Monday, October 22, 2007

On number 3

Why number 3? It is peculiar to notice that several numbers such as 3 keep on recurring not only in every walk of our life, but also along historic lines. Space has 3 dimensions; every color is construed in terms of 3 primary colors (red, green, blue); there are 3 genders in most of the phonetic Indo-European languages; the most commonly encountered geometric figure is a triangle; and many more such examples.

In 2005, a study of 115 different alphabets found that most languages average 3 strokes a character. The researcher, Mark Changizi, said this is no coincidence because the number 3 happens to be the biggest number human brain can recognize without having to count.

An investigation into the origins of sacred or holy number should exclude the consideration of numbers used in merely classificatory and conventional relations, as those which naturally flow from the decimal, duodecimal, and other systems of numeration; and also the cabalistic, occult, or mystic employment of numbers, so common in the secret philosophies, as these were conscious fabrications or adaptations, in a social condition far removed from that of primitive thought.

While this study will expound more on the number 3 and things connected to it, it will be useful for a reader to know that what is universally considered a sacred number in all sciences and cultures is usually either 3 or 4 or derived from those two. This study will also include largely “unconscious” reflections of great scientists, politicians, philosophers, and scholars who tended to think, classify and divide things in 3s, without any special objective or aim. The number of “unconscious” divisions of rituals, beliefs, traditions, gods, and other cultural-religious and social aspects of human life will as well be observed. The number 3 derives its “sacredness” from the abstract, subjective operations of the intelligence, and has its main application in the imaginary and non-phenomenal world. The number 4 derives its “sacredness” from the concrete and material relations, from external perceptions, and has its application in the objective and phenomenal world.

The associations which attach sacredness to these numbers arise in the human mind and are of the same character, everywhere and at all times, hence no theory is needed to explain identities or similarities in this respect.

Ethnic character, however, tends potently to develop especially either the one or the other, either the abstract symbolism of the 3 and its derivatives, or the concrete symbolism of the 4 and its derivatives.

Here we will concentrate more on the number 3 and leave out the 4.

All operations of mind, all acts of intelligence, necessarily proceed in accordance with the 3 fundamental laws of thought, expressed in logic as the laws of Identity, Diversity, and Excluded Middle. These ever-present laws, though rarely recognized, constantly exert their power in impressing a triple form of reasoning. The form of the syllogism or the logic of Hegel with its two antitheses reconciled by a higher synthesis or the trilogies of the philosophy of Auguste Comte all bearing witness to the phenomenon.

When, as in mathematical logic of a famous British mathematician and philosopher George Boole (1815 - 1864), the syllogism is expressed in algebraic terms it is found to be represented invariably by an equation of 3 numbers, for example,

a = b + c, a symbolic notation which proves the triune nature of all subjective operations of the intelligence.

The two universal categories of understanding (or modes of perception), Space and Time, invariably present themselves in a threefold aspect: Time as the past, the present, the future, as expressed in the grammar of every language; Space as length, breadth and thickness. The primitive (letting apart mainly the plasma) perceptions of matter are likewise threefold: as solid, the earth; fluid, the water; and gaseous, the air or wind. The applications of these conceptions in mythology are most marked.

Time is represented as the past, the present, and the future. As the effects of time conceived under this threefold aspect, we have the mythical concept of the threefold energy of the gods. For example, the Indian Trimurti: Brahma, creating; Vishnu, preserving; Shiva, destroying; and the Egyptian triad, Isis, Horus, Osiris – birth, life, death. These are what the Vedas call “the 3 paths of the Being.”

From the necessary threefold relation of space and position come such expressions as “Indra, Lord of the Three Worlds;” “Creator of the Three Worlds;” the “Threefold World,” and alike; in the Latin poets “mundus triformis,” “mundus triplex,” “Jovis regnum triplex,” etc.; also the division of the Space into the Upper World, the Under World, and the Earth Plane, of which we find a primitive conception in every continent.

The Christian doctrine of Trinity (inspired by Gnostic Trinity) as well as the trinities of Buddhism and many less important faiths are well-known. According to William Westcott (1848 - 1925), a distinguished esotericist, magician and Freemason, “It is impossible to study any single system of worship throughout the world without being struck with the peculiar persistence of the triple number in regard to divinity.”

