Enhancing Sense-Perception Through Thinking by Olive Whicher

ENHANCING SENSE-PERCEPTION THROUGH THINKING

By Olive Whicher

An article from the 1994 Edition of the Golden Blade

An Anthroposophical Scientific Journal
https://www.waldorflibrary.org/images/stories/Journal_Articles/Golden_Blade__1994.pdf

Life on earth today affords experiences concerning space as never before; there flood in on all hands pictures and experiences, which encourage spatial ways of reacting and thinking. This calls for ways of thinking, which come clearly to grips with the experiences demanded by life in a body moving around the earth-space. As children, we learn to stand upright, to cope with the law of gravity, rising above it
in running and climbing. By observing the actions of others, we copy and try and try again, so that, all being well and in good time, we become proficient. The speed of modem life demands all this as never before, especially for those who live and grow up in cities.

Walking in the street, driving to work, hearing about or watching news of shootings, explosions, and rioting, even if only in the imagination — all this has an effect, particularly on the very young, which is of the same quality as the physical force involved in any of these activities. These forces, coming to expression through substance, originate from some centre and involve an outward movement towards a point of impact in the surrounding space. There is, however, a difference between an inorganic and an organic force. The first may be clearly and fully described by a physicist; not so the force resulting in the physical movement of a living organism.

The modem analytical physicist is equipped through his education with the kind of thinking, such as that provided by algebra, the most efficient tool at the core of analytical mathematics, which takes away pictorial thinking and reduces the facts to symbolism. This kind of mathematical thinking has led to the most wonderful achievements in technology; life on earth has been greatly changed, with the development of telecommunication, travel, the distribution of goods all over the world, and so on. Significantly enough, though, the very pictorial element, which this aspect of mathematics has taken away, modem technology has given back in a very specific way in television, the pros and cons of which are not always evident to an undiscriminating public today. Not only the violence portrayed in the pictures, but the technological process itself, which involves the destruction of the original picture and its apparent reconstruction in the form of dots
on the screen, has a detrimental effect on the life-forces of the viewer.

The development of the living sciences, with the notable exception of medical techniques in the operating theatre, and in methods of diagnosis, has not kept pace with the development of technology. Apart from important successes in immunization and certain aspects of biological control, disease threatens the extinction of plants and animals, and causes great concern also in humans. Environmental concems point to a deterioration in the life of the planet itself, raising questions in the minds of eminent scientists in regard to the very nature of the earth. Is the universe simply a great mechanism, with relatively solid bodies moving round in the space occupied by all the other bodies, such as sun, moon, stars and galaxies, in ways which vary with the various theories? Or are there other ways of thinking about it all?

We see what we think we see!

A recent article in the Daily Telegraph (March 22, 1993) reviews the ‘changing fashions’ in theories concerning urgent environmental issues, in particular, the phenomenon of acid rain and the acidification of the soils. The article is accompanied by the head-on photograph of a pregnant cow, the sad face staring out from an enormously extended, heavy body, hanging from the horizontal vertebral column, sup
ported by comparatively inadequate-looking shoulders and legs. The caption runs: ‘Poor cow: manure releases ammonia, which ultimately turns to nitrate in the soil result: acidification.’ With this we are led to follow the origins of acid emissions from power generators to cow-pats, the product of a living organism. From such an analysis it would seem that there is no difference between the inorganic emission and
the product of a living organism, such as has sustained life on this earth for thousands of years. It is of course, this very way of thinking purely quantitatively and materialistically about substance, whether inorganic or organic, which led to the chemical fertilizer industry in the first place, and of much else of an inorganic chemical nature used now in foodstuffs, pharmaceutical products, also of course, in clothing. What is the difference between organic products and synthetic ones? Maybe, in their wisdom, the poor cows are also asking this question!

Perhaps the very mind-boggling successes in the physical sciences arising through analytical mathematics have resulted in eclipsing the fact that mathematics includes quite other ways of thinking, the study and practice of which educates the mind towards quite different ways of approach to phenomena. Mathematics contains all manner of answers. The unportant thing is to put the right question, in order to get the
right answer to questions concerning observed phenomena. A question couched in thoughts, which will suit the phenomena of physics, will not necessarily result in a satisfactory answer to a question concerning living processes. In fact, we see what we think we see! Very much depends on becoming aware of the way we have been educated to think and, today, in taking our own thinking in hand and, where necessary,
transforming it.

