When the phenomenon of thinking in terms of numbers actually began will possibly never be known. How it began, however, is not difficult to conjecture. In fact, there are many evidences which confirm the following speculation on how man conceived a number system.

In separateness there is confusion. The mind always seeks to synthesize, to tie together its experiences for simplicity and understanding. As for events, they are experiences existing in a period of human consciousness. A period of human consciousness may be from the time one awakens in the morning until he closes his eyes in sleep at night. Each event that occurs during such a period may be quite clear in itself in the mind. At night before losing consciousness in sleep, we are quite aware that many such events occurred during the conscious period, or the day. The mind struggles to know just how many there were. In other words, it seeks to group them into a whole or an order of quantity, which we call numerical.

The mind also seeks to find some symbol of this unity as a guide, that is, something which appears as a whole yet actually consists of the grouping of separate things. The hand is such a symbol. It contains five fingers grouped into a unity. The first attempt at counting, therefore, must have been on the fingers, just as children do today. Quantity was determined by comparison to these ten fingers. Things or events, if they exceeded the total fingers, or ten, were determined as twice two hands or three times two hands, and so on. Similar methods of counting are prevalent among aborigines in various parts of the world today.

The actual history of mathematics began with the Ionian Greeks about the fifth century B.C. However, the Greeks undoubtedly inherited much of mathematics from the investigations of their venerable predecessors, the ancient Egyptians and Phoenicians. In fact, Greek tradition pays homage to the Egyptians for the rudiments of geometry. Also the sicence of numbers was declared by them to be an attainment of the Egyptians. For centuries, the only indication of this inheritance of the science of numbers by the Greeks was the references to it by the ancient Greek and later historians.

Herodotus, father of history, relates how the Heliopolitan priests told him they were the first discoverers of the solar year, and that they divided this year into a mathematical arrangement of twelve parts or months, each month having thirty days. To each year they added five days, so that the seasons would uniformly repeat themselves. The Egyptians accomplished this feat of the calendar approximately 4000 B.C.! Then Strabo, Greek historian of the First Century B.C., says in his geography of Egypt: "And here it was, they say, that the science of geometry originated, just as accounting and arithmetic originated with the Phoenicians, because of their commerce."

Ancient Manuscript Found

 

During the early part of the present Twentieth Century, the first direct information on Egyptian knowledge of mathematics came to light. In the British Museum a hieratic (abbreviated hieroglyphs) papyrus, part of the Rhind collection of antiquities, was translated. It was disclosed that it was written by a Scribe known as Ahmes, approximately 1000 years B.C. This papyrus was an emendation of a text still a thousand years earlier. The title of this papyrus is "Direction for Knowing All Dark Things." It is a discourse on arithmetic and geometry. It contains a series of questions and their answers, or problems and their solutions. It appears that at this time the Egyptians were having some little difficulty with fractions. Scribes could only operate with fractions having one as a numerator, the only exception being 2/3rds. Multiplication was accomplished by multiplying a given number by two, for example, and then doubling that total and continuing in this manner until the required sum was had. Strange symbolical signs were used in their calculations. A figure of a person walking forward indicated addition--backward indicated subtraction. A flight of arrows also denoted subttraction.

The Egyptians applied geometry to practical needs. There is little direct evidence that they were much concerned with abstract geometry, as were the Greeks. For example, the Egyptians used the science of geometry for determining the contents of circular granaries, which they did with great accuracy. The ground plan of the Great Pyramid, that is, its square base, was accomplished with wonderful skill. Also the orientation of it according to the cardinal points of the compass displayed amazing mathematical exactitude, comparing favourably with calculations by instruments today.

How were the signs of the numerals decided upon? Why do we calculate in units of ten, each decade beginning again and progressing through a next higher series of nine? Is it an accidental arrangement, or is there more than a mathematical meaning underlying such a system?

Our present numerical symbols are known as the Gobar Arabic, and were evolved by the Arabs from much earlier forms. One theory is that the numerals 5, 6, 7 and 9 were derived from the first letters of Indo-Bactrian words corresponding to them. The Bactrians were an ancient Iranian people who came into India and were undoubtedly of the original Aryans and brought their language with them. For example, the symbol for 5 is said to be the first letter of the Bactrian word for five. The symbols for 1, 2 and 3, respectively, are said to be derived from "parallel pen strokes, cursively connected."

