911:Geometry
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- Occult symbolism Intro
- History of oppression
- Social terrorism
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Intro
(todo)
Wave dynamics
(To fix: "waving" is a verb. Waves need a medium. Adapt/integrate the various wave theories to/in the concepts of the electromagnetic "rope theory")
- Universal patterns:
- Periodicity: Cyclic energy flows (in, neutral-center, out)
- Sympathetic vibrations <-> Resonance (todo: "law of octaves" observations in various energy-mass spectra)
- Complexity through simplicity (fractal recurrence, infinite states, few rules)
- Relativity (no absolute, true beginning and end are elusive - "the serpent bites its tail")
- Equilibrium dynamics (Entropy functions from the smallest to the largest scales)
- Meaning/intention and its information communication process (see also: Semiotics)
- Communication and Language (in its broadest sense):
- Symbolism (the coding of the concepts of communication into a more narrow band of possibilities):
- Forms of communication: kinetic, phonetic, optical (with subsets: symbolic signs, letters), non-optical spectrum
- Electromagnetic waves are the basis for any form of communication
- Information gathering / processing / rendering
- Vortices flows.png
"A vortex can spin in only one direction. Parity demands that for every vortex there must be a countervortex. This is why all dynamic structures are created, like men and women, in equal and opposite numbers. Two vortices spinning in the same direction flow in opposite directions along their interface, Therefore, if pushed together. they will annihilate each other. This is why when particle meets antiparticle, they are transformed into radiant energy. The closer two vortices spinning in the same direction are pushed together, the more energy is brought into opposition along their interface. Therefore, all vortices rotating in the same direction will tend to move away from each other until they are spaced equally apart." [1]
- Wave flow basics.png
Standing wave flow basics [2]
"universal ratio mathematics [4]
"Chladni figures for circular plate, sorted by number of (diameters, circles) in each pattern. These patterns can appear at any orientation on the plate. Each distinct pattern has a unique vibration frequency. The vibration frequency therefore offers a rotation invariant representation of the pattern present on the plate." [5] (See also: Cymatics)
Harmonic resonance theory [6]
Wave behavior
- Waves (Category:Waves): "Disturbances which propagate through space and time, usually with transference of energy."
- Wave mechanics/theories:
- Standing wave: "A wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions."
- Running wave:
- Soliton
- S-wave:
- "The S-wave, secondary wave, or shear wave, sometimes called an elastic S-wave, is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: S-waves, like waves in a rope, as opposed to waves moving through a slinky, the P-wave."
- P-wave:
- "P-waves are a type of elastic wave, also called seismic waves, that can travel through gasses (such as sounds), elastic solids and liquids, including the Earth. P-waves can be produced by earthquakes and recorded by seismometers. The name P-wave stands for primary wave, as the P-wave is the fastest among the elastic waves, compared to the S-waves. In isotropic and homogeneous solids, the polarization of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy."
- Transverse wave
- Longitudinal wave
- Rayleigh wave:
- "They are distinct from other types of seismic waves, such as P-waves and S-waves, which are both body waves, or Love waves, another type of surface wave. Rayleigh waves are generated by the interaction of P- and S- waves at the surface of the earth. The Rayleigh wave travels with a velocity that is lower than the P-, S-, and Love wave velocities. Emanating outward from the epicenter of an earthquake, Rayleigh waves travel along the surface of the earth at about 10 times the speed of sound in air"
- S-wave:
- Soliton
- See also:
- de Broglie hypothesis and Bohm interpretation
- Wave mathematics:
Wave phenomena
- Natural frequency
- Resonance (See also: "The Frequency Resonsant")
- Entrainment
- Electromagnetic radiation
- Absorption
- Diffraction
- Interference
- Redshift [43] and Blue shift
- Doppler effect
- Gravitational lens
- Holography
- Coandă effect
- Countercurrent exchange
- Lorentz force
- Eddy current (Foucault current)
- Biefeld–Brown effect (video's)
- Electrohydrodynamics
- Centrifugal force and Torque
- Brownian motion
Music theory
- Auditory sensations:
- Science of music:
- "Musical Mathematics", Cristiano M.L. Forster
- Dmitri Tymoczko research
- Rythm:
Self-organizing systems
Dynamical systems
- Video lecture: "Chaos, Fractals and Dynamical Systems"
- Dynamics:
- Attractor: "is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed."
