Geometry And The Quest For Reality

[Principium Nexus]

The quote below is from the book A Beginner's guide to Constructing the Universe - The Mathematical Archetypes of Nature, Art and Science, A voyage from 1 to 10 by Michael S. Schneider. Even though it's for the book, it's interesting to read and might make you more interested into Geometry or the book.

"Sooner or later there comes a time in life when you start thinking about Reality and where to find it. Some people tell you there is no such thing, that the world has nothing permanent in it, and, as far as you are concerned, consists merely of your fleeting experiences. Its framework, they say, is the random product of a natural process, meaningless and undirected.

  Other believe that the world was made by a divine Creator, who continues to guide its development. This sounds a more interesting idea, but, as skeptics point out, every religion and church that upholds it does so by faith alone. If you are naturally faithful and can accept without question the orthodoxy of your particular religion or system of believes, you will feel no need to inquire further and this book will appear superfluous. It was written for those of us who lack or have lost the gift of simple faith, who need evidence for our beliefs. We cannot help being attracted by religious view, that the world is a harmonious, divinely ordered creation in which, as Plato promised the uninitiated, "things are taken care of far better than you could possibly believe." Yet superficially it is a place of confusion and chaos, where suffering is constant and the ungodly flourish.

This is where we begin the quest for Reality. Looking closely at nature, the first insight we obtain is that, behind the apparently endless proliferation of natural object, there is a far lesser number of apparent fixed types. We see, for example, that through every generation cats are cats and are programmed for catlike behavior. In the same way, every rose has the unique characteristics of a rose and every oak leaf is definitely an oak leaf. No two specimens of these are ever exactly the same, but each one is clearly a product of its own formative type. If it were not so, if animals and plants simply inherited their progenitors' characteristics, the order of nature would soon dissolve into an infinite variety of creatures, undifferentiated by species and kinship's.

  This observation, of one type with innumerable products, give rise to the old philosophical problem of the One and the Many. The problem is that, whereas the Many are visible and tangible and can be examined at leisure, the One is never seen or sensed, and its very existence is only inferred through the evident effect it has upon its products, the Many. Yet, paradoxically, the One is more truly real than the Many. In the visible world of nature all is flux. Every thing is being born or dying or moving between the two processes. Nothing ever achieves the goal of perfection or the sate of equilibrium that would allow it to be described in essence. The phenomena of nature, said Plato, are always "becoming", never actually "are". Our five senses tell us that they are real, but the intellect judges differently, reasoning that the One, which is constant, creative, and ever the same, is more entitled to be called real than its ever-fluctuating products.

  The search for Reality leads us inevitably towards the type, the enigmatic One that lies behind the obvious world of the Many. Immediately we encounter difficulties. Being imperceptible and existing only as abstractions, types cannot be apprehended by the methods of physical science. A number of modern scientists, perceiving the influence of type in nature, have attempted to bring them within the range of empirical study. Rupert Sheldrake, author of A New Science of Life and other works, has take a bold step in that direction. In an earlier age, the Pythagorean's worked on systematizing the types by means of numerical formulae. Yet Plato, who wrote at length on the subject of constant types (referred to as "forms"), was carefully ambigious in defining them and never made clear the means by which they influence the world of appearances.

  Plato did, however, give instructions on the procedure towards understanding the nature and function of the types. In the Republic he described the ascent of the mind through four different stages. It begins in Ignorance, when it does not even know that there is anything worth knowing. The next stage is Opinion, the stage in which TV chat-shows particularly are forever stuck. This is divided into two subcategories, Right Opinions and Wrong Opinion. Above that is the level of Reason. By education and study, particularly, in certain mind-sharpening subjects, the candidate is prepared for entry into the fourth stage, which is called Intelligence (nous). One can be prepared for it but with no guarantee of success, for it is a level that one can only achieve on one's own, the level of heightened or true understanding, which is mental level of an initiate.

  The studies that Plato specified as most effective in preparing the mind for understanding are the so-called mathematical subjects, consisting of number itself, music, geometry, and astrononmy. These were the main studies of Pythagoras and his followers, who anticipated the realization of modern physics in proclaiming that all scales and departments of nature were linked by the same code of number. Geometry is the purest visible expression of number. In Platonic terms, the effect of its study lead the mind upward from Opinion onto the level of Reason, where its premises are rooted. It then provides the bridge or ladder by which the mind can achieve its highest level in the real of pure Intelligence.

  Geometry is also the bridge between the One and the Many. When you draw one of its basic figures - a circle, say, or a triangle or regular polygon- you do not copy someone else's drawing; your model is the abstract ideal of a circle or triangle. It is the perfect form, the unchanging, the unmanifest One. Below it are the Many - the expressions of that figure in design, art, and architecture. In nature also the One circle gives rise to the Many, in the shapes and orbits of the planets, in the roundness of berries, nests, eyeballs, and the cycles of time. On every scale, every natural pattern of growth or movement conforms inevitably to one or more of the simple geometric types. The pentagon, for example, lies behind each specimen of the five-petaled rose, the five fingered starfish, and many other living forms, whereas the sixfold, hexagonal type, as seen in the structure of snowflakes and crystal generally, pertains typically to inanimate nature.

  As soon as you enter upon the world of the sacred, symbolic, or philosophical geometry - from your first, thoughtful construction of a circle with a circumference divided into natural six parts - your mind is opened to new influences that stimulate and refine it. You begin to see, as never, before, the wonderfully patterned beauty of Creation. You see true artistry, fare above any human contrivance. This indeed is the very source of art. By contact with your aesthetic senses are heightened and set upon the firm basis of truth. Beyond the obvious pleasure of contemplating the works of nature - the Many - is the delight that comes through the philosophical study of geometry, of moving towards the presence of the One.

  Michael Schneider is an experienced teacher and, as you are entitled to expect, a master of his geometric craft. No one less qualified could set out its basic principles so clearly and simply. His much rarer asset is appreciation of the symbolic and cosmological symbolism inherent in geometry. That is the best reason for being interested in the subject, and it is the reason why the philosophers of ancient Greece, Egypt, and other civilizations made geometry and number the most important of their studies. The traditional science taught in their mystery schools is hardly known today. It is not available for study in any modern place of education, and there is very little writing on the subject. In this book you will find something that cannot be obtained elsewhere, a complete introduction to the geometric code of nature, written and illustrated by the most perceptive of its modern investigators."

I want to open this topic to discuss/post literature or media regarding to geometry found in nature or in general. Anything regarding geometry is welcome!

[Principium Nexus]

 

Edited July 7, 2017 by Principium Nexus