EM education | Platonic formation of the Æther

What is Electromagnetic Education?

pentakisdodecahedron: the aetheric waters

– Platonic formation of the Æther –

IN exploring the cultural significance of electromagnetism more subtle approaches can sometimes offer perspectives for understanding that cannot be found in more purely technical investigations, such as with electronics.

ONE such rewarding venture can be found in exploring the ideas of electromagnetism though geometry. The knowledge needed is largely accessible online and through books that can be loaned from a library, and the only requirement is a general level of appreciation for, and literacy of, how the material world is composed of mathematical abstractions and their connection to the ideas of philosophy which culminate in the geometrical structures of molecules and atoms.

AN elegant background is provided in the book The Architecture of Molecules by Linus Pauling. Though a more specifically geometrical investigation can be found in the book Platonic & Archimedean Solids by Daud Sutton, which provides a visual overview of the construction of certain geometrical forms and their remarkable interrelationships.

Platonic & Archimedean Solids.
Daud Sutton. ©2002. Wooden Books.

IN general, the connection between electromagnetism and geometry is less overtly described than simply exists as the context for major ideas which have sought to describe and define the world as it is found to exist, over the millennia.

PLATO's discovery or communication of the mathematical relationships of five geometric forms (the Platonic solids) is well-known as a cosmology of various states of matter. As outlined in the Timaeus, Plato establishes a connection between 'the elements' of the material world within a universal geometrical framework. Therefore the material elements of fire, earth, water, and air are given form, as is the immaterial quintessence. Millennial later these formations were revealed in crystallographic structures of atoms and molecules bound together by shared electrons.

IN addition, the idea of a quintessence or '5th Element specifically relates to still-existing questions of electromagnetic understanding, and lack therof, and its significance remains a universal mystery even in this day.

materials needed: glue and wooden sticks.

TO begin a tangible exploration of these ideas, all that is needed is craft glue and a bag of equal sized wooden sticks, (although other sticks could be used and air-drying clay could be an improved method of construction in retrospect). The important thing to remember is that in deciding to build the Platonic forms all sticks must be of equal size. The fact of using a single scale to make all five forms will help make sense of why the following constructions and their discovery are so remarkable. And now, onto the forms…

tetrahedron: fire. (4 triangular faces)

A tetrahedron is a pyramid of 4 triangular faces, made of 6 sticks which meet in 4 places. It was said by Plato to be like fire because of its "penetrating acuteness" and "it is the simplest and most fundamental of the regular solids" (Daud).

cube: earth. (6 square faces)

A cube is composed of 6 square faces, made of 12 sticks which meet in 8 places. It was said by Plato to be like earth because of its directionality, stability, and its relation to the first perfect number, six (Daud). (Note: all models are constructed using the same sized wooden sticks in different geometrical structures, as are the following more complex shapes…)

octahedron: air. (8 triangular faces)

AN octahedron is composed of 8 triangular faces, made of 12 sticks which meet in 6 places. Its triangular form was said by Plato to exist between those of fire and water, and was thus said to be air (Daud). The notion of symmetry is unique in this form, as a Star of David (sculpture) is visible when seen 'face on'. So too, the role of the flattening of 3 dimensional objects into 2 dimensional shadows or projections is another attribute that can be explored in every form.

icosahedron: water. (20 triangular faces)

AN icosahedron is composed of 20 triangular faces, made of 30 sticks which meet in 12 places. It is the largest of the triangular forms, and Plato associated it with water, "the densest and least penetrating of the three fluid elements" (Daud), which includes fire (tetrahedron) and air (octahedron).

dodecahedron: æther. (12 pentagonal faces)

THE dodecahedron is composed of 12 pentagonal faces, made of 30 sticks which meet in 20 places. It is the form that is closest that of a perfect sphere, and is the only form completely based on the number 5, though the icosahedron contains a pentagon within its structure. It was considered by Plato the quintessence or "fifth being," "Heaven above," a mysterious "5th element" which represents the cosmos.

'As "quintessence" it isn't above the four elements, the configured states of matter, but encompasses them, infusing the force of life and excellence throughout their structures." - A Beginner's Guide to Constructing the Universe. Michael Schneider. ©1994, p.107.

SUFFICE it to say that the æther conceptually equates with this notion of the quintessence which has also had a central role in the science and culture. For example, one of Einstein's experiments centers around the idea of the æther, and a recent popular movie entitled The Fifth Element centers around a mystical connection in the fabric of the universe that has yet to be fully revealed. (For more information on the æther hypothesis, please visit: The Æther FAQ, and Modern Scientific Theories of the ancient Aether, offsite.)

