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Space & Counterspace through Projective Geometry

Renewing Spatial Concepts via Projective Geometry:
- https://cgunn3.blogspot.com/2017/11/projective-geometry-2017-context.html

Space & Counterspace (3 Parts):
- Part 1: https://cgunn3.blogspot.com/2020/10/space-and-counterspace-i.html
- Part 2: https://cgunn3.blogspot.com/2020/10/space-and-counterspace-ii.html
- Part 3: https://cgunn3.blogspot.com/2020/10/space-and-counter-space-i.html

Scientific thinking has achieved much in the inorganic realm yet faces visible limitations addressing global problems like climate change and social unrest. Its materialistic orientation treats matter as the underlying source of all phenomena. Quantum mechanics, however, dissolved matter from "stuff filling space" into abstract mathematical formulas. The concept of space itself remained fixed despite this transformation. Projective geometry emerged during the scientific revolution as a response to perspective painting phenomena, discovered by Desargues and receiving renewed emphasis around 1820. It offers potential to heal the spatial one sidedness afflicting modern consciousness by making our concept of space whole.

Rudolf Steiner identified projective geometry's healing role and emphasized developing negative space to balance ordinary Cartesian space. In his light course he claimed life phenomena required forces originating from space's periphery, acting planar from without. He termed these universal forces to distinguish them from classical physics' central forces. In his warmth course he described the solid state as corresponding to familiar objects filled with stuff while the gas state represented negative space obtained by turning standard space inside out. Fluid states balanced between them. He repeatedly stressed that expanding natural science concepts this way was essential for renewed social thinking. George Adams, Olive Whicher, Louis Locher Ernst, and Ernst Lehrs developed these ideas. Their work ended in the early 1960s. Progress since then has been modest despite consequences from one sided spatial thinking growing more severe.

Projective geometry works through duality. A dictionary of duality creates partner configurations and translates descriptions into dual partners. This extends to Euclidean geometry, producing the Euclidean plane and its partner, the dual Euclidean plane. A hexagonal pattern of colored dots shows this concretely. Each colored point in the central grid corresponds to a line of the same color in the outer figure. Translations fix an ideal point and move all other Euclidean points perpendicular to this fixed point. They generate corresponding dual translations that fix the dual ideal line. When a hexagonal pattern translates rightward and the ideal point moves beyond the grid boundary, the dual pattern shifts. It appears crowded and asymmetric, concentrated on the opposite side of the origin. The six boundary lines of the dual pattern form a hyperbola when viewed through Euclidean eyes. Yet they remain a circle when viewed through dual Euclidean eyes. The grid of lines stays rigidly connected as the hexagonal pattern translates.
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Crystallographic patterns extend this duality through families of parallel lines with specific directions. A regular 2D crystal of rhombi extending from the origin exhibits three different directions or ideal points. The dual pattern reverses this relationship. All points now lie on one of three ideal lines passing through the origin. Parallel lines in the Euclidean pattern maintain uniform spacing through identical Euclidean steps. Corresponding dual points maintain equal spacing through dual Euclidean steps, approaching but never reaching the ideal point. X ray diffraction patterns of table salt arranged in a cubic lattice resemble the counterspace partner of 2D crystals in Euclidean geometry. George Adams explored whether x ray crystallography produces a counterspace lattice. Through Fourier transform analysis he concluded x ray crystallography implements transformations in ordinary space rather than counterspace. The mathematical parallels remain notable.

