START A PETITION 27,000,000 members: the world's largest community for good
START A PETITION
x
Group Discussions
Pythagoras
10 years ago
The Life and Philosophy of Pythagoras http://www.sacred-texts.com/eso/sta/sta15.htm The Life and Philosophy of Pythagoras WHILE Mnesarchus, the father of Pythagoras, was in the city of Delphi on matters pertaining to his business as a merchant, he and his wife, Parthenis, decided to consult the oracle of Delphi as to whether the Fates were favorable for their return voyage to Syria. When the Pythoness (prophetess of Apollo) seated herself on the golden tripod over the yawning vent of the oracle, she did not answer the question they had asked, but told Mnesarchus that his wife was then with child and would give birth to a son who was destined to surpass all men in beauty and wisdom, and who throughout the course of his life would contribute much to the benefit of mankind. Mnesarchus was so deeply impressed by the prophecy that he changed his wife's name to Pythasis, in honor of the Pythian priestess. When the child was born at Sidon in Phťnicia, it was--as the oracle had said--a son. Mnesarchus and Pythasis named the child Pythagoras, for they believed that he had been predestined by the oracle. Many strange legends have been preserved concerning the birth of Pythagoras. Some maintained that he was no mortal man: that he was one of the gods who had taken a human body to enable him to come into the world and instruct the human race. Pythagoras was one of the many sages and saviors of antiquity for whom an immaculate conception is asserted. In his Anacalypsis, Godfrey Higgins writes: "The first striking circumstance in which the history of Pythagoras agrees with the history of Jesus is, that they were natives of nearly the same country; the former being born at Sidon, the latter at Bethlehem, both in Syria. The father of Pythagoras, as well as the father of Jesus, was prophetically informed that his wife should bring forth a son, who should be a benefactor to mankind. They were both born when their mothers were from home on journeys, Joseph and his wife having gone up to Bethlehem to be taxed, and the father of Pythagoras having travelled from Samos, his residence, to Sidon, about his mercantile concerns. Pythais [Pythasis], the mother of Pythagoras, had a connexion with an Apolloniacal spectre, or ghost, of the God Apollo, or God Sol, (of course this must have been a holy ghost, and here we have the Holy Ghost) which afterward appeared to her husband, and told him that he must have no connexion with his wife during her pregnancy--a story evidently the same as that relating to Joseph and Mary. From these peculiar circumstances, Pythagoras was known by the same title as Jesus, namely, the son of God; and was supposed by the multitude to be under the influence of Divine inspiration." This most famous philosopher was born sometime between 600 and 590 B.C., and the length of his life has been estimated at nearly one hundred years. The teachings of Pythagoras indicate that he was thoroughly conversant with the precepts of Oriental and Occidental esotericism. He traveled among the Jews and was instructed by the Rabbins concerning the secret traditions of Moses, the lawgiver of Israel. Later the School of the Essenes was conducted chiefly for the purpose of interpreting the Pythagorean symbols. Pythagoras was initiated into the Egyptian, Babylonian, and Chaldean Mysteries. Although it is believed by some that he was a disciple of Zoroaster, it is doubtful whether his instructor of that name was the God-man now revered by the Parsees. While accounts of his travels differ, historians agree that he visited many countries and studied at the feet of many masters. "After having acquired all which it was possible for him to learn of the Greek philosophers and, presumably, become an initiate in the Eleusinian mysteries, he went to Egypt, and after many rebuffs and refusals, finally succeeded in securing initiation in the Mysteries of Isis, at the hands of the priests of Thebes. Then this intrepid 'joiner' wended his way into Phoenicia and Syria where the Mysteries of Adonis were conferred upon him, and crossing to the valley of the Euphrates he tarried long enough to become versed in, the secret lore of the Chaldeans, who still dwelt in the vicinity of Babylon. Finally, he made his greatest and most historic venture through Media and Persia into Hindustan where he remained several years as a pupil and initiate of the learned Brahmins of Elephanta and Ellora." (See Ancient Freemasonry, by Frank C. Higgins, 32░.) The same author adds that the name of Pythagoras is still preserved in the records of the Brahmins as Yavancharya, the Ionian Teacher. Pythagoras was said to have been the first man to call himself a philosopher; in fact, the world is indebted to him for the word philosopher. Before that time the wise men had called themselves sages, which was interpreted to mean those who know. Pythagoras was more modest. He coined the word philosopher, which he defined as one who is attempting to find out. After returning from his wanderings, Pythagoras established a school, or as it has been sometimes called, a university, at Crotona, a Dorian colony in Southern Italy. Upon his arrival at Crotona he was regarded askance, but after a short time those holding important positions in the surrounding colonies sought his counsel in matters of great moment. He gathered around him a small group of sincere disciples whom he instructed in the secret wisdom which had been revealed to him, and also in the fundamentals of occult mathematics, music, and astronomy, which he considered to be the triangular foundation of all the arts and sciences. (continued next post)
Life and Philosophy of/Mathematics
10 years ago
When he was about sixty years old, Pythagoras married one of his disciples, and seven children resulted from the union. His wife was a remarkably able woman, who not only inspired him during the years of his life but after his assassination continued to promulgate his doctrines. As is so often the case with genius, Pythagoras by his outspokenness incurred both political and personal enmity. Among those who came for initiation was one who, because Pythagoras refused to admit him, determined to destroy both the man and his philosophy. By means of false propaganda, this disgruntled one turned the minds of the common people against the philosopher. Without warning, a band of murderers descended upon the little group of buildings where the great teacher and his disciples dwelt, burned the structures and killed Pythagoras. Accounts of the philosopher's death do not agree. Some say that he was murdered with his disciples; others that, on escaping from Crotona with a small band of followers, he was trapped and burned alive by his enemies in a little house where the band had decided to rest for the night. Another account states that, finding themselves trapped in the burning structure, the disciples threw themselves into the flames, making of their own bodies a bridge over which Pythagoras escaped, only to die of a broken heart a short time afterwards as the result of grieving over the apparent fruitlessness of his efforts to serve and illuminate mankind. His surviving disciples attempted to perpetuate his doctrines, but they were persecuted on every hand and very little remains today as a testimonial to the greatness of this philosopher. It is said that the disciples of Pythagoras never addressed him or referred to him by his own name, but always as The Master or That Man. This may have been because of the fact that the name Pythagoras was believed to consist of a certain number of specially arranged letters with great sacred significance. The Word magazine has printed an article by T. R. Prater, showing that Pythagoras initiated his candidates by means of a certain formula concealed within." Pythagorean Mathematics http://www.sacred-texts.com/eso/sta/sta16.htm CONCERNING the secret significance of numbers there has been much speculation. Though many interesting discoveries have been made, it may be safely said that with the death of Pythagoras the great key to this science was lost. For nearly 2500 years philosophers of all nations have attempted to unravel the Pythagorean skein, but apparently none has been successful. Notwithstanding attempts made to obliterate all records of the teachings of Pythagoras, fragments have survived which give clues to some of the simpler parts of his philosophy. The major secrets were never committed to writing, but were communicated orally to a few chosen disciples. These apparently dated not divulge their secrets to the profane, the result being that when death sealed their lips the arcana died with diem. Certain of the secret schools in the world today are perpetuations of the ancient Mysteries, and although it is quite possible that they may possess some of the original numerical formulŠ, there is no evidence of it in the voluminous writings which have issued from these groups during the last five hundred years. These writings, while frequently discussing Pythagoras, show no indication of a more complete knowledge of his intricate doctrines than the post-Pythagorean Greek speculators had, who talked much, wrote little, knew less, and concealed their ignorance under a series of mysterious hints and promises. Here and there among the literary products of early writers are found enigmatic statements which they made no effort: to interpret. The following example is quoted from Plutarch: "The Pythagoreans