Chapter 2: SCIENCE OF THE FUTURE
Section 13 – Goethean Science and Modern Geometry
Our task will be to seek for Ideas, which correspond just as exactly to the phenomena of plant forms and growth as do the familiar laws of physics to the pheonomena of inorganic nature. To this end, we shall bring to bear on the morphology of plant life a realm of achievement of the spirit of modern thought which has hitherto run alongside natural science, without having had any great influence on it. This is the modern Synthetic or Projective Geometry, the development of which took place in the beginning of the nineteenth century. Today, many mathematicians consider this beautiful realm of geometry to be classical and already superseded, in fact, it is but the seed of quite new directions in mathematics, containing as it does potent possibilities in relation to living nature and the science of life in all aspects.
The new geometry has a close relationship to the quality of thinking of the great artist-scientist Goethe.  It cultivates a qualitative, picture-forming aspect of mathematics, which approaches closely the Goethean experience of nature. For Goethe seeks the explanation of something living, not merely in the logically thought-out relationship of cause and effect, but through what he call anschauende Urteilskraft. The term which comes near the rendering of this idea into English is perceptive judgement, meaning: a perceiving of the truth within the whole, while observing, so as to reach the archetypal picture or Idea, to which the phenomenon relates.
It is to such a method that Projective Geometry is akin. Not only in the method, but in the content of the new geometry, we find significant possibilities of bridging the gulf between Goethe’s qualitative and completely phenomenological way of approach to Nature and the natural science of our time, permeated as it is with so much mathematical thought. Modern Geometry provides a way of experiencing space and spatial forms, so that the importance Goethe attaches to polarity in nature – light and darkness in the Theory of Colours, expansion and contraction in the Metamorphosis of Plants – may be approached through the transparent and exactitude of mathematical thought. Much that the biologist, who is imbued with the ideal of Goethe’s theory of knowledge strives for, can be realized through the clarity and precision of studies in morphology based on modern projective geometry.
Unhappily, the one-sided insistence on the use of analytical mathematics as a tool for biologists has had a profoundly formative effect on the biological sciences and on the minds even of younger scientists, some of whom, however, know instinctively that a purely materialistic approach to the secrets of life yields no real progress, and are at their wits’ end to find a way out of the impasse. The key to the phenomena – or else, if it does not, the key is not to be found. The biologist, beholding the wonderful regularities of pattern in the forms of life, tends to assume that if a rational explanation is to be found it must be via the atomic, ultra-microscopic realm which in the quality of its forms is only senses. A striving to perceive the phenomena of life though the whole,, rather than through the part, receives no help from the ancient, Euclidian, finite geometry inherited from the past. This why there is a tendency in biology to borrow basic ideas from physics, for though in general the old conception of space is adequate for the understanding of inorganic nature, it is so only to a greater ideal freedom than the biologist. This dependence upon physics has undoubtedly been a hindrance the proper development of biology. It has even been said that while biology in its efforts to be an exact science has taken the basis of its ideas from physics, in future the laws of physics would reveal themselves to be special cases of the more universal biological laws awaiting discovery in the future. 
The general lack of interest and understanding of the potential which is inherent in the thought-forms of the new geometry results in a lack of the right kind of mathematical tool to complement the old forms and lead to a truer understanding of organic processes. Yet, through the discovery in modern geometry of the Principle of Duality – better described as the Principle of Polarity – which bears on all ideas concerning space and spatial formations, the relationship between “Centre and Periphery” can be qualitatively experienced in quite a different way than before, and the needs of biology are met with an exact, scientific mode of thought.