From the point of view of this theory, the numeral 2 was written like the Z of the alphabet. The upper and lower parallel lines denoted 2. The oblique vertical line was the cursive or written manner of connecting the two parallel lines. The original figure 3 consisted of two horizontal parallel lines, and then one vertical stroke directly beneath. These were connected together by little loops similar to the way in which the numeral appears today.

It is said that in some languages the names for the entire first ten digits are from the fingers used to denote them. In fact, it is related that the words five and hand, in most languages, are dereived from the same root. The Roman numeral X is said to be composed of two V's, with apex to apex; in other words, one V standing upon the point of the other.

According to the Rosicrucian conception, the circle represents the periodicity of nature's phenomena or is a symbol of the cycles in nature. The circle, the Rosicrucians say, is numerically expressed by the numeral nine, the square of three, or the equilateral triangle. Consequently, in any expression of nature or cycle, we advance from 1 to 9. The second period begins with 1 again. The zero after the numeral 1, or the figure 10, means the beginning of the second period--20, for example, means the beginning of the fourth, and so on.

Pythagorean Number System

 

With the Greeks and ancient Hebrews, numbers had more than a utilitarian value. They became symbols for philosophical abstractions and mystical and occult principles. The numbers were esoteric keys to truths and laws of nature. In some instances these symbols of laws were thought to have a secret latent efficacy in themselves. In fact, it was often believed that they exerted influence on all who wore them or who used them in a certain manner.

To Pythagoras goes much of the credit for the esoteric meaning of numbers. He was born on the island of Samos about 569 B.C. He travelled to Egypt to study there with the learned priesthood of the Mystery Schools. The classical scholar Stanley, in his biographies of the philosophers, says of Pythagoras' studies in Egypt: "Coming to (Pharaoh) Amosis, Amosis gave him letters to the priests, and first going to those of Heliopolis, they sent him to the priests of Memphis, as the most ancient. From Memphis, upon the same pretense, he was sent to Thebes. They enjoined him very hard precepts, wholly different from the institutions of Greece, which he readily performed, to their great admiration, that they gave him power to sacrifice to the gods, and to acquaint himself with all their studies which was never known to have been granted to any foreigner besides."

About 529 B.C., Pythagoras moved to Crotona, a colony in the south of Italy. He opened schools which were crowded with enthusiastic students. His teachings were expounded to two groups of students--probationers and Pythagoreans. The latter received his most profound philosophical views and were bound by oath into a brotherhood. Though Pythagoras inherited his fundamental ideas in geometry from Egypt, he exceedingly elaborated upon them and evolved them into a philosophy. The impact of Pythagoras upon Greek philosophy was tremendous. The discoveries accredited to him, which are indubitably his, constituted a great contribution to human knowledge. Even the very words mathematics and philosophy are said to have been originated by him.

Pythagoras divided numbers into odd and even. The odd numbers he termed gnomons. The harmony of nature had greatly impressed itself upon him. He discovered that the division of a musical string corresponded to the octaves of music; namely, the sound coming from a vibrating string, depends upon its length. He finally conceived that all manifestations in nature are according to number or mathematical proportion. He believed that if one knew the numerical essence, the mathematical harmony of substance, he could control it at will. In fact, he believed that certain numbers corresponded to properties or substances in nature. Plutarch says in his essay on Pythagorean arithmetic, "For Pythagoras thought number the greatest power and reduced everything to numbers--both the motions of stars and the creation of living beings, and he established two supreme principles--one finite, united, and the other infinite, duality. The one, the principle of good, the other evil. For the nature of unity being innate in what surrounds the whole creation, gives order to it, to souls virtue, to bodies health, to cities and dwellings praise and harmony, for every good thing is conversant with concord.... So he demonstrates of all of the successive numbers that the even are imperfect and barren--but that the odd are full and complete--because joining to the even they preserve their own character. Nor in this way is the odd number super, but also added to itself, it generates an even number. For it is creative, it keeps the original force and does not allow a division, since per se the mind is superior. But even added to itself, neither produces the other, nor is indivisible."

Pythagoras also assigned moral qualities to numbers. These meanings were not understood by the uninitiated, and taken literally or without further qualification, they often seemed ludicrous. That the Pythagoreans had a more extensive and lucid meaning is known only to those shcools of esotericism as the Rosicrucians, who are traditional affiliates of the ancient Pythagorean School at Crotona. Pythagoras regarded the numeral ONE as the source of all numerals. It was the point of beginning, the self-contained, the absolute. It likewise, therefore, depicted the reason, the mind cause. Two stood for opinion. Four represented justice and stability of character. Five represented marriage, because it consisted of the unity of the odd and even numbers two and three. Five was also held to be the key to the laws of colour. The sphere was completion, that without beginning or end. Perfect numbers are those whose division add up to the number itself. For example, six is divided by one, two, and three, and these all add up to six.