The field's advancement requires addressing an education challenge. Most participants lack sufficient grounding in projective geometry fundamentals to engage in research. Projective geometry is not typically taught in universities. This results in uneven preparation among self taught participants. Difficulty maintaining continuous thematic impulse in collaborative efforts follows from this. Proposed solutions include regular courses offered periodically throughout the year as online videos with integrated platforms for remote learning, discussion forums, and homework assignments. Major research themes needing development include establishing an overview of counterspace versions and applications, investigating Nick Thomas's counterspace work, exploring path curves and surfaces for counterspace connections, and understanding Fibonacci numbers and golden ratios in plant forms. George Adams' work on path curve surfaces for purifying moving water requires revival. Physics investigations should address the polarity of kinematics and dynamics. The question of whether quantum mechanics paradoxes disappear when counterspace integrates into mathematical foundations deserves exploration. Non locality might look different through geometric frameworks where planes are primitive entities. Astronomical themes including planetary orbits as circles in counterspace merit investigation. Dark matter hypotheses might be explained using levity forces based in counterspace pulling toward space's periphery. Goethe and mathematics connections suggest projective geometry provides the ideal spatial vocabulary for Goethe's method. This bridges mainstream and phenomenological approaches. The polarity of center and periphery requires concrete differentiation. Peripheral nature in environmental systems, DNA organization, and Rudolf Steiner's indication that human higher ego resides in periphery rather than bodily organization all need consideration.
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Mechanics in Space & Counterspace
- https://pubs.aip.org/aip/jmp/article-abstract/41/10/6995/396130/Mechanics-in-space-and-counterspace

- Download the full article here: https://annas-archive.org/md5/46d2e7bb765c3bd540054bea8f25a77d

Oliver Conradt develops a formulation of classical mechanics using the completely dual approach to Clifford algebra. This embeds Lagrangian and Hamiltonian mechanics into the dual framework of space and counterspace. The projective split is enlarged by introducing a pictorial representation for the Pauli algebra. The Pauli algebra appears as phase space extended by time as a scalar and energy as a pseudoscalar. Positions are represented by pointlike vectors and momenta by planelike vectors. Phase space obtains new interpretation through this duality. Central mechanical concepts like phase space and symplectic metric gain geometric meaning, demonstrating that the framework works with classical mechanics' basic principles.

Lagrangian and Hamiltonian mechanics take shape through the dual framework where canonical momenta become bivectors in the Pauli algebra. The canonical momentum is defined through partial derivatives of the Lagrangian with respect to velocities. Examples including n body systems with potential forces, independent body motion, the harmonic oscillator, and Kepler motion show the approach's strength. For the harmonic oscillator, position trajectories and momentum trajectories divide the phase space curve. For the two dimensional harmonic oscillator, the end plane of the momentum planelike vector remains orthogonal to the velocity at each moment. This reveals a relationship between position and momentum trajectories that holds throughout the motion.

Canonical transformations in the dual framework preserve Hamiltonian equations' structure. Four different generating functions connect through Legendre transformations. Symplectic functions form the symplectic group preserving the skew symmetric symplectic metric. The metric's geometric meaning reveals the intercept theorem from elementary geometry. It shows the metric between a plane and a point as a distance such that the plane is incident with a multiple of the point and the point is incident with a multiple of the plane. Liouville's theorem asserts unit determinant for phase flow differential. It follows from symplectic preservation. Symplectic transformations preserve incidence between positions and momenta and symplectic distance between nonincident point plane pairs.
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Principles and Practice of Radiesthesia | Abbé Mermet

Radiesthesia is fundamentally about detecting radiations that emanate from all bodies, whether living or nonliving, using pendulums or rods as instruments. Every material object emits its own distinct undulations and radiations into the environment. When a human becomes the conductor for radiesthetic flux through the sympathetic nervous system, the pendulum or rod responds by translating these hidden forces into visible movement. This interaction reveals both discrete elements and continuous currents within the radiesthetic field. The discrete elements include magnetic lines, fundamental rays, mental rays, luminous rays, witness rays, vertical columns, images, serial numbers, spirals, and designs that the pendulum can trace. Meanwhile, continuous aspects flow through mental or solar rays. Even seemingly minor factors like temperature, color, and chain length can influence how a pendulum responds.

The methodology operates in four primary ways when working on site. Detection occurs through lines of force, luminous rays, mental rays, or by tracking specific oscillations. These approaches incorporate techniques for measuring both distance and depth, often employing plumb line methods or quick estimation techniques. Yet radiesthesia extends beyond physical location to encompass teleradiesthesia, a practice that permits exploration regardless of whether targets are nearby or thousands of miles away. This requires the practitioner to possess photographs, maps, or plans of the area in question. The reliability of such remote work hinges on having accurate plans, favorable atmospheric conditions, and vigilance about parasitic radiations that could interfere with detection. Environmental disturbances can completely disrupt the process, as occurred during the 1933 Japan tidal wave when all radiesthetic function ceased for several hours.