- Bifurcation theory: "bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour."
- Complex analysis (topics)
- Complex plane (mathematics)
Cymatics
- "Cymatics is the study of wave phenomena. It is typically associated with the physical patterns produced through the interaction of sound waves in a medium."
- See also:
- Examples:
Natural shapes:
Synthetic shapes:
Picture of tortoise beside cymatic sound pictures at 1021 Hz, 2041 Hz, 1088 Hz and 1085 Hz. [8]
Magnetohydrodynamics shapes:
Ferrofluid in a rotating and axial magnetic field (video).
- Synergetics
- "Synergetics is an interdisciplinary science explaining the formation and self-organization of patterns and structures in open systems" ... "As a consequence, self-organization means an enormous reduction of degrees of freedom (entropy) of the system which macroscopically reveals an increase of 'order' (pattern-formation). This far-reaching macroscopic order is independent on the details of the microscopic interactions of the subsystems. This is why Synergetics explains the self-organization of patterns in so many different systems in physics, chemistry, biology and even social systems."
- Tensegrity - an applied mechanical concept of synergetics.
Crystallization
- Various notes:
- Snowflake photos (by Mark Cassino)
- To research:
- Piezoelectricity and other (derived) electro-magnetic functions of crystals.
- The large selenite crystals of the Naica Mine ("Crystal Cave of Giants") in Mexico. (see also: [44])
Snow crystals
Fractals
- Fractal generation classes:
- Escape-time Fractals: Mandelbrot set, Julia set, Nova fractal.
- Iterated Function Systems: Cantor set, Koch snowflake, Sierpinski carpet.
- Random Fractals
- "In random fractals, we see dendritic fractals demonstrate the fundamental natural property of diffusion-limited aggregation (DLA). DLA is best illustrated in the physical manifestations of fern growth, ice crystals, tree branch growth and electrical discharges." [45]
- Strange attractors
- Generated by iteration of a map or the solution of a system of initial-value differential equations that exhibit chaos.
- See also:
- video: "Fractals in Science, Engineering and Finance (Roughness and Beauty)"
- Multifractal system
- "Grand Unified Fractal Theory"
- "The Thumb Print of God: A Spiritual Exploration Through Fractal Mathematics"
- flickr.com: fractalists pool
- jmckennonmth212s09.wordpress.com
- FractalAnimation.com
- "Study of Chaotic Motions"
Structure of a leaf [10]
Cellular automata
- Various notes:
- See also:
"Rule 110" cellular automaton, which is Turing complete.
Information concepts
- Modes and attributes:
- Entropy: "It quantifies the information contained in a message, usually in bits or bits/symbol. It is the minimum message length necessary to communicate information."
- Geometry
- Symmetry, Self-similarity, Similarity (as-above-as-below, "binary-triplets")
- Chirality: "In geometry, a figure is chiral if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. A non-chiral figure is called achiral."
- Symmetry, Self-similarity, Similarity (as-above-as-below, "binary-triplets")
- Recursion: "a transformation in which the transformation being used is applied within its own structure."
- Duplication
- Variation
- Transformation
- Other informational topics:
- Patterns
- Information theory - pioneered by Claude Elwood Shannon
- Kolmogorov complexity - by Andrey Kolmogorov
- Animal behaviour and Kolmogorov complexity: "Dialog with black box - Using Information Theory to study animal language behaviour", by Zh. I. Reznikova
- Gödel's incompleteness theorems - by Kurt Gödel
- Turing machine - by Alan Turing
Mathematics
High-level divisions of mathematics.
Truth
Quantity
- Numeral system (see also: Grapheme)
Structure
- Algebra
- Linear algebra
- Associative algebra
- Clifford algebra ("is a very convenient representational and computational system for geometry. It is going to be the way computer science deals with geometrical issues. It contains, in a fully integrated manner, linear algebra, vector calculus, differential geometry, complex numbers and quaternions as real geometric entities, and lots more. This powerful language is based in Clifford algebra." [46]). See also: "Why do I like Clifford Algebras?".
