed hitherto – notably in the theory of continuous transformation-groups, where the invariant elements are of very diverse kinds – is rich in morphological possibilities, clearly akin to the phenomena of living growth. ⁴¹ But one must first be freed from the one-sidedly pointwise bias which is as foreign to this more mobile geometry as indeed it is to the phenomena themselves.

Science asks the question: how by the convex and outward growth of each single cell, by cell-division, does it come about that the microscopic parts grow in precisely the extent and the directions which the organism as a whole requires? More and more as time goes on, the scientist begins to think in terms of fields and areas of biological activity in mutual interplay. But also an important reversal of spatial imagination is here required.

Where the idea of physical space is instinctively, exclusively maintained it goes without saying that the larger whole will not be understood until the microscopic parts are; they, after all, are like the bricks of which the whole must be built up. But this is not the logic of ethereal construction: here on the contrary we are more likely to learn the elementary truths by contemplating the entire form, visible to the naked eye, and, from the lessons thus learned, in course of time press forward to understand Nature’s technique in making the microscopic parts serve the whole. We may conceive that there are a multitude of “differential” ether-spaces following an archetypal pattern – each with its
“infinitude within”, – their phases of activity waxing and waning to serve the whole.

In every living cell, in every embryonic tissue, there is a primitive potentiality of growth. Where the true balance of a living body is impaired, often a local tendency to spherical and outward growth will become rampant. In the healthy organism this tendency would be held in check, only allowed to function in so far as it served the whole. We may thus gain a new conception of a well-known biological fact: the greater or lesser predisposition of a higher organism to infection or parasitic attack by a lower.

The archetypal germinating centre is none other than the point-at-infinity of an ethereal space pure and simple. To live at all, in every growing part the higher organism must be giving birth to such centres. If it is healthy they are held in balance, inducing their several outward growths only to the extent that the organism as a whole requires. But if in one part or another the localized ethereal centres become too strong, it may only be a relative question whether the excessive life finds vent as it were of its own accord, or whether the ethereal focus
becomes occupied by the specific seed or spore of some other organism, bearing another morphological archetype and able to make use of the unbalanced ether forces of the host.

The geometrical idea of spatial forces – pointwise or planar – and of their static and dynamic balance does not lose all definition at this level. Even in the mechanical realm, for instance in the statics of a rigid body, there are important truths of a purely projective nature – invariant not only in the rigid space to which these particular forces belong, but under all projective transformations. This shows that the wonderful harmony between the forces of Nature and the forms of space is more deeply rooted, and it encourages the further development of a purely projective theory of forces – a subject to which mathematicians have already devoted some attention.

Moreover, it is precisely at this level that science will one day understand the relationships of the microscopic with the astronomical phenomena. The question of the relation of the Earth’s ethereal field to lunar rhythms, to the other planets, as well as to the Sun, will find answers, when science has conceived the true Idea of an organism: a composite field of more or less balanced interplay between polar formative forces and principles. In this book, we shall concentrate to begin with on the fundamental polarity of Earth and Sun, for this 1s archetypal. Then this idea has been fully experienced and scientifically understood, the way will be open to perceive in detail how the true nature of the plant reveals also the true nature of the galaxy- of the great organism within which all life on Earth take place. The plant must reveal herself in all her glory- an ethereal form clothed in earthly substance, living, unfolding, metamorphosing between Earth and Sun”, amid the sun-like, though differentiated cosmic forces of the planets and the stars. ⁴³

34 – Cone as Intensive Form in Counterspace

The ethereal counterspace is, like physical space, to be thought of as being three dimensional – only negatively; it is to be thought of planewise from without inward, instead of pointwise from within outward. In physical, Euclidean space, the two-dimensional element is the plane and the one-dimensional the straight line; it is natural for the understanding of this space that one learns two dimensional geometry in a Euclidean plane.