Water prospection, mineral detection, petroleum location, and medical diagnosis represent the primary domains where radiesthesia finds practical application. In France, water springs at specific depths were successfully located in areas like Vercel and Clermont sur Oise. Petroleum operations benefited from these methods too. Depths and output predictions made through radiesthetic assessment proved accurate in Tliouanet, Algeria and Eastern Galicia. Similarly, gas sources emerged in Cuarny, Switzerland and Arcachon following both on site and mental prospection.

Beyond resource discovery, medical practitioners employed pendular diagnosis to identify tuberculosis, cancer, and various other conditions, often detecting them months or years before conventional medicine could. Harmful radiations from subterranean water flowing through different geological layers were shown to cause chronic illness in residents living above them. Simply displacing beds or furniture once radiesthetic examination identified exposure zones frequently resolved health problems. The reach of these methods extended further still through telediagnosis using photographs, signatures, or handwritten letters, enabling practitioners to assess conditions from hundreds or thousands of miles away. Vatican authorities consulted on archaeological research while multiple documented cases confirmed the accuracy of distant medical evaluations.
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Karl Schappeller Device - Primary Physics

Karl Schappeller (1875 to 1947) was an Austrian inventor who developed a potential "free energy" device that attracted considerable attention around 1930. He rose from poverty to owning a castle while conducting experiments in energy as a lay scientist, culminating in a spherical device meant to tap what he called aether energy or Raumkraft, meaning space energy. The sphere was not intended to be a working machine but rather to demonstrate principles of what Schappeller called Reverse Thermodynamics, which operates in opposition to the Second Law of Thermodynamics.

The core component, the stator, consists of a spherical shell made from two airtight steel half shells. Two iron bar magnets are positioned internally on opposite poles with a hollow center between them. Inside this hollow area, two coils constructed from hollow copper tubes filled with electret material originate at the magnet poles and terminate at the center, then connect to the rotor through conventional copper wire. The electret, a permanent magnet far stronger than ferromagnetism or electromagnetism, was kept in a strong electric field during slow baking until it solidified. All air was pumped from the hollow core before operation. The rotor is a steel wheel of a particular design mounted with magnets that respond to the stator's force through attraction and repulsion.

When activated through a battery and earth connection, the device generates glowing magnetism at the center gap between the split bar magnets. Cyril W. Davson, who visited Schappeller and spent three years studying his work, reported this glowing magnetism is one thousand times more powerful than ordinary magnetism and represents what he termed primary physics rather than secondary physics. After initial stimulation, no further battery input is required. Energy is drawn directly from the surrounding aether, bound through the magnetic electret material in the hollow copper coils, then radiated outward as heat, electricity, magnetism, or mechanical work. The device functions as an implosion mechanism at the energy level, drawing energy toward the center through the magnets into the glowing magnetism field before radiating outward.

Aether physics forms the theoretical foundation, viewing the universe as a sea of energy with aether serving as a non compressible medium transmitting field energy. All energy is radiant energy according to this model, including gravity, which is understood as a push from aether radiation rather than a pull. The Bloch Wall, a transition layer between adjacent ferromagnetic domains, holds importance in energy radiation. At the point where north and south pole magnetism spins meet in opposite directions, where magnetism is zero and reversal occurs, energy radiates outward. The conjunction of two dipolar force field vectors creates a quadropole force field or gravity that radiates in a circular 360 degree pattern.

Schappeller's concept of Reverse Thermodynamics distinguishes his work from mainstream academia. A combustion machine following the Second Law of Thermodynamics increases entropy and disorder. A Reverse Thermodynamic machine operates through cold stressed conditions that increase order and decrease entropy. The device absorbs heat rather than producing it, making it implosive rather than explosive. This process mirrors biological systems. A tree absorbs energy from sunlight and combines it with water and carbon dioxide to form wood, following Reverse Thermodynamic principles governed by a template pattern like a seed. This life giving cold force was called Vril by those who adopted Schappeller's ideas.
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By 1930, the German Weimar Republic through the Reichsarbeitsgemeinschaft planned to use multiple Schappeller devices in a broadcast energy distribution system throughout Germany that would replace the electrical grid entirely. Schappeller discussed powering Royal Navy ships with a representative of the British Admiralty and met with SS Reichsführer Heinrich Himmler in Vienna in 1933. Medical uses included pendular diagnosis to identify tuberculosis, cancer, and conditions months or years before conventional detection. The device was also envisioned as a levitation mechanism for flying machines and was researched near the end of World War II for possible weaponry applications.
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Louis Turenne's Radiesthetic Wave System

