Exploring Negative Space by Nick Thomas

Exploring Negative Space
by Nick Thomas
Article Sourced from the Vortex of Life Forum Archives
This paper explores an approach to science based on the interaction of two distinct spaces in contrast to the usual assumption of a single complicated manifold. The idea follows on the work of Steiner, Adams and Edwards (Refs 1 and 5). Cayley showed (Ref. 4) that a metric geometry may be derived from projective geometry by selecting an invariant conic section, which may be extended to an invariant quadric surface in three dimensions. The distance between two points A,B is then defined by relating it…

https://www.aetherforce.energy/exploring-negative-space-by-nick-thomas/

#projectivegeometry #counterspace #ethers #ether #nickthomas #steiner #aetherforce

Counterspace Research – Nick Thomas

Counterspace Research
Nick Thomas
Article Sourced from the Vortex of Life Forum Archives
Rudolf Steiner produced about 50 written works and gave nearly 6,000 lectures. It is important to work with them as research reports rather than ‘bibles’. Indeed he urged us (Ref. 1) not to treat him as an authority because in the spiritual realm that approach to a spiritual teacher is today not just inappropriate but damaging. Research in the physical realm is relatively easy as we are free there, and a wrong thought
remains abstract and soon shows itself to be false. But in the spiritual realm…

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#steiner #projectivegeometry #ethers #nickthomas #counterspace

Space and Counterspace - A chapter from Ernst Lehr's Man or Matter

https://www.aetherforce.energy/space-and-counterspace-by-ernst-lehrs/

Conceived dynamically, as projective geometry requires, Point and Plane represent a pair of opposites, the Point standing for utmost contraction, the Plane for utmost expansion. As such, they form a polarity of the first order. Both together constitute Space. Which sort of space this is, depends on the relationship in which they are envisaged. By positing the point as the unit from which to start, and deriving our conception of the plane from the point, we constitute Euclidean space. By starting in the manner described above, with the plane as the unit, and conceiving the point from it, we constitute polar-Euclidean space.

The realization of the reversibility of the relationship between Point and Plane leads to a conception of Space still free from any specific character. By G. Adams this space has been appositely called archetypal space, or ur-space. Both Euclidean and polar-Euclidean space are particular manifestations of it, their mutual relationship being one of metamorphosis in the Goethean sense.

Through conceiving Euclidean and polar-Euclidean space in this manner it becomes clear that they are nothing else than the geometrical expression of the relationship between gravity and levity. For gravity, through its field spreading outward from an inner centre, establishes a point-to-point relation between all things under its sway; whereas levity draws all things within its domain into common plane-relations by establishing field-conditions wherein action takes place from the periphery towards the centre. What distinguishes in both cases the plane at infinity from all other planes may be best described by calling it the all-embracing plane; correspondingly the point at infinity may be best described as the all-relating point.

In outer nature the all-embracing plane is as much the ‘centre’ of the earth’s field of levity as the all-relating point is the centre of her field of gravity. All actions of dynamic entities, such as that of the ur-plant and its subordinate types, start from this plane. Seeds, eye-formations, etc., are nothing but individual all-relating points in respect of this plane. All that springs from such points does so because of the point’s relation to the all-embracing plane. This may suffice to show how realistic are the mathematical concepts which we have here tried to build up.

#aetherforce #ether #counterspace #space #levity #gravity #polarity #projectivegeometry #steiner #goethe #manormatter

Introduction to Path Curve Geometry by Nick Thomas
https://tpow.app/59d3a5dc

George Adams suggested in 1950 that one variety of the path curves discovered by Felix Klein could apply to natural forms, particularly the spirals found on the egg-shaped surfaces of plant buds and cones, and also birds eggs. Lawrence Edwards, while teaching this to the children in his mathematics class in Edinburgh, began to wonder whether it was just a nice story or whether it was actually true. This is not an easy matter as it is all too easy to dismiss practical research to test it as mere “curve fitting”. However that is far from the truth as it lives within a thought context or paradigm from which it derives its meaning, namely the application of Rudolf Steiner’s discovery of Counterspace to a deeper understanding of the subtle aspects of Nature.

#aetherforce #ether #counterspace #projectivegeometry #celestialbotany

Chemical Ether (or Tone/Number Ether) works on a microscopic level, structuring matter through chemical synthesis and molecular bonding. Its influence governs interactions like covalent and hydrogen bonding, facilitating organization at a fundamental level. Geometrically, it interacts with counterspatial harmonics, shaping matter with intrinsic order rather than external forces like electricity. Undines mediate chemical ether within water, integrating and balancing its structuring processes to ensure harmony in material synthesis.

Chemical Ether Geometry
- Relies on harmonic relationships and counterspatial structuring.
- Uses geometric transformations tied to symmetry in chemical interactions.

Life Ether transcends the boundaries of macro and micro-organization, integrating these levels into a unified whole. It orchestrates living systems, enabling growth, healing, and the functional unity of organisms. Its geometric manifestations include lemniscates and logarithmic spirals, reflecting self-referential and recursive forms. Gnomes mediate life ether, channeling its upward and integrative energy to harmonize living processes and align diverse elements into cohesive systems.

Life Ether Geometry
- Embodies recursive, self-organizing shapes like lemniscates and spirals.
- Links macro- and micro-dynamics in a cohesive, integrative framework.

