Fibonacci Vectors in TokenSpace
Fibonacci Vectors in TokenSpace
Vhttp://en.wikipedia.org/wiki/Fibonacci_number#Identity_for_doubling_n
Vector space
The term Fibonacci sequence is also applied more generally to any function g from the integers to a field for which g(n+2) = g(n) + g(n+1). These functions are precisely those of the form g(n) = F(n)g(1) + F(n-1)g(0), so the Fibonacci sequences form a vector space with the functions F(n) and F(n-1) as a basis.
More generally, the range of g may be taken to be any abelian group (regarded as a Z-module). Then the Fibonacci sequences form a 2-dimensional Z-module in the same way
*****
From this it is possible to generalize, "Fibonacci sequence", of F(n) w/ g(1), F(n-1)g(0), to "Fibonacci progression": E(n), D(n), C(n), B(n), A(n) with g(1). etc.., each letter preceding the constant "g" as the function sign standing for a (1) - (0) base. If these seven (6, under "g") are taken as a Fibbonacci string 1-1-2-3-5-8 (for A-B-C-D-E-F), the 13 is G/g: the form of forms as a unity taken up from lower-to-higher case level, showing the octave's return to "Do" in the progression of tones of the musical scale. With repetitions of these, sounded out with rhythm, lyrics, timbres and harmonics from all ends of the scale come all the music modulations we experience. The stacked squares in the Fibonacci rectangles up to 13, from which the line spiraling in begins, successively curling counter-clockwise through smaller squares until returning to alignment with point of entry at the centre. This line would traverse all vectors of planes in TokenSpace. It's seven notes, or moments, are the vibrations in Space/time energy/matter as a S*tring of consciousness. The F(n) vectors in TokenSpace, along the diagonal from center-to-upper left on the two-dimensional surface, traverses the fields of predicates from the starry heaves above to the moral law within through which the totality of experienced..
If, inverting lower for higher case ("G" for "g": "f" for "F" etc.) letters, to indicate orders of form vs. matter, text vrs tokens, predicates vs. names, G is taken as most inclusive (as in "The G-word": God), all things (n) are shown in the wheel of communication under the curve through square 13, entering square 8, the field of human visual sense perception, as light. All 'f(x) are G", the class of all truths when "f" is any predicate applying to any object x (as an n). The class of G's includes whatever is given as individuals under any predicate: propositions in general, a unity in duality. It is the predicate of all predicates applied truly to subjects, taken up as the "is" relation into the form (higher level) inherent in form (lower level) of (forms,...) of individuals.
These notes unifying the description of what transpires along a line through solids stacked in the F(n) way, spiraling down, in and through from G to A. This is the model-map of the Wheel of Communication along its radius from center to circumference. It is also an interpretation of the Ray of Creation (Ouspensky) with conscious S*trings as "worlds" of nested space-time scales of matter-energy ratios.
The seven Notes are mounted on a circle spiraling inward to a terminus near the center.but a little below right. Retracing the spiral from there, within, outward, through each square successively, to arrive at actual Sign-use, begins: where neurophysiology goes over into the lowest-conscious level, in sleep, as dreams. These are brought back into waking state by conscious effort (or relaxation of effort), but are already organized templates of reproduced scenes in imagination allowing displacement and condensation of feeling situations to occur.
It is at this lowest-level boundary that trauma, and imprints of content under pain-of-recollection screen out/ disguize and distort some "dark" thoughts from the feeling domain, so easily suppressed. (When these can no longer be brought back to consciousness due to 'resistances', they go over to 'repressed' content. They can continue to draw cathexis in the unconscious, and skew relations that depend on continuity for consciousness. This is basically what neurosis is, in Freudian terms.) The spiraling-in energy entering as light into the perceived visual world is pulled downward, and into, the chthonic depths of organic pulsation; then this energy spiraling out, from those depths into articulate Token-(then Outer)- Space, become higher "light" for consciousness. "God", the highest, most complete, powerful., nurturant, containing text-token,
is at the circumference, but also at the center of this inward-outward spiral line, the same form of unity under and through the sequence of predicates. It is the most pretentious token, or token of most pretentiousness. The unity of the Ray of Creation, passing through, and out of, the human anatomical incarnation.