Take for example the puzzling question of the morphogenetic processes in the early stages of embryonic development, which seem to be determined not from the inside of the material organism, but from the surface, taking place from the periphery inward. Gurwitch seeks for the Idea of the peripheral, formative fields, partly enveloping the organism and working on its surface.  “Study” he says “the processes of growth and embryonic development in their early stages – invaginations, folding, and the like – and we shall find the typical formations determined without exception by the contours of the outer surface, not by the internal structure.” He and others have tried to deduce the specific character of the “morphogenetic field” purely from the phenomena of growth and form, leaving open the question of its source. Stress is laid on the surface-character of many typical phenomena of development, suggesting that the formative factor does not proceed, like the kind of causation with which we are most familiar in the inorganic world, from within outward, but the other way round. The elaboration of the “field” concept in physics encouraged scientists to look in this direction and attempts are naturally made to ascribe the field to the physicochemical factors observed in the cells and tissues. The interrelation of cause and effects is, however, by no means clear, and whole realm is wide open to research.
For such problems and phenomena of the living world, the Principle of Polarity in modern geometry provides a new and essential key; it awakens in the mind quite other powers of imaginative insight. Expressed briefly, the polarities of pure geometry suggest: Wherever the point, there too the plane – the plane which in contrast to the teeming world of atoms is related to the vast expanse of the spatial cosmos. Over against the point-centered elements hitherto known to physics, we are led to consider the thought of elements or processes planar in character, which by their very nature are akin to the celestial periphery, even as every centre of gravity is akin to the centre of the Earth. A schooling in this geometrical discipline gives to the mind capacities in thinking of a unique kind when applied to the observation of Nature; it offers the inclusion of the plane and of planes moving from the periphery, as form – and space-creative entities, side by side with the point and its centric and contracted nature. The Goethean terms of “expansion and contraction” acquire a deeper meaning than the merely spatial one, for the Principle of Polarity leads beyond the conception implied by these terms in the old geometry. The law provides the leitmotif for the idea of metamorphosis. Metamorphosis is possible in the changing interplay of polarities.
14. Universal Forces – Rudolf Steiner’s Indications
Goethe’s achievements in biology, as well as in the theory of colours and with this leading into realms of physics, are being taken far more seriously in recent decades. Yet humanity today is in a very different situation, and is struggling both in natural science and in regard to the social questions arising from it, with the problems hardly to be imagined in Goethe’s lifetime. Until the end of the nineteenth century, the revelations of natural science were concerned with the material world. Deep spiritual powers lie at the basis of this realm of outer phenomena. “Space, Time, and Matter” do not in fact form an absolute ground for science. Modern physics has come so far as to dissolve the seemingly stable aspect of matter, and to penetrate this, but in a one-sided and therefore certainly dangerous manner. Space itself, in which matter has its existence, is in reality the result of the polar interplay of centric and peripheral components. The recognition of this, which is reached with perfect clarity in the new geometry , has, however, not yet had the right and proper influence which it should have had upon natural science.
Man in his researches into nature’s laws asks earnest questions; the universe answers him according to the nature of this questions. The one-sidedly centric forms of thought which have dominated physics and chemistry since the seventeenth century have opened up more and more the idea of the centric (atomistic) component of natural existence. Twentieth-century physics has long recognized that this component is of the nature of pure thought, and is not to be grasped with ideas derived from sense perception, as though the atom were a minute particle of matter. But there is as yet no recognition of the fact that natural existence also contains the polar aspect, even in matter and the substance-creating processes. To the centric, pointwise component belongs the other pole – the peripheral component. The ideas derived from modern geometry make it abundantly logical at least to widen the form of the question we put to nature. The peripheral component has to do with those cosmic powers, which in past times were experienced as the cosmic, ethereal and therewith the life-giving forces, the echoes of which are still to be found, particularly in Eastern traditional wisdom, though not accepted by modern science. It becomes more and more essential for the healthy development of mankind’s culture that the knowledge of such cosmic forces be renewed, but in a modern scientific way. Rudolf Steiner  showed how to this end the necessary capacities and powers of knowledge can and must be developed on the sound basis of natural-scientific thinking and research. Especially towards the end of his lifetime, in response to questions from trained scientists, he gave indication concerning the ways in which a dominantly materialistic science must be transformed. Thoughts inherently related and applicable to the living processes have to be developed and applied in the observation of life, just as this has been done for the inorganic sciences. The laws of the inorganic world alone are just not sufficient to explain the secrets of the organic, and we must pass on from a stage in science in which far-reaching results have been achieved in mechanics and physics (and also in the mechanical aspects of medicine, in surgery) to a scientific era in which new thought-forms may be found, with which to approach more truly the physics and chemistry of the world of life.