Transforming our thinking

To transform one’s thinking so as to reach beyond the realm of measure, number and weight requires an inner moral force, and here the word ‘force’ has no spatial connotation, only an inner reality. The forces of will are still required, but the object is no longer in space. To quote
Rudolf Steiner: ‘The highest form of individual life is that of conceptual thinking without reference to a definite conceptual content.’ ¹ Here we are faced with an activity of will in quite a different world — in the inner space of our own spiritual activity of thinking. Thinking is an inner force, of which the human being through his own initiative is capable today.

Mathematics itself embodies this inner activity of thinking, and Steiner immersed himself in it at a very early age. But, while analytical mathematics, together with its offspring, the computer, has resulted in such a quantitatively assessed and ordered world, Steiner had already in the very early decades of this century seen the value of modern synthetic projective geometry, frequently urging the scientists among his pupils to look for the qualitative further development of pictorial mathematical thinking and imagination along these lines.

Essentially important in education, this aspect of mathematical and morphological thinking provides the key to an understanding and a scientific description of what is involved in Rudolf Steiner’s conception of the forces at work in all aspects of life. He saw these creative, formative forces as related the to sun and working through the elements of warmth, light, air and water into all substances and into the
earth as a whole.

Such forces work contrary and are polar opposite to the gravitational force of earth, and the understanding of them involves the conception of a type of space, which is polar opposite to the three-dimensional space of the earth. If earth-space is centric, formed outward from the gravitational centre, the living space of the sun is peripheral; we think not of point-centres, but of planes and surfaces, forming and
creating from the periphery inward. It is no easy task to understand scientifically what Steiner means by the ‘etheric formative forces.’

The law of polar reciprocation

This law of polar reciprocation was formulated geometrically as late as in the first third of the nineteenth century and is expressed in the culminating theorem of modem projective synthetic geometry. ² As indicated in Figure 4.1, the theorem states that for any line in the plane of a circle (or any of its transformations) there is a companion point (and vice versa). Line and point take on a mutual relationship. Move the one inward towards to the centre and the other will move out to the periphery. Practice it and see that the polar line and its pole will meet on the circle itself and take on the aspect of tangent and its point of contact We are also led to an ultimate conclusion, namely, that we must think of a line, which is polar to the central point, and that this line is at infinity.

One appreciates an aspect of the circle, which complements the one-sided way we have usually thought of a circle — as the locus of a point, which, while moving round, maintains fixed distance from a centre.

We see that a circle may just as well be created by its enveloping lines or tangents as by its points. Furthermore, the circle reveals an exact reciprocal relationship — an actual pairing — among all the points and lines, which lie in its plane. What a picture, involving the idea of social relationships!

Incarnated as we are in a physical body on the earth, the picture of a circle and its central point is very real. Each step must be taken outward from a central point; wherever we go we carry our central point with us and, normally speaking, each step is of the same length. We are at home in this form of repetitive measurement, and can justifiably call it ‘step-measure.’ We build and we weigh according to this pointwise
aspect of mathematics. The idea of quantity rules here.

Contemplate with the mind’s eye the family of circles in Figure 4.2 and a new vista of thought is opened up. Not only are the circles so plastically formed by their tangent lines, but the measure which relates them to one another is very different. It involves two infinitudes; the outer line-at-infinity, and now at the same time, the innermost point also takes on the quality of an infinitude. This point functions as an inner infinitude, because the measure between the circles is not additive, but it is multiplicative. In other words, the proportion between two consecutive steps remains constant, not the steps themselves. We call this ‘growth-measure.’

This is in fact the kind of measure to be found in all aspects of the living world, and it is especially visible in plants. Not only does the ‘star-point’ in the centre of Figure 4.2 represent an innermost essence of negative measurement, but also the tangential aspect of the circles, pictured plastic ally from without, gives the true image of the space into which, as Steiner described it, the ‘formative forces’ of the etheric world work. They pour creatively into the inner spaces, wherever new, young life is developing. These are not purely physical, earthly spaces; they are sun-like spaces, into which the life-giving forces of the stars and the planets can work. We begin to understand in modem terms the fact that in older times the inner organs of the body were related to the planets — heart to the sun, liver to Jupiter, and so on

It is, of course, necessary to picture Figure 4.2 in its fulness, in terms of spheres, created by their tangent planes. Setting aside for our present purpose, the proof of this theorem of polar reciprocation, which a study of higher mathematics can bring, it can be said that it gives mathematical justification for the study of morphology in a way which is truly described by the word ‘wholeness.’

