911:Geometry

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Contents

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

Wave behavior

  • 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"

Wave phenomena


Music theory

Self-organizing systems

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."

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."


Natural shapes:


Synthetic shapes:


Magnetohydrodynamics shapes:

  • 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

Fractals

Cellular automata

Information concepts

  • Modes and attributes:

Mathematics

High-level divisions of mathematics.

Truth

Quantity

Structure

Space

Change

Metamathematics

Applied mathematics

Geometry

Spirals

Natural spirals

Scientific spirals

Cultural spirals

Abstractions

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


Natural analogies:

Tree of life

Earthly representations if the tree of life?

Polyhedron

Uniform polyhedron

Platonic solids

Metatron cube

Literature

Links

Various:

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