Tradition holds that over the entrance to Plato’s Academy was written the words:
“Agewmetrhtoz mhdeiz eisitw”
[If one were to convert the font above to Greek letters, it would read:]
“Only he who is familiar with geometry shall be admitted here.”
(Apparently a knowledge of the Greek language was also important.)
This website is not quite so stringent, and will happily admit any she who is interested in entering. (The guys will, of course, still need to know some geometry.) Alternatively, anyone who can carry a tune may also enter -- in a bucket or by any other means. Music is, after all, based on geometry and mathematics.
For anyone who doesn’t think of themselves as being “familiar with geometry,” the words attributed to Plato’s school might be considering insulting, and thereby construed to have little or no validity. Any grapes from the discourteous must inevitably be sour.
This circumstance is indeed unfortunate in that anyone who is not familiar with geometry, anyone who does not appreciate the premise that Philosophy is about understanding the meaning of a mathematical ratio (the Golden Mean), and anyone who adheres exclusively to a literal interpretation of spiritual teachings... Such an individual might find it difficult to fully comprehend and appreciate the exquisite beauty of the universe. One might even miss the underlying delights in sacred geometry jewelry.
One appealing aspect of geometry is that it constitutes A Graphic Description of the universe, one which is easily visualized, and in some cases can even be aesthetically pleasing. Mathematics in general can often get bogged down in jargon, i.e. abstract symbols which tend to hide the meaning of an equation. But geometrical figures have body, depth, width and the advantage that a picture is worth a thousand words.
At its most fundamental level, Philosophy may be said to involve the use of reason and interactive communications in seeking truth and knowledge. This laudable goal is undertaken in an attempt to understand reality: i.e. the causes and nature of things, the principles governing existence, the material universe, the perception of physical phenomena, and the analysis of human behavior. Which, when you think about it, is quite inclusive. Philosophy is also notably distinct from the mundane -- the dull, routine, of-this-world boredoms, all of which include: work, sports, politics, money, lack of money, and whatever else that distracts us from studying philosophy.
The word, philosophy, derives from the Latin philosophia, and can be written as phi-lo-sophia in order to investigate the meaning of the word based on its parts (using the philosophical tools of “reason and interactive communications”). The first portion, “phi” is simply the Greek letter F or f (equivalent to F or f in the English alphabet). Meanwhile, “lo” (according to the Oxford dictionary) is an archaic form of “calling attention to an amazing sight” (as in “lo and behold”). “Sophia”, on the other hand -- besides being the Goddess of Wisdom (and to which the biblical Book of Proverbs is essentially dedicated) -- is considered to be a combining form meaning “knowledge”, “thought”, or “wisdom”.
The end result is that philosophia -- or Phi lo Sophia -- can be viewed as the wisdom, knowledge, or calling attention to the amazing sight of Phi. Which is precisely what sacred geometry is all about.
A dedicated study of a simple Greek letter might appear to the unenlightened as something short of an illuminating quest. This allegedly simple Greek letter, however, is a mathematical symbol for what is known as the Golden Mean -- a mathematical ratio which is enormously influential in understanding everything from the universe and nature, to ancient cultural monuments and esoteric traditions, to the rise and fall of hemlines or stock prices. The Golden Mean (or phi) is by its nature the essential ingredient in Sacred Geometry, Numerology, and as it turns out, Connective Physics and science in general.
The inherent connection between philosophy, sacred geometry, and numbers is manifested in numerous ways. There is the Geometry of Alphabets, i.e. the Hebrew, Greek, and Arabic alphabets being sacred and the first five books of the Bible being representations of sacred geometry. Much of this understanding was contained in the Ha Qabala, an aspect of Jewish and Christian mysticism which is worthy of prolonged and concentrated study.
It has also been said that "Sacred Geometry exists beyond religion, belief or nationality. It unites us all in the belief of the one. By understanding the concept of the one each of us can take control over our own lives and break free of the circle of chaos in the material world which Judaism calls the world of lies." [quoted from ka-gold's Age of Aquarius article] This is significant stuff!
For just an inkling of what Sacred Geometry is all about, consider just one facet of it, the Golden Mean or Golden Number. The latter website provides a wealth of information in a very nicely designed web-package.
The idea that philosophy is inherently mathematical might not be construed as good news for mathematically uninclined philosophers. But as pointed out in A Non-Mathematical Digression, it might be a good idea to momentarily address this potential obstacle.
Given that disclaimer, the amazing phenomenon of Fibonacci Numbers (complete with “bunnies”), the Golden Mean (a very rewarding subject), Golden Mean Mathematics (for those so unwise or so inclined), The Great Pyramids (a really big subject), Nines (e.g. cloud addresses), Transcendental Numbers (for those who really want to get above the crowd), Cycles, Music, and the Harmony of the Spheres (harmonies of all kinds being a good thing)... All of these glories await your click of the mouse.
For the more sophisticated mathematicians, an excellent beginning commentary can be found at <http://mathworld.wolfram.com/GoldenRatio.html>. As an initial example, the referenced website describes the Golden Mean (Ratio) as “A number often encountered when taking the ratios of distances in simple geometric figures such as the pentagram, decagon and dodecagon. It is denoted phi, or sometimes tau (which is an abbreviation of the Greek “tome,” meaning “to cut”). Phi is also known as the divine proportion, golden mean, and golden section and is a Pisot-Vijayaraghavan constant. It has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers.”