The “Divine” Number
Egyptian mathematics was restricted basically to solutions of practical, geometric problems [4]. On the other hand, the cuneiform tablets discovered and read in the last 200 years provide the evidence that Babylonian mathematics dealt with much deeper notions concerning numbers. We can reliably assume that Pythagoras may have been taught in geometry by the Egyptian priests. Among that what he has borrowed from Babylon, however, if any, was definitely the best knowledge available about numbers.
Pythagoras was regarded as a semi-divine, mystical person by his Greek contemporaries and followers. A strange statement of his is that ‘there is nothing in the world that is genuinely new: everything repeats itself in regular intervals‘ (emphasis is mine) (quoted from Porphyrius, Vita Pythagorae 18 in [5]). I cannot help relating this idea to the ELS of the Bible code. Talking about codes, we must mention the fact that he invented a system of communication so that ‘mathematicians’ – from the Greek ‘mathema’: knowledge - could talk together without being understood by those that are not in the secret.
But what is most important, Pythagoras introduced the notion that numbers exist as objects and that everything in the universe, both material and spiritual, could be described with numbers. He has demonstrated this idea first in music, with the ratios of the lengths of vibrating strings producing different tones. This idea appeared to be so profound that its echo could be perceived in modern physics. Pythagoreans believed that even the tiniest particles in the whole cosmos are interlinked through the laws of harmony represented by numbers. Generally, they would assert in modern terms, we can say about the physical objects that individual lengths of vibrating entities yield octaves. Undoubtedly, more yield derivations emerge as ratios… Mathematics expresses laws of deep yet achievable by the human mind natures. Melody, the individual characteristic and thus the quintessence of music, is not only an expression of the harmony describable by numbers. It can cure body and soul [5].
On the basis of this, we can assume that Pythagoras brought to the Aegean world a new understanding of the nature of the numbers. And this notion was so novel and at the same time so well defined that it must have been borrowed from a civilization that has had the potential as time and space to develop it. Egypt having been ruled out, the only civilization that matches the requirement is Babylon. At this point we may ask the next question: Is there a particular number that is characteristic for the whole civilization? And, if yes, what it is likely to be?
Babylonians were successors to even more ancient civilizations. The origin can be traced back to the Sumerians, whose civilization flourished about 3,000 BC, that is, immediately after the Flood. Interestingly, the sexagesimal number system can also be traced back to the Sumerians. And there is something else that has its roots in their civilization that reached our times through the Babylonians: astrology.
Although sun and moon as well as the other planets visible by naked eye are well documented as objects of worship, one of them is prominent as specifically Chaldean: Venus. This planet was an object of very deep religious respect. The English word ‘veneration’ (from Latin venerare adore, revere; compare also to Venereus = of Venus) is a distant echo of this heritage and reflects the influence of the Babylonian civilization on the Western culture. And what is most characteristic for Venus from astronomical point of view is its appearance at regular intervals in certain points in the celestial sphere. There are five such points that Venus visit every eight years with an accuracy of a fraction of a day! If we connect these points the result will be a pentagram. The pentagram is a figure inscribed in a regular pentagon (Figure 5). Both pentagram and pentagon were widely used symbols as signs of protection, the latter being the shape of choice for the design of fortresses.
Pythagoras definitely has brought these geometric figures, which became signs of his secret society, the Pythagoreans. But Pythagoras or his disciples were the first to understand the nature of the irrational numbers. And there is historical evidence that this understanding came through a specific relation between the sides and diagonals of a regular pentagon. This relation is expressed as a number, which value is 1.6180339887….. This number is called the Golden Ratio and can be illustrated on a line cut in such way that the ratio of the length of the longer segment to that of the shorter one is the same as the length of the line to the length of the longer segment:
The Golden Ratio is
BC/AC = AB/BC = 1.6180339887…..
The story of the Golden Ratio is described vividly by Prof. Mario Livio in his recent book [6], which I recommend to those readers who would like to consider the subject on a higher level. Therefore we will not discuss it here. The Golden Ratio amazed every mathematician that explored it. It appeared as a result in various problems famous for their beauty both in geometry and algebra. The Golden Ratio is so much peculiar in many aspects, so elusive for understanding and so deep in meaning that, engrossed by its fascinating properties, the mathematician Clifford A. Pickover suggested that in a specific rectangle a point that is defined by the Golden Ratio to be referred to as “The Eye of God”.