In three-dimensional counterspace, there are two- and one-dimensional aspects also but here the extensive and intensive spatial experience is reversed. The one-dimensional is still the straight line, but as a manifold of planes instead of points (Fig 28). The negative two-dimensional is the point as manifold of lines and planes. Here we have an intensive two-dimensional element; polar to the extensive, two-dimensional plane of Euclidean space. Thus there are not only polyhedral, discrete forms (as, for instance, in Fig. 26), but also plastic forms
resulting (as in Fig. 42 ) from a continuous sequence of lines (so-called generators) and tangent planes or planes of contact. These are conical forms of various kinds, held in a point, which are polar to the plane-curves of ordinary geometry (see also Plate IV). ²⁰

Take, for example, the spiral curve drawn in perspective at the top of Plate VI, which is like the plane-spiral in Fig. 51. Out of it there arises the spiral cone in the point below. (The spiral above is only drawn to make visible this cone formation, at least to some extent.) The conical surface spirals in infinitely many furls towards the innermost – in this case, vertical – line; just as a plane-spiral uncurls towards the infinitely distant line of its plane. Following the conical surface as it unfurls (impossible to include in the drawing), it opens out, becoming more and more horizontal, towards the horizontal plane indicated in the drawing; just as a spiral in a plane curves ever inward towards its mid-point.

The concentric circles (Plate X) have their polar reciprocal picture: a family of concentric circular cones (Plate IV). As the circles grow infinitely outward in growth-measure towards the infinitely distant line of their plane, or inward towards the centre, so the cones grow “inward” towards the vertical  middle line and “outward” towards the horizontal plane.

In Euclidean space, there are two kinds of plane: the infinitely distant one and all the others. Their measures and form-relationships arise from the fact that in each plane a single line governs, namely, the line that plane has in common with the infinitely distant plane. (In the infinitely distant plane itself, all lines are infinitely distant. Through this, and because of the imaginary circle, there are other measures related more with spherical trigonometry.)

In counterspace, there are two kinds of point: the all-relating point and all other points. Also here, every “other point” bears a singular line, namely, the line which that point has in common with the all-relating point. This line also functions as an infinitude, but from within rather than from without. We experience it clearly as an infinitude within, and precisely this concept is a significant guide towards the understanding of the ethereal nature of the forms which appear in the growing shoot of the plant.

The cone forms in Plate IV are to be regarded in this sense; they are forms in counterspace. The point bearing the cones is not the all-relating point; the latter would be somewhere on the vertical line above this point. (How far above is for the moment immaterial.) This line, then, represents the line-at-infinity within of the “cone-space”. For the concentric circular cones in Plate IV, the horizontal plane towards which the cones open out, is the “ethereal median plane”, and is .comparable with the central point of a family of concentric circles in physical
space.

In this sense, the family of concentric cones is to be thought of in counterspace. Following them as they become ever slimmer and slimmer, from without inward, we should not experience them as shrinking; on the contrary, it is an inward growth-process, towards the line-at-infinity within, exactly comparable to the growth of the circles in Plate X outward towards the infinitely distant line. Change the direction, and the circles shrink into their mid-point; this compares with the opening of the cones into their median plane. This opening out in the counterspace must be experienced, not as outward growth, but as a lessening in the cone-space; as such it disappears into nothing, as
it flattens completely into the plane, just as the circular space in the plane of the concentric circles is reduced to nothing in the central point. (Compare paragraphs 20 and 21, Chapter Ill.)

We are so easily confined to words which express the familiar properties of a physical, pointwise space. As well as the word concentric, we must become used to the word co-planar, which indicates, not a central point, but a planar, peripheral middle realm of an ethereal space.

The ethereal, negative two-dimensional geometry in the point is of infinite significance in the study of plant morphology and growth-processes. When Goethe writes to Herder : ” Forward and backward, the plant is ever leaf, inseparably united with the germ of the future plant, so that the one is unthinkable without the other”, the relating of leaf and germ, or leaf and eye, is ideally none other than the relation of the extensive and intensive two-dimensional elements.