indeed go farther than this, and honour even numbers and geometrical diagrams with the names and titles of the gods. Thus they call the equilateral triangle head-born Minerva and Tritogenia, because it may be equally divided by three perpendiculars drawn from each of the angles. So the unit they term Apollo, as to the number two they have affixed the name of strife and audaciousness, and to that of three, justice. For, as doing an injury is an extreme on the one side, and suffering one is an extreme on the on the one side, and suffering in the middle between them. In like manner the number thirty-six, their Tetractys, or sacred Quaternion, being composed of the first four odd numbers added to the first four even ones, as is commonly reported, is looked upon by them as the most solemn oath they can take, and called Kosmos." (Isis and Osiris.) Earlier in the same work, Plutarch also notes: "For as the power of the triangle is expressive of the nature of Pluto, Bacchus, and Mars; and the properties of the square of Rhea, Venus, Ceres, Vesta, and Juno; of the Dodecahedron of Jupiter; so, as we are informed by Eudoxus, is the figure of fifty-six angles expressive of the nature of Typhon." Plutarch did not pretend to explain the inner significance of the symbols, but believed that the relationship which Pythagoras established between the geometrical solids and the gods was the result of images the great sage had seen in the Egyptian temples. Albert Pike, the great Masonic symbolist, admitted that there were many points concerning which he could secure no reliable information. In his Symbolism, for the 32░ and 33░, he wrote: "I do not understand why the 7 should be called Minerva, or the cube, Neptune." Further on he added: "Undoubtedly the names given by the Pythagoreans to the different numbers were themselves enigmatical and symbolic-and there is little doubt that in the time of Plutarch the meanings these names concealed were lost. Pythagoras had succeeded too well in concealing his symbols with a veil that was from the first impenetrable, without his oral explanation * * *." (continued next post)
Pythagorean Mathematics, continued
10 years ago
This uncertainty shared by all true students of the subject proves conclusively that it is unwise to make definite statements founded on the indefinite and fragmentary information available concerning the Pythagorean system of mathematical philosophy. The material which follows represents an effort to collect a few salient points from the scattered records preserved by disciples of Pythagoras and others who have since contacted his philosophy. METHOD OF SECURING THE NUMERICAL POWER OF WORDS The first step in obtaining the numerical value of a word is to resolve it back into its original tongue. Only words of Greek or Hebrew derivation can be successfully analyzed by this method, and all words must be spelled in their most ancient and complete forms. Old Testament words and names, therefore, must be translated back into the early Hebrew characters and New Testament words into the Greek. Two examples will help to clarify this principle. The Demiurgus of the Jews is called in English Jehovah, but when seeking the numerical value of the name Jehovah it is necessary to resolve the name into its Hebrew letters. It becomes יהוה, and is read from right to left. The Hebrew letters are: ה, He; ו, Vau; ה, He; י, Yod; and when reversed into the English order from left to right read: Yod-He-Vau-He. By consulting the foregoing table of letter values, it is found that the four characters of this sacred name have the following numerical significance: Yod equals 10. He equals 5, Vau equals 6, and the second He equals 5. Therefore, 10+5+6+5=26, a synonym of Jehovah. If the English letters were used, the answer obviously would not be correct. The second example is the mysterious Gnostic pantheos Abraxas. For this name the Greek table is used. Abraxas in Greek is Ἀβραξας. Α = 1, β = 2, ρ = 100, α = 1, ξ =60, α = 1, ς = 200, the sum being 365, the number of days in the year. This number furnishes the key to the mystery of Abraxas, who is symbolic of the 365 Ăons, or Spirits of the Days, gathered together in one composite personality. Abraxas is symbolic of five creatures, and as the circle of the year actually consists of 360 degrees, each of the emanating deities is one-fifth of this power, or 72, one of the most sacred numbers in the Old Testament of the Jews and in their Qabbalistic system. This same method is used in finding the numerical value of the names of the gods and goddesses of the Greeks and Jews. All higher numbers can be reduced to one of the original ten numerals, and the 10 itself to 1. Therefore, all groups of numbers resulting from the translation of names of deities into their numerical equivalents have a basis in one of the first ten numbers. By this system, in which the digits are added together, 666 becomes 6+6+6 or 18, and this, in turn, becomes 1+8 or 9. According to Revelation, 144,000 are to be saved. This number becomes 1+4+4+0+0+0, which equals 9, thus proving that both the Beast of Babylon and the number of the saved refer to man himself, whose symbol is the number 9. This system can be used successfully with both Greek and Hebrew letter values. The original Pythagorean system of numerical philosophy contains nothing to justify the practice now in vogue of changing the given name or surname in the hope of improving the temperament or financial condition by altering the name vibrations. There is also a system of calculation in vogue for the English language, but its accuracy is a matter of legitimate dispute. It is comparatively modern and has no relationship either to the Hebrew Qabbalistic system or to the Greek procedure. The claim made by some that it is Pythagorean is not supported by any tangible evidence, and there are many reasons why such a contention is untenable. The fact that Pythagoras used 10 as the basis of calculation, while this system uses 9--an imperfect number--is in itself almost conclusive. Furthermore, the arrangement of the Greek and Hebrew letters does not agree closely enough with the English to permit the application of the number sequences of one language to the number sequences of the others. Further experimentation with the system may prove profitable, but it is without basis in antiquity. The arrangement of the letters and numbers is as followssee diagram on link) The letters under each of the numbers have the value of the figure at: the top of the column. Thus, in the word man, M = 4, A = 1, N = 5: a total of 10. The values of the numbers are practically the same as those given by the Pythagorean system. AN INTRODUCTION TO THE PYTHAGOREAN THEORY OF NUMBERS (The following outline of Pythagorean mathematics is a paraphrase of the opening chapters of Thomas Taylor's Theoretic Arithmetic, the rarest and most important compilation of Pythagorean mathematical fragments extant.) The Pythagoreans declared arithmetic to be the mother of the mathematical sciences. This is proved by the fact that geometry, music, and astronomy are dependent upon it but it is not dependent upon them. Thus, geometry may be removed but arithmetic will remain; but if arithmetic be removed, geometry is eliminated. In the same manner music depends upon arithmetic, but the elimination of music affects arithmetic only by limiting one of its expressions. The Pythagoreans also demonstrated arithmetic to be prior to astronomy, for the latter is dependent upon both geometry and music. The size, form, and motion of the celestial bodies is determined by the use of geometry; their harmony and rhythm by the use of music. If astronomy be removed, neither geometry nor music is injured; but if geometry and music be eliminated, astronomy is destroyed. The priority of both geometry and music to astronomy is therefore established. Arithmetic, however, is prior to all; it is primary and fundamental. (continued next post)
Pythagorean Mathematics, continued
10 years ago
Pythagoras instructed his disciples that the science of mathematics is divided into two major parts. The first is concerned with the multitude, or the constituent parts of a thing, and the second with the magnitude, or the relative size or density of a thing. Magnitude is divided into two parts--magnitude which is stationary and magnitude which is movable, the stationary pare having priority. Multitude is also divided into two parts, for it is related both to itself and to other things, the first relationship having priority. Pythagoras assigned the science of arithmetic to multitude related to itself, and the art of music to multitude related to other things. Geometry likewise was assigned to stationary magnitude, and spherics (used partly in the sense of astronomy) to movable magnitude. Both multitude and magnitude were circumscribed by the circumference of mind. The atomic theory has proved size to be the result of number, for a mass is made up of minute units though mistaken by the uninformed for a single simple substance. Owing to the fragmentary condition of existing Pythagorean records, it is difficult to arrive at exact definitions of terms. Before it is possible, however, to unfold the subject further some light must he cast upon the meanings of the words number, monad, and one. The monad signifies (a) the all-including ONE. The Pythagoreans called the monad the "noble number, Sire of Gods and men." The monad also signifies (b) the sum of any combination of numbers considered as a whole. Thus, the universe is considered as