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.
Could someone please interpret this for me. I only speak English.
Acartia,
If you work it out, maybe you can explain it to me.
I think it might be an attempt to start a new mystical religion based on the effective components of homeopathic medicine.
I thought that it might be talking about pyramid power.
All I want to know is, what’s the polarity of the Time Cube?
You should know that circles, ellipses, and parabolas are conic sections, and what you are calling a conic section is in fact a cone. Good start.
Homeopathic geometry? Thin stuff.
It’s quite a simple concept.
Here are my thoughts:
There is a polarity between physical matter and the so called fifth element, the quintessence, the ether. What we think of as empty space is actually the ether. The material substance of modern physics is governed by point-wise, centric forces. The etheric realm is the polar opposite, governed by planar, peripheral forces. What used to be considered as empty space may seem empty in a physical sense, but as we are finding out it is not really empty, it is the domain of etheric forces.
In abandoning any thoughts of the ether, modern science has ignored one half of reality and expended all its efforts into examining the remaining half, the material half.
Are you not a mathematician? Have you heard of projective geometry?
No. But after reading this I am on the verge of projectile vomiting.
No I am not talking about a cone. The examples above are single static representations of conic sections. The conic section I am talking about is is the general, dynamic form which encompasses all of the above forms. Think of a circle changing to an ellipse, moving through the form of a parabola to a hyperbola and back again. This ever changing form is the conic section that I am talking about.
This dual polarity crap ignores half of reality:
EARTH HAS 4 CORNER
SIMULTANEOUS 4-DAY
TIME CUBE
WITHIN SINGLE ROTATION.
4 CORNER DAYS PROVES 1
DAY 1 GOD IS TAUGHT EVIL.
IGNORANCE OF TIMECUBE4
SIMPLE MATH IS RETARDATION
AND EVIL EDUCATION DAMNATION.
Yes.
Your post uses the term “projective geometry”. But, apart from the words, I didn’t find anything.
Sorry, I’m not interested in your Time Cube.
So you didn’t listen to any of the video I linked to?
So two-dimensional! 🙂
A video of a lecture about homeopathy? No, I did not listen.
Its not about homeopathy, it is about the nature of science.
Below is a summary of the lecture with a few additions of my own:
He begins by discussing the history of homeopathy in relation to the development of modern science, how the rise of atomic theory supplanted the earlier vitalism. The materialism from the 17th century boosted by exact experiments and the “intellectual clarity” and “probity” of mathematical thinking dominated scientific thinking. But he asks how many ideated elements, in other words spiritual elements are built into this thinking. After all “mathematics is an activity of pure thought” Newton, Descartes, Liebniz then Faraday and Clerk Maxwell brought geometric clarity and mathematical thought. Physics gains its strength from mathematics. And this type of thinking resulted in the industrial revolution.
But up until the twentieth century space was treated as the space of Euclid. It was considered to be a vast empty chamber in which material, point centred bodies moved about. Infinite distance was the concern of philosophers, it was outwith the domain investigated by science. Space is just the background field in which material point-centred bodies interact with each other. Take the bodies away and you are left with nothing. Space is just a medium in which bodies exist.
But at the same time as modern science was developing in its materialistic manner, a new form of projective geometry was arising among the mathematicians. Adams begins to discuss this new form of geometry at around the 20 minute mark in the video. It had its beginnings in the likes of Kepler and Pascal. It took off through the works of French mathematicians. Projective geometry, like Euclidian geometry, as well as having an aspect of pure mathematics also has a side in which practical experience is manifest.
Measurement in Euclidean geometry takes its start from tangible objects related to our bodies, such as inches, feet and the like. But tactile experiences of distance is very restricted compared with our visual experiences. With sight we can look up at the night sky and into the vast distances of space. We can look towards the periphery which is the source of the complimentary planar forces.
