Icosahedral -
Dodecahedral Structure Of The Universe
A Number is the essence of all things, and
the organization of the Universe in all its definitions represents in general
the harmonic system of numbers and their ratios". - Aristotle
About what ratios spoke
Aristotle? Responding this question it is necessary to tell about two
achievements of the Pythagorean science: (1) about the "Principle of
multiple relations""division of the line segment in extreme and
middle ratio" called later by the "golden section".
The number of 10 is considered
by the Pythagoreans as the highest value. They called it as a
"tetraxis". As is known the "tetraxis" can be presented as
the sums of four first natural numbers (10 = 1 + 2 + 3 + 4) and it carried a
special ideological load in the Pythagorean doctrine. The unit or
"Monada" of 1, according to Pythagor, meant a spirit and all visible
world follows from it. From the unit of 1 the "deuce" or the
"dyad" (2 = 1 + 1) symbolized the material atom followed. By taking
in itself the unit 1, the "dyad" was transformed into the
"triad" (3 = 2 + 1) symbolized the alive world. The alive world (the
"triad") plus the unit of 1 produces the "tetrad" (4 = 3 +
1) symbolized the Whole, that is, the visible and invisible world. As the
"tetraxis" 10 = 1 + 2 + 3 + 4, it meant that it expressed by itself
"Everything".
As it appeared, the internal
proportions of the "teraxis" find out among many natural phenomena of
the objective world, in particular, in the law of the cord oscillation. The
musical row proportions constructed on this basis provided the best, harmonic
consonance: the ratio of each member of the "tetraxis" to the
previous one gave the "octave" (2:1), the "quinte" (3:2),
the "quarto" (4:3). So, on the example of the sound wave process for
the first time in the history of science the major property of all sound waves,
their multiplicity, was revealed. The "Musical harmony " discovered
by means of the "tetraxis" analysis was confirmed in experience with
a traditional cord; in the sounds "generated" by vessels filled by
water in the given proportions; in the sounds "generated" by the
blacksmith's hammers of different weights etc.
A conviction in universality of
the "tetraxis" principle ripened step-by-step and this prepared the
basis for transferring of this model on the Cosmos.
PLATONIC SOLIDS
Now about the second
achievement of the Pythagorean doctrines. According to the remark of the
commentator of the last issuing of Plato's works for him "all cosmic
proportionality is based on the principle of the "golden or harmonic
proportion". Plato's cosmology is based on the regular polyhedrons called
"Platonic Solids". Each Plato's Solid symbolized some of the five
"beginnings" or "elements": tetrahedron - the body of fire,
octahedron - the body of air, a hexahedron (cube) - the body of the Earth,
regular icosahedron - the body of water, dodecahedron - the body of the
Universe.
A representation about the
"through" harmony of the Universe invariably was associated with its
implementation in these regular polyhedrons. And the fact that the
dodecahedron, the main "cosmic" figure, was based on the golden
section gave to the latter a sense of the main proportion of the Universe.
"Euclid did not intend to
write the systematic tutorial on geometry. He set as a goal to write the work
about the regular polyhedrons intended for the beginners by virtue of what he
set forth all necessary information" - the joke of the known English
geometer d'Arci Thompson, as well as any good sharpness, contains in itself a
grain of true. According to Proclus, the commentator of the "Euclidean
Elements", Euclid considered the methods of construction of the Platonic
Solids as the "crown" of all thirteen books of the
"Elements". And he placed just this major mathematical information in
the concluding, thirteenth book.
Plato's cosmology became the
basis of the so-called icosahedro-dodecahedral doctrine, which by red thread
passes through all human science. The essence of this doctrine consists of the
fact that the dodecahedron and regular icosahedron are typical forms of the
nature in all its manifestations starting since cosmos and finishing by
micro-cosmos.
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| Dodecahedron |
The problem about the form of
the Earth permanently took minds of scientists since the antique times. And
when the hypothesis about the spherical form of the Earth got scientific
grounds there arose the idea that the Earth represents by itself the
dodecahedron by the form. So, already Plato wrote: "The Earth, if to look
at it from above, is similar to the ball consisting of 12 skin's pieces".