In relation to the Goethean conception of “expansion and contraction”, we quote here the Dutch botanist F. H. julius,44 who wrote: “The outer, visible rhythm of growth is interpenetrated by another, invisible rhythm of growth forces, which runs in just the opposite direction …. The more contracted the material, the more intensive are the possibilities of growth. The more the material expands, the more these possibilities ebb away.” Julius calls the realm of the creative, formative forces “the realm of the Idea“, which lies at the fount of the becoming and growing of the living organism. In this sense he goes on: “There is also to be found expansion and contraction in the realm of the Idea ,
but not spatially; rather as a greater or lesser potential of creative force. Where there is spatial expansion, there is ideal contraction; where spatial contraction, . there is ideal expansion.” With “spatial” is meant here, positive space, expressed in the usual terms. If one is familiar with the relationship of the formative forces with ethereal or negative spaces, then in these words exactly that is described which is revealed to perceptive judgement, when one lifts the experience of the spaces and forms of the plant-shoot to that realm in which one also perceives the ethereal spaces as such.

35 – Negative Content – “Sun-spaces”

To understand the plant according to this way of thinking we must become more familiar with a sun-like space. Until now we have concerned ourselves mainly with the spatial-counterspatial form as such, and have hardly touched on the aspect of substance. In positive space, the volume, say, of a sphere or a cube provides a natural vessel in which to contain substance. It is however, in the nature of the case that such finite, spatial contents do not accumulate in a counterspace determined by an all-relating point.

The question arises: Is there for the ethereal spaces something analogous to the filling of physical space with material substance? Spiritual science answers this question in the affirmative. Let us answer it, to begin with, with a scientific hypothesis, which, if we are content to follow the direction of the idea, can lead to some enlightenment in the contemplative experience of natural phenomena. We will formulate the idea somewhat radically:

The filling of physical spaces with ponderable matter represents only one pole in a polar process. It cannot be that in some places in the universe ponderable, positive space-filling matter accumulates, if not somewhere else a balance is being held. In the totality of universal
processes, there is physical, weighable matter on the one hand and “negative “,  imponderable, – anti-ponderable – “ether-substance” on the other.

Negative substantiality is in its spatial aspect planar; it “fills” space planewise. Using the two upper pictures in Plate X as a guide, think of a physical sphere filled to its surface with ordinary matter. Then picture the polar opposite sphere: here the “negative substance” formed of planes ” fills” the space from the world-periphery inward, as far inward as the surface of the sphere. What would normally be called the inner space of the sphere remains empty; it is hollow. The space filled with planes from the world-circumference inward is considered as negative space, finite; it is not infinite in content. Infinite is, however the hollow, inner space of the sphere, for there in the heart of it is the all-relating star-point the infinitude within.

Leaving open the question as to whether quantitative concepts have any meaning at all in relation to ethereal substance, we can at least be clear that according to the purely mathematical idea, the planewise space of the sphere, from the periphery inward, is certainly finite .

The same concept comes to our aid, when we think of a materially filled sphere, like the Earth, and then consider how the material aspect becomes less and less as we pass out through the Earth’s atmosphere towards the world periphery. Correspondingly, then one can form  form the opposite picture: a sphere with a maximum of intensity in the periphery, which tends to diminish and gradually disappear towards the all-relating point in the infinitude within .

One must recognize that somewhere in a living organism there may be a point or a localized region, functioning as focus for ethereal-substantial content. Then the laws described in paragraph 30 come into question. In such a realm, we do not look for the ethereal content, but rather for a receptive realm, a space infinitely capable of receiving the ethereal content, which according to its nature, fills the surrounding, peripheral space.

For the concept “substantial content” in physical space, we have to substitute the idea of a nothing-nothingness-in ethereal space. It is an empty, hollowed-out space. There, where in physical space one is used to finding substance, there is none; whereas in the surrounding space, where one expects to find an empty nothing, there it is. The sun-space, or counterspace is in relation to ordinary space a negative space. The two are related as the stamp is to the seal.