All bodies emit waves traveling on carried waves, with sound, light, radioactive bodies, atomic bombardment, and the human body all emitting and receiving waves. Ondes entretenues (sustained waves) form foundational carrying waves generated through magnetic bombardment striking the ether, creating antenna phenomena like wireless telegraphy. Ondes pendulaires (carried waves) differ as carried waves requiring a carrying wave to manifest, traveling upon sustained waves as secondary phenomena. Colors represent ondes (waves) traveling on light rays ceasing with nightfall. Every phenomenon emerges through creation of ventres (antinodes) and nœuds (nodes), identical to how violin strings vibrate under the virtuoso's finger, with cold and heat representing only vibrations. Bodies halt these waves creating rebounds comparable to sound echoing from walls or light reflecting from mirrors, with secondary waves rebounding alongside primary waves generating colored images. Turenne classified bodies into three families: radioactive bodies containing both positive and negative electricity producing atomic bombardment; bodies containing only positive electricity; bodies containing only negative electricity. Detectors employing the baguette (dowsing rod) and pendule (pendulum) permit resonance with all wave types, extending perception beyond the five senses into the sixth sense dedicated to wave detection.

The three planes of induction constitute the electromagnetic architecture underlying all wave phenomena. One horizontal plane contains positive and negative poles analogous to compass poles while two vertical planes orient North-South and East-West perpendicular to each other. Ondes horizontales (horizontal waves) occurring without radioactivity indicate non-radioactive bodies while ondes verticales (vertical waves) in North-South and East-West directions indicate disintegrating bodies and electrical phenomena. Four successive alternating movements between swinging and rotation at the intersection point signify radio-magnétisme (radio-magnetism). These three planes appear constantly across magnetized needles, electromagnetic radiations from sun and stars, mineral matter, living organisms, and atmospheric conditions. Every body positioned between these planes generates characteristic wave patterns detectable through apparatus orientation. Water detected vertically produces ondes verticales négatives (negative vertical waves) at 8 meters wavelength. Standing water above contaminated ground exhibits negative wave characteristics with 45-degree angle line patterns radiating from water edges. Radioactive mineral waters emit horizontal waves at 8 meters characteristic of living organisms supplemented with vertical positive and negative components from dissolved mineral constituents. Foreign substances contacting radioactive water impose their characteristic spectrum while reducing water's wavelength, demonstrating contaminant absorption of water's energy signature.
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Color radiation demonstrates the linear law of the electromagnetic spectrum from infrared through seven fundamental colors to ultraviolet, spanning a complete 10 meter distance. Seven fundamental colors arranged from violet through indigo, blue, green, yellow, orange to red each occupy precise positions at 1 meter intervals. Red produces concentric circles at 2 meter diameter while orange through violet display progressively elongating ellipses with semi-major axes expanding systematically at 0.50, 1.00, 1.50 and 2.00 meters. White generates radioactivity throughout a 10 meter radius sphere while black manifests as perpendicular crossing lines coinciding with terrestrial magnetic poles. Complementary color pairs when superimposed in proper proportions generate white light while displaying their distinct wave characteristics. Green occupies the central radioactive position where vertical plane inversions occur. Frequencies measured in billions of kilocycles confirm Turenne's centimeter scale measurements amplify actual radiation wavelengths approximately 2.5 million times. All seven fundamental colors display characteristic pendular wave groupings of four, repeated four times around each color in both horizontal and vertical orientations. Horizontal magnetic waves occupy the left half spectrum while vertical electrical waves present opposite polarity distributions. Infra-red extends from black toward red through superimposition of black and red ribbons in varying proportions while ultraviolet extends from violet toward white through proportional white-violet superimposition. Homeopathic dilutions emit waves following identical height laws regardless of body composition with lengthened wavelengths under heating and shortened wavelengths under cooling.