Both modern science and naturalistic art were inspired by the same love of nature and the same desire to understand the secrets of nature. Da Vinci and Durer studied the science of perspective and this led to projective geometry. And this geometry deals not only with the tangible but also with the infinite represented by vanishing points. This brought the infinite into the realm of science in a way that Euclidean geometry never did. This brought about the study of mobile types of form as opposed to the rigid shapes of Euclidean geometry. (John Harshman take note) Listen to the video from around the 26 to 27 minute mark if you are interested. He compares the conic section of projective geometry with Goethe’s archetype in the 29th minute and thus ties it in with the metamorphosis of living form. That is the practical aspect.
There is a polarity of expansion and contraction. We have two fundamental sources, the point and the plane, neither one of which is more fundamental than the other. The polarity of a magnet is a polarity of opposing forces which are both point-wise, The polarity of point and plane is a polarity of complimentary forces.
Modern science, with its emphasis on genes and strings of DNA, treats the point-wise source as fundamental while ignoring the planar aspect. By this method it can only arrive at half-truths. Now that science is beginning to observe the effects of fields which are planar and peripheral, a more complete picture will emerge. These forces work in the opposite direction to the point-wise in which the causes are thought of as emanating from particles such as DNA molecules, Morphology and embryology is governed and sustained by overarching planar forces. The activities of the genome provide the material on which these forces work.
After the 20th minute he mainly discusses projective geometry and It is not until the 53rd minute that he brings homeopathy back into the discussion.
At 58 minutes he states that there is no physical material that has not ultimately arisen from the interplay of centric and peripheral forces. From the forces of earthly origin and the forces of cosmic origin.
I get the feeling that gene-centred thinking is far too ingrained in the minds of some participants here to even contemplate or consider what I am talking about.
CharlieM,
You make it all sound like mysticism — which is why I am not enthusiastic about watching that video.
That’s okay, it’s your choice.
IMO mysticism involves personal introspection which has a lot to do with subjective feelings. I would say that studying polarity as was done by George Adams is an objective enquiry carried out in the scientific spirit.
Further to this reply I would like to add the following:
The circles, ellipses, and parabolas that you are talking about are figures that can be measured in the tradition of Euclidean geometry.
The conic section I am talking about cannot be pinned down to a specific measurement. It is considered from the aspect of projective geometry in like manner to the way living forms are treated in Goethean science.
Then you’re really bad at expressing yourself. A conic section is just the intersection of a plane with a cone. If you move the plane, the nature of the section changes. Big deal.
Charlie, you might enjoy reading “The Universe in the Rear View Mirror: How Hidden Symmetries Shape Reality” by Dave Goldberg.
You can pick up a used copy for about 5 bucks on Amazon.
Incidentally, a point and a line are both conic sections.
That’s a bit harsh, I’ll settle for just bad at expressing myself 🙂
Spoken like a true reductionist.
If a geometry teacher treats these figures in isolation then the kids do not see the connections, the relationship between them is lost. It is basically teaching them to be reductionist thinkers. If the teacher begins with the mobile conic section, the different figures can be obtained by the manipulation of this section, the relationship can be understood. It is always best to begin with the general case and to work out from there how the individual examples are obtained from it. That way they can see the connections.
And what about an infinite plane?
Thanks, I’ll look into it.
What about it? It’s not a conic section, if that’s the question.
Can an infinite plane ever be regarded as a conic section?
Take a plane slicing through a cone and describing a circle. Without tilting it move it up towards infinity and down towards the point. Are you saying that when it is positioned at the infinitely small point it remains a conic section but when it reaches the plane at infinity it ceases to be a conic section? If so can you explain your reasoning?
Not with the normal meaning of “plane” and the normal meaning of “conic section.”
Projective geometry works better without all of the silly mystification.
Those evil materialistic mathematicians won’t ever allow you to reach infinity. They’re ignoring an infinite portion of reality
So what about a point at infinity, do you agree with John that it can be regarded as a conic section?
I agree. That’s why I haven’t given you any silly mystification.
A point at infinity. LOL. Misunderstanding infinity seems to be a requirement for cranks.
