The ethers, formative forces, and elements, as presented in the philosophy of Rudolf Steiner, are the basic creative components. in the structure of the universe. All forms of nature can be defined by these inseparable concepts. When combined with the practice of geometry, we find a reenforcement of these ideas and an interconnectedness in which geometry, ether, and form, become one.
Light, warmth, tone, and life, the four ethers, are the universal principles; the superior and unifying archetypes giving birth to the formative forces. The corresponding geometric function which represents the ethers is the square root of two. This is the transformative and generative function where one becomes two and creates the endless potential of multiplicity, which can be observed in the division of a square cut by its diagonal.
Although we may not have the ability to perceive the ethers directly, we can, by observing the differences between the physical and the etheric, begin to understand the nature of the formative forces. All formations of plants, trees, crystals, water, etc., can be viewed as objects of action embodied in formative force. The square root of three displays its formative character in the geometric configuration of the Vesica Piscis, and can be constructed by drawing two equal circles in which the center of each overlies the circumference of the other. These overlapping circles are an excellent representation of a cell in the midst of division exhibiting the active se ~~ ration of the ethers and formative forces. The hexagon, when viewed in relationship to the square root of three and the Vesica Piscis, brings into existence the ordered formation of crystals, especially those of the carbon bonding type which allow for the creation of all organic substances.
The elements, earth, air, fire, and water, are the basis for the physical and give it prevalence. Through the ethers, formative forces, and elements, are created the substances and forms of organic life. These are individualizing and regenerative, symbolized by the double square or square root of five rectangle. The square root of five function is inseparably related to the Golden Ratio of the Fibonacci sequence which can be observed throughout nature.
The relationships of the three square root functions presented here are the only essentials in the formation of the five regular solids (Platonic) which are the basis for all volumetric forms. Given this, in conjunction with the ethers, elements, and formative forces, we can readily observe and define all forms displayed in nature.