Along the psychosemiotic vectors generated in TokenSpace through consciousness by Sign-use will be found templates for
God-use
Logos (philosophy)
Ego-istics (existential "I" uses)
Moral Agency
Embodied Eros
aesthesis (incl. drama narrative)
Dreams (psycho-neural threshold)
_____
These are successively squared text-token predicate levels in the Wheel. Dreams and the pre-conscious neuro-physiological substrate are the 1 -1 duality of the Fibonacci process, the self-texting unconscious, transcribing images of how we feel from one context to another (as in mini-flashbacks, using primary-process memory). The "2" square is post-birth, mind-body consciousness (Descartes). "3" square, touching the side of the 2 where the 1's are doubled, adds Eros to Aesthesis, as in pursuit of reproduction with orgasmic acme. "5" doubles this, taking up into itself both mind and body under judgment of right or wrong action -- added whenever reproduction is put in the context of the larger completing whole. "8", then, adds the double of the moral (good will) and non-, or im-moral domains, as conscious individual personal being. This is completed at 13 by the arc of logos/light/reason penetrating the earth-sky diameter, connecting Isis (as Sirius; w/ the Sothic calendar) to existential totality, and completion in the square 21.
THE HIERAQRCHY OF INTENTIONAL TYPES
In any formally elaborated language of the Principia Mathematica sort, strict observance of the distinction between names and predicates is required in order to avoid violation of the Theory of Logical Types. invoking predicates of predicates -- "F", as predicate of x's, subtituting for one of x's it ranges over ("F" for "x" in "F(x)", to give "F(F)". In formal deductions, this generates self-contradiction* -- see below. In ordinary grammar, however, the doubling of predicates on themselves occurs often and importantly: to fold back, or fold into, the use of a sign as text (meaning) what is communicated through it as token. This occurs everytime a sentence calls attention to itself, the word "word" is used for a word, communication commences about communication, ... pursued until finally consciousness comes into view, per se under Sign-Use (S*). Philosophy could not exist without language about language, thought about thought, representation of what is (being). How do these two things go together?
A general system of what exists, as a totality, under a basic predicate-subject form, if it is to avoid paradox, self contradiction and internal turmoil, must theoretically bestow an asymmetrical, transitive stipulation for the relation of F-E-D-C-B-A to g(n), as substitutes. F's, as forms of E-level individuals, are not E's; E's are not D's, etc. At the top, "God", as chief text in TokenSpace for all the S* in its field cannot stand for an object in the field of consciousness, except as a token for a text referring outside and beyond it as its field of completion. (Whether "God exists" or not cannot be asked; do Fibonacci sequences?). Similarly, the Forms Plato depicts so beautifully in Republic 6 as contents of the upper part of the upper part of the divided line cannot themselves be objects appearing in the sensible world, though the motions of sun, moon and planets in Ptolemyic approximated perfected circles, the Greeks thought. Nor, pursuing the theme of formal transgression further, can Forms and dynamics of such enormous cosmological objects; nor the Forms and dynamics of micro-objects composing the cells, tissues, organs of the personal body, until it becomes conscious to itself and others using signs...Nor can the unity of this (S*5) level of predicate -- the "I" itself, as it is to itself, become an objective entity observed in the world by others, except through the body.
Here, again, is the Upper Triad of Sign-Uses S*7 = God/TokenSpace
S*6 = (Ql-types: 5,4,3,2,1; v) ("v " for a vivifying energy-constant as part of any content of consciousness.) (Totality of Contents of Consciousess)
S*5 = ("I"5* (4,3,2,1); v ) (Totality of contents of my* consciousness.
In the Hierarchy of Intentional Types, S*4 is the domain of conscious agency, where the form of will under S*7,6,5 (upper triad) intersects, and interacts with, actual physical movements of the body (as S*3,2,1: the lower triad levels of sign-use. Let these correlate with:
S*3 -- S*entence-to-S*entence relations (implication)
S*2 - Predicates to objects -
S*1 - threshold objects
Great care must be taken to instal this basic framework as a metaphysical analytic as accurately as possible. The seven-tiered hierarcy of predicates of predicates, of ....objects spiraling in and spiraling out of the universal TokenSpace Globe, relating to its own progression as upper and lower triads meeting at the 4th of each -- body responding to communication of thought through consciousness each completing the other ... is the format for universal TokenSpace proposed in the Wheel of Communication.
The work of the three sectors of the lower triad, S*3,2,1 is correlated through the Fibonacci rectangles through 1,1 and 2: The 2 is a square of the two 1's, taken as body/consciousness (actual sign-use) events. This is the totality portended by S*5, under which it can be figured as a sequence like "I S IS ISIS". proceeding from S*4 "I Do" (as double text-token: doing what it says).
