There was a lecture given by George Adams entitled, “The Lost Tapes – Potentization & Peripheral Forces” which is read in this video.
This lecture was given to the British Homeopathic Congress in London in 1961. It begins on the theme of homeopathy, but this is just one narrow area of the subject matter of the lecture. He discusses projective geometry in general and how it applies to the natural world.
He talks about the rise of projective geometry:
At the time while physicists and astronomers were busily applying the ancient geometry of Euclid to their problems modified by the newer analytical methods of Descartes, Leibniz and Newton. While this was going on a new form of geometry was arising among the pure mathematicians. A new form of geometry which while including the Euclidian among its other aspects. A new form of geometry was arising which is far more comprehensive than the Euclidian, far more beautiful and far more profound. I refer to that school of geometry which is known variously as projective geometry, modern synthetic geometry or the geometry of position. In the seventeenth century the truths of this new synthetic geometry were beginning to be apprehended by the astronomer Kepler, also by the mystical philosopher Pascal, also by Pascal’s teacher Girard Desargues, a less known but a very important historical figure.
He explains how in Euclidian geometry, figures such as circles, ellipses and parabolas are represented as distinct forms whereas in projective geometry the conic section is treated as primal and the above figures are derivatives of this dynamic form in much the same way as all plant forms are derived from Goethe’s archetypal plant.
Projective geometry therefore naturally deals not only with tangible and finite forms but it deals with the infinite distance of space represented as these are by the vanishing lines and the vanishing points of perspective. And so in the new geometry the infinitely distant is treated realistically in a way which was foreign to the classical geometry of Euclid and the Greeks. A bold step was taken when there was added to the finite space distance elements the infinitely distant elements referred to as the ideated elements of space. This was a bold step in thought. This bold step in thought was rewarded by a twofold insight which was most important for the understanding of a science of living things. In the first place attention was focused no longer on the rigid forms such as the square or the circle. But attention was focused on mobile types of form changing into one another in the diverse aspects of perspective, or in other kinds of geometrical transformation. In Euclid for instance we take our start from the rigid form of the circle, sharply distinguished from the ellipse, and the ellipse is sharply distinguished from the parabola, and the parabola is sharply distinguished from the hyperbola. Now in projective geometry it is the conic section in general of which the pure idea arises in the mind, and of which various constructions are envisaged. Now as in real life the circular opening of a lamp shade will appear in many forms of ellipse while you move about a room. The opening of a bicycle lamp projects onto the road in front sundry hyperbolic forms. In a similar way in pure thought we can follow the transformations from one form of conic section to another form of conic section. Now strictly speaking the conic section of projective geometry is neither a circle nor an ellipse nor a parabola nor a hyperbola. The conic section of projective geometry is a purely ideal form out of which all these arise, out of which the conic section of the circle the ellipse the parabola the hyperbola can arise, as much as in Goethe’s botany the archetypal leaf is not identical with any particular variety or metamorphosis of leaf but underlies all these metamorphoses.
In projective geometry there is a fundamental duality between the point at infinity and the plane at infinity. And neither is more fundamental than the other.
Projective geometry recognises as the deepest law of spacial structure, it recognises an underlying polarity which to begin with in simple and imaginative language can be called a polarity of expansion and contraction. And this being used in a qualitative and very mobile sense…
Speaking qualitatively the point is the quintessence of contraction, the plane is the quintessence of expansion. From the point of view of the new geometry three dimensional space can equally well be formed from the plane inward, or you can form the three dimensional plane from the point outward. One approach is no more basic than the other.
Because it pays little regard to the peripheral planar forces present day atomism and materialism are one-sided and incomplete.