- Set theory
- Abstract algebra
- Boolean algebra
- Group
- Category of groups (types of groups: finite, infinite, discrete, continuous, multiplicative, additive, abelian, cyclic, simple, solvable)
- Group theory
- Abelian group
- Galois theory ("Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.")
- Group theory
- Category of groups (types of groups: finite, infinite, discrete, continuous, multiplicative, additive, abelian, cyclic, simple, solvable)
- Ring theory
- Hypercomplex number
- Polynomial
Space
- Geometry
- Symmetry
- Classical geometry
- Classical geometry
- Möbius transformation (see also: video: [47])
- Euclidean geometry (see also: "A mathematician sculpts solids point by point")
- Euclidean space (see also: Topological space)
- Euclidean plane geometry
- Euclidean solid geometry
- Pythagorean theorem
- Bisected hexagonal tiling
- Euclidean space (see also: Topological space)
- Classical geometry
- Trigonometry
- Topology
- Topological space
- Continuous function
- Topological algebra (see also: abstract algebra)
- Geometric topology
- Manifold
- Lie group
- E8 (see also: "An Exceptionally Simple Theory of Everything", disinfo hype?)
- Lie group
- Manifold
Change
- analysis
- Mathematical optimization
- Complex analysis (topics)
- Harmonic analysis
- Computational complexity theory
- Numerical analysis
- Calculus (calculus is the study of change)
- Net (intended to unify the various notions of limit and generalize them to arbitrary topological spaces)
- Probability theory
Metamathematics
Applied mathematics
Geometry
- Various:
- video: "Geometry of Life" (part 1-4)
- History of geometry
- 'Sacred' geometry
- Tetractys (see also: Quincunx)
- "Sacred geometry, Metatron's cube and the platonic solids"
- Metatron
- Platonic solids
- Doubling the cube ("The Delian Problem")
- Noncommutative geometry
- 'Magic' shapes
- Magic square
- see also: Sudoku
- Magic circle
- Magic square
Spirals
- Various notes:
- See also:
- Numerology: Phi
- Energy: Electromagnetism
- Occult symbolism: Energy spiral
- Occult symbolism: Serpent
- "The Mystic Spiral: Journey of the Soul" (see Literature list below)
- "In the Garden"
- "Electro-fractal Universe"
- Vortex (contraction => center => expansion)
- See also:
Natural spirals
- Todo:
- 'images' of DNA, telomere and enzyme helix structures.
- Blood flow vortexes
- Solar Parker spiral
Pinwheel Galaxy (see also: Spiral galaxy)
North pole of planet Mars
- Waterspout.jpg
Sea life near vents at volcano V-1 in the Tonga Arc. [13]
Ram horns
Red cabbage internal spiral [15]
Nautilus shell
See also: Pheidian spirals research.Vine tendril
Daisy flower (parabolic spiral) [18]
Pine cone (bottom)
See also: Occult symbolism: Pine conePine cone (side)
(see previous) [20]
Note: the double helix."Cross section through an axoneme of Actinosphaerium near the axopod base. Two spiral rows of microtubules are coiled about a central axis in a precise geometrical arrangement. Scale marker 1 µm." [22]
Paraffin carborundum crystal [24]
Scientific spirals
Spiral periodic table [25]
Note: "This arrangement of the elements focuses on the increasing atomic number in an ordered sequential fashion." ... "hydrogen is at the center and all elements radiate out from it." [26]
See also: Languages: Electrochemical"All direction is curved, all motion is spiral" by Walter Russell (1871–1963)
"Ten octaves of integrating light" by Walter Russell (1871–1963)
Cultural spirals
- Various notes:
- See also:
- Swastika:
- "The Swastika" (by Thomas Wilson Curator, Department of Prehistoric Anthropology, U.S. National Museum, 1894)
- See also Fylfot
- abrahadabra.com forum: Reclaiming Ancient Symbols: The Swastika
- "The Swastika" (by Thomas Wilson Curator, Department of Prehistoric Anthropology, U.S. National Museum, 1894)
Altar at the Tarxien temple complex in Malta. (estimated at ~2800 BC.).