Vhttp://en.wikipedia.org/wiki/Fibonacci_number#Identity_for_doubling_n
Vector space
The term Fibonacci sequence is also applied more generally to any function g from the integers to a field for which g(n+2) = g(n) + g(n+1). These functions are precisely those of the form g(n) = F(n)g(1) + F(n-1)g(0), so the Fibonacci sequences form a vector space with the functions F(n) and F(n-1) as a basis.
More generally, the range of g may be taken to be any abelian group (regarded as a Z-module). Then the Fibonacci sequences form a 2-dimensional Z-module in the same way
*****
From this it is possible to generalize, "Fibonacci sequence", of F(n) w/ g(1), F(n-1)g(0), to "Fibonacci progression": E(n), D(n), C(n), B(n), A(n) with g(1). etc.., each letter preceding the constant "g" as the function sign standing for a (1) - (0) base. If these seven (6, under "g") are taken as a Fibbonacci string 1-1-2-3-5-8 (for A-B-C-D-E-F), the 13 is G/g: the form of forms as a unity taken up from lower-to-higher case level, showing the octave's return to "Do" in the progression of tones of the musical scale. With repetitions of these, sounded out with rhythm, lyrics, timbres and harmonics from all ends of the scale come all the music modulations we experience. The stacked squares in the Fibonacci rectangles up to 13, from which the line spiraling in begins, successively curling counter-clockwise through smaller squares until returning to alignment with point of entry at the centre. This line would traverse all vectors of planes in TokenSpace. It's seven notes, or moments, are the vibrations in Space/time energy/matter as a S*tring of consciousness. The F(n) vectors in TokenSpace, along the diagonal from center-to-upper left on the two-dimensional surface, traverses the fields of predicates from the starry heaves above to the moral law within through which the totality of experienced..
If, inverting lower for higher case ("G" for "g": "f" for "F" etc.) letters, to indicate orders of form vs. matter, text vrs tokens, predicates vs. names, G is taken as most inclusive (as in "The G-word": God), all things (n) are shown in the wheel of communication under the curve through square 13, entering square 8, the field of human visual sense perception, as light. All 'f(x) are G", the class of all truths when "f" is any predicate applying to any object x (as an n). The class of G's includes whatever is given as individuals under any predicate: propositions in general, a unity in duality. It is the predicate of all predicates applied truly to subjects, taken up as the "is" relation into the form (higher level) inherent in form (lower level) of (forms,...) of individuals.
These notes unifying the description of what transpires along a line through solids stacked in the F(n) way, spiraling down, in and through from G to A. This is the model-map of the Wheel of Communication along its radius from center to circumference. It is also an interpretation of the Ray of Creation (Ouspensky) with conscious S*trings as "worlds" of nested space-time scales of matter-energy ratios.
The seven Notes are mounted on a circle spiraling inward to a terminus near the center.but a little below right. Retracing the spiral from there, within, outward, through each square successively, to arrive at actual Sign-use, begins: where neurophysiology goes over into the lowest-conscious level, in sleep, as dreams. These are brought back into waking state by conscious effort (or relaxation of effort), but are already organized templates of reproduced scenes in imagination allowing displacement and condensation of feeling situations to occur.
It is at this lowest-level boundary that trauma, and imprints of content under pain-of-recollection screen out/ disguize and distort some "dark" thoughts from the feeling domain, so easily suppressed. (When these can no longer be brought back to consciousness due to 'resistances', they go over to 'repressed' content. They can continue to draw cathexis in the unconscious, and skew relations that depend on continuity for consciousness. This is basically what neurosis is, in Freudian terms.) The spiraling-in energy entering as light into the perceived visual world is pulled downward, and into, the chthonic depths of organic pulsation; then this energy spiraling out, from those depths into articulate Token-(then Outer)- Space, become higher "light" for consciousness. "God", the highest, most complete, powerful., nurturant, containing text-token,
is at the circumference, but also at the center of this inward-outward spiral line, the same form of unity under and through the sequence of predicates. It is the most pretentious token, or token of most pretentiousness. The unity of the Ray of Creation, passing through, and out of, the human anatomical incarnation.