a monad, but the individual parts of the universe (such as the planets and elements) are monads in relation to the parts of which they themselves are composed, though they, in turn, are parts of the greater monad formed of their sum. The monad may also be likened (c) to the seed of a tree which, when it has grown, has many branches (the numbers). In other words, the numbers are to the monad what the branches of the tree are to the seed of the tree. From the study of the mysterious Pythagorean monad, Leibnitz evolved his magnificent theory of the world atoms--a theory in perfect accord with the ancient teachings of the Mysteries, for Leibnitz himself was an initiate of a secret school. By some Pythagoreans the monad is also considered (d) synonymous with the one. Number is the term applied to all numerals and their combinations. (A strict interpretation of the term number by certain of the Pythagoreans excludes 1 and 2.) Pythagoras defines number to be the extension and energy of the spermatic reasons contained in the monad. The followers of Hippasus declared number to be the first pattern used by the Demiurgus in the formation of the universe. The one was defined by the Platonists as "the summit of the many." The one differs from the monad in that the term monad is used to designate the sum of the parts considered as a unit, whereas the one is the term applied to each of its integral parts. There are two orders of number: odd and even. Because unity, or 1, always remains indivisible, the odd number cannot be divided equally. Thus, 9 is 4+1+4, the unity in the center being indivisible. Furthermore, if any odd number be divided into two parts, one part will always be odd and the other even. Thus, 9 may be 5+4, 3+6, 7+2, or 8+1. The Pythagoreans considered the odd number--of which the monad was the prototype--to be definite and masculine. They were not all agreed, however, as to the nature of unity, or 1. Some declared it to be positive, because if added to an even (negative) number, it produces an odd (positive) number. Others demonstrated that if unity be added to an odd number, the latter becomes even, thereby making the masculine to be feminine. Unity, or 1, therefore, was considered an androgynous number, partaking of both the masculine and the feminine attributes; consequently both odd and even. For this reason the Pythagoreans called it evenly-odd. It was customary for the Pythagoreans to offer sacrifices of an uneven number of objects to the superior gods, while to the goddesses and subterranean spirits an even number was offered. Any even number may be divided into two equal parts, which are always either both odd or both even. Thus, 10 by equal division gives 5+5, both odd numbers. The same principle holds true if the 10 be unequally divided. For example, in 6+4, both parts are even; in 7+3, both parts are odd; in 8+2, both parts are again even; and in 9+1, both parts are again odd. Thus, in the even number, however it may be divided, the parts will always be both odd or both even. The Pythagoreans considered the even number-of which the duad was the prototype--to be indefinite and feminine. The odd numbers are divided by a mathematical contrivance--called "the Sieve of Eratosthenes"--into three general classes: incomposite, composite, and incomposite-composite. The incomposite numbers are those which have no divisor other than themselves and unity, such as 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and so forth. For example, 7 is divisible only by 7, which goes into itself once, and unity, which goes into 7 seven times. The composite numbers are those which are divisible not only by themselves and unity but also by some other number, such as 9, 15, 21, 25, 27, 33, 39, 45, 51, 57, and so forth. For example, 21 is divisible not only by itself and by unity, but also by 3 and by 7. The incomposite-composite numbers are those which have no common divisor, although each of itself is capable of division, such as 9 and 25. For example, 9 is divisible by 3 and 25 by 5, but neither is divisible by the divisor of the other; thus they have no common divisor. Because they have individual divisors, they are called composite; and because they have no common divisor, they are called in, composite. Accordingly, the term incomposite-composite was created to describe their properties. (continued next post)
Pythagorean Mathematics, continued
10 years ago
Even numbers are divided into three classes: evenly-even, evenly-odd, and oddly-odd. The evenly-even numbers are all in duple ratio from unity; thus: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1,024. The proof of the perfect evenly-even number is that it can be halved and the halves again halved back to unity, as 1/2 of 64 = 32; 1/2 of 32 = 16; 1/2 of 16 = 8; 1/2 of 8 = 4; 1/2 of 4 = 2; 1/2 of 2 = 1; beyond unity it is impossible to go. The evenly-even numbers possess certain unique properties. The sum of any number of terms but the last term is always equal to the last term minus one. For example: the sum of the first and second terms (1+2) equals the third term (4) minus one; or, the sum of the first, second, third, and fourth terms (1+2+4+8) equals the fifth term (16) minus one. In a series of evenly-even numbers, the first multiplied by the last equals the last, the second multiplied by the second from the last equals the last, and so on until in an odd series one number remains, which multiplied by itself equals the last number of the series; or, in an even series two numbers remain, which multiplied by each other give the last number of the series. For example: 1, 2, 4, 8, 16 is an odd series. The first number (1) multiplied by the last number (16) equals the last number (16). The second number (2) multiplied by the second from the last number (8) equals the last number (16). Being an odd series, the 4 is left in the center, and this multiplied by itself also equals the last number (16). The evenly-odd numbers are those which, when halved, are incapable of further division by halving. They are formed by taking the odd numbers in sequential order and multiplying them by 2. By this process the odd numbers 1, 3, 5, 7, 9, 11 produce the evenly-odd numbers, 2, 6, 10, 14, 18, 22. Thus, every fourth number is evenly-odd. Each of the even-odd numbers may be divided once, as 2, which becomes two 1's and cannot be divided further; or 6, which becomes two 3's and cannot be divided further. Another peculiarity of the evenly-odd numbers is that if the divisor be odd the quotient is always even, and if the divisor be even the quotient is always odd. For example: if 18 be divided by 2 (an even divisor) the quotient is 9 (an odd number); if 18 be divided by 3 (an odd divisor) the quotient is 6 (an even number). The evenly-odd numbers are also remarkable in that each term is one-half of the sum of the terms on either side of it. For example: 10 is one-half of the sum of 6 and 14; 18 is one-half the sum of 14 and 22; and 6 is one-half the sum of 2 and 10. The oddly-odd, or unevenly-even, numbers are a compromise between the evenly-even and the evenly-odd numbers. Unlike the evenly-even, they cannot be halved back to unity; and unlike the evenly-odd, they are capable of more than one division by halving. The oddly-odd numbers are formed by multiplying the evenly-even numbers above 2 by the odd numbers above one. The odd numbers above one are 3, 5, 7, 9, 11, and so forth. The evenly-even numbers above 2 are 4, 8, 16, 32, 64, and soon. The first odd number of the series (3) multiplied by 4 (the first evenly-even number of the series) gives 12, the first oddly-odd number. By multiplying 5, 7, 9, 11, and so forth, by 4, oddly-odd numbers are found. The other oddly-odd numbers are produced by multiplying 3, 5, 7, 9, 11, and so forth, in turn, by the other evenly-even numbers (8, 16, 32, 64, and so forth). An example of the halving of the oddly-odd number is as follows: 1/2 of 12 = 6; 1/2 of 6 = 3, which cannot be halved further because the Pythagoreans did not divide unity. Even numbers are also divided into three other classes: superperfect, deficient, and perfect. Superperfect or superabundant numbers are such as have the sum of their fractional parts greater than themselves. For example: 1/2 of 24 = 12; 1/4 = 6; 1/3 = 8; 1/6 = 4; 1/12 = 2; and 1/24 = 1. The sum of these parts (12+6+8+4+2+1) is 33, which is in excess of 24, the original number. Deficient numbers are such as have the sum of their fractional parts less than themselves. For example: 1/2 of 14 = 7; 1/7 = 2; and 1/14 = 1. The sum of these parts (7+2+1) is 10, which is less than 14, the original number. Perfect numbers are such as have the sum of their fractional parts equal to themselves. For example: 1/2 of 28 = 14; 1/4 = 7; 1/7 = 4; 1/14 = 2; and 1/28 = 1. The sum of these parts (14+7+4+2+1) is equal to 28. The perfect numbers are extremely rare. There is only one between 1 and 10, namely, 6; one between 10 and 100, namely, 28; one between 100 and 1,000, namely, 496; and one between 1,000 and 10,000, namely, 8,128. The perfect numbers are found by the following rule: The first number of the evenly-even series of numbers (1, 2, 4, 8, 16, 32, and so forth) is added to the second number of the series, and if an incomposite number results it is multiplied by the last number of the series of evenly-even numbers whose sum produced it. The product is the first perfect number. For example: the first and second evenly-even numbers are 1 and 2. Their sum is 3, an incomposite number. If 3 be multiplied by 2, the last number of the series of evenly-even numbers used to produce it, the product is 6, the first perfect number. If the addition of the evenly-even numbers does not result in an incomposite number, the next evenly-even number of the series must be added until an incomposite number results. The second perfect number is found in the following manner: The sum of the evenly-even numbers 1, 2, and 4 is 7, an incomposite number. If 7 be multiplied by 4 (the last of the series of evenly-even numbers used to produce it) the product is 28, the second perfect number. This method of calculation may be continued to infinity. (continued next post)
