(Speculations Very Much In Process)

**The Mathematical Perspective**

1. In cosmos, there exist entities of all grades and orders, and in all dimensions.

2. There are, it is hinted in the *Old Commentary*, ten major dimensions. Within these dimensions (most of them entirely intangible to man, imprisoned as he is on the cosmic physical plane), entities live and move and have their beingi.e., they *express* their natures.

3. A fundamental axiom: the qualitative nature of all entities can be expressed in *number.*

4. The fundamental ENTITY WHO/WHICH is the GROUND OF ALL BEING and the SUBSTRATUM OF COSMOS is really an indefinable a NON-ENTITY, and is correlated to no number at all, or rather to the ZERO.

5. All entities (forever-past, instantaneous present, or forever future) have been, are, or will be derivative from this ENTITY/NON-ENTITY.

6. All entities in cosmos are *numerical*.

7. The Fundamental Entities of cosmos are those from Whom/Which all other entities within the Universal Process are derived

8. These Fundamental Entities *are*, in fact, the Fundamental Numbers, the Fundamental or Simple Integers. The first nine numbers, the Simple Integers, are the *Primary Cosmic Gods. *The Greatest Gods in Cosmos are the first Nine Integers, and the mysterious *Tenth* which is, in a mysterious way, the *First*.

9. Each successive Integer (or, more suggestively, *Integer-God*) is mysteriously derived from the Integer preceding it. (Refer to *Infinitization of Selfhood* for an attempt to describe with relative fulness the cosmo-psychological process).

10. All integers are really Integer-Gods, just as all entities within cosmos are, essentially, *gods.* For the sake of clarity, however, we will refer to the first *nine* (or possibly *ten*) integers as the *Primary Integer Gods* because all other integers/entities/gods are derived from them

11. Integer-Gods create other Integer Gods our of their own nature. This creative process should be called *emanation.* Some of the created/emanated Integer Gods are *successive* and *sequential *but most are some are not.

12. The creativity of each Integer-God proceeds through the addition of the Monad (the Number One) to itself. This addition arises through an Integer-Gods *sight* or *cognition* of its own *integrity.* Its own subjectivity or *subjective quantity, *plus *is objective self-sight or self-cognition* creates the next, successive Integer-God. (Other arithmetic processes of *self-multiplication,* *self-subtraction,* and *self-division,* are also present in the Universal Process and can be correlated with various psycho-spiritual processes exhibited by both macrocosmic and micro-cosmic entities.) Let us say, however, that the fundamental practice of *addition*psycho-spiritually consideredthe *addition* of *self* to *Self*is the fundamental modus-operandi of *emanation.* Once the *emanative process* has presented the fundamental Universal Structure, the other arithmetic operations (and their mathematical extensions) find their application.

13. Thus, Numerical Sequence arises through what we will call, *emanative Self-reflective generation.* Each Number arises through an act of Self-perception.

14. The Number One arises through *reductive SELF-Perception.* (Infinitude is *reduced* to One).

15. All Numbers greater than One arise through expansive* additive-thus-multiplicative Self-perception.* (Parenthetically, the reverse processthat of obscuration or absorptionproceeds through what can be called *subtractive-thus-divisional self-rejection.* Emanatively, I *add* *selves* to the *Self. *Obscuratively, I *subtract* or *reject* lesser *selves* from the field of consciousness and return to the *Self.* Outgoingly, *I am more and more.* Incomingly, *I am less and less.*)

16. The *quality* of each of these Number-Gods is related to its numerosity i.e., to is *quantity.* Really, *numerosity* connotes rather more that quantity; it is quantity and resultant quality combined.

17. The numerosity of a Number-God is determined by the collection of Monads distinctive of that Number-God, and, hence, to its *ordinal place* in the infinite sequence of Number-Gods.

18. The number of Monads distinctive of any Number-God is one *more* than the number of acts of Self-perception implicit in that Number-God.

19. For instance, there are *two* Monads in the Number-Two, but it took only* one act Self-perception* to generate/emanate the Number Two.

