Flyin' Fibonacci, Batman! Feel Pyth's Pain
Flying Fibonacci, Batman!
Feel Pythagoras’ pain?
... was transported by the followers of Cambyses as a prisoner of war. Whilst he was there he gladly associated with the Magoi ... and was instructed in their sacred rites and learnt about a very mystical worship of the gods. He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians...
However, history records he wasn’t particularly well received by local Samians when he returned to turn them on. (worth pointing out again)
... he tried to use his symbolic method of teaching which was similar in all respects to the lessons he had learnt in Egypt. The Samians were not very keen on this method and treated him in a rude and improper manner.
No soap for the savior. Not to be outdone,
... he formed a school in the city [of Samos], the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics .
Initiates were required to study 5 years in silence, before being allowed to say anything at all (in highest counsel assemblies). In Hegel’s historical model of the incarnate Spirit – one free (kingship), some free (Greek democracy, all free (Enlightenment) – Pythagoras’ brotherhood is a throw-back to “None free”. Almost: the Epyptian-priesthood caverns of secret knowledge of The One, through Thoth, resonates through this ‘semicircle’. (? – curved-line/time boundary?) Or, rather, when “freedom”, as Hegel understood it, coming over from the Enlightenment into the Third millennium, didn’t apply. According to the oldest histories, men originally served the Gods, and were “granted” kingship at Kish, in Sumer, before Babylon rose after Marduk. The advanced sexigesimal number system by which stupendously accurate calculations of planetary orbits, eclipses, and other night-sky phenomena were ordered, dates to the earlier epoch, and was considered sacred communication objectively connecting heavens-earth (the sacred precincts were called EN.DUR.ANKI). It was the sort of information that to know was to be a part and conduit of; therefore “not (for) free”. Not for “the free”, if that meant “excused from relating to reality in an objective way.” Unfortunately for humanity, despite the best efforts of the Pythagoreans, the original Hermetic schools at Alexandria (where the Emerald Tablets of Thoth The Atlantean were kept, and scientific studies originating before Thales of Miletus, Athens, Rome), the Templars and FreeMasons, ….despite the best efforts of the best, the “freedom now” crowd has demanded, and usually got, its way in history regarding freedom from the bondage of objective knowledge (wrong!) until the venerable old vehicles designed to communicate them become useless. Mere words; rituals, weird and eerie programs taking place outside the field of clear and distinct communication. And deliberately kept so. Then it seems as the Giant World Clock has quit ticking, while its hands continued their silent, slow seni-circling… the forms the world shows to consciousness drift by, as in dreams, with all instances drained of any but cardboard-front life-in-the-moment. Then it moves on. In Pythagoras’ world, as I get it, this is compatible with saying there is no movement at all, only “seeming”. This would go with his identifications of things with numbers, the number of the male principle “3”: The Father of numbers (One in the Three) and Father of humans (through the First and Second Adam) are the same in the eternity of the principle unfolding, ever unfolded, in three stages, leading to the Fourth. This is a paradox in Pythagoras’ system. The unfolding in time, through beginning, middle, end, is, for itself, outside time, or under the arc of its circumference. And that perpetually.
****.
The metaphysical importance of Pythagoras as a Thinker/Savior/Mediator lies in this: His thought and view of the universe intersected the fundamental metaphysical opposites represented by straight and curved lines. The accumulated data of astronomy was the objective empirical verification of the meanings given use of both lines in constructing starlobe maps. It is in this Vorstellung combining of arithmetic and geometry, particularly triangles, squares, cubes and spheres (posited by Ptolemy), that a humanly wrought scientific account of the universe originated. Could a fundamental flaw have been built into the very way these earliest diagram represented reality? – creating a ‘glitch’ in the mental adjustment of humans on planet earth to their environment destined to blossom into full-scale psychotic breakdown, over the long haul? – based on the sheer contradiction between realty in itself , versus reality (in Hegel’s terms) for itself (through subjective delusions projected as objective through ‘the Spirit’)? (“Vorstellung” is the German notion of representation not confined to text, but as in: “religious Vorstellung” are “the basis of unity of the Church” – Hegel; contrasted with “philosophical”, or “fascist corporate” Vorstellungen, etc.)
Hypothesis here: A glitch indeed, can be spotted in their use of number-geometry signs in Tokenspace, when internalizes as mental “maps” defining actual space-time relations through the body. (Perhaps others spot other glitches.) .