Even in ancient times when primitive peoples that inhabited the world started to take stock of their surroundings and to try to understand natural phenomena, one of first thoughts that must have certainly occurred to them was to realize that all things (trees, mountains, birds) appear in more than one instance. This thought gave birth to “counting” things. Early humans started marking the number of appearances of same or similar things. They marked on leafs, on trees, on sand, on stones. Marks made on stone were more enduring and thus, among other things, gave birth to much of cave art in later times. First durable “memories” for humans – number of their game, of their provisions of food, etc. – were engraved on stone. Thus it would have been obviously difficult to deploy an elaborate system of marking signs on stone. First humans, unconsciously, devised many fairly primitive sign-systems. And it happened that those first contemporary, evolution-wise, humans started to think, count, and mark in 3s, its multiples, and derivatives.

The Sumerian number system, the first known number system that existed in written form, used the base 60, 3 times 20 – number of fingers on both hands and feet. Mayan numerals were written with only 3 symbols: a dot for one; a line, which is a five, and the glyph of a sea shell to represent zero. Even then time and space have come to be “classified” and counted in 3s. Mayan timekeeping employed 3 different measures of time. Early Indian mathematical texts contain long discussions of the infinite, where they divide infinity in one, two and most importantly 3 dimensions – the perfection case.

The careful student of the Scriptures (in Christianity as well as Islam, Judaism, Buddhism, Hinduism, Jainism, and even some pagan faiths such as Wicca) must be struck with the frequency of the use of number 3, in connection with sacred ideas and things, from Genesis to Revelation. Orthodox Christian doctrine is based on the principle of Trinity. It is also curious that oaths are traditionally repeated 3 times. 3 is the mystic number of unity, but it is what some have called a "plural unit," a threefold symbol of unity. Frederic Farrar (1831-1903), a notable English clergyman and writer, said: “3 was to the Jews the sacred number, the number of spirit, and the number of the life of God.” 3, then, means greatness, excellence, and perfection. “3 measures” means a complete, a great measure. In the Latin and Greek tongues 3, according to Thomas Wemyss, was also mystical, owing to “its supposed perfection, because, containing a beginning, middle and end, it seemed to signify all things in the world . . . the power of all the gods, who are divided into 3 classes.”

Not only in religions, but also in many cultures the 3 is of special significance. While in many cultures such as Babylonian, Mayan, and Egyptian triads are numerous, none serves a more flagrant example than a much admired and unique Manchu (in China) culture. According to Manchu shamanism, there are 3 regions of the cosmos with 3 levels each. In many Manchu clans, from the earliest times 3 Cosmic Goddesses have been worshiped. In contemporary shamanic rituals, representations of gods in most clans are made of pieces of cloth which are placed on altar. According to the time at which rituals are held for different gods, Manchu classify their home gods into 3 types. Manchu also conceive the souls as of being composed of 3 parts (as also Babylonians, Sumerians, and ancient Greeks – starting with Plato who split the soul into three parts: the appetitive, the spirited, and the rational – did). Manchu traditional music usually consists of 3 dominant notes plus a few subsidiary notes. Some pieces of Manchu music consist of 3 notes only.

3 was also a frequent visitor to minds of religious leaders, philosophers, kings, writers, poets and even simple individuals who dared to look back and evaluate human existence in terms of history, progress, and evolution. Ever since, many of social, political and natural sciences have been conceived and systematized having many 3s in them. Those who advocated these sciences and were instrumental in their development never ceased to express themselves “unconsciously” in 3s. Not surprisingly, numerous figures in the past have viewed, for example, history as a tripartite system, evolving around 3 grand ideas, ages, principles, and events.

Joachim of Fiore (c. 1135 - 1202) argued that there have been 3 epochs, presided over by God the Father, God the Son, and the Holy Spirit respectively, during which the Old Testament, the New Testament and the “spiritual eternal Gospel” will be in force. Jean Bodin (c. 1530 - 1596), a French philosopher, divided history into 3 periods – the history of Oriental peoples, the history of Mediterranean peoples, and the history of northern peoples.

In 1620 Francis Bacon, the first person who conceived the intellectual history as such, identified 3 discoveries that set his age apart from the ancient times. “It is well to observe the force and virtue and consequences of discoveries. These are to be seen nowhere more conspicuously than in those 3 which were unknown to the ancients, and of which the origin, though recent, is obscure and inglorious; namely, printing, gunpowder, and the magnet.”

Thomas Hobbes (1588 - 1679), Bacon’s amanuensis, argued that 3 branches knowledge outweighed all others in explanatory power: physics, which studies nature; psychology, which studies man as individual; and politics, which deals with artificial and social groupings of mankind.

With the advent of the Industrial Revolution, beginning in England and spreading all over the Europe and later to the rest of the world, the number of distinctly brilliant individuals who talked in 3s dramatically increased. So, for example, many famous European philosophers and historians of 18th and 19th century constantly reminded the public in their works of the importance of the number 3, and its utmost relevance to all dimensions of social and political life of the world.