20. Remember, however, all Monads are really, always and forever *one* Monad. (But for practical purposes, there are as many Monads as there are Numbers)

21. From the Number One (the Integer-God, One) all complexity arises.

22. Let it be remembered, however, that though no Number-God (no matter how complex) is different from the Monad, for all Number-Gods *are* Monads*and*, ultimately, *The Monad. *

23. All Numbers are *distinctive units,* and hence they are a *one.* No matter what their numerosity, they are still and always a *one.* And, metaphysically, the *one* that they are, cannot be distinguished from the one and only Universal Onethe Primary Integer-Godthe Number *One*.

24. *Categorical distinctiveness* *in quantity*, however, exists only among the first Nine Integer-Gods. While the Number Eight is different from Nine, the Number Ten (through different from the Number Nine) is not *categorically distinct* from the Number One. Similarly, the Number Eleven, while different from the Number Ten (and the Number One) is not categorically distinct from the Number Two.

25. If a Number-God can be reduced through numerological addition (or normal division) to the numerosity of one or more Number-Gods from previous ninefold sequences, such reducible Number-Gods do not have *categorical distinctiveness*.

26. *Only the Numbers One through Nine have categorical distinctiveness*.

27. Thus, no matter how complex may be a Number-God, if that Number-God is *not* one of the First Nine Integers, it is necessarily related to either a Number-God from a previous ninefold sequence or to an Integer God from the Original Ninefold Sequence *and* (of course) to the Number One.

28. In fact, all Number-Gods (even the first Nine Primary-Integer-Gods) are not only *related* to the Number One (which composes them), but *are* the Number One. There is but One Monad in all of cosmos, and all entities generated from that Monad (by Self-sight, or Self-cognition) are both (apparently) different from it and yet the *same* as it. All are One.

29. By a *vertical* process of successive, sequential emanation (and, also, by a *horizontal* process *combination*), the entire entified universe in all its complexity, is generated.

30. *Vertically* considered, simple Numbers-Gods become more complex Number-Gods through *emanative Self-addition* (which is also a process of Self-multiplication). *Horizontally*, complex numbers (for our purposes, defined as Numbers with high numerosity) also arise through the *combination* of various Number-Gods (and numbers) representative of various levels of numerosity.

31. *Number-Gods *and *numbers* are not the same. Number-Gods are *archetypal* and permanent-in-cosmos, whereas, *numbers* *arise through combination* rather than

*emanation**.*

32. What we call *numbers* are really *reflections* of archetypal Number-Gods.

33. Every Number-God has many *reflections* in cosmos due to the combinations which arise through Law of Attraction, and the affiliativeness which arises between different Number-Gods.

34. Once emanatively generated, any Number-God can combine with any other Number-God to create a number. This act of union will produce another *two*, and also a number equal to the numerosity of a particular Self-emanated Number-God.

35. For instance, if the Number-God Two combines with (or is added to) the Number-God Five, then the result is a new being, or associative entity, the number seven. But this new being will not *be* the Number-God Seven (which is itself, alone), but only *reflective of* the Number-God, Seven. Further, the combination of the Number-Gods Two and Five has produced through their union, a twofold entity, which is *not* the Number-God, Two, but which is only reflective of the Number-God Two. When two combine a *two* arises; when three combine a *three* arises, etc.

36. In all of Cosmos there is only One *Archetypal* Number One, One *Archetypal* Number Two, One *Archetypal* Number Three, etc., etc, ad infinitum.

37. Yet the number of combinations between these Number-Gods is potentially infinite (through never demonstrably infinite) because *infinitude* is never *actually demonstrable*only *trends* towards infinitude are demonstrable.

38. Every time Number-Gods combine, they create an entity (a number) characterized by 1) the number of Number-Gods involved in the combination; and 2) the numerosity of the combination (based on the sum of the numbers characteristic of the Number-Gods involved.)