Fig. 58 shows some enlarged photographs of microscopic sections through buds in very early stages of development, showing the rudimentary beginning of growth in which even the Hower-bud of a future season is being laid down; Cranberry (Vaccinium vitis-idaea), Cherry (Prunus avium) and Arctic Blackberry (Rubus arcticus). Such pictures speak eloquently to the imagination concerning the hidden, inner, receptive centres – the ethereal infinitudes deep in the womb of Nature.

Each time a man plants a seed in the Earth, it is not the little pointwise seed which contains the ethereal substance. In the seed lies the receptive centre, thirsty for form. And the spot on the Earth where the seed is planted is not the place where the ethereal substance is to be found, for this substance is not pointwise, it is planewise, peripheral substance. Here, where the plant will grow, become visible, and show forth its ethereal organs, is the hollowed-out, negative space, the inward emptiness, into which the ethereal forces will stream, to fill it with
living, nutritional substance. We touch here the realm of divine magic, and may understand that in less materialistic times than ours, the deeds of sowing and reaping are accompanied by acts of prayer and worship, in the recognition that here is a realm of human activity, which reaches beyond man into the spiritual depths of all earthly existence.

36 – Weight and “Leichte” – Earth and Sun

The concept of interwoven polarities now enables us to look more deeply into the greatest polarity of all – that of Earth and Sun. To the Earth, physical and material as it obviously is, we have also attributed an ethereal space, with the point-at-infinity at or near the Earth’s centre. We saw it in terms of the two pictures of Plate X, placed one upon the other concentrically, but with the left-hand picture predominating. In the same dual aspect we now see the Sun, only with the ethereal – the negative-space quality of the right-hand picture – predominating. The sympathy, the organic, life-begetting interplay of Sun and Earth is due to the fact that each in some degree shares the other’s nature; none
the less, they are polar to each other, so that a mighty activity is engendered. If Earth and Sun, as most cosmologies agree, were once united, the bonds were loosed in such a way that the Sun took with it a preponderance of Light, and the Earth of Darkness. But they were not irrevocably sundered, and through the countless seasons of Earth’s separate existence, life on this planet still bears witness to their kinship.

The concept of ethereal space, interpreting what is known of living form and function- and above all, of the plant in its relation to the sunlight-reveals a new and fundamental aspect of the sun itself. It is as follows:

In the spatial universe of which we have experience on Earth, ruled as it is by the great polarity of point and plane, the ethereal or negatively spatial aspect has its most essential, macrocosmic focus in the centre of the Sun. Mighty peripheral activities pour in towards this macrocosmic focus. Of all ethereal spaces, this of the Sun is the most powerful and the most ancient. It is organically related to the planet Earth, and to the living creatures which the Earth brings forth . Therefore there is a primary infinity between the ethereal spaces formed by living organisms upon Earth, and the vast cosmic space of the Sun itself. The life-giving power of the Sun’s radiations is due, not only to outer physical causation making its way hither through external space, but to this primary, inherent kinship.

The proposition has been stated with all care. Therefore we say, at the very outset, “in the spatial universe of which we have experience on Earth”. From the aspect of other stars and galaxies, although their light is manifest in our space, it may be different. Again it is not implied that the ethereal aspect of the Sun is the only one. The proposition contradicts no established facts, such for example as  the relation of Sun and Earth in the aspect of physical space or of “celestial mechanics”; it adds a complementary aspect, leaving to future discovery the
question of the full relationship between the two.

In the mechanics of the physical world, the most important concept is that of a “centre of gravity”. For every material body or given distribution of matter, this is a definite, even calculable point, between which and the centre of the Earth we conceive the force of gravity to work. For the community of all earthly-material bodies, the centre of the Earth is like an archetypal centre of gravity to which all others relate.

Physical matter is ruled by the force of gravity, the archetypal instance of the centric forces – and by those forces closely allied to it, such as pressure and contraction. These forces express themselves ultimately in the power to move matter or to withstand and counterbalance the mechanical type of force, which is also characteristically centric.

We have been led to the clear conception that the primary force of an ethereal space will be the precise opposite of gravitation, or of a force of pressure. It will be levitational, suctional, expansive.