The forces at work in living processes

It was Goethe’s scientific method of-observation, developed in the eighteenth century, and still not taken seriously by scientists, which Steiner recognized and developed further (himself also not being widely recognized as a scientist). We should realize how new the task is: to understand and provide a mathematically sound basis for the interpretation of the forces at work in living processes. Materialism was, indeed, necessary, in order to reach a degree of freedom and individuality in thinking. Even the resulting technological civilization, belongs essentially to our time. Old beliefs from the past had to be overcome, in order to find truth at a different level. No dogma can help us today; but the way opened up by a mathematics which rests primarily on synthesis rather than analysis breaks very valuable new ground. Gradually, what appeared to belong to the past, takes on new life for science in the future.

What a picture this is, in comparison to the one provided in the textbooks of biology today! And yet, today, we shall still be understood, if we say that our neighbour has a heart of gold! Goethe, the great artist, who was also a scientist, wet further and said :

‘What is more splendid than gold? — Light — What is more refreshing than Light? — Conversation.’

Conversation! Only human beings are capable of it! The poor cow can only speak dumbly, hoping that we humans, by looking and perceiving and thinking more truly, will learn to hear. Words may echo to us seemingly from the past ‘Where two or three are gathered together, there am I in the midst.’ These words belong to past, present and future. A ‘sun-space,’ sun-circles are created, wherever human beings meet, as so many do today, attempting together to solve the world’s problems. In recognition of each other’s capacity for sacrifice, human beings are saying, ‘Where there is a will, there is a way.’

Rudolf Steiner in a lecture cycle given in 1923 ³ describes how, if we go back to very ancient times, we find that human beings took very little notice of measure, number and weight in earthly things, for they understood the world through their original clairvoyant capacities. They took less notice of measure, number and weight, but gave themselves up more to the colours and tones of earthly things.

‘Just think!’ he says, ‘that it is only since Lavoisier, only rather more than a hundred years, since chemistry has been reckoning according to weights. The idea of weight is first used at the end of the eighteenth century!’ Earlier humanity was given over to the colour-carpet of the world and to the weaving of tones and waves. One lived in all of this, even while one lived in the physical world.

Through this, he says, one had the possibility of seeing human beings, not as we see them now, but as the result of the converging forces of the whole universe. The human being was more than just the man standing on a little spot of earth; he was like a picture of the whole world, given colour from all sides. The harmony of the spheres sounded through the human being and gave him form.

Steiner goes on to describe how the picture given of the human form and of the human heart by modern science would have seemed to the teachers of the ancient mystery wisdom like knitting a stocking! They said:

‘The human heart is the result of the gold, which lives everywhere in the light, streaming in from the universe and forming it. Light weaves through the world and light bears the gold. Everywhere the gold is in the light; gold lives and weaves in the light. And when the human being stands there in life, then is his heart made, not out of gherkins and salad and lamb-chops and the like, but it is created out of the gold in the light. The salad and the lamb-chop only serve to help us to learn that the human heart is created out of the whole world.”

Perhaps it is easier to follow Rudolf Steiner speaking in this vein than it is to understand him when he was speaking to scientists and mathematicians, for there we allow poetry to come to our aid, whereas to transform our scientific way of thinking is much more demanding. Yet the mathematical thinking, which underlies the concept of physical and ethereal spaces and forces has proved to be a very fruitful way of
approach to living phenomena, provided we use all three powers, which we have at our disposal: thinking, feeling and willing. The clarity of thinking must never be lost, always coming to terms with measure, number and weight. The light of thought becomes penetrated with the warmth of feeling called forth by the phenomena; and with the activity of willing we must press on across all thresholds of understanding. The intellect is our tool, but how we use it is our responsibility.

To stroke the warm rotundity of that extended belly of the cow helps in the perception of the creative worlds at work under the stars. In the many stomachs and inner spaces of bovine production within the living form, the forces are so different from what takes place on the factory production line! As scientists concerned with procreation in animal and plant and even in the realm of human thinking, we can learn
to think according to the laws of the outer forms and also according to the quite different laws at work in the inner paces of life, laws which accord with the way the celestial worlds work creatively into physical substances in physical pace. Rudolf Steiner used the word Gegenraum (counterspace) to describe ethereal space.” ⁴

How to think differently

The key to the transformation of thinking required in order to move from the picture of physical space to that of negative or ethereal space is to change from thinking of points to thinking of planes or surfaces, which mould forms from outside. ⁵Practice putting surfaces in the mind’s eye, instead of points.