AS such the æther can function, symbolically and pragmatically, as the 'cosmic' reality of electromagnetic phenomena which remains in the realm of the unknown.

The Platonic Solids in order of volume, small to large: fire, earth, air, water, æther.
In this sequence, the æther is the fifth and largest volume of the elements.
(note: the Star of David found within the triangles the octahedron.)

THE value of modeling the Platonic Solids is realized when comparing the forms in relation to one another after they are constructed. It is critically important to remember that all forms are created using an identical size and shape of wooden stick, and these are the five geometries that result. Vastly different and yet sharing similarities among themselves, they are truly universal forms that have since been found as organizational patterns in the material world of atoms, molecules, and crystal structures; in addition to the designs of other material forms. e.g. the methane molecule has a tetrahedral structure; an apple slice has pentagonal symmetry as does the dodecahedron.

The Platonic Solids in order of density, simple to complex: fire, earth, air, æther, water.
In this sequence, water is the most complex construction as it has the most facets.
(note: the Star of David found within the triangles of the icosahedron.)

ARRANGEMENT of the Platonic Solids in a different sequence can reveal an interesting perception of the same elements: the æther may not literally be an actual 'fifth' element if considering the complexity of the forms, instead it could be 'fourth' if considering the dodecahedron has 12 faces versus the 20 of the icosahedron. In addition, the icosahedron has both triangular and pentagonal geometrical structures which adds additional complexity. Also, each element's name is based on the number of their faces (tetra equals 4, etc.) so that this number (icosa = 20 versus dodeca = 12) would appear more significant than the number of edges (sticks) or vertices (places of intersection), which in the latter cases the æther (dodecahedron) is equally or more numerous in construction.

IN any case, such a sequence visually appears 'out of order' though it may be a legitimate and logical ordering. Reading the original cosmology in the Timaeus by Plato would likely help to resolve some of these questions that are not readily addressed in subsequent accounts, and these models could be considered a preparation for that.

ESSENTIAL to appreciating the beauty of the five regular polyhedra, or Platonic Solids, is to grasp their geometric interrelationships with one another. Each of the five forms can hold every other form within, it in a structured way.

Platonic & Archimedean Solids. Page 54. Wooden Books.
Each of the five Platonic forms relate to one another.
.edu fair-use, scan by electronetwork.org, 2005.

RELEVANT to the nesting of geometries inside one another is that the concept of 'scale' applies, in that the wooden sticks used to model each of the forms in one scale would need to be a variety of sizes/scales to achieve such constructions. It is an approach that can be explored using a robust modeling tool such as Zome (which enables Kepler's model of the universe to be built, which nests the five elements one inside another).

THOUGH there is still much that can be explored using a single scale, in this case using wooden sticks of equal size, explorations are ultimately limited only by imagination.

air (octahedron) and earth (cube) and earth-air (tetrakishexahedron):
consisting of 24 triangles, 36 sticks, 14 intersections.

FOR instance, upon building the Platonic Solid representing water, the octahedron, it was realized that it contains the shape of a square which exactly matches that of the cube, representing earth. It was then possible to merge these two forms into one, in the same scale, to achieve a hybrid element: earth-air, a tetrakishexadedron.

water (icosahedron) and aether (dodecahedron) and aether-water
(pentakisdodecahedron): 60 triangles, 90 sticks, 32 intersections.

LIKEWISE, in exploring the idea of constructing a model of the æther, it was noticed that water, an icosahedron, contains a pentagon within its structure. Matching this pattern at the same scale as the dodecahedron, made of pentagons, adds a layer of triangular forms and thus creates the hybrid element: aether-water, a pentakisdodecahedron, which could relate poetically to ideas such as the aetheric wind and aetheric ocean of the cosmos.

tetrakishexadedron and pentakisdodecahedron.

tetrakishexahedron (earth-air) and pentakisdodecahedron (aether-water).

THUS, in exploring the formation of the Platonic Solids a new perception of the ideas of the æther emerges, if only to offer a descriptive ability for conceptualizing material states and how they relate. Especially with regard to electromagnetism, itself the fundamental connection between all five elements in the structure of atoms and molecules and 'forms,' in addition to their original conceptual formation: these geometrical structures tell the story of the cosmos and are a worthwhile exploration for those interested in investigating both new and old ideas in a single, universal context of cosmic mystery. (bc 3.18.2005)

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