A paragraph formulated and written down by Rudolf Steiner in March 1924,  indicated clearly the path which must be trodden in science:
“When we look out on lifeless Nature, we find a world full of inner relationships and find in them the content of the ‘Laws of Nature’. We find, moreover, that by virtue of these laws lifeless Nature forms a connected whole with the entire Earth. We may now pass from this earthly connection, which rules in all lifeless things, to contemplate the living world of plants. We see how the universe beyond the Earth sends in from distances of space the forces which draw the Living forth out of the womb of the Lifeless. IN all living things we are made aware of an element of being which, freeing itself from the mere earthly connection, makes manifest the forces that work down on to the Earth from realms of cosmic space. As in the eye we become aware of the luminous object which confronts it, so in the tiniest plant we are made aware of the nature of the Light from beyond the Earth. Through this ascent into contemplation, we can perceive the difference of the earthly and physical which holds sway in the lifeless world, from the extra-earthly and ethereal which abounds in all living things.”
On the one hand the study of lifeless nature has resulted in the formulation of the “Laws” according to which things relate to one another on and around the Earth; the stone rolls down the mountainside, the pendulum swings to and fro, the apple falls to the ground.
But how, indeed, does the apple get to the top of the tree in the first place? Is not the fact that it falls a secondary, rather than a primal phenomenon in the household of Nature?
In living processes, phenomena are to be seen which take place in an altogether different and usually quite opposite way from those which are familiar in the inorganic world. Substances move about in living tissues, rise upward as well flowing downward; they may even interpenetrate, without losing their identity, which is impossible in the world of solid bodies. What is actually happening, when the rootlet pierces the integument of the seed, reaches down into the soil and draws substances upward from the dark Earth? How do the changes take place in living tissues, allowing the young shoot to grow upward, instead of downward? Is the process called photo-synthesis fully understood in all detail?
What is it we see when, in Rudolf Steiner’s words we “contemplate the world of living plants”? For the greater majority of trained scientists, the passage quoted above will be nonsensical, even embarrassing; and yet science today is asking questions, which, not so very long ago, would have been considered to be impossible. Here it is said: “In all living things we are made aware of an element of being which , freeing itself from the mere earthly connection, makes manifest the forces that work down on to the Earth from realms of cosmic space.” What can this mean? How are forces that work down on to the Earth from realms of cosmic space.” What can this mean? How are forces that work down on to the Earth from realms of cosmic space made manifest? And what is the nature of such forces? Such questions are crucial today; they are being asked, and answers are being bandied about on all hands. But still more crucial for the life and well-being of man and the planet Earth is that the questions are rightly asked, that man researching into nature’s laws asks the right questions and is ready to receive the right answers.
Rudolf Steiner took up and developed further the scientific method of Goethe. As a young man he edited and annotated Goethe’s scientific works  and in the essay entitled The Nature and Significance of Goethe’s Writings on Organic Morphology, he refers to and explains Goethe’s description of the capacity by means of which organic nature may be comprehended, which he called anschauende Urteilskraft – the perceptive power of thinking (cf. p. 35) Goethe established in his morphological works the theoretical basis and the method of the study of organic forms and processes. The qualities perceived by the senses in a living form are the result of something which is not perceptible to the senses. What is perceived by the senses is not by itself sufficient to explain the total phenomenon. To do this it is necessary conceptually to grasp the whole – the Idea of totality – as well as that which appears to the senses in space and time.
Such a morphological study requires intensive training in observation and thinking. To an awakened mind, the very forms themselves, their changing shapes and gestures “make manifest” their source and origin. It is the kind of knowledge, reaching to the impulsating, all-sustaining principle of life, which Spinoza called scientia intuitivia.