See the beautiful, moving surfaces in water, the surface of a body which swims on water, the uniquely moulded surfaces of an individual human head or face. Draw them, model them, picture them, always in movement and change. In time we learn to see with the mind’s eye more actively than before; we leam to perceive in both spaces at once — the space of measure, number and weight, and the ether-spaces of the living, moving forms. The convexities and concavities of a living form begin to become eloquent; thought is raised into the spiritual ‘dimension’ of the etheric body, which is linked, not to the gravitational centre, but to the infinite periphery of the world. Human thought itself is an etheric power, a spiritual power, which we must learn to use rightly today, in order to find our true balance.

The laws inherent in the etheric formative forces are peripheral, working inward into living, inner spaces, in contrast to the way substance can be caused to explode outward. The life-forces, working inward, draw substance upward, contrary to the force of gravity. In the plant, for instance, it is evident that enormous masses of substance are drawn upward every spring, providing food, not only for the body, but —
we hope — also for the mind. These are real forces, and our scientific task today is not only to leam to understand how they work, but also to realize that in the very process of using them, we are working towards the necessary balance in scientific thinking. This is the task to which George Adams devoted his life.

Adams, who had originally put the question to Rudolf Steiner conceming the relevance of synthetic geometry, created many pictures and contributed much in writing to wards helping to bring about a change of scientific thinking. A picture which is most helpful in the awakened study of plant morphology is shown in Figure 4.3. A horizontal plane is tangent to a sphere; on it is indicated a family of circles, are concentric in the point of contact of the plane with the sphere. The circles in the plane are arranged in a measure, which is predominant in the plant kingdom. It is geometrical progression, in other words, proportional growth; we call it ‘Growth Measure.’ To each circle in the
plane has been drawn its polar form — a cone, each in thepoint of contact with the sphere. ⁶

Here we meet the need to go beyond the ordinary way of spatial thinking; these cones are not ‘double’; each is a single cone, and it is deemed to be ‘in’ a point, for all its lines and planes are ‘in’ the point of contact, just as all the lines and points of the circles are in the horizontal plane. This is a quite new way of thinking, which cannot be fully illustrated in the picture; we need to employ active, pictorial and imaginative thinking to comprehend the dynamic of this picture.

Furthermore, our thinking must go beyond the limits of Euclidian space in realizing that each cone reaches and passes through the plane-at-infinity. Moreover, if the circles range in growth-measure between their innermost point and the line at-infinity of the plane in which they lie, then we must see that in the family of cones-in-a-point, the innermost line will function as an inner infinitude, while, as the cones open out they tend to flatten towards the horizontal plane, which then functions as an ‘outer’ infinitude in this planar type of space.

To follow such processes is a valuable exercise in mobile thinking, which adds wings to our powers of observation. We leam to see what we think we see in two worlds at once, the material and the ethereal. In the physical movements of a living organism, such as the vertical human form, this way of human thinking, which also involves feeling and willing, gives vital access to Rudolf Steiner’s descriptions of the worlds in
which we live and make our experiences.

Rudolf Steiner, in his efforts to draw the attention of scientists to the necessity of thinking in this way about the way the etherical forces work, used as mathematical examples the Cassini curves (Plate 8, opposite page 65, the lemniscate and the curves in and around it) and also the Apollonian circles (Plate 9, curves of division), both of which are drawn between two foci, one being considered positive and the other negative. Both of these curve families are, however, conceived only pointwise

Path-curve surfaces

George Adams continued his research after Steiner’s death in 1925, until his own death in 1963. During the Second World War, while doing non-combatant service in the BBC, he was able to research intensively in the British Library. He found work done by earlier German mathematicians concerning curves and surfaces in which the quality of the tangent (line or surface), is paramount and far exceeds the pointwise aspect. ⁷

Adams was able to instruct Lawrence Edwards in calculating and picturing such curves and surfaces, for which he coined the name ‘path curve’ and ‘path-curve surface’ (Plate 10, opposite page 65). In later years, after the death of George Adams, Lawrence Edwards succeeded in applying this mathematical process to plant metamorphosis and also to the forms of animal and human organs.