The body, house of insipient consciousnesses, has always posed a problem for science. But there it is: see Da Vinci’s fascination, the great early Florentine Greek sculptors, heaven-projected Adam Kadmon of kabalah … the Human Form, in all its glory. The sacred, whatever else it might be, is in that; not apart from it, as modern Marcianists hold. Such was the Renaissance creed. (This again approaches Christology as the hinge of history; cf. previous post.) Scientists themselves, ever eager to square things up so they can calculate the diameters, gravitate toward a Leibnizean/Monad metaphysic inside of which each and all can be “free”, in order to explain themselves and the possibility of knowledge (Kant). When pressed to turn from method to metaphysics, they hem and haw. Some, such as Einstein, use God to refute Quantum Theory. Appropriately, since forms of energy so miniscule as barely affecting the behavior of single neutrons can be assigned the metaphysical status of 0.000001, as affecting forms of cellular, organic and social life mediated by sign-use. But hardly “scientifically” (“God doesn’t play dice with the universe,” he quipped, rejecting the metaphysics of probability theory Quantum theory used. Er… as if someone though “He” did? -Einstein doing “G-d” for the Jews, although I am sure he wouldn’t have put it that way. But, as was recently pointed out to me, neither do terrorists call themselves “terrorists”.)
The reason they hem and haw, jive and jig-a-boo, is because they aren’t for sure some important truth about the cosmos wasn’t known, and forgotten, precisely as is argued here, under the way of being recognized as sacred. As a way of being. Through the body. That is the challenging, absurd idea. There WAS a glitch, they secretly divine, but to straighten it out requires a metaphysical overhaul, reconstructing sign-use, and reinventing the wheel of communication. That is what this is about.
Slicing the Pi, and Squaring the Circle
Pythagorean metaphysics came to grief over the problem of ‘irrational numbers’, the incommensurability of units of straight lines to curved lines, illustrated by the common denominator 3.1416…. as ratio of length of diameter to the circumference of any circle. This is a non-terminating fraction, calling upon the mind to either admit that an infinite sequence of diminishing discriminations existed ….Aristotle would say “potentially infinite”, … or give up the idea that the same units of space that measure straight lines also measures curves, apparently contradicting Pythagoras’ identity of things and numbers.
The received science came to use models that jammed together rational and irrational ratios – terminating and non-terminating fractions – to accommodate measurements of both diameters and circumferences on the Vorstellung of events in space and time, calculated from the body. These were put together in the mathematical “calculus” of Leibniz and Newton. Thus. the problem of Pi, the history of which is traced to Sumer and Babylon, gets grammatized into the language of science. The stage is set for what is called “relativity theory”, “quantum theory”, “Big Bang and String theory”, and the like, which rest applying irrationals in reality measurement.
There is another model, an alternate theory of space-time-universe form under geometry and numbers (but without words). It is the Enneagram, as taught in original Gurdjieff schools, and Chapter 14 of P.D. Ouspensky’s “In Search of the Miraculous”. (not: as personality diagnostic). One major unique feature is its use of the fraction 0.142857, which is the digital expansion of One (1) divided into Seven (7) equal parts (“7/1” – “7 into 1”). The values obtained by continuing the division on the right hand side of the decimal repeat the sequence interminably: 0.142857142857142857 etc., etc, ad infinitum. Though the grade of texture becomes finer and finer, the pattern can never vary. This provides a schema for taking 6 progressively arranged series of 7/1 as “squaring the circle”, as in:
1 divided into 7 parts =
0.142857 1/7
0.285714 2/7
0.428571 3/7
0.571428 4/7
0.714285 5/7
0.857142 6/7
1. 7/7
If ‘One” is the unity of All, as Pythagoras held, the seven equal parts represent a succession of worlds arithmetically potential in it. The unbounded (potentially infinite extension of series at every level) is contained within the bounded. The moving through each of the segments from One, to Seven completes a circle of circles ascending from 1/7 to 1, descending from 7/7 to 0.
Fibonacci introduced the decimal system using Arabic numerals in the 13th century; before that, this first step in the construction of the Enneagram could not be laid out visually. However, it does correspond to the arithmetic of the seven-tone musical scale known to Pythagoras. Fibonacci, who saw sequences in numbers as Pythagaoras did, did not, apparently, make a physical/geometrical application of sequences. This is required to compress the repetitions in nature of One in 7 --in hues of color, musical notes, atomic-molecular weight proportions, and days of the week (the 7th being sacred). Just threw the last in there to set the stage for a Hegel connection later. It is impossible to overestimate the extent to which the metaphysics of space, time, number, geometry and measurement go together under the same set of Vorstellung.
The Fibonnaci sequence is 1-1-2-3-5-8-13-21-34-65 – etc., repeating the operation of addition to each additional number, after doubling ‘1’. If a sequence of operations were specified – say, alternately add the last, and next-but last; then, changing that, but lawfully, etc., 7 times – this would built the framework of an infinite framework in which all finite totalities were subsumed under triads within the One of every unit, which is the Enneagram. More later.