In the areas of anthroposophical scientific work, based on the indications given by Rudolf Steiner particularly towards the ends of his lifetime, research has been going on for some decades into the organic realm, attempting to demonstrate the etheric or ethereal forces. In comparison with the “centric” forces of classical physics, they have been called by Rudolf Steiner the “universal” or “cosmic” forces.
The vast field of phenomena revealed by modern science, for instance in anatomy, zoology, botany, embryology, in earth-sciences and so on, can be approached with the renewed insight. Experimentally, new techniques are being evolved and developed further in order to demonstrate the action of ethereal, cosmic forces in relation, for instance, to the effect of moon and other cosmic rhythms, or of high potencies, on living organisms. Research is undertaken into processes which are known, but are without scientific explanation, because the idea of peripheral or universal forces is lacking. Such experiments are being carried out particularly as the result of the practical needs of medicine, pharmacy and agriculture, where the healing aspect of Rudolf Steiner’s indications is being more and more recognized today.
Although Rudolf Steiner gave many indication as to how to proceed in these various realms, he made it clear that the rediscovery of the ethereal realm of life must take place in a modern scientific way, and must not be confused by vague, traditional conceptions of the nature of these forces. It is necessary to redefine in scientific terms the realm o=and nature of the forces that shape and sustain living forms. He showed how it will be possible to form a clear conception of the ethereal entities and forces, which, he contended, would open up a field of true research, and, in a higher sense, of direct perception. 
It is in this context that the present work relates to Rudolf Steiner’s scientific aims, bringing to the researches already in progress modern mathematical thought-forms and procedure. The specific direction taken, which develops the idea of a peripheral type of space and formative process on the basis of modern projective geometry (cosmic as opposed to earth-space), is due to concentrate indication Rudolf Steiner gave, when he asked for the mathematical formulation of what he called “Negative of Counter-Space” (Gegenraum). As we as using the word “cosmic”, he often referred to “etheric space” and to “sun space” in the same context. He repeatedly pointed out the need to complement of transmute the conception of space, which is ideally formalized by three cartesian axes, in order to overcome or supersede the one-sidedly centric and physically spatial thought-forms of natural science. Hence the formulation of a polar Euclidian type of space by George Adams (Kaufmann), which he published first in German under the title :”Von dem Aetherischen Raume” and then in English: Physical and Ethereal Spaces, both in 1933.  Later, the same concept was worked out by Professor Louis Locher-Ernst, called by him “Polar Euclidian Space” and published in 1957 in his book Raum und Gegenraum. 
Thus in recent decades the further steps have been taken in projective geometry, which set forth the mathematical statement of spaces absolutely complementary to the rigid and finite space of Euclid. Projective geometry had discovered that the ideal structure of three-dimensional space does not proceed one-sidedly from the point alone, but from two opposite entities – point and plane – which play a fully equivalent part in the fundamental structure. Already in the 1820’s and 30’s the “non-Euclidian” geometries had been discovered; moreover, spaces of more than three dimensions had been thought out and the classical a priori of a rigid and right-angled three-dimensional space as being the only possible way of thinking about space was shaken. A still further change was wrought by the increasing effort of nineteenth-century science to penetrate into the working of Nature’s forces and to adapt the forms of thought to the phenomena discovered. No longer could researches concerning “real” objects and events in Space and Time remain within the framework of the classical concept of three-dimensional space, nor accord with Newton’s idea of the uniform flow of Time. Thence came Einstein’s Theory of Relativity and other subsequent developments. The idea of a conception of space polar to Euclidian space was therefore theoretically close at hand, but furthermore the was was also open to the clear mathematical concept of forces polar to the conventional, centrically conceived forces of physics.