Once again it is difficult to find words to express adequately the unfamiliar concepts and phenomena, and, as so often, the more flexible German language provides the best answer. The German word “Leichte“, which is not quite the same as “Leichtigkeit“· or “lightness” has a quality, which makes it preferable toany other, and we like to use it. The ethereal forces are not light and empty, in the sense simply of a lack of physical weight; they have their own kind of “antiweight”, which the word “Leichte” comes nearest to expressing, -better, perhaps,
than the word “levity”. ^{36, 37}

Thus, analogous to the centre of gravity of a material body we can speak of a plane of Leichte (or levity), of a form of negative substantiality, in other words, of ethereal content. A median plane in the realm of ethereal substantiality holds the balance over against the concept of a mid-point in materially filled space. And as we have seen in paragraph 31, through the mobility of projective geometry, we are not restricted to the idea of ethereal concentric spheres, as depicted in Plate X, where the Leichte-plane is the plane at infinity of physical space itself. We recognize it again in the excentric form of ethereal concentric spheres as represented by the horizontal line (Plate IX), and also in the
horizontal plane in the “Cone-space” in Plate IV.

It is helpful to consider in this context the concepts: centrifugal and centripetal. In regard to physical matter, gravity functions centripetally. Nevertheless, through the resulting tendency towards concentration of matter, the opposite quality is manifested; for all matter, as soon as one tries to lessen the space it occupies, reacts with outward pressure. Both qualities are inherent in all matter and this comes to expression in the “specific weight” and the “specific volume”. In solid substance it is largely the former which predominates, in airy or gaseous
substance certainly the latter, where, in the absence of a pressure from without, the space-filling tendency continues more or less indefinitely.

It is in the nature of the case that in the filling of space with matter, the one aspect, however dominating it may be, cannot be present without the other. For example, were the force of gravity alone to operate, every material body would collapse into its own centre of gravity – or towards the centre of gravity of the Earth. The centrifugal tendency must work in some way or other against the centripetal force. (According to the theories of modern physics, it is the hypothetical “intra-molecular force” which plays this part. We are, however, not concerned at the moment with the theories, but are simply considering the facts of the phenomena.)

In the case of ethereal substance in counterspace, we must think in the opposite way. Leichte works centrifugally, drawing or sucking living substance upward and away from the all-relating point or relative centre of the living process, towards the Leichte-plane. Here, too, there is the balancing, centripetal process, for the ethereal forces seek the relative centre, their tendency is to give, to bestow their life-awakening qualities. The ethereal forces do not simply follow their natural, cosmic tendency, and float away into the periphery, but offer their living forces inward, towards the living, growing centre, the infinitude within.

The peripheral, etheric forces work inward and unite with the physical, but in doing so, the levitational force draws or sucks the physical outward. The expansive process does not come about through pressure from within, but through a planewise “suction” from without. One could formulate it thus: The physical, held by gravity, draws the ethereal in towards itself ( germination, invisible prelude to growth). The ethereal, carried by Leichte or levity, draws the physical out with it (outwardly visible growth).

We become aware that the concepts centrifugal and centripetal have a double meaning in this context; they correspond to the qualitative process and not merely to the outward appearance. The idea of expansion and contraction in the realm of growth is more subtle in the Goethean sense than in the Newtonian. The true polarity in the realm of the living is the expression of the centrifugal in the one realm, together with the centripetal in the other, and vice versa.

In the science of cosmology, it is of fundamental importance to allow the hypothesis that in the real processes of the universe there may be both positively and negatively filled spaces. ⁴⁵ One meets the phenomena of the spatial cosmos with quite other expectations. Until now, the cosmological theories of the scientific era were based quite as a matter of course on the idea of a one-sidedly pointwise, Euclidean-type universe. In spite of the general Theory of Relativity and various other developments in recent time, this deeply rooted presupposition has not changed as radically as the conception of space and counterspace would require.