Charlie: Can you give a single equation that arises from this stuff ?
Oh dear, I watched some randomly selected bits of the video. Oh dear, Oh dear.
So, we now have J-Mac, Byers, and CharlieM.
Well I could have been clearer and called it the apex which is a dimensionless point. Although in projective geometry the point can be seen as the intersection of an infinite number of planes or equally as the intersection of an infinite number of lines. A straight line is the intermediary between point and plane. It can be viewed either as composed of an infinite number of points or equally valid as the convergence of an infinite number of planes.
Do you agree with John that this point is a conic section? I am interested to know what people think about this, even though we are getting caught up in details.
As John says, a point is a conic section.
Euclidean geometry is a subset of projective geometry so anything that can be applied to Euclidean geometry can also be applied to projective geometry.
No constructive criticism from you then.
What about the base of an infinitely long cone, is there any stage when it ceases to be a conic section?
A cone is not a conic section. It is a cone.
I’m not making sense of “base of an infinitely long cone”.
All points are dimensionless (zero area)
3 planes are enough in a 3 dimensional space
or just 2 lines
Of course. What’s controversial about that? imagine a plane that intersects the cone at its apex. Or at the tangent of the base. The section is the intersection: a single point
A ‘cone’ that extends indefinitely doesn’t have a base. You can’t have a plane intersect the cone “at infinity” because you can’t define a plane with X, Y or Z coordinates at infinity, as you would for example for a plane X=3.
Whats geometry got to do with Homeopathy ?
Homeopathy is plane stupid
I think CharlieM is imagining a cone with a base. Thus the intersection of a horizontal plane with this “base” is a filled circle, rather than an open circle. Make the cone’s base big enough, and he thus thinks you get a plane, rather than a big circle…
There’s a failure to understand what a ‘section’ is, and what a ‘cone’ is.
The inscription at the entrance to Plato’s Academy is said to have been, “Let no-one ignorant of geometry enter here.” For Plato a grasp of mathematics was the best training for understanding reality.
The beauty about the conic section we are discussing is that it we are able to grasp ideal truths in our minds. But not only are they ideal, they are also objective. Because they are not dependent on our personal opinions we should be able to come to an agreement about them. And if we don’t then one of us must have an inaccurate idea of the subject.
So what can we agree on regarding conic sections:
1. A conic section is any curve produced by the intersection of a plane and a right circular cone.
2. We begin with a cone and its mirror image.
3. These cones are thought of as extending to infinity.
4. A plane with infinite extension dissecting these cones in any position and at any angle will produce a conic section.
5. It is meaningless to talk of these cones having bases.
6. The conic section can describe a circle, an ellipse, a parabola or a hyperbola.
7. If the plane passes through the apex the conic section can be a dimensionless point, a straight line or a hyperbola depending on its orientation.
Points we may not agree on
1. We gain an understanding of conic sections through pure thought.
2. The idea of the conic section is objective and singular. We all grasp the same idea which does not change no matter how many minds grasp it.
3. The general conic section is fundamental. The various figures obtained are specific examples of the fundamental nature of conic sections.
4. Both cones extend to the same plane at infinity, there are not two separate planes..
5. It is good exercise our minds if we think about the intersecting plane changing its position relative to the cones.
I welcome any sensible comments.
That should be: a point, a line, or a pair of intersecting straight lines.
You do not get a hyperbola if the plane goes through the apex.
You are right, thankyou 🙂
Yes we agree. Zero length, zero area, zero volume.
Yes in Euclidean geometry three planes are sufficient to define a point in the same way that two points are sufficient to define a straight line.
An infinite number of lines would be in relation to the plane at infinity.
I’m not trying to be controversial. We agree that the point is included as a conic section.
We agree yet again.
You would need to listen to the video to understand where Adams makes the connections.
You insist on making zero sense with “planes at infinity”
Also I would say only axioms are “fundamental” in mathematics. Your new found infatuation with cones doesn’t make them fundamental