The animism of numbers--namely, that they were imbied with spirit--is attributed also to Pythagoras. However, scholars are inclined to disclaim that Pythagoras ever taught anything which now goes under the guise of animistic numerology. In antiquity, when the development of symbols to represent numbers was in its formative stage, letters of the alphabet were often used for such a purpose. Consequently the letters of words would add up to certain sums. Words or names having greater sums were thought to possess more of the efficacy believed inherent in numbers. Since numbers had sex--that is, were male or female, or odd and even--certain words acquired a masculinity or femininity, because of their numerical otal. Omens were ascribed to words having certain numerical value, just as 13 is considered unlucky by the superstitious today. To the true occultist and the mystic, however, such words were but mere keys for numerical values, word symbols for numbers.

Esoteric Meaning of Numbers

From out of these origins have come an abundance of meanings attributed to numbers. Some are obviously mystical and philosophical allegories. Others are but rank superstitions which have been superimposed on the pristine meanings. The following few may prove interesting.

THE MONAD or the number 1: The point of beginning, the indivisible, the prime cause, the absolute--God--the first of all things.

THE DUAD or the number 2: The contraries or opposites in nature, by which realities are generated. It alludes to such universal diversities as positive and negative, rest and motion, good and evil. The extremities between which the creative force in the universe operates.

THE TRIAD or the number 3: The first odd number, therefore the first perfect number. The point of unity or equilibrium of those opposites which the duad represents. They key to the laws of material creation, is expressed in the sciences, the symbol of the Rosicrucian "law of the triangle."

THE TETRAD or the number 4: The fountain of nature. The symbol of permanency or stability in nature. It also represents the four primal elements--air, earth, fire, and water. Further, it depicts the four cardinal virtues--prudence, temperance, fortitude, and justice.

THE PENTAD or the number 5: It is called the spherical number, because at every multiplication it restores itself or terminates the number and begins a new cycle, as for example: 5 X5=25; 9X5=45; or 5X2=10; or 5X4=20. This repetition or cyclical function causes it to become a symbol for the external motion of light through the cosmos. It is also the symbol for the unity of positive and negative qualities, because it unites the first even number, 2 and the first odd number, 3. Consequently, it was referred to as the "Sign of Marriage." To the alchemist, it depicted the quintessence, because it was derived from the other four elements.

THE HEXAD or the number 6: It is often called the perfection of parts. This appellation was given it because when it is multiplied into itself it always itself appears in the unit place. Thus, for example, 6, 36, 216, etc. This is supposed to be reflected in the tradition that the world was created in six periods or days. Man is likewise said to have been created on the sixth day. Jesus died on the cross on the sixth day of the week. The Hexad or 6 also represents the double triangle, or Hexagram. One apex or point up, and one with the point down, the combination being a symbol of the spiritual and material forces of the cosmos united in harmony.

THE HEPTAD or the number 7: Signifies abundance; it combines the four boundaries of matter--point, line, superfices, and solid, with the three intervals: length, breadth, and depth. It is also related to the various cycles and periods of human development; in other words, the ages of man, the various stages through which he passes are said to be 7 in number. The body has 7 obvious points--head, chest, abdomen, two legs, and two arms.

THE OGDOAD or the number 8: It is a mystical symbol of regeneration--888is the special number of Jesus Christ, as "He who is the resurrection and the life," and Jesus is the opposite of 666, the number of the beast. The Ogdoad also is a symbol of justice, because it consists of "even evenly numbers," and on account of its equal divisions.

THE ENNEAD or the number 9: It is said to be like the horizon "because all of the other numbers are bounded by it." It is also called perfect, because it is generated from the Triad, likewise called perfect. It was often held to be the symbol of the indestructibility of matter, the reason being that 9 multiplied by any number always reproduces itself. For example: 9X2=18, and 8+1=9.

THE DECADE or the number 10: It is the apex of numbers. It is "the accomplishment of numbers." To increase the sum, one must retrograde from the decade to the monad; in other words, back to one again, and begin over. It is likewise called the cosmos or the universe, the self-contained, of which all numbers are but expressions or manifestations. The ten Sephiroth of the Hebrew Kabbala (see article entitled, What exactly is the Kabbala?) are said to be the prototype, the essence of all things, spiritual and material, which emanate from the godhead.

Hosted by www.Geocities.ws