Concerning the significance for science of the concept of Polarity in the so called “Principle of Duality” in modern geometry, the English mathematician Professor Turnbull ⁴⁰ (who published the letters of Isaac Newton) wrote : “The two aspects are not in contradiction, but are mutually in one another. They are complementary and simultaneously true. And yet it is possible to research into either realm without finding it necessary to keep the other in mind at the same time.” Professor Turnbull draws attention to the new morphological method
employed in this book: “In the formation and growth of organisms, both modes of analysis are important (by this is meant the pointwise and the planewise method of observation). Seed, stem and leaf ask that the three dimensional plant form be studied in two aspects, – not only pointwise and microscopically, but also planewise.”

The ideas of the new geometry lead to an organic world conception. The external, additive concepts of size, and the rather primitive eighteenth-century concept of cause and effect, which still persists, in which entities in space push and pull one another, are overcome. The laws whereby the planet Earth and the Sun are related are described not only according to the spatial astronomical thought forms of Kepler, or according to the laws of inertia in the sense of Newton or even Einstein. They are also revealed by the living plant, when we learn to understand her laws aright.

37 – The Peripheral Component in Light, Heat, & Chemical Processes

The ethereal aspect of radiant energy will be revealed in its life-giving functions. In the organic cosmology resulting from the fundamental concept of spaces positive and negative, the relation of the Sun to the green plant on Earth will guide us in discerning the ethereal character of the Sun itself. What the polarity of space suggests will here go hand in hand with a very simple observation of phenomena.

In physical space, the apparent source of radiation is, to begin with, a point-centred body- a candle-flame, a glowing ember. With its potential effects the radiation fills the surrounding space, tending towards the infinite periphery, the effects becoming less intense in proportion to the inverse square of the Euclidean distance from the source. The radiation becomes perceptible by its effects on matter. It is reflected from the surface of material objects. Absorbed in these or in the medium that fills the space, it gives rise to heat, raising the
temperature and thus inducing other changes. Its relation to dark matter is symptomatically shown by the Bunsen flame. Non-luminous and scarcely visible until the stream of air is cut off, the flame then grows relatively smoky and at the same time shines forth brightly, the dark particles of carbon becoming incandescent.

In physical space and in relation to matter, radiation manifests centrifugally. This is a simple description of the phenomena, quite apart from any ascertainment of the so-called “velocity of light”. It fills the space to the remotest material barrier. The heat which it engenders when absorbed brings about thermal expansion and nearly always increases solubility; in the solution it enhances the outward, space-filling tendency known as osmotic pressure.

If we now try to imagine the ethereal or polar counterpart of this centrifugal picture, it will be a radiant activity of which the active source is in the infinite periphery of space. Once more we have the two contrasting pictures of concentric spheres in Plate X, of which the left-hand one clearly represents the naïve physical idea of radiation. On the ethereal side we have to picture the concentric spheres not in their pointwise or radial but in their planar or tangential aspect. The planar tendency is inward and centripetal, but in describing it as such there is no need to think of it realistically as though the planar entities were travelling inward. The relation of space and time in this realm is on another level. ⁴⁶ The essence of the matter is that the active source is in the periphery, whilst in the centre, where in the aspect of physical space we should expect the source, is the infinitude into which the ethereal or negative radiation is being spent.

Turning now to the phenomena, it is precisely this centripetal tendency which the processes of life, in their relation to radiant energy, suggest. Apart from what comes to Earth directly from Sun and stars, the primary source of radiant energy as known to men on Earth is fire, burning the fuel-wood or coal or oil -which has been formed by living things. Directly or indirectly, it is the outcome of the relation of the green plant to the cosmic sunlight. Now the formation of sugar, starch and cellulose in the leaves and other organs of the plant is a phenomenon, not of expansion but of contraction. The chemical constituents of which these carbohydrates are formed – carbon dioxide of the air and water raised from the soil – are specifically lighter than the resulting product in the body of the plant. The chemical process itself is endothermic and therefore cooling and contracting. Even the polymerization, forming the di- and polysaccharides, the different forms of starch, cellulose and lignin, is a condensing process.