Next metaphysical Question to consider: What us Justice?
Feel Pythagoras’ pain?
... was transported by the followers of Cambyses as a prisoner of war. Whilst he was there he gladly associated with the Magoi ... and was instructed in their sacred rites and learnt about a very mystical worship of the gods. He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians...
However, history records he wasn’t particularly well received by local Samians when he returned to turn them on. (worth pointing out again)
... he tried to use his symbolic method of teaching which was similar in all respects to the lessons he had learnt in Egypt. The Samians were not very keen on this method and treated him in a rude and improper manner.
No soap for the savior. Not to be outdone,
... he formed a school in the city [of Samos], the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics .
Initiates were required to study 5 years in silence, before being allowed to say anything at all (in highest counsel assemblies). In Hegel’s historical model of the incarnate Spirit – one free (kingship), some free (Greek democracy, all free (Enlightenment) – Pythagoras’ brotherhood is a throw-back to “None free”. Almost: the Epyptian-priesthood caverns of secret knowledge of The One, through Thoth, resonates through this ‘semicircle’. (? – curved-line/time boundary?) Or, rather, when “freedom”, as Hegel understood it, coming over from the Enlightenment into the Third millennium, didn’t apply. According to the oldest histories, men originally served the Gods, and were “granted” kingship at Kish, in Sumer, before Babylon rose after Marduk. The advanced sexigesimal number system by which stupendously accurate calculations of planetary orbits, eclipses, and other night-sky phenomena were ordered, dates to the earlier epoch, and was considered sacred communication objectively connecting heavens-earth (the sacred precincts were called EN.DUR.ANKI). It was the sort of information that to know was to be a part and conduit of; therefore “not (for) free”. Not for “the free”, if that meant “excused from relating to reality in an objective way.” Unfortunately for humanity, despite the best efforts of the Pythagoreans, the original Hermetic schools at Alexandria (where the Emerald Tablets of Thoth The Atlantean were kept, and scientific studies originating before Thales of Miletus, Athens, Rome), the Templars and FreeMasons, ….despite the best efforts of the best, the “freedom now” crowd has demanded, and usually got, its way in history regarding freedom from the bondage of objective knowledge (wrong!) until the venerable old vehicles designed to communicate them become useless. Mere words; rituals, weird and eerie programs taking place outside the field of clear and distinct communication. And deliberately kept so. Then it seems as the Giant World Clock has quit ticking, while its hands continued their silent, slow seni-circling… the forms the world shows to consciousness drift by, as in dreams, with all instances drained of any but cardboard-front life-in-the-moment. Then it moves on. In Pythagoras’ world, as I get it, this is compatible with saying there is no movement at all, only “seeming”. This would go with his identifications of things with numbers, the number of the male principle “3”: The Father of numbers (One in the Three) and Father of humans (through the First and Second Adam) are the same in the eternity of the principle unfolding, ever unfolded, in three stages, leading to the Fourth. This is a paradox in Pythagoras’ system. The unfolding in time, through beginning, middle, end, is, for itself, outside time, or under the arc of its circumference. And that perpetually.
****.
The metaphysical importance of Pythagoras as a Thinker/Savior/Mediator lies in this: His thought and view of the universe intersected the fundamental metaphysical opposites represented by straight and curved lines. The accumulated data of astronomy was the objective empirical verification of the meanings given use of both lines in constructing starlobe maps. It is in this Vorstellung combining of arithmetic and geometry, particularly triangles, squares, cubes and spheres (posited by Ptolemy), that a humanly wrought scientific account of the universe originated. Could a fundamental flaw have been built into the very way these earliest diagram represented reality? – creating a ‘glitch’ in the mental adjustment of humans on planet earth to their environment destined to blossom into full-scale psychotic breakdown, over the long haul? – based on the sheer contradiction between realty in itself , versus reality (in Hegel’s terms) for itself (through subjective delusions projected as objective through ‘the Spirit’)? (“Vorstellung” is the German notion of representation not confined to text, but as in: “religious Vorstellung” are “the basis of unity of the Church” – Hegel; contrasted with “philosophical”, or “fascist corporate” Vorstellungen, etc.)
Hypothesis here: A glitch indeed, can be spotted in their use of number-geometry signs in Tokenspace, when internalizes as mental “maps” defining actual space-time relations through the body. (Perhaps others spot other glitches.) .