Because of the one-sidedly mechanistic and materialistic direction of applied mathematics, which has served science well in the direction of atomism, it appears that no one, apart from the researchers following Rudolf Steiner’s indications, has deemed it worth while to work out the formulation of polar Euclidian spaces, let alone to develop concepts concerning the forces which might apply in such a space. Yet this is precisely what is needed to fie to the concept of etheric formative forces – processes at work in the building up of living tissues and forms – a clear mathematical basis. In other words, what may be revealed through observation by the process of “perceptive judgement”, when an underlying truth or Idea has been perceived, can be described and explained in terms required by the modern scientist – provided, that is, that he has acquired the necessary mathematical skill and imagination.
In the present work the attempt is made to bring these new ideas to bear on the morphological phenomena of living nature, and in particular of the higher pant. Our underlying method is primarily morphological. In the observation of the living forms in all their detail and beauty, we shall be seeking to read the ideal – even mathematical – significance of the visible, macroscopic phenomena of plant life and function. Moreover we shall approach the plant as a whole, – its changing forms, the way it creates its own spaces as it lives and grows through the seasons.
Our work relates to what can be seen with the naked eye; we shall leave aside the details of cells structure, the phenomena of cell division, and so on, although, of course, we are conscious that this is a lack. It is, however, in the nature of the new method, to approach at first the whole and then its parts. According to the old spatial conceptions, it is natural to think first of the parts and then to put them together to make up the whole. One thought instinctively that as the whole is made up of smaller parts, it is therefore to be explained by a study of these parts. The cell structure of the leaf revealed by the microscope, for instance, must surely contain the explanation as to how the whole leaf has come about. The structure of the protoplasm, seen by means of a stronger magnification as plastids, cholorplasts, chromoplasts, nucleus and so on, must, we tend to think, contain the explanation of the cell as a whole. Finally, one hopes to find explanations for theses smaller particles by penetrating to the still smaller molecular structure with the electron microscope. This line of thought has indeed, particularly in recent times, led to important knowledge; but the deeper insight into the type of spatial concept afforded by modern geometry leaves the question open as to whether perhaps the explanation for microscopic phenomena may not just as well be sought in the phenomena of the whole. Many phenomena point neither in the one nor in the other direction; to an ordinary spatial mode of observation it is indeed a puzzle that the same kind of cell-structure and process of cell-division should exist in the myriad forms of both animal and plant life. This fact alone might well be an indication of the insufficiency of this manner of explanation.
We shall be led by our study of plant life and also by the spirit of the new geometry, with its deeper conception of space, to experience spatial formations – even space itself – as evolving processes, rather than as being already given and ready made. This directs us towards a way of approach to knowledge concerning which one can become convinced that it will be just as characteristic of the science of the future as was the predominantly spatial mode of approach for science hitherto.
As well as seeing Nature as a series of objects and processes spread out in space and taking place in the indifferent passage of time, we shall begin to recognize Nature herself as a time-organism uniting earthly and cosmic polarities. Universal epochs of time are super-imposed one on another in Nature’s laboratory. Just as in the human soul experiences of the present moment – joys and sorrows – live together with memories reaching back through years and decades, so it is in the space-time existence of Nature. Things which co-exist in space and in the immediate flow of present time – particularly when it is a question of different orders of size – can correspond to different cosmic times. It becomes a matter of recognizing the signature of Time at every stage. Then the explanation can no longer be a spatial one, not even one which, in the sense of Einstein, includes Time as a dimension within the spatial structure.
It is in this sense that a morphological study, which takes it start from the visible forms and growth processes of plants and leaves aside for the moment the histological and cytological phenomena, is justified. It must, however, be said that to investigate this realm also with the help of the ideas of Space and Counterspace, once the first steps have been laid in the study of the whole, will be an extremely important task. The question must be asked, how the unfolding development characteristic of a particular type of plant, say, a Rose, is related to the cell-structure, how the one and the other aspect are mutually interdependent – how, perhaps, in the play and interplay of the Nature forces, the plant in its wholeness comes about not because of, but in spite of the cytological aspect.
This article was an excerpt, specifically Chapter 2 of George Adams and Whicher’s book Plant between the Sun and Earth.
It is a rare text and subsequent chapter will be released and linked to this chapter.
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