When afterwards the wood is burned, radiant heat and light are emitted, and in its physical manifestation the outcome is once more expansive thus the relation of the cosmic sunlight to the green shoot suggests that m this living process light is associated with a centripetal activity, to which the building of these life sustaining and combustible substances is due. The release of radiant energy with its expansive physical effects when the wood is burned is the reasons. The polar relation of projective geometry is here realized by Nature on a gigantic scale, but the one element of the dual process can only be grasped with scientific thinking when the idea of ethereal or negative space has been developed.

To understand what is here intended, it is essential to unburden the mind of atomistic preconceptions, not with a view to their elimination, but in order that the visible and tangible phenomena may tell what they have to tell from another aspect. By far the greater part of our atomistic world picture is not phenomenon at all and cannot be; it is idea. This makes it no less real if the idea is true, but it should not become a “fixed idea”, barring the way to others which the intuitive mind may also read from the phenomena directly, and which may prove no less essential. The planar realm when found will complement the pointwise; the one idea will help interpret what is enigmatic in the other.

It is in physical space and above all in inorganic matter – or matter which, like  burning wood or coal, has fallen out of the living process – that those expansive, dissipating tendencies are manifest which are at last summed up in the Second Law of Thermodynamics. A classical example – the Irreversible diffusion of gases, each of them tending to fill the available space till its own partial pressure is balanced- shows how the Second Law is connected with the expansive, space filling tendencies which are evoked by heat, and therefore by radiant energy as
such, in inorganic matter. But in the realm of life, if we are unbiassed – if observation and thinking are truly poised between the two “dual” possibilities which we now know to be inherent in the very nature of space – we shall associate radiant energy with a centripetal and not only with a centrifugal tendency. Seeing how life renews the differentiated forms and substances which death disperses, we shall not unduly universalize the Second Law.

The concept of ethereal space makes it possible to conceive in a simple way both the inward and the outward tendencies of radiation. (See again the top right-hand picture ‘in Plate X, supposing the apparent “source”. to be in the region of the point-at-infinity within.) The outward tendency is like a primary phenomenon of levitation, evoking once agam the kmsh1p of Leichte – “light” and “lightness” – suggested by the genius of language. The plane of levity is the plane-at-infinity of physical space. The inward on the other hand, of which we have been speaking, is a space-filling tendency in negative space, working from the periphery towards a boundless realm within which in comparison to matter filled space is like a space that is “more than empty”. The outward and inward tendencies balance one another; the space is filled with
ethereal light, which may well be of many kinds; the dynamic balance here suggested may be established in many different ways.

A “space of light”, thus conceived, is indeed like the “negative” of air- of the Earth’s atmosphere which finds its balance between the centrifugal, space-filling tendency of gases, and the centripetal of its own weight. The interplay is manifest in atmospheric pressure; the balance is established in a gradient of pressure. So in the corresponding realm of ethereal space and substance, the interplay will manifest in an ethereal or planar field of force for which the proper word is “suction”. Unlike most “suctions” that occur in physical mechanics, this is,
however, a true, qualitative force of suction, not the mere outcome of a difference of pressures. Be it observed that in this polar comparison of “light” and “air”, the centripetal tendency of the one corresponds to the centrifugal of the other and vice versa.

All these things indicate that in radiation there is a primary activity peripheral m nature, tending inward and not only outward. The physical centrifugal effects are in the nature of a polar-opposite response. Once again the relation of centre and periphery is mutual.

The implications for physics and chemistry are far-reaching. The numerical rhythms and harmonies shown in the spectroscopic phenomena, deeply related as they are to the laws of chemical affinity and structure, will have their origin not only in sub-microscopic world of atoms, but in this interplay of centric and peripheral activities. As in projective geometry the pure relations of number working in the ideal interplay of point, line and plane are found to govern the enhancement of ever more complex forms, so will the primary rhythms, manifested in the differentiations of matter and radiant energy, be working in the cosmic realm of Light and Dark – using the Goethean terms in their wider
meaning. If then the spectral lines are an indication of these cosmic rhythms, antecedent to matter though embodied in it, the discovery of the same lines in the light of Sun and stars does not oblige us to infer that matter, ready-made and preop1tated into Euclidean space, is present yonder as it is on Earth. What it makes certain is that the formative forces to which the earthly matter is due, are also there in the great universe.