Pythagorean Mathematics, continued
10 years ago
Perfect numbers when multiplied by 2 produce superabundant numbers, and when divided by 2 produce deficient numbers. The Pythagoreans evolved their philosophy from the science of numbers. The following quotation from Theoretic Arithmetic is an excellent example of this practice: "Perfect numbers, therefore, are beautiful images of the virtues which are certain media between excess and defect, and are not summits, as by some of the ancients they were supposed to be. And evil indeed is opposed to evil, but both are opposed to one good. Good, however, is never opposed to good, but to two evils at one and the same time. Thus timidity is opposed to audacity, to both [of] which the want of true courage is common; but both timidity and audacity are opposed to fortitude. Craft also is opposed to fatuity, to both [of] which the want of intellect is common; and both these are opposed to prudence. Thus, too, profusion is opposed to avarice, to both [of] which illiberality is common; and both these are opposed to liberality. And in a similar manner in the other virtues; by all [of] which it is evident that perfect numbers have a great similitude to the virtues. But they also resemble the virtues on another account; for they are rarely found, as being few, and they are generated in a very constant order. On the contrary, an infinite multitude of superabundant and diminished numbers may be found, nor are they disposed in any orderly series, nor generated from any certain end; and hence they have a great similitude to the vices, which are numerous, inordinate, and indefinite." THE TABLE OF THE TEN NUMBERS (The following outline of the Pythagorean numbers is a paraphrase of the writings of Nicomachus, Theon of Smyrna, Proclus, Porphyry, Plutarch, Clement of Alexandria, Aristotle, and other early authorities.) Monad--1--is so called because it remains always in the same condition--that is, separate from multitude. Its attributes are as follows: It is called mind, because the mind is stable and has preeminence; hermaphrodism, because it is both male and female; odd and even, for being added to the even it makes odd, and to the odd, even; God, because it is the beginning and end of all, but itself has neither beginning nor end; good, for such is the nature of God; the receptacle of matter, because it produces the duad, which is essentially material. By the Pythagoreans monad was called chaos, obscurity, chasm, Tartarus, Styx, abyss, Lethe, Atlas, Axis, Morpho (a name for Venus), and Tower or Throne of Jupiter, because of the great power which abides in the center of the universe and controls the circular motion of the planers about itself. Monad is also called germinal reason, because it is the origin of all the thoughts in the universe. Other names given to it were: Apollo, because of its relation to the sun; Prometheus, because he brought man light; Pyralios, one who exists in fire; geniture, because without it no number can exist; substance, because substance is primary; cause of truth; and constitution of symphony: all these because it is the primordial one. Between greater and lesser the monad is equal; between intention and remission it is middle; in multitude it is mean; and in time it is now, because p. 72 eternity knows neither past nor future. It is called Jupiter, because he is Father and head of the gods; Vesta, the fire of the home, because it is located in the midst of the universe and remains there inclining to no side as a dot in a circle; form, because it circumscribes, comprehends, and terminates; love, concord, and piety, because it is indivisible. Other symbolic names for the monad are ship, chariot, Proteus (a god capable of changing his form), Mnemosyne, and Polyonymous (having many names). The following symbolic names were given to the duad--2--because it has been divided, and is two rather than one; and when there are two, each is opposed to the other: genius, evil, darkness, inequality, instability, movability, boldness, fortitude, contention, matter, dissimilarity, partition between multitude and monad, defect, shapelessness, indefiniteness, indeterminate ness, harmony, tolerance, root, feet of fountain-abounding idea, top, Phanes, opinion, fallacy, alterity, diffidence, impulse, death, motion, generation, mutation, division, longitude, augmentation, composition, communion, misfortune, sustentation, imposition, marriage, soul, and science. In his book, Numbers, W. Wynn Westcott says of the duad: "it was called 'Audacity,' from its being the earliest number to separate itself from the Divine One; from the 'Adytum of God-nourished Silence,' as the Chaldean oracles say." As the monad is the father, so the duad is the mother; therefore, the duad has certain points in common with the goddesses Isis, Rhea (Jove's mother), Phrygia, Lydia, Dindymene (Cybele), and Ceres; Erato (one of the Muses); Diana, because the moon is forked; Dictynna, Venus, Dione, Cytherea; Juno, because she is both wife and sister of Jupiter; and Maia, the mother of Mercury. While the monad is the symbol of wisdom, the duad is the symbol of ignorance, for in it exists the sense of separateness--which sense is the beginning of ignorance. The duad, however, is also the mother of wisdom, for ignorance--out of the nature of itself--invariably gives birth to wisdom. (continued next post)
Pythagorean Mathematics, continued
10 years ago
The Pythagoreans revered the monad but despised the duad, because it was the symbol of polarity. By the power of the duad the deep was created in contradistinction to the heavens. The deep mirrored the heavens and became the symbol of illusion, for the below was merely a reflection of the above. The below was called maya, the illusion, the sea, the Great Void, and to symbolize it the Magi of Persia carried mirrors. From the duad arose disputes and contentions, until by bringing the monad between the duad, equilibrium was reestablished by the Savior-God, who took upon Himself the form of a number and was crucified between two thieves for the sins of men. The triad--3--is the first number actually odd (monad not always being considered a number). It is the first equilibrium of unities; therefore, Pythagoras said that Apollo gave oracles from a tripod, and advised offer of libation three times. The keywords to the qualities of the triad are friendship, peace, justice, prudence, piety, temperance, and virtue. The following deities partake of the principles of the triad: Saturn (ruler of time), Latona, CornucopiŠ, Ophion (the great serpent), Thetis, Hecate, Polyhymnia (a Muse), Pluto, Triton, President of the Sea, Tritogenia, Achelous, and the Faces, Furies, and Graces. This number is called wisdom, because men organize the present, foresee the future, and benefit by the experiences of the fast. It is cause of wisdom and understanding. The triad is the number of knowledge--music, geometry, and astronomy, and the science of the celestials and terrestrials. Pythagoras taught that the cube of this number had the power of the lunar circle. The sacredness of the triad and its symbol--the triangle--is derived from the fact that it is made up of the monad and the duad. The monad is the symbol of the Divine Father and the duad of the Great Mother. The triad being made of these two is therefore androgynous and is symbolic of the fact that God gave birth to His worlds out of Himself, who in His creative aspect is always symbolized by the triangle. The monad passing into the duad was thus capable of becoming the parent of progeny, for the duad was the womb of Meru, within which the world was incubated and within which it still exists in embryo. The tetrad--4--was esteemed by the Pythagoreans as the primogenial number, the root of all things, the fountain of Nature and the most perfect number. All tetrads are intellectual; they have an emergent order and encircle the world as the Empyreum passes through it. Why the Pythagoreans expressed God as a tetrad is explained in a sacred discourse ascribed to Pythagoras, wherein God is called the Number of Numbers. This is because the decad, or 10, is composed of 1, 2, 3, and 4. The number 4 is symbolic of God because it is symbolic of the first four numbers. Moreover, the tetrad is the center of the week, being halfway between 1 and 7. The tetrad is also the first geometric solid. Pythagoras maintained that the soul of man consists of a tetrad, the four powers of the soul being mind, science, opinion, and sense. The tetrad connects all beings, elements, numbers, and seasons; nor can anything be named which does not depend upon the tetractys. It is the Cause and Maker of all things, the intelligible God, Author of celestial and sensible good, Plutarch interprets this tetractys, which he said was also called the world, to be 36, consisting of the first four odd numbers added to the first four even numbers, thus: 1 + 3 +5 +7 = 16 2 + 4 + 6 + 8= 20 which