This Plato's hypothesis found further scientific development in works of
physicists, mathematicians and geologists. So, the French geologist de Bimon
and the well-known mathematician Poincare considered that the form of the Earth
represents by itself the deformed dodecahedron.
The Russian geologist Kislitsin
also used in his researches the idea about the dodecahedral form of the Earth.
He put forward the hypothesis that 400-500 million years ago the geo-sphere of
the dodecahedral form was turn into the geo-icosahedron. However, such
transformation appeared not full and uncompleted. As the result the geo-dodecahedron
appeared to be inscribed into the frame of the icosahedron.
In the last years the
hypothesis about the icosahedro-dodecahedral form of the Earth was subjected to
verification. For this purpose the scientists combined the axis of the
dodecahedron with the axis of the terrestrial globe and, gyrating around of it
this polyhedron, paid attention that its edges coincide with gigantic
disturbances of Earth's crust. By taking then regular icosahedron as a
polyhedron, they established that its edges coincide with more small-sized
partitionings of Earth's crust (mountain ranges, breaks etc.). These
observations confirm the hypothesis about proximity of the tectonic framework
of Earth's crust with the forms of the dodecahedron and icosahedron.
The hubs of the hypothetical
geo-crystal are as though centers of certain anomalies on the planet: in them
all global centers of extreme atmospheric pressure, regions of the hurricanes
origin are arranged; in one of the hubs of the regular icosahedron (in Gabon)
the natural nuclear reactor worked 1,7 million years ago was found. The
gigantic mineral deposits (for example, Tyumen field of oil) are dated for many
hubs of the polyhedrons, anomalies an animal pattern (the lake of Baikal),
centers of development of cultures of mankind (Ancient Egypt, Northern Mongolia
etc.).
All these examples confirm
surprising insight of Plato's intuition.
A long time it was considered,
that in the inorganic nature were not used almost dodecahedron and regular
icosahedron having so-called "pentagonal" symmetry axis, but the
"pentagonal" symmetry axis is a constant "satellite" of
life. The regular icosahedron is geometric object, which form are used by
viruses, that is, the icosahedral form and pentagonal symmetry are fundamental
in organization of living material.
The discovery of the
quasi-crystals (based on the regular icosahedron) made in 1984 by Israeli
physicist Dan Shechtman became the outstanding event in modern physics, as this
discovery shows that the "pentagonal" symmetry and the icosahedral
form play also a fundamental role in crystallography.
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| Building Blocks |
The works of the
American researcher Winter heading the group "Planetary Palpitations"
became the quintessence of geometrical ideas about all being. He is a preacher
of the ideal form, unitary "golden section", which like to the
"golden chain" connects the gene and the Universe. Accepting the
concept of the icosahedro-dodecahedral form of the Earth, Winter develops it
further. He pays attention on the fact that the angle described by the Earth's
spin axis during its precession for 26 000 years is equal to 32°. It exactly is
equal to that angle, under which it is necessary to incline the cube, that,
gyrating it then around of the axis (with five stops) to get the dodecahedron.
In Winter opinion, the power skeleton of the Earth represents by itself the
dodecahedron inscribed into the icosahedron, which, in turn, is inscribed into
the second dodecahedron. The geometrical ratios between the indicated
polyhedrons are represented by the golden section.
Dodecahedral structure, in
Winter's opinion, is inherent not only in the power skeleton of the Earth, but
also in the constitution of living material. So, during division of the ovule
it is formed at first the tetrahedron from four cells, then the octahedron, the
cube, and, at last, the icosahedro-dodecahedral frame of the gastrula. And at
last, perhaps, it is the most important: the structure of the life genetic code
represents by itself the four-dimensional development (on the time axis) of a
rotating dodecahedron! Thus, it appears, that all Universe from the Meta-Galaxy
up to the living cell is constructed by one principle - infinitely entered each
to other dodecahedron and icosahedron being among themselves in the proportion
of the golden section!