Along the psychosemiotic vectors generated in TokenSpace through consciousness by Sign-use will be found templates for
God-use
Logos (philosophy)
Ego-istics (existential "I" uses)
Moral Agency
Embodied Eros
aesthesis (incl. drama narrative)
Dreams (psycho-neural threshold)
_____
These are successively squared text-token predicate levels in the Wheel. Dreams and the pre-conscious neuro-physiological substrate are the 1 -1 duality of the Fibonacci process, the self-texting unconscious, transcribing images of how we feel from one context to another (as in mini-flashbacks, using primary-process memory). The "2" square is post-birth, mind-body consciousness (Descartes). "3" square, touching the side of the 2 where the 1's are doubled, adds Eros to Aesthesis, as in pursuit of reproduction with orgasmic acme. "5" doubles this, taking up into itself both mind and body under judgment of right or wrong action -- added whenever reproduction is put in the context of the larger completing whole. "8", then, adds the double of the moral (good will) and non-, or im-moral domains, as conscious individual personal being. This is completed at 13 by the arc of logos/light/reason penetrating the earth-sky diameter, connecting Isis (as Sirius; w/ the Sothic calendar) to existential totality, and completion in the square 21.
THE HIERAQRCHY OF INTENTIONAL TYPES
In any formally elaborated language of the Principia Mathematica sort, strict observance of the distinction between names and predicates is required in order to avoid violation of the Theory of Logical Types. invoking predicates of predicates -- "F", as predicate of x's, subtituting for one of x's it ranges over ("F" for "x" in "F(x)", to give "F(F)". In formal deductions, this generates self-contradiction* -- see below. In ordinary grammar, however, the doubling of predicates on themselves occurs often and importantly: to fold back, or fold into, the use of a sign as text (meaning) what is communicated through it as token. This occurs everytime a sentence calls attention to itself, the word "word" is used for a word, communication commences about communication, ... pursued until finally consciousness comes into view, per se under Sign-Use (S*). Philosophy could not exist without language about language, thought about thought, representation of what is (being). How do these two things go together?
A general system of what exists, as a totality, under a basic predicate-subject form, if it is to avoid paradox, self contradiction and internal turmoil, must theoretically bestow an asymmetrical, transitive stipulation for the relation of F-E-D-C-B-A to g(n), as substitutes. F's, as forms of E-level individuals, are not E's; E's are not D's, etc. At the top, "God", as chief text in TokenSpace for all the S* in its field cannot stand for an object in the field of consciousness, except as a token for a text referring outside and beyond it as its field of completion. (Whether "God exists" or not cannot be asked; do Fibonacci sequences?). Similarly, the Forms Plato depicts so beautifully in Republic 6 as contents of the upper part of the upper part of the divided line cannot themselves be objects appearing in the sensible world, though the motions of sun, moon and planets in Ptolemyic approximated perfected circles, the Greeks thought. Nor, pursuing the theme of formal transgression further, can Forms and dynamics of such enormous cosmological objects; nor the Forms and dynamics of micro-objects composing the cells, tissues, organs of the personal body, until it becomes conscious to itself and others using signs...Nor can the unity of this (S*5) level of predicate -- the "I" itself, as it is to itself, become an objective entity observed in the world by others, except through the body.
Here, again, is the Upper Triad of Sign-Uses S*7 = God/TokenSpace
S*6 = (Ql-types: 5,4,3,2,1; v) ("v " for a vivifying energy-constant as part of any content of consciousness.) (Totality of Contents of Consciousess)
S*5 = ("I"5* (4,3,2,1); v ) (Totality of contents of my* consciousness.
In the Hierarchy of Intentional Types, S*4 is the domain of conscious agency, where the form of will under S*7,6,5 (upper triad) intersects, and interacts with, actual physical movements of the body (as S*3,2,1: the lower triad levels of sign-use. Let these correlate with:
S*3 -- S*entence-to-S*entence relations (implication)
S*2 - Predicates to objects -
S*1 - threshold objects
Great care must be taken to instal this basic framework as a metaphysical analytic as accurately as possible. The seven-tiered hierarcy of predicates of predicates, of ....objects spiraling in and spiraling out of the universal TokenSpace Globe, relating to its own progression as upper and lower triads meeting at the 4th of each -- body responding to communication of thought through consciousness each completing the other ... is the format for universal TokenSpace proposed in the Wheel of Communication.
The work of the three sectors of the lower triad, S*3,2,1 is correlated through the Fibonacci rectangles through 1,1 and 2: The 2 is a square of the two 1's, taken as body/consciousness (actual sign-use) events. This is the totality portended by S*5, under which it can be figured as a sequence like "I S IS ISIS". proceeding from S*4 "I Do" (as double text-token: doing what it says).
posted by Sid Thomas | 2:07 AM
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