together equal 36. Keywords given to the tetrad are impetuosity, strength, virility, two-mothered, and the key keeper of Nature, because the universal constitution cannot be without it. It is also called harmony and the first profundity. The following deities partook of the nature of the tetrad: Hercules, Mercury, Vulcan, Bacchus, and Urania (one of the Muses). The triad represents the primary colors and the major planets, while the tetrad represents the secondary colors and the minor planets. From the first triangle come forth the seven spirits, symbolized by a triangle and a square. These together form the Masonic apron. The pentad--5--is the union of an odd and an even number (3 and 2). Among the Greeks, the pentagram was a sacred symbol of light, health, and vitality. It also symbolized the fifth element--ether--because it is free from the disturbances of the four lower elements. It is called equilibrium, because it divides the perfect number 10 into two equal parts. The pentad is symbolic of Nature, for, when multiplied by itself it returns into itself, just as grains of wheat, starting in the form of seed, pass through Nature's processes and reproduce the seed of the wheat as the ultimate form of their own growth. Other numbers multiplied by themselves produce other numbers, but only 5 and 6 multiplied by themselves represent and retain their original number as the last figure in their products. The pentad represents all the superior and inferior beings. It is sometimes referred to as the hierophant, or the priest of the Mysteries, because of its connection with the spiritual ethers, by means of which mystic development is attained. Keywords of the pentad are reconciliation, alternation, marriage, immortality, cordiality, Providence, and sound. Among the deities who partook of the nature of the pentad were Pallas, Nemesis, Bubastia (Bast), Venus, Androgynia, Cytherea, and the messengers of Jupiter. The tetrad (the elements) plus the monad equals the pentad. The Pythagoreans taught that the elements of earth, fire, air, and water were permeated by a substance called ether--the basis of vitality and life. Therefore, they chose the five-pointed star, or pentagram, as the symbol of vitality, health, and interpenetration. (continued next post)
Pythagorean Mathematics, continued
10 years ago
It was customary for the philosophers to conceal the element of earth under the symbol of a dragon, and many of the heroes of antiquity were told to go forth and slay the dragon. Hence, they drove their sword (the monad) into the body of the dragon (the tetrad). This resulted in the formation of the pentad, a symbol of the victory of the spiritual nature over the material nature. The four elements are symbolized in the early Biblical writings as the four rivers that poured out of Garden of Eden. The elements themselves are under the control of the composite Cherubim of Ezekiel. The Pythagoreans held the hexad--6--to represent, as Clement of Alexandria conceived, the creation of the world according to both the prophets and the ancient Mysteries. It was called by the Pythagoreans the perfection of all the parts. This number was particularly sacred to Orpheus, and also to the Fate, Lachesis, and the Muse, Thalia. It was called the form of forms, the articulation of the universe, and the maker of the soul. Among the Greeks, harmony and the soul were considered to be similar in nature, because all souls are harmonic. The hexad is also the symbol of marriage, because it is formed by the union of two triangles, one masculine and the other feminine. Among the keywords given to the hexad are: time, for it is the measure of duration; panacea, because health is equilibrium, and the hexad is a balance number; the world, because the world, like the hexad, is often seen to consist of contraries by harmony; omnisufficient, because its parts are sufficient for totality (3 +2 + 1 = 6); unwearied, because it contains the elements of immortality. By the Pythagoreans the heptad--7--was called "worthy of veneration." It was held to be the number of religion, because man is controlled by seven celestial spirits to whom it is proper for him to make offerings. It was called the number of life, because it was believed that human creatures born in the seventh month of embryonic life usually lived, but those born in the eighth month often died. One author called it the Motherless Virgin, Minerva, because it was nor born of a mother but out of the crown, or the head of the Father, the monad. Keywords of the heptad are fortune, occasion, custody, control, government, judgment, dreams, voices, sounds, and that which leads all things to their end. Deities whose attributes were expressed by the heptad were Ăgis, Osiris, Mars, and Cleo (one of the Muses). Among many ancient nations the heptad is a sacred number. The Elohim of the Jews were supposedly seven in number. They were the Spirits of the Dawn, more commonly known as the Archangels controlling the planets. The seven Archangels, with the three spirits controlling the sun in its threefold aspect, constitute the 10, the sacred Pythagorean decad. The mysterious Pythagorean tetractys, or four rows of dots, increasing from 1 to 4, was symbolic of the stages of creation. The great Pythagorean truth that all things in Nature are regenerated through the decad, or 10, is subtly preserved in Freemasonry through these grips being effected by the uniting of 10 fingers, five on the hand of each person. The 3 (spirit, mind, and soul) descend into the 4 (the world), the sum being the 7, or the mystic nature of man, consisting of a threefold spiritual body and a fourfold material form. These are symbolized by the cube, which has six surfaces and a mysterious seventh point within. The six surfaces are the directions: north, east, south, west, up, and down; or, front, back, right, left, above, and below; or again, earth, fire, air, water, spirit, and matter. In the midst of these stands the 1, which is the upright figure of man, from whose center in the cube radiate six pyramids. From this comes the great occult axiom: "The center is the father of the directions, the dimensions, and the distances." The heptad is the number of the law, because it is the number of the Makers of Cosmic law, the Seven Spirits before the Throne. The ogdoad--8--was sacred because it was the number of the first cube, which form had eight corners, and was the only evenly-even number under 10 (1-2-4-8-4-2-1). Thus, the 8 is divided into two 4's, each 4 is divided into two 2's, and each 2 is divided into two 1's, thereby reestablishing the monad. Among the keywords of the ogdoad are love, counsel, prudence, law, and convenience. Among the divinities partaking of its nature were Panarmonia, Rhea, Cibele, CadmŠa, Dindymene, Orcia, Neptune, Themis, and Euterpe (a Muse). The ogdoad was a mysterious number associated with the Eleusinian Mysteries of Greece and the Cabiri. It was called the little holy number. It derived its form partly from the twisted snakes on the Caduceus of Hermes and partly from the serpentine motion of the celestial bodies; possibly also from the moon's nodes. The ennead--9--was the first square of an odd number (3x3). It was associated with failure and shortcoming because it fell short of the perfect number 10 by one. It was called the called the number of man, because of the nine months of his embryonic life. Among its keywords are ocean and horizon, because to the ancients these were boundless. The ennead is the limitless number because there is nothing beyond it but the infinite 10. It was called boundary and limitation, because it gathered all numbers within itself. It was called the sphere of the air, because it surrounded the numbers as air surrounds the earth, Among the gods and goddesses who partook in greater or less degree of its nature were Prometheus, Vulcan, Juno, the sister and wife of Jupiter, PŠan, and Aglaia, Tritogenia, Curetes, Proserpine, Hyperion, and Terpsichore (a Muse). (continued next post)
Pythagorean Mathematics, continued
10 years ago
The 9 was looked upon as evil, because it was an inverted 6. According to the Eleusinian Mysteries, it was the number of the spheres through which the consciousness passed on its way to birth. Because of its close resemblance to the spermatozoon, the 9 has been associated with germinal life. The decad--10--according to the Pythagoreans, is the greatest of numbers, not only because it is the tetractys (the 10 dots) but because it comprehends all arithmetic and harmonic proportions. Pythagoras said that 10 is the nature of number, because all nations reckon to it and when they arrive at it they return to the monad. The decad was called both heaven and the world, because the former includes the latter. Being a perfect number, the decad was applied by the Pythagoreans to those things relating to age, power, faith, necessity, and the power of memory. It was also called unwearied, because, like God, it was tireless. The Pythagoreans divided the heavenly bodies into ten orders. They also stated that the decad perfected all numbers and comprehended within itself the nature of odd and even, moved and unmoved, good and ill. They associated its power with the following deities: Atlas (for it carried the numbers on its shoulders), Urania, Mnemosyne, the Sun, Phanes, and the One God. The decimal system can probably be traced back to the time when it was customary to reckon on the fingers, these being among the most primitive of calculating devices and still in use among many aboriginal peoples.