All 92 chemical elements organize into eight distinct families each exhibiting characteristic height values at 13, 19, 25, 50, 55, 62, 68 and 80 centimeters measured on Turenne's meter. When radium serves as reference standard at zero, any test substance displays a single disappearing secondary wave with disappearance of all 92 periodic table secondary waves except one uniquely identifying the element by atomic number with absolute precision. Corresponding wave length ranges from zero to 1.55 meters depending on chemical state, purity and thermodynamic conditions. Eight family groupings precisely mirror the seven fundamental colors' linear law establishing concordance between elemental atomic structure and electromagnetic frequency characteristics. The 44 metals present in human blood and cellular structure manifest 8 meter wavelength harmonically or directly. Cancer exhibits anomalous wavelength behavior with normal body cells generating wavelengths around 8 meters while cancer displays altered wavelength of reduced dimension coupled with capacity to reverse electrical polarity alternating between positive and negative character. Geometric forms produce characteristic radioactive patterns with rectangles, triangles, circles, parabolas, ellipses and hyperbolas emitting radioactive tracing lines along their geometric construction paths. Two vertical planes separating soils demonstrate helium emission at bottom and argon emission at top of any vertical surface establishing the foundation of atmospheric stratification.
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Medical applications employ the law of similars (loi des semblables) through testimony methods and wave correspondence. Disease conditions manifest specific electromagnetic wave signatures at particular heights and lengths while appropriate remedies display identical or complementary frequencies establishing resonance conditions promoting cellular healing or pathogen neutralization. Heavy waters exhibiting characteristic penetrating electromagnetic properties restore mineral water vitality. Individual organisms establish characteristic personal spectral signatures termed temoins individuels (individual witnesses) permitting distant medical analysis through blood serum containing all organ wave emissions. Toxic emanations manifest wavelengths below 8 meters while beneficial influences maintain or restore 8 meter optimization. Mining and geological prospecting employ telluric wave mapping using radium as antenna exciter on scaled maps with vertical penetrating wave patterns overlaying geological structure revealing ore deposits, petroleum reserves and uranium concentrations through characteristic electromagnetic signatures. Long-distance diagnosis operates through witness resonance principles where personal wave imprints establish electromagnetic connection spanning thousands of kilometers with fluctuations in witness wave behavior precisely corresponding to instantaneous physiological changes. Acupuncture meridians correspond to seven functions organized as seven groupings of metals drawn from the 44 body metals with 14 meridians total containing elements 97 and 84 plus functional metal groupings. The human body functions as electromagnetic antenna emitting and receiving waves across three perpendicular induction planes with characteristic radio-active points at eyes, hands, sympathetic nervous system, brain, liver, ovaries, testicles and spinal cord emitting superior intensity waves toward south and west. Auras surrounding human forms consist of void with infra and ultra-wave components acting as biological condensers transforming vertical injurious waves into horizontal less-injurious waves.

Bibliography of Louis Turenne's Radiesthetic Works
- Turenne, Louis. Book 1. Continuous Waves and Pendular Waves. 1931.
- Turenne, Louis. Book 2. Treated Waves, Pendular Waves: Light, Colors. 1931.
- Turenne, Louis. Book 3. On the Law of Similars and the Waves of Illness. 1933.
- Turenne, Louis. Book 4. Water, Zoology, Botany. 1934.
- Turenne, Louis. Book 5. Waves of Geometric Forms, Minerals, Reading the Plane, Evolution of Matter. 1935.
- Turenne, Louis. Book 6. Waves of Arab Numerals, Series, Human Waves, Heavy Water, Mineral Water. 1942.
- Turenne, Louis. Book 7. Waves in Arithmetic and Geometry, Transuranic Physics, Disintegration, Mummification. 1943.
- Turenne, Louis. Book 8. Medicine and Waves. 1952.
- Turenne, Louis. Book 9b. Annex of Scientific Radiesthesia. 1958.
- Turenne, Louis. Book 10. Final Wave Studies. 1962.
- Turenne, Louis. Book 11. Scientific Radiesthesia: A Complete Introduction. 1976.
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