Post by Indilwen on Jul 10, 2012 11:05:22 GMT 12
Pythagorean Mathematics:
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 formulæ, 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 * * *."
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 Æons, 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.
continued reading: 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 formulæ, 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 * * *."
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 Æons, 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.
continued reading: www.sacred-texts.com/eso/sta/sta16.htm