The Pythagorean Theory of Music and Color
10 years ago
http://www.sacred-texts.com/eso/sta/sta19.htm HARMONY is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form. The universe is made up of successive gradations of good, these gradations ascending from matter (which is the least degree of good) to spirit (which is the greatest degree of good). In man, his superior nature is the summum bonum. It therefore follows that his highest nature most readily cognizes good because the good external to him in the world is in harmonic ratio with the good present in his soul. What man terms evil is therefore, in common with matter, merely the least degree of its own opposite. The least degree of good presupposes likewise the least degree of harmony and beauty. Thus deformity (evil) is really the least harmonious combination of elements naturally harmonic as individual units. Deformity is unnatural, for, the sum of all things being the Good, it is natural that all things should partake of the Good and be arranged in combinations that are harmonious. Harmony is the manifesting expression of the Will of the eternal Good. THE PHILOSOPHY OF MUSIC It is highly probable that the Greek initiates gained their knowledge of the philosophic and therapeutic aspects of music from the Egyptians, who, in turn, considered Hermes the founder of the art. According to one legend, this god constructed the first lyre by stretching strings across the concavity of a turtle shell. Both Isis and Osiris were patrons of music and poetry. Plato, in describing the antiquity of these arts among the Egyptians, declared that songs and poetry had existed in Egypt for at least ten thousand years, and that these were of such an exalted and inspiring nature that only gods or godlike men could have composed them. In the Mysteries the lyre was regarded as the secret symbol of the human constitution, the body of the instrument representing the physical form, the strings the nerves, and the musician the spirit. Playing upon the nerves, the spirit thus created the harmonies of normal functioning, which, however, became discords if the nature of man were defiled. While the early Chinese, Hindus, Persians, Egyptians, Israelites, and Greeks employed both vocal and instrumental music in their religious ceremonials, also to complement their poetry and drama, it remained for Pythagoras to raise the art to its true dignity by demonstrating its mathematical foundation. Although it is said that he himself was not a musician, Pythagoras is now generally credited with the discovery of the diatonic scale. Having first learned the divine theory of music from the priests of the various Mysteries into which he had been accepted, Pythagoras pondered for several years upon the laws governing consonance and dissonance. How he actually solved the problem is unknown, but the following explanation has been invented. One day while meditating upon the problem of harmony, Pythagoras chanced to pass a brazier's shop where workmen were pounding out a piece of metal upon an anvil. By noting the variances in pitch between the sounds made by large hammers and those made by smaller implements, and carefully estimating the harmonies and discords resulting from combinations of these sounds, he gained his first clue to the musical intervals of the diatonic scale. He entered the shop, and after carefully examining the tools and making mental note of their weights, returned to his own house and constructed an arm of wood so that it: extended out from the wall of his room. At regular intervals along this arm he attached four cords, all of like composition, size, and weight. To the first of these he attached a twelve-pound weight, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight. These different weights corresponded to the sizes of the braziers' hammers. Pythagoras thereupon discovered that the first and fourth strings when sounded together produced the harmonic interval of the octave, for doubling the weight had the same effect as halving the string. The tension of the first string being twice that of the fourth string, their ratio was said to be 2:1, or duple. By similar experimentation he ascertained that the first and third string produced the harmony of the diapente, or the interval of the fifth. The tension of the first string being half again as much as that of the third string, their ratio was said to be 3:2, or sesquialter. Likewise the second and fourth strings, having the same ratio as the first and third strings, yielded a diapente harmony. Continuing his investigation, Pythagoras discovered that the first and second strings produced the harmony of the diatessaron, or the interval of the third; and the tension of the first string being a third greater than that of the second string, their ratio was said to be 4:3, or sesquitercian. The third and fourth strings, having the same ratio as the first and second strings, produced another harmony of the diatessaron. According to Iamblichus, the second and third strings had the ratio of 8:9, or epogdoan. (continued next post)
The Pythagorean Theory of Music and Color, continued
10 years ago
The key to harmonic ratios is hidden in the famous Pythagorean tetractys, or pyramid of dots. The tetractys is made up of the first four numbers--1, 2, 3, and 4--which in their proportions reveal the intervals of the octave, the diapente, and the diatessaron. While the law of harmonic intervals as set forth above is true, it has been subsequently proved that hammers striking metal in the manner described will not produce the various tones ascribed to them. In all probability, therefore, Pythagoras actually worked out his theory of harmony from the monochord--a contrivance consisting of a single string stretched between two pegs and supplied with movable frets. To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws. Having once established music as an exact science, Pythagoras applied his newly found law of harmonic intervals to all the phenomena of Nature, even going so far as to demonstrate the harmonic relationship of the planets, constellations, and elements to each other. A notable example of modern corroboration of ancient philosophical reaching is that of the progression of the elements according to harmonic ratios. While making a list of the elements in the ascending order of their atomic weights, John A. Newlands discovered at every eighth element a distinct repetition of properties. This discovery is known as the law of octaves in modern chemistry. Since they held that harmony must be determined not by the sense perceptions but by reason and mathematics, the Pythagoreans called themselves Canonics, as distinguished from musicians of the Harmonic School, who asserted taste and instinct to be the true normative principles of harmony. Recognizing, however, the profound effect: of music upon the senses and emotions, Pythagoras did not hesitate to influence the mind and body with what he termed "musical medicine." Pythagoras evinced such a marked preference for stringed instruments that he even went so far as to warn his disciples against allowing their ears to be defiled by the sounds of flutes or cymbals. He further declared that the soul could be purified from its irrational influences by solemn songs sung to the accompaniment of the lyre. In his investigation of the therapeutic value of harmonics, Pythagoras discovered that the seven modes--or keys--of the Greek system of music had the power to incite or allay the various emotions. It is related that while observing the stars one night he encountered a young man befuddled with strong drink and mad with jealousy who was piling %#&!*% about his mistress' door with the intention of burning the house. The frenzy of the youth was accentuated by a flutist a short distance away who was playing a tune in the stirring Phrygian mode. Pythagoras induced the musician to change his air to the slow, and rhythmic Spondaic mode, whereupon the intoxicated youth immediately became composed and, gathering up his bundles of wood, returned quietly to his own home. There is also an account of how Empedocles, a disciple of Pythagoras, by quickly changing the mode of a musical composition he was playing, saved the life of his host, Anchitus, when the latter was threatened with death by the sword of one whose father he had condemned to public execution. It is also known that Esculapius, the Greek physician, cured sciatica and other diseases of the nerves by blowing a loud trumpet in the presence of the patient. Pythagoras cured many ailments of the spirit, soul, and body by having certain specially prepared musical compositions played in the presence of the sufferer or by personally reciting short selections from such early poets as Hesiod and Homer. In his university at Crotona it was customary for the Pythagoreans to open and to close each day with songs--those in the morning calculated to clear the mind from sleep and inspire it to the activities of the coming day; those in the evening of a mode soothing, relaxing, and conducive to rest. At the vernal equinox, Pythagoras caused his disciples to gather in a circle around one of their number who led them in song and played their accompaniment upon a lyre. The therapeutic music of Pythagoras is described by Iamblichus thus: "And there are certain melodies devised as remedies against the passions of the soul, and also against despondency and lamentation, which Pythagoras invented as things that afford the greatest assistance in these maladies. And again, he employed other melodies against rage and anger, and against every aberration of the soul. There is also another kind of modulation invented as a remedy against desires." (See The Life of Pythagoras.) (continued next post)