Giambattista Vico (1668 - 1744), a famous Italian philosopher, distinguished the age of the gods, the heroic age and the human age (he borrowed some of his ideas from Herodotus and Varro). He also distinguished 3 “instincts” which, he argued, shaped history, and 3 “punishments” that shaped civilization. The 3 “instincts” were a belief in Providence, the recognition of parenthood, and the instinct to bury the dead, which gave mankind the institutions of religion, family and sepulture. The 3 punishments were shame, curiosity and the need to work, which caused rise various societies, social values, and most importantly of art and science.

The French statesman Anne Robert Jacques Turgot (1727 - 1781) claimed that civilization is the product of geographical, biological and psychological factors. Yet another Frenchman, Marquis de Condorcet (1743 - 1794), believed there were 3 outstanding issues in history – the destruction of inequality between nations, the progress of equality within one and the same nation, and the perfecting of mankind.

William Godwin (1756 - 1836), an English anarchist, thought that the 3 chief ideas that would produce the all-important goal in life were literature, education, and (political) justice. Another Englishman, Thomas Carlyle (1795 - 1881), an essayist and historian, noted that “the 3 greatest elements of modern civilization [are] gunpowder, printing, and the Protestant religion.” The third Englishman, Sir James Frazer, an anthropologist, distinguished ages of magic, religion and science.

Auguste Comte (1798 - 1857) idealized 3 stages in history – theological-military, metaphysical-legalistic, and scientific-industrial.

Going further and looking upon natural sciences and those derived from those sciences. From Atomic Physics, it is known that atoms consist of three constituents: protons, neutrons, and electrons. In Mathematics, the triangle is the most durable shape possible, the only "perfect" figure, which, if all endpoints have hinges, will never change its shape unless the sides themselves are bent.

Some Economists also thought in 3s. In the Wealth of Nations (1776), Adam Smith (1723 - 1790) offered a pioneering analysis of the fundamental division of income into rents, wages and profits of stock, identifying their respective owners as the landlord, the wage-earner and the capitalist, the “3 great, original and constituent orders of every civilized society.” Even Marxism can be reduced to the number 3: an age when man knows neither surplus nor exploitation, when both surplus and exploitation are pervasive, and when surplus remains but exploitation is ended. Karl Polanyi, in The Great Transformation (1944), distinguished 3 great economic epochs – reciprocity, redistribution and the market.

Contemporary historians, economists, philosophers and politicians also seem to be prone to this “tendency” of 3.

Ernest Gellner in his book Plough, Sword and Book (1988), divides history into 3 major phases – hunting/gathering, agrarian production, and industrial production, and that these fitted with the 3 great classes if human activity – production, coercion, cognition. In 1991, Richard Tarnas, in The Passion of the Western Mind, argued that Western philosophy can be divided into 3 great epochs – as largely autonomous during the classical period, as subordinate to religion during the dominant years of Christianity, and as subordinate to science ever since.

Isaiah Berlin, the Oxford political philosopher, thought there were 3 great political/psychological turning-points in history. The first came after the death of Aristotle, when the philosophical schools of Athens “ceased to conceive of individuals as intelligible only in the context of social life … and suddenly spoke of men in terms of inner experience and individual salvation.” The second turning-point was inaugurated by Machiavelli, which involved the recognition that there is division “between the natural and the moral virtues, the assumption that political values are not merely different from, but may in principle be incompatible with, Christian ethics.” The third turning-point was the advent of romanticism.

The list of 3s can go on and on and on…


In the American (indigenous) and Mongolian races the 4 and its derivatives are almost exclusively the “ruling” holy bodies, whereas the numerous triads and trilogies of the “white” races such as Egyptians, Greeks, ancient Germans, Celts, Slavs, and Aryan Indians have been pointed out and identified by numerous scholars.

Ancient Babylonians seem to have had a decided preference for the 4 and its derivatives, and from them probably, the early Semites drew the superior sacredness which, as it is seen in the Old Testament, they so pointedly assigned to that series. This profound ethnic contrast, original or derived, perhaps prevented them, when the religious sentiment reached a high development, from accepting the Christian doctrine of Trinity.

It is thus evident that the deep-rooted notions of 3 have to do not only with cultural-religious aspects of different peoples but also, due to the “unconscious” nature of many observations and classifications, mentality and possible patterns of human thought, still vaguely explained by natural and social sciences. This, if true, would mean that these numbers, and most notably 3, and their derivatives will keep on recurring in all aspects of human life also in future, as they did in past and do in present. After all, the great Hermes Trismegistus (“thrice the great”), the father of Orphics, was a strong believer in the power of numbers, and the 3 was of vital value in his theories.

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