Thinking of Sun and Earth, and of radiation in its relation to matter, we have approached the Goethean polarity of Light and Dark. Goethe meant not merely visible light; the purest and most incandescent white was for him already an outcome of the interplay of light and darkness. ⁴⁷ Moreover the dark was for him associated not only with unsubstantial shadows, but with the very essence of the matter which throws the shadows. In “Light and Darkness”, he divined an ideal polarity, fundamental to the structure of the world; the visible phenomena were an outcome of the interplay of both components. This does not mean ultimate dualism, any more than does the geometrical Principle of Duality. The more one enters into Goethe’s concept of polarity, the more deeply does one see it to be related to the projective geometry which in his lifetime was only just beginning. Today, when his scientific work- including the Theory of Colour – is being taken more seriously than in recent generations, one cannot but confess that his idea of the realm of light, near as it is to our immediate experience of Nature, is
foreign to the existing theories, whether in their corpuscular or in their undulatory aspect. The discrepancy may be resolved when it is seen that these theories refer to the physically spatial effects of light – effects which are only brought about when light is already caught and held, so to speak, in darkness. ⁴⁸

Using the Goethean ideal concepts, physical or pointwise space as such belongs, in effect, to the “dark” pole, and negative or planar space to the “light”. Yet the polarities of the world are so interwoven that the former is sustained by an unique plane – an unique entity of light – and the latter by an unique point or entity of darkness. Formative, crystal-begetting light from the infinite plane “informs” the Euclidean spatial world, the space of darkness. And in the dark fertile earth every living seed or germinating centre is the receptive focus for a vast space of light- the planar space which bears the archetype of the organic form that is here seeking realization.

We have thus approached the phenomenon of radiation from two polar aspects. Let us think again of the typical and familiar example, – a candle flame! We contemplate it and think as follows: It radiates light, heat and chemical effects. In this process, not only the radiation from within outward is at work; for the candle can only radiate outward, because in the ether-space of which the all relating point is in the candle flame, the ethereal forces work inward from the world-periphery. The flame is a receptive centre: only thus can it radiate, bestowing light and warmth. Centre and periphery work together in active and mutual interplay.

The radiation in this case is connected with a chemical process. If our hypothesis holds true, we can gain through it a new insight into this process. The chemical interchange consists not just in the moving around of pointwise (atomistic) particles in physical space, but in a process of becoming and passing away again (Werden und Entwerden). The substance which is burning – now in space – originally came into being from the periphery. It has come to rest in a quite definite, rhythmically determined, qualitative-quantitative equilibrium between centre and periphery. Now, through the chemical process engendered in the flame, an inroad has been made into this restful state. The substance is
being “eaten up”, and a new equilibrium is coming about in the new substance which is being engendered.

Heat in its very nature is always delicately in the balance, in the interplay of ethereal and physical spaces; it is at the threshold between the ponderable and the imponderable or “anti-ponderable”. The view held by the nineteenth century scientists, as expressed in the Theory of Gases, came nicely to expression in the famous, classical textbook of the English physicist Tyndall: Heat as a Mode of Motion. Rudolf Steiner answered this in the following words: “Yes, it is movement, but not outward, spatial extensive movement – not just a hopping about of the molecules, and so on – but intensive movement, ⁴⁹ whereby is meant an inpouring of the peripheral into the centric, and a working outward of the centric into the periphery; an interplay of physical and ethereal spaces.”

The idea that in all processes of radiation peripheral space plays a part is to be grasped in this sense. Underlying the active process, which appears to come from a radiating centre, is the equally important part played by the universal forces, which work in from the periphery. Yes, the original source or origin is to be sought in the periphery rather than in the centre.

Gallery with All Plate Images from Beginning of the Book

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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