The Playing Board of the Egyptian Game Mehen
Newgrange passage tomb entrance stone (with trispiral and single spiral engravings), Ireland (estimated at ~3500 BC.). See also: [27], More images from that site.
Reask stone, near Kerry, Ireland. [30]
Väskinde cemetery (Sweden) [31]
The marble pedestal patterns on the imperial guardian lion (also called a "Fu Lion", "Foo Dog", "Lion of Buddha".) at the Forbidden City, China.
Nazca Lines monkey, Peru.
Swastika examples
Trojan, Onchan (Isle of Man), and Roman artwork
Cyprus Roman Mosaic (~50BCE)
Note: 4-pointed star, 6-pointed star and Double squareVatican staircase
Note: the octagon ceiling.Thule Society emblem
Emblem of the Nazi SS Panzer Division "Wiking"
US Naval Construction Force Base. Coronado island, San Diego, California USA. [34]
Drawing by M.C. Escher
Advertisement of Coka Cola in the early 20d Century. [35]
Abstractions
- Various notes:
- See also:
- "Vortex Simulations" (research paper) (based on Contour-advective semi-Lagrangian algorithms)
- See also:
See: Energy
"Schematic of dominant unisonal vortex with an elongated dual-core vortex eye in a progressive vortical paradigm arrangement with vortical spokes and vortical spiral arms" [36]
Hopf fibration (or "Hopf map") describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931. Hopf found a many-to-one continuous function (or "map") from the 3-sphere onto the 2-sphere such that each distinct point of the 2-sphere comes from a distinct circle of the 3-sphere. [37]
"A basic one dimensional depiction of the "Tube Torus" shape is formed by ratcheting the Seed of Life and duplicating the lines in its design. In Physics, the Tube Torus is considered a basic structure in the study of Vortex forms. Some say the Tube Torus contains a code of vortex energy that describes light and language in a unique way, perhaps as something of an Akashic Record." [38]
- Vortex math.jpg
Marko Rodin's vortex mathematics.
Fermat spiral (see also: "Spiral Mandela's")
Fibonacci sequence in the Sunflower
Ulam spiral (or "Ulam rose", see also the next image) ranging from number 1 to 121. All points starting from the center are numbered from one and go in a anti-clockwise spiral outwards. Note how the points tend to line up along diagonal lines.
Ulam spiral ranging from number 1 to 3,996,001. Prime numbers are white; composites are black. Note how the points tend to line up along diagonal lines. [39]. See also: video's.
Riemann surface for the square root function.
Riemann surface for the cube root function.
Seed of Life
- Various notes:
- "The Seed of Life is formed from seven circles being placed with sixfold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design."
- "The first circle at the center including its twelve petals, is called The Germ Of Life and the second concentric circle is called The Seed Of Life. The third concentric circle holds the very important Flower Of Life and the fourth, The Fruit Of Life." [48]
Flower of Life
- Various notes:
- The center of each circle is on the circumference of six surrounding circles of the same diameter. The pattern looks flower-like, hence the name. The Flower of Life pattern contains the basis of Metatron's Cube. From this pattern, all five of the Platonic solids can be derived.
- The Flower of Life is a geometrical figure composed of multiple evenly-spaced, overlapping circles, that are arranged so that they form a perfect pattern with a six-fold symmetry like a hexagon. It is their ultimate secret!! [49]
- "The Flower of Life is a geometric pattern inscribed on many of the world's great Pyramids, Temples and Cathedrals dating back over 6000 years." [50]
- "Flower of Life symbols: Found in India & other locations"
- "Sacred Geometry: Flower of Life"
... as interference ripples from its center.
3D-spherical Flower of Life [40]
Natural analogies:
The process of mitosis in cell division.
There are 4 types of cell division: binary fission for the simpler Prokaryotic cell types, and cytokinesis, mitosis and meiosis for Eukaryotic cell types.
Tree of life
- Various notes:
- video: "Extreme Kabbalah: The Tree of Life" (todo: research this 2D/3D node representation thesis)
Tree of Life derived from the Flower of Life.
The Caduceus on the Tree of Life.