In the early sixties, while working in the Institut fur Stromimgswissenschaften, which he helped to found together with Theodor Schwenk and other friends, Adams calculated a number of path-curve surfaces and had them made by the sculptor, John Wilkes, who with great skill was able to translate pages of figures into actual shapes from which he could make casts. This formed the seed-ground from which Wilkes
was later able to develop his Flowforms, still with the aim of water purification, though without the underlying mathematics of the path-curve surfaces. This work, too, is being developed further now, with the aid of Nick Thomas. ⁸

Quite recently, Adams’ work with these higher order surfaces has been taken into the practical field by Georg Sonder, who has transformed the process, whereby the pharmaceutical firm Helixor creates a remedy for cancer. Instead of a cylinder, as previously used, the mixing process now takes place within the egg-shaped form of a path-curve surface. The indications given by Dr. Steiner for this remedy ask for the mixing of the juices of mistletoe berries picked in sum er and berries picked in winter to be carried out in some way outside the influence of the force of gravity? ⁹Cancer is an illness of our time, in which the formative and controlling influence of the etheric formative forces is weakened, resulting in the physical proliferation of the cells. One solution was the centrifuge developed in Arlesheim, Switzerland, and used to create the medicament Iscador, with which Adams was also originally connected. In both methods, it is the anti-gravitational, etheric, cosmic force, which must be allowed to function, unassailed by the force of gravity, during the process of mixing.

It is fascinating to realize that the enormously varied shapes of birds’ eggs are all mathematical path curve surfaces — typically ethereal space-forms! The same may be said of the water-vortex and no doubt of the vortical eddies in the air, which are sometimes visible in the swirling leaves of autumn. Warmth, too, is a field of research, which responds well to this new way of thinking.

It is to be hoped that the science of the ‘path-curve surfaces’ will be further developed in techniques concerned with living processes; an example might be in the mixing of the biodynamic preparations. This way of thinking mathematically certainly helps to explain why Steiner gave instructions for making these preprations in the way he did.

Just as biodynamic farming methods take organic farming further, so also anthroposophical medicine, which is partly allopathic and partly homeopathic, reaches further than both. Our task reaches into the future, to build a firm bridge between analytical science and spiritual science.

References
1. Steiner, Philosophy of Spiritual Activity, Chapter IX, The Idea of Freedom.‘
2. For a basic introduction to projective synthetic geometry, see Olive Whicher, Projective Geometry, Rudof Steiner Press 1985, which is fully
annotated, giving classical and modem authors. [TO BE PUBLISHED ON AETHERFORCE.ENERGY SOON] … See George Adams, Physical and Ethereal Spaces, Rudolf Steiner Press 1965, for the mathema tical formulation of the laws of space and counterspace.
3. Steiner. Lecture of July 28, 1923 in Domach.
4. Steiner first used the word Gegenraum (Anti-space or counterspace) in the lecture course given on Astronomy and its relationship to the other sciences, 1—18, I92I …See also the Warmth Course, Mercury Press, Spring Valley, NY 1988.
5. George Adams: Physical and Etheral Spaces.
6. Adams and Whicher: The Plant between Sun and Earth, Rudolf Steiner Press 1980. [Chapters 1 & 2 published on Aether Force, with Chapter 3 to be published soon. Others will be published in due time.]
7. Adams discovered some little known mathematical work by Sophius lie and Felix Klein and developed it in order to supersede the use of the pointwise Cassini curves and the Apollonian circles. He called the curves and the surfaces he was able to develop ‘path-curves* and ‘path-curve surfaces’, and was attracted to them, because they involve a highly tangential and planewise way of thinking: ideally suited to the picturing of ethereal or negative space-forms. The surfaces in Plate 10 are pictured and must be thought of in this kind of space. They are poised between the vertical line, which functions as an inner infinitude, and the horizontal line-at-infinity, towards which the surfaces would develop, if the drawing were to be continued. One can imagine the whole of this ether eal space woven through and through with the planes, which mould the surfaces from without. At every point on every curve there is a hyperosculating creative plane, which cannot, of course, be drawn.
8. See Theodor Schwenk, Sensitive Chaos, Rudolf Steiner Press 1963. John Wilkes developed the Wirbela Flowforms at Emerson College, Sussex.
9. Rudolf Steiner’s indications concerning the development of a cancer remedy were developed after his death, by Dr Alexander Leroi in Arles heim, Switzerland. This remedy, Iscador, is produced by Weleda in Switzerland. The pharmaceutical firm Helixor in Germany has developed another method of mixing the Juices using a vessel created in the form of a path-curve surface.