The Pythagorean Theory of Music and Color, continued
10 years ago
It is probable that the Pythagoreans recognized a connection between the seven Greek modes and the planets. As an example, Pliny declares that Saturn moves in the Dorian mode and Jupiter in the Phrygian mode. It is also apparent that the temperaments are keyed to the various modes, and the passions likewise. Thus, anger--which is a fiery passion--may be accentuated by a fiery mode or its power neutralized by a watery mode. The far-reaching effect exercised by music upon the culture of the Greeks is thus summed up by Emil Nauman: "Plato depreciated the notion that music was intended solely to create cheerful and agreeable emotions, maintaining rather that it should inculcate a love of all that is noble, and hatred of all that is mean, and that nothing could more strongly influence man's innermost feelings than melody and rhythm. Firmly convinced of this, he agreed with Damon of Athens, the musical instructor of Socrates, that the introduction of a new and presumably enervating scale would endanger the future of a whole nation, and that it was not possible to alter a key without shaking the very foundations of the State. Plato affirmed that music which ennobled the mind was of a far higher kind than that which merely appealed to the senses, and he strongly insisted that it was the paramount duty of the Legislature to suppress all music of an effeminate and lascivious character, and to encourage only s that which was pure and dignified; that bold and stirring melodies were for men, gentle and soothing ones for women. From this it is evident that music played a considerable part in the education of the Greek youth. The greatest care was also to be taken in the selection of instrumental music, because the absence of words rendered its signification doubtful, and it was difficult to foresee whether it would exercise upon the people a benign or baneful influence. Popular taste, being always tickled by sensuous and meretricious effects, was to be treated with deserved contempt. (See The History of Music.) Even today martial music is used with telling effect in times of war, and religious music, while no longer developed in accordance with the ancient theory, still profoundly influences the emotions of the laity. THE MUSIC OF THE SPHERES The most sublime but least known of all the Pythagorean speculations was that of sidereal harmonics. It was said that of all men only Pythagoras heard the music of the spheres. Apparently the Chaldeans were the first people to conceive of the heavenly bodies joining in a cosmic chant as they moved in stately manner across the sky. Job describes a time "when the stars of the morning sang together," and in The Merchant of Venice the author of the Shakesperian plays writes: "There's not the smallest orb which thou behold'st but in his motion like an angel sings." So little remains, however, of the Pythagorean system of celestial music that it is only possible to approximate his actual theory. Pythagoras conceived the universe to be an immense monochord, with its single string connected at its upper end to absolute spirit and at its lower end to absolute matter--in other words, a cord stretched between heaven and earth. Counting inward from the circumference of the heavens, Pythagoras, according to some authorities, divided the universe into nine parts; according to others, into twelve parts. The twelvefold system was as follows: The first division was called the empyrean, or the sphere of the fixed stars, and was the dwelling place of the immortals. The second to twelfth divisions were (in order) the spheres of Saturn, Jupiter, Mars, the sun, Venus, Mercury, and the moon, and fire, air, water, and earth. This arrangement of the seven planets (the sun and moon being regarded as planets in the old astronomy) is identical with the candlestick symbolism of the Jews--the sun in the center as the main stem with three planets on either side of it. The names given by the Pythagoreans to the various notes of the diatonic scale were, according to Macrobius, derived from an estimation of the velocity and magnitude of the planetary bodies. Each of these gigantic spheres as it rushed endlessly through space was believed to sound a certain tone caused by its continuous displacement of the Šthereal diffusion. As these tones were a manifestation of divine order and motion, it must necessarily follow that they partook of the harmony of their own source. "The assertion that the planets in their revolutions round the earth uttered certain sounds differing according to their respective 'magnitude, celerity and local distance,' was commonly made by the Greeks. Thus Saturn, the farthest planet, was said to give the gravest note, while the Moon, which is the nearest, gave the sharpest. 'These sounds of the seven planets, and the sphere of the fixed stars, together with that above us [Antichthon], are the nine Muses, and their joint symphony is called Mnemosyne.'" (See The Canon.)This quotation contains an obscure reference to the ninefold division of the universe previously mentioned. The Greek initiates also recognized a fundamental relationship between the individual heavens or spheres of the seven planets, and the seven sacred vowels. The first heaven uttered the sound of the sacred vowel Α (Alpha); the second heaven, the sacred vowel Ε (Epsilon); the third, Η (Eta); the fourth, Ι (Iota); the fifth, Ο (Omicron); the sixth, Υ (Upsilon); and the seventh heaven, the sacred vowel Ω (Omega). When these seven heavens sing together they produce a perfect harmony which ascends as an everlasting praise to the throne of the Creator. (See IrenŠus' Against Heresies.) Although not so stated, it is probable that the planetary heavens are to be considered as ascending in the Pythagorean order, beginning with the sphere of the moon, which would be the first heaven. (continued next post)
The Pythagorean Theory of Music and Color, continued
10 years ago
Many early instruments had seven Strings, and it is generally conceded that Pythagoras was the one who added the eighth string to the lyre of Terpander. The seven strings were always related both to their correspondences in the human body and to the planets. The names of God were also conceived to be formed from combinations of the seven planetary harmonies. The Egyptians confined their sacred songs to the seven primary sounds, forbidding any others to be uttered in their temples. One of their hymns contained the following invocation: "The seven sounding tones praise Thee, the Great God, the ceaseless working Father of the whole universe." In another the Deity describes Himself thus: "I am the great indestructible lyre of the whole world, attuning the songs of the heavens. (See Nauman's History of Music.) The Pythagoreans believed that everything which existed had a voice and that all creatures were eternally singing the praise of the Creator. Man fails to hear these divine melodies because his soul is enmeshed in the illusion of material existence. When he liberates himself from the bondage of the lower world with its sense limitations, the music of the spheres will again be audible as it was in the Golden Age. Harmony recognizes harmony, and when the human soul regains its true estate it will not only hear the celestial choir but also join with it in an everlasting anthem of praise to that Eternal Good controlling the infinite number of parts and conditions of Being. The Greek Mysteries included in their doctrines a magnificent concept of the relationship existing between music and form. The elements of architecture, for example, were considered as comparable to musical modes and notes, or as having a musical counterpart. Consequently when a building was erected in which a number of these elements were combined, the structure was then likened to a musical chord, which was harmonic only when it fully satisfied the mathematical requirements of harmonic intervals. The realization of this analogy between sound and form led Goethe to declare that "architecture is crystallized music." In constructing their temples of initiation, the early priests frequently demonstrated their superior knowledge of the principles underlying the phenomena known as vibration. A considerable part of the Mystery rituals consisted of invocations and intonements, for which purpose special sound chambers were constructed. A word whispered in one of these apartments was so intensified that the reverberations made the entire building sway and be filled with a deafening roar. The very wood and stone used in the erection of these sacred buildings eventually became so thoroughly permeated with the sound vibrations of the religious ceremonies that when struck they would reproduce the same tones thus repeatedly impressed into their substances by the rituals. Every element in Nature has its individual keynote. If these elements are combined in a composite structure the result is a chord that, if sounded, will disintegrate the compound into its integral parts. Likewise each individual has a keynote that, if sounded, will destroy him. The allegory of the walls of Jericho falling when the trumpets of Israel were sounded is undoubtedly intended to set forth the arcane significance of individual keynote or vibration. THE PHILOSOPHY OF COLOR "Light," writes Edwin D. Babbitt, "reveals