Earthly representations if the tree of life?
Polyhedron
Uniform polyhedron
Platonic solids
- See also:
- Stella octangula (derived from 2 intersecting Tetrahedra)
- Merkabah (Two intersected Tetrahedra)
- video: "13 Masonic Secrets, Part 8 of 13"
- Merkabah (Two intersected Tetrahedra)
- Compound of five tetrahedra
- Stella octangula (derived from 2 intersecting Tetrahedra)
Icosahedron
"The icosahedron is bounded by twenty equilateral triangles. It has the largest volume for its surface area and represents the property of wetness. The icosahedron corresponds to water."Octahedron
"The octahedron is bounded by eight equilateral triangles. It rotates freely when held by two opposite vertices and corresponds to air."Tetrahedron
"The tetrahedron is bounded by four equilateral triangles. It has the smallest volume for its surface and represents the property of dryness. It corresponds to fire." [42]Merkabah - which is formed by two intersecting Tetrahedra.
Hexahedron
"The hexahedron is bounded by six squares. The hexadedron, standing firmly on its base, corresponds to the stable earth."Dodecahedron
"The dodecahedron is bounded by twelve equilateral pentagons. It corresponds to the universe because the zodiac has twelve signs corresponding to the twelve faces of the dodecahedron."
Metatron cube
- The Metatron cube (derived from the "Flower of Life") holds all the 5 Platonic solids.
- See: [51] & [52]
- See: Occult symbolism XV: District of Columbia ( Washington, D.C. masonic street plan. )
Literature
- 1924:
- Marcotone: The Science of Tone-Color [53], Edward Maryon
- 1967:
- Cymatics - A Study of Wave Phenomena and Vibration - volume 1, volume 2, Hans Jenny, ISBN 1-888-13807-6
- 1974:
- The Mystic Spiral: Journey of the Soul, Jill Purce, ISBN 978-0500810057
- 1982:
- 1994:
- Homage to Pythagoras: Rediscovering Sacred Science, Christopher Bamford (and others: Robert Lawlor, ...), ISBN 0940262630
Links
- Geometric Properties of Masonic Symbols
- Plasma Cosmos Planet (blog aggregation on various cosmology topics)
- Goldenmean.info (Dan Winter)
- Charles Gilchrist (videos)
- 2dcurves.com
- Hyperflight.com
- Vedic mathematics (see also: JainMathemagics.com)
- Geometrycode.com
- "Systems of Proportion in Design and Architecture"
- "Museum of Harmony and the Golden Section: Mathematical connections in Nature, Science and Art"
- 3D visualization of wave spectrum-usage
- Reconciliation of Science and Religion (blog)
- Heliotropodeluz.wordpress.com
- Coralcastlecode.com
- Sacredscience.com
- Sacred-geometry.com
- Halexandria.org
- Humanresonance.org
- Tony Smith
- "Stuff and Style of the Universe"
- "Patterns in Nature"
- James Furia's geomusic (video's, audio interview)
- Pyramidmatrix.com (by Carl P. Munck)
- "Phi Sound Healing"
- 2012forum.com
- "Ripening, Maturity and Cosmic Influences"
- "Isomorphic-like Magic Stars"
- "Freemasonry Geometry"
- Flow-field-cycle visualizations:
Various:
- Cyclesresearchinstitute.org
- Foundation for the Study of Cycles
- oregonite.blogspot.com
- biogenesislab.blogspot.com
- Trivortex.com (Brian David Andersen)
- Earthmatrix.com
- Spaceandmotion.com
- RexResearch.com
- Feandft.com
- Metaspherical.com
- thecleaver.blogspot.com
- Holographic Universe
- Spirasolaris.ca
- Lawofone.info
- Lambdoma.com
- "Stoa del Sol"
- Borderlands.com
- unamity.com ("Millennium Twain")
- EarthHarmonics.blogspot.com
- "The prehistoric alignment of world wonders"
- Ray Tomes' Cycles in the Universe
- Biowaves.com
- Crop Circle Language
- Atlascoelestis.com (Catholic astronomy image archive)
- Soundhealingnetwork.org
- Sacred Geometry and Illumination