911:Geometry and numerology
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Contents |
[edit] Intro
(todo)
- See also:
[edit] 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
[edit] Mathematics
High-level divisions of mathematics.
[edit] Truth
[edit] Quantity
- Numeral system (see also: Grapheme)
- Numbers
- Arithmetic
- Number theory
- Integer
- Rational number
- Real number
- Irrational number
- Imaginary unit
- Complex number
- Imaginary number (complex number whose squared value is a real number not greater than zero)
- Complex number
- Imaginary unit
- Fraction
- Logarithm
- Cardinal number (size of sets)
- Ordinal number (order type)
- Operations
- Number theory
- Arithmetic
- Numbers
[edit] 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." [27]). 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
[edit] Space
- Geometry
- Symmetry
- Classical geometry
- Euclidean geometry
- Euclidean space (see also: Topological space)
- Euclidean plane geometry
- Euclidean solid geometry
- Pythagorean theorem
- Bisected hexagonal tiling
- Euclidean space (see also: Topological space)
- Euclidean 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
[edit] Change
- analysis
- Dynamical systems theory
- 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
[edit] Metamathematics
[edit] Applied mathematics
[edit] Self-organizing systems
[edit] 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:
- 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.
[edit] Geometry
- Various:
- Tetractys (see also: Quincunx)
- "Sacred geometry, Metatron's cube and the platonic solids"
- Metatron
- Platonic solids
- See also: Doubling the cube ("The Delian Problem")
- Noncommutative geometry
- 'Magic' shapes
[edit] 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." [28]
[edit] Flower of Life
- Various notes:
- "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." [29]
- "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 [1] |
Natural analogies:
The process of mitosis in cell division. |
[edit] Tree of life
Tree of Life derived from the Flower of Life. |
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The Caduceus on the Tree of Life. |
[edit] Spiral waves
[edit] Natural
North pole of planet Mars (See also: "Mystery of Mars' Polar Spirals") |
Cyclone (Typhoon, Hurricane) |
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Nautilus shell |
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Daisy flower (parabolic spiral) [3] |
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"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." [6] |
Paraffin carborundum crystal [8] |
[edit] Cultural
- Various notes:
- See: Plasma cosmos
- 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.) |
Mycenaean Tholos 'tomb' chamber ceiling decoration at the Orchomenos site in Greece. [19] |
Newgrange passage tomb entrance stone (with trispiral and single spiral engravings), Ireland (estimated at ~3500 BC.). See also: [20], More images from that site. |
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Reask stone, near Kerry, Ireland. [23] |
Väskinde cemetery (Sweden) [24] |
The marble pedestal patterns on the imperial guardian lion (also called a "Fu Lion", "Foo Dog", "Lion of Buddha".) at the Forbidden City, China. |
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Swastika examples |
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Trojan, Onchan (Isle of Man), and Roman artwork |
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Thule Society emblem |
Emblem of the Nazi SS Panzer Division "Wiking" |
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US Naval Construction Force Base. Coronado island, San Diego, California USA. [26] |
[edit] Abstractions
Dual torus (Double vortex + Torus) [9] |
(see previous) [10] |
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. [11] |
"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." [12] |
Marko Rodin's vortex mathematics. |
Fermat spiral (see also: "Spiral Mandela's") |
Fibonacci sequence in the Sunflower |
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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. [13]. See also: video's. |
Riemann surface for the square root function. |
Riemann surface for the cube root function. |
[edit] Polyhedron
[edit] Uniform polyhedron
[edit] Platonic solids
Icosahedron |
Octahedron |
Tetrahedron |
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Hexahedron |
Dodecahedron |
[edit] Metatron cube
- The Metatron cube (derived from the "Flower of Life") holds all the 5 Platonic solids.
- See: [30]
[edit] Numerology
[edit] Phi
- Various notes:
- Alternative names: Φ (the Greek letter Phi), Golden ratio
- Approximation: 1.6180339887
- "The Golden Rectangle and the Golden Ratio"
- goldennumber.net
[edit] 1
- Various notes:
- Whole, all, unity, onement (see also: Atonement or "at-onement")
- See also: circle symbolism
[edit] 2
- Various notes:
- (todo)
[edit] 3
- Various notes:
- See also: 3-Pointed Star
Trilateral Commission logo. Note: also forms pyramid |
- "M" as the number 3
[edit] Pi
- Various notes:
- Alternative names: π (the Greek letter for Pi)
- Approximation: ~ 3.1415926535
- See also: circle symbolism
- "Pi and the Great Pyramid"
[edit] 4
- Various notes:
- See also: 4-Pointed Star
[edit] 5
- Various notes:
- Dodecahedron and Small stellated dodecahedron
- The 5 root races/epochs ideology:
- "Root Race (or Epochs to subsequent authors) is a term first used in the late 19th century by Helena Petrovna Blavatsky in her book The Secret Doctrine. The word designates the large time periods in her esoteric cosmology and symbolizes stages in human evolution. The large time periods of the root races can be compared to the geological time periods or to the Yugas in Hindu Mythology."
- "The Theosophical Root Races"
Olympic Games. (see also: Occult symbolism II: Intertwined circles) |
[edit] 6
- Various notes:
- See also: 6-Pointed Star
[edit] 7
- Various notes:
- See also: 7-Pointed Star
- 7 days of the week: sun-day, moon-day, (Norwegian "Tyr") Mars-day, Woden-day (Mercury), Thor-day, Fri-day (free-day, Venus), Saturn-day
Planetary weekday heptagram? |
[edit] 8
- Various notes:
- See also: 8-Pointed Star
The 2008 Summer Olympics in China starts at: Fri, Aug 08, 2008 8:08 PM. [16] |
[edit] 9
- Various notes:
- See also: 9-Pointed Star
[edit] 10
- Various notes:
- See also: 10-Pointed Star
[edit] 11
- Various notes:
- See also: 11-Pointed Star
- One of the most important numbers in the occult
Marlboro cigarettes. The letters "l" and "b" together form the number 11 |
[edit] 12
- Various notes:
- Devine number, the circle is used in astrology/science measurements:
- 12 signs of the zodiac, 12 months, 12 hours.
- 12 months of the year: januari, februari, march, april, may, june, juli, august, september, october, november, december.
- See also: 11-Pointed Star
The Chromatic scale is a musical scale with 12 pitches. [17] |
3D 12-star (stained-glass art from: [18]) |
European flag with 12 (5-pointed) stars. |
[edit] 13
- devine number + 1 (representing "divinity", or "the creator" overlooking the creation)
- Friday the 13th - "... the superstition derived from the massacre of the Knights Templar on Friday October 13, 1307. King Philip IV of France ordered the destruction of the Templars, after having claimed that they were engaged in heretical practices."
The Great Seal of the United States. |
Defense Intelligence Agency |
U.S. Army |
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