Even a plastic surface or a curve in space consists of an infinite and continuous sequence not only of points but of canted lines and tangent or oscillating planes. The mutual balance of these aspects namely point-wise and planar with a line-wise aspect intermediating. The mutual balance of these aspects gives us a deeper insight into the essence of plasticity than the old-fashioned one-sided point-wise treatment. Part of this is this, that whatever geometrical form or law we can conceive there will always be a sister form. A sister law equally valid in which the roles of point and plane are interchanged… This principle is a master key among the truths of projective geometry. It can be known as the principle of duality or the principle of polarity. This principle of polarity in its cosmic aspect is one of the essential keys to the manifold polarity of nature. And when you recognise that you can lead to a form of scientific thinking which can transcend one-sided atomism and can transcend the materialistic bias.
Science of today with its one-sided emphasis on point-wise forces is quite suitable for inorganic physics and chemistry, but the biological sciences, by borrowing from these sciences are hindered in their attempt to understand the organic realm.
We have to invert our customary ideas of centre and periphery to get the right notion. A physical force emanating from a centre needs the surrounding space in which to ray out. The infinite periphery has to be there to receive it. Likewise an etherial or peripheral force needs the living centre towards which it works. it springs from the periphery from the vast expanse and tends towards the living centre. Just as a physical force springs from a centre, from a plane of concentration works outward…If there were only rigid and finished forms then the old Euclidian geometry might be sufficient for us. But to understand the genesis and the metamorphosis of living forms we need a more mobile thinking, we need a thinking that reveals the balance between the centric and the peripheral, between the architectural aspect and the plastic aspect. Yet even the most rigid of nature’s forms, that is the crystal, this is understood in a far deeper way when we perceive how the crystal lattice derives from an archetypal pattern in the infinitely distant plane. The infinite periphery of universal space. Now in the realm of living form when once the new geometrical idea had been awakened in the mind then morphology and embryology confirm what is known to us by simple everyday experience from the world of the plants, namely how life on earth is sustained by the forces flowing inwardly from the surrounding heavens. Up ’till now biology has been trying to understand these things with concepts, derived from the inorganic world where centric forces predominate. It has been a hindrance to biological thinking to have to borrow its basic concepts from the non-biological sciences of physics and physical chemistry. Ideas no less scientifically exact should be derivable directly from the study of living phenomena just as the ideas of mechanics and electro-magnetics have been derived from the study of non-living things. To an open minded contemplation nature reveals on every hand the forms and the signature of active forces. nature reveals not only centric forces but peripheral planar forces…
If I’m right in the main thesis I put before you a new chapter will be opened out tending to bring our science nearer to life, nearer above all to human life.
Adams also wrote the following book with Olive Whicher, which deals with the same subject:
The Plant Between Sun and Earth, and the Science of Physical and Ethereal Spaces
The fundamental hypothesis of this book ‘is to attribute to the idea of Polarity a universal significance for the spatial structure of the world, not only in pure thought but in the real structures of Nature.’
From the book:
In their instinctive way, people in times past were well aware that the plant draws not only from the Earth and from its physical surroundings but in its ordered rhythms of life receives from the universe of Sun and stars; they husbanded their land accordingly. Along the lines here suggested this too may become scientific knowledge, giving much-needed guidance to those who feel the need to treat both plant and soil in the way a living entity deserves. Experience has shown that disappointing and even destructive results may be obtained when the powerful methods of modern chemistry are applied directly to the living world. Greater and greater care is being exercised in this respect. Arising out of such experience, the need is felt for a more integral approach. The molecular pictures of chemistry are too remote from what is seen and known in the immediate contact with nature.
The tentative idea here put forward concerning the substantial function of the life of plants will, if confirmed, shed a new light on questions of nutrition, for all earthly creatures. Not only the archetype of form is of a cosmic nature; but the very substance by which the creature lives is renewed and regenerated, inward from the periphery, from the celestial universe.
While these initial suggestions may need to be greatly modified, this much is certain. When the polarities of the spacial universe – expressed in the geometrical Principle of Polarity (Duality) – have duly penetrated into the thoughts and imaginations of science, a cosmic outlook will arise, which will also lead to a new sense of responsibility towards the life of the Earth-planet.
I presume this was written when this was first published in 1952.