Defining Geometric Linkages
Linkages as elements simultaneously existing in both Euclidean space and counterspace, facilitating their dynamic interaction. The core types of linkages and their characteristics include:

Pointwise Linkages
Pointwise linkages connect specific locations in Euclidean space with their counterparts in counterspace. A point in Euclidean space translates into a system of lines and planes in counterspace. Thomas describes how objects linked through points undergo transformations governed by counterspatial metrics, resulting in strain and stress when these metrics conflict with spatial geometry. For instance, a cube linked at a point will deform along counterspatial principles, even as it retains its Euclidean form​​.

Surface Linkages
These linkages emphasize the interaction of surfaces between space and counterspace. They describe transformations that occur across two-dimensional planes, allowing for dynamic relationships like oscillations and rhythm. For example, in biological systems, surface linkages mediate the spatial spread of chemical or etheric forces, shaping growth and form through counterspatial patterns​.

Volumetric Linkages
Volumetric linkages describe the interplay of space and counterspace within three-dimensional volumes. These linkages govern expansive and compressive phenomena, such as the elasticity observed in gases or fluid dynamics. Thomas highlights the importance of volumetric linkages in explaining phenomena like spiral motions or vorticity in fluids, where counterspatial metrics introduce novel behaviors like long-range forces​.

Dynamic or Kinematic Linkages
These linkages capture the movement and transformation of objects as they obey the metrics of both spaces. Thomas explains that such dynamics often result in rotational transformations, which minimize stress in systems linked to counterspace. For example, rotation about an axis through the counterspatial point at infinity represents a stress-free transformation, illuminating why rotation appears so ubiquitously in natural phenomena​​.

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#geometry #projectivegeometry #pathcurvegeometry #ethers #formativeforces #nickthomas #counterspace #steiner #goetheanscience #polarity #anthroposophy

Part 3 of 3

I have already called your attention to the basis upon which rests the perception, the subjective experiences of temperature. We really experience the difference between our own temperature and the temperature of the environment, which, indeed, is what the thermometer does — I have drawn this to your attention. But perception depends precisely on this that we have within us a certain condition and that which lies outside this condition constitutes our perception. We cannot be a thing and perceive it at the same time. But we must always be other than the conditions we are experiencing. Suppose we consider tone. Insofar as we are tone, we cannot experience tone. If we would answer without prejudice the question: what are we as experiencers of tone, we come to the conclusion that we simply experience one potential difference while we are the other potential difference. We experience the Y - X′ difference; we do not experience the Y - Y′ difference because that is part of our being in time. It accompanies our perception of tone. It is an orderly inner chemical process in our fluid nature and is a part of our being. What causes chemical effects within us produces certain orderly effects in the world itself. It is by no means without interest to picture the following to yourselves. You know well that the human body consists only of a small degree of solid constituents. More than 90 percent of it is water, what plays through us as a delicate chemical process while we listen to a symphony is an inner continually phosphorescent marvel in this fluid nature. We are in our inner nature what these chemical processes reflect from tone. And we become aware of the tone world through the fact that we are chemically the tone world in the sense I have presented to you.

Our understanding of man himself is really much broadened, you see, if we bring an understanding of physical problems to bear on the human body. But the thing we must strive for is not to form abstract concepts of which physics is so fond today Rather, we must force our way through the concepts really woven into the world, the objective world.

Fundamentally everything that spiritual science is striving to bring into the conceptual world and especially what it is striving to do to promote a certain way of thinking, has for its object to bring back into human development thought permeated with reality. And it is indeed necessary for this to happen. For this reason we must prosecute vigorously such studies as have been presented here during the last few days.

We have in every case tried to emerge from the old theoretical point of view and enter into a point of view that is real, so that our concepts will be saturated with reality. This will yield technical results quite different from those attained up to the present. Practice and theory hang together inwardly. And when we see in any one case what reform is needed as in the case of physics, for instance, we can understand what must happen. Since the time has come when we must separate, I wish to emphasize that I have only indicated to you in these lectures what you are to see, to stimulate you to develop these things further. You will be able to develop them. Our mathematical physicists, whom we have among our number will be able to give new life to the old formulae. And they will find, when they apply to these old formulae the ideas I have indicated to you, that certain transformations can be made that are real metamorphoses. From these will grow much that will be of enormous importance technically for the further development of mankind. This is, of course, something which cannot be gone into in detail, but only can be indicated at this time."

#steiner #warmthcourse #anthroposophy #goetheanscience #warmth #counterspace #ether

- Metabolic & Limb System: The metabolic-limb system relates to the spiral-lemniscatory paths of the outer planets (Mars, Jupiter, Saturn), which move in more peripheral or spherical directions rather than radially. Their wider orbital movements through cosmic space parallel the metabolic processes of substance transformation and limb mobility.

The planetary system exhibits qualities of a living organism:
- The ratios between planetary orbital periods are incommensurable (cannot be expressed in finite numbers)
- This incommensurability prevents the system from becoming rigid and maintains its "aliveness"
- If the orbital periods were commensurable, the system would have reached rigidity long ago due to cumulative disturbances

The system maintains itself through cosmic nutrition:
- Comets act as food for the planetary system, bringing carbon and nitrogen
- The entire system moves toward the constellation of Hercules while continuously losing and replacing substance
- This movement affects the planetary system similar to how work affects humans - requiring substance replacement

He suggests a cosmic breathing process in relation to the 18 year nutation (wobbling) cycle of the Earth's axis corresponding to the Moon's orbital patterns with the the precession of the equinoxes, mirroring the human breathing rhythm of 18 breaths per minute, while both align with the larger 25,920-year cycle of the precession of equinoxes that mirrors the total number of breaths in one human day.

#steiner #astronomy #anthroposophy #goetheanscience #cosmology #counterspace #sun #planets