The body, house of insipient consciousnesses, has always posed a problem for science. But there it is: see Da Vinci’s fascination, the great early Florentine Greek sculptors, heaven-projected Adam Kadmon of kabalah … the Human Form, in all its glory. The sacred, whatever else it might be, is in that; not apart from it, as modern Marcianists hold. Such was the Renaissance creed. (This again approaches Christology as the hinge of history; cf. previous post.) Scientists themselves, ever eager to square things up so they can calculate the diameters, gravitate toward a Leibnizean/Monad metaphysic inside of which each and all can be “free”, in order to explain themselves and the possibility of knowledge (Kant). When pressed to turn from method to metaphysics, they hem and haw. Some, such as Einstein, use God to refute Quantum Theory. Appropriately, since forms of energy so miniscule as barely affecting the behavior of single neutrons can be assigned the metaphysical status of 0.000001, as affecting forms of cellular, organic and social life mediated by sign-use. But hardly “scientifically” (“God doesn’t play dice with the universe,” he quipped, rejecting the metaphysics of probability theory Quantum theory used. Er… as if someone though “He” did? -Einstein doing “G-d” for the Jews, although I am sure he wouldn’t have put it that way. But, as was recently pointed out to me, neither do terrorists call themselves “terrorists”.)
The reason they hem and haw, jive and jig-a-boo, is because they aren’t for sure some important truth about the cosmos wasn’t known, and forgotten, precisely as is argued here, under the way of being recognized as sacred. As a way of being. Through the body. That is the challenging, absurd idea. There WAS a glitch, they secretly divine, but to straighten it out requires a metaphysical overhaul, reconstructing sign-use, and reinventing the wheel of communication. That is what this is about.
Slicing the Pi, and Squaring the Circle
Pythagorean metaphysics came to grief over the problem of ‘irrational numbers’, the incommensurability of units of straight lines to curved lines, illustrated by the common denominator 3.1416…. as ratio of length of diameter to the circumference of any circle. This is a non-terminating fraction, calling upon the mind to either admit that an infinite sequence of diminishing discriminations existed ….Aristotle would say “potentially infinite”, … or give up the idea that the same units of space that measure straight lines also measures curves, apparently contradicting Pythagoras’ identity of things and numbers.
The received science came to use models that jammed together rational and irrational ratios – terminating and non-terminating fractions – to accommodate measurements of both diameters and circumferences on the Vorstellung of events in space and time, calculated from the body. These were put together in the mathematical “calculus” of Leibniz and Newton. Thus. the problem of Pi, the history of which is traced to Sumer and Babylon, gets grammatized into the language of science. The stage is set for what is called “relativity theory”, “quantum theory”, “Big Bang and String theory”, and the like, which rest applying irrationals in reality measurement.
There is another model, an alternate theory of space-time-universe form under geometry and numbers (but without words). It is the Enneagram, as taught in original Gurdjieff schools, and Chapter 14 of P.D. Ouspensky’s “In Search of the Miraculous”. (not: as personality diagnostic). One major unique feature is its use of the fraction 0.142857, which is the digital expansion of One (1) divided into Seven (7) equal parts (“7/1” – “7 into 1”). The values obtained by continuing the division on the right hand side of the decimal repeat the sequence interminably: 0.142857142857142857 etc., etc, ad infinitum. Though the grade of texture becomes finer and finer, the pattern can never vary. This provides a schema for taking 6 progressively arranged series of 7/1 as “squaring the circle”, as in:
1 divided into 7 parts =
0.142857 1/7
0.285714 2/7
0.428571 3/7
0.571428 4/7
0.714285 5/7
0.857142 6/7
1. 7/7
If ‘One” is the unity of All, as Pythagoras held, the seven equal parts represent a succession of worlds arithmetically potential in it. The unbounded (potentially infinite extension of series at every level) is contained within the bounded. The moving through each of the segments from One, to Seven completes a circle of circles ascending from 1/7 to 1, descending from 7/7 to 0.
Fibonacci introduced the decimal system using Arabic numerals in the 13th century; before that, this first step in the construction of the Enneagram could not be laid out visually. However, it does correspond to the arithmetic of the seven-tone musical scale known to Pythagoras. Fibonacci, who saw sequences in numbers as Pythagaoras did, did not, apparently, make a physical/geometrical application of sequences. This is required to compress the repetitions in nature of One in 7 --in hues of color, musical notes, atomic-molecular weight proportions, and days of the week (the 7th being sacred). Just threw the last in there to set the stage for a Hegel connection later. It is impossible to overestimate the extent to which the metaphysics of space, time, number, geometry and measurement go together under the same set of Vorstellung.
The Fibonnaci sequence is 1-1-2-3-5-8-13-21-34-65 – etc., repeating the operation of addition to each additional number, after doubling ‘1’. If a sequence of operations were specified – say, alternately add the last, and next-but last; then, changing that, but lawfully, etc., 7 times – this would built the framework of an infinite framework in which all finite totalities were subsumed under triads within the One of every unit, which is the Enneagram. More later.
Next metaphysical Question to consider: What us Justice?
posted by Sid Thomas | 5:37 AM
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