the glories of the external world and yet is the most glorious of them all. It gives beauty, reveals beauty and is itself most beautiful. It is the analyzer, the truth-teller and the exposer of shams, for it shows things as they are. Its infinite streams measure off the universe and flow into our telescopes from stars which are quintillions of miles distant. On the other hand it descends to objects inconceivably small, and reveals through the microscope objects fifty millions of times less than can be seen by the naked eye. Like all other fine forces, its movement is wonderfully soft, yet penetrating and powerful. Without its vivifying influence, vegetable, animal, and human life must immediately perish from the earth, and general ruin take place. We shall do well, then, to consider this potential and beautiful principle of light and its component colors, for the more deeply we penetrate into its inner laws, the more will it present itself as a marvelous storehouse of power to vitalize, heal, refine, and delight mankind." (See The Principles of Light and Color.) Since light is the basic physical manifestation of life, bathing all creation in its radiance, it is highly important to realize, in part at least, the subtle nature of this divine substance. That which is called light is actually a rate of vibration causing certain reactions upon the optic nerve. Few realize how they are walled in by the limitations of the sense perceptions. Not only is there a great deal more to light than anyone has ever seen but there are also unknown forms of light which no optical equipment will ever register. There are unnumbered colors which cannot be seen, as well as sounds which cannot be heard, odors which cannot be smelt, flavors which cannot be tasted, and substances which cannot be felt. Man is thus surrounded by a supersensible universe of which he knows nothing because the centers of sense perception within himself have not been developed sufficiently to respond to the subtler rates of vibration of which that universe is composed. (continued next post)
The Pythagorean Theory of Color, continued
10 years ago
Among both civilized and savage peoples color has been accepted as a natural language in which to couch their religious and philosophical doctrines. The ancient city of Ecbatana as described by Herodotus, its seven walls colored according to the seven planets, revealed the knowledge of this subject possessed by the Persian Magi. The famous zikkurat or astronomical tower of the god Nebo at Borsippa ascended in seven great steps or stages, each step being painted in the key color of one of the planetary bodies. (See Lenormant's Chaldean Magic.) It is thus evident that the Babylonians were familiar with the concept of the spectrum in its relation to the seven Creative Gods or Powers. In India, one of the Mogul emperors caused a fountain to be made with seven levels. The water pouring down the sides through specially arranged channels changed color as it descended, passing sequentially through all shades of the spectrum. In Tibet, color is employed by the native artists to express various moods. L. Austine Waddell, writing of Northern Buddhist art, notes that in Tibetan mythology "White and yellow complexions usually typify mild moods, while the red, blue, and black belong to fierce forms, though sometimes light blue, as indicating the sky, means merely celestial. Generally the gods are pictured white, goblins red, and devils black, like their European relative." (See The Buddhism of Tibet.) In Meno, Plato, speaking through Socrates, describes color as "an effluence of form, commensurate with sight, and sensible." In TheŠtetus he discourses more at length on the subject thus: "Let us carry out the principle which has just been affirmed, that nothing is self-existent, and then we shall see that every color, white, black, and every other color, arises out of the eye meeting the appropriate motion, and that what we term the substance of each color is neither the active nor the passive element, but something which passes between them, and is peculiar to each percipient; are you certain that the several colors appear to every animal--say a dog--as they appear to you?" In the Pythagorean tetractys--the supreme symbol of universal forces and processes--are set forth the theories of the Greeks concerning color and music. The first three dots represent the threefold White Light, which is the Godhead containing potentially all sound and color. The remaining seven dots are the colors of the spectrum and the notes of the musical scale. The colors and tones are the active creative powers which, emanating from the First Cause, establish the universe. The seven are divided into two groups, one containing three powers and the other four a relationship also shown in the tetractys. The higher group--that of three--becomes the spiritual nature of the created universe; the lower group--that of four--manifests as the irrational sphere, or inferior world. In the Mysteries the seven Logi, or Creative Lords, are shown as streams of force issuing from the mouth of the Eternal One. This signifies the spectrum being extracted from the white light of the Supreme Deity. The seven Creators, or Fabricators, of the inferior spheres were called by the Jews the Elohim. By the Egyptians they were referred to as the Builders (sometimes as the Governors) and are depicted with great knives in their hands with which they carved the universe from its primordial substance. Worship of the planets is based upon their acceptation as the cosmic embodiments of the seven creative attributes of God. The Lords of the planets were described as dwelling within the body of the sun, for the true nature of the sun, being analogous to the white light, contains the seeds of all the tone and color potencies which it manifests. There are numerous arbitrary arrangements setting forth the mutual relationships of the planets, the colors, and the musical notes. The most satisfactory system is that based upon the law of the octave. The sense of hearing has a much wider scope than that of sight, for whereas the ear can register from nine to eleven octaves of sound the eye is restricted to the cognition of but seven fundamental color tones, or one tone short of the octave. Red, when posited as the lowest color tone in the scale of chromatics, thus corresponds to do, the first note of the musical scale. Continuing the analogy, orange corresponds to re, yellow to mi, green to fa, blue to sol, indigo to la, and violet to si (ti). The eighth color tone necessary to complete the scale should be the higher octave of red, the first color tone. The accuracy of the above arrangement is attested by two striking facts: (1) the three fundamental notes of the musical scale--the first, the third, and the fifth--correspond with the three primary colors--red, yellow, and blue; (2) the seventh, and least perfect, note of the musical scale corresponds with purple, the least perfect tone of the color scale. (continued next post)
The Pythagorean Theory of Color, continued
10 years ago
In The Principles of Light and Color, Edwin D. Babbitt confirms the correspondence of the color and musical scales: "As C is at the bottom of the musical scale and made with the coarsest waves of air, so is red at the bottom of the chromatic scale and made with the coarsest waves of luminous ether. As the musical note B [the seventh note of the scale] requires 45 vibrations of air every time the note C at the lower end of the scale requires 24, or but little over half as many, so does extreme violet require about 300 trillions of vibrations of ether in a second, while extreme red requires only about 450 trillions, which also are but little more than half as many. When one musical octave is finished another one commences and progresses with just twice as many vibrations as were used in the first octave, and so the same notes are repeated on a finer scale. In the same way when the scale of colors visible to the ordinary eye is completed in the violet, another octave of finer invisible colors, with just twice as many vibrations, will commence and progress on precisely the same law." When the colors are related to the twelve signs of the zodiac, they are arranged as the spokes of a wheel. To Aries is assigned pure red; to Taurus, red-orange; to Gemini, pure orange; to Cancer, orange-yellow; to Leo, pure yellow; to Virgo, yellow-green; to Libra, pure green; to Scorpio, green-blue; to Sagittarius, pure blue; to Capricorn, blue-violet; to Aquarius, pure violet; and to Pisces, violet-red. In expounding the Eastern system of esoteric philosophy, H. P, Blavatsky relates the colors to the septenary constitution of man and the seven states of matter as follows: COLOR PRINCIPLES OF MAN STATES OF MATTER Violet Chaya, or Etheric Double Ether Indigo Higher Manas, or Spiritual Intelligence Critical State called Air Blue Auric Envelope Steam or Vapor Green Lower Manas, or Animal Soul Critical State Yellow Buddhi, or Spiritual Soul Water Orange Prana, or Life Principle Critical State Red Kama Rupa, or Seat of Animal Life Ice This arrangement of the colors of the spectrum and the musical notes of the octave necessitates a different grouping of the planets in order to preserve their proper tone and color analogies. Thus do becomes Mars; re, the sun; mi, Mercury; fa, Saturn; sol, Jupiter; la, Venus; si (ti) the moon. (See The E. S. Instructions.) Harmony: please see illustrations, charts and diagrams on the links associated with these pages for more complete information.