39. For instance, if five Number-Gods unite to create a new entity (or number), that entity will be characterized by fivefoldness (reflective of the Number-God Five), and will also have a *reflective numerosity* which is the sum of the numerosities of all Number-Gods who thus combined. For instance NG 1, plus NG 6, plus NG 17, plus NG 32, plus NG 97, yields a fivefold entity characterized by the reflective numerosity of 153. This, number, in numerology, is called the *alpha number.*

40. The entity 153, thus derived, is *not* the Number-God 153 (who is the Archetypal 153), but is a combination *exactly resonant* to Archetypal 153.

41. The concept of *resonance* is crucial in the understanding of universal meta-physiology and, consequently, of *astrology.*

42. Metaphysically, *resonance* is the process by which one Number-God (or number) affects another Number-God (or number) *without* dampening the vibratory freedom of the Number-God (or number) thus affected.

43. Exact resonances and harmonious resonances are also to be distinguished. For instance, any emanation or combination producing the number 4 is harmoniously resonant to the Number-God 24, but only a combination producing the number 24, is *exactly resonant* to the Number-God 24.

44. Of course, the possibility of resonances between combinations of numbers must also be taken into consideration, and not only resonances between a combination of number and a Number-God.

45. In fact, resonances between Number-Gods themselves are foundational to all other forms of resonancewhich must be considered derivative.

46. Examining the number 153, we see it will be related to the Number-Gods 144, 135, 126, 117, 108, 99, 90, 81, 72, 63, 54, 45, 36, 27, 18, and ultimately, 9.

47. The Integer-God Nine is the Primary Archetype of the Number-God 153, though Number-God 153 is also an Archetype (of a derivative nature)for there are Primary Archetypes (1 9/10) and *derivative* Archetypes, (11 towards the largest demonstrable number in any finite system).

48. The Number-Gods (or combinative numbers) to which any given Number-God (or combinative number) is related, can be derived by 1) adding or subtracting the reduced alpha number of the Number-God to itself, or 2) by multiplying or dividing the numerosity of the Number-God by its own reduced alpha number.

49. Since Number-God 153 sums to 9 (reduced alpha number), successive subtractions of 9 will produce related (and more potent) Number-Gods (like 144, or 135), and successive additions of 9 will produce resonantly related (yet less potent) Number-Gods (like 162, or 171). Similarly, division (in this case, of 153 by 9, yielding 17) will produce a more potent Number-God than multiplication of 153 by 9, yielding 1377.

50. The greater the numerosity, the less fundamental and potent the Number-God.

51. Number-Gods in combination may, however, be thought of differently with regard to their potency. In a certain sense (*objectively* and *materially*), the greater the combinative number, the more potent the resultant entity. The obvious conclusion isany combination producing the highest allowable number in a given cosmos (as no cosmos is actually or demonstrably infinite no matter how potentially infinite the potential combinations of its entities), achieves *wholeness* and thus returns to the power of the number *one.* Ultimately, the maximum combinative number is allied to the most potent Archetypal Numberthe Number One.

52. For instance, in a way, a million men are more powerful than ten men (depending, of course, on their the *quality* of the men). When *all* are included in any combination, the maximum potency of the *aggregative kind* is reached. The forces of all units will be united, and thus the *objective strength* will be greatest. But this is not the same as saying that the Number-God One Million is *archetypally greater* than the Number-God Ten. *Subjectively* and *metaphysically, *it is just the other way around.

53. Archetypally, *less is more.* * *The smaller the numerosity of the Number-God, the closer it is (hence, the more *like* it is) to the Archetypal *One, the Father of all Number-Gods. *In terms of *combinative strength,* however, less is less, and more is morethe *quality factor being equal.*

54. Thus, the smaller the numerosity of a Number-God, the more powerful is that God, and the more fundamental or foundational. to the infinite sequence of Number-Gods.

55. More could be developed along this line both mathematically and philosophically, however, we want to look at the dynamics of *astrology* in this numerological context.

56. Reviewing: Integer-Gods and Number-Gods are all *archetypal* (i.e., foundational to the structure of cosmos)*. *The Primary Number-Gods are the Integer-Gods (IGs) and are the Pythagorean Decad.

57. Reviewing: That which we call a number, however, is created by *combination* {whether 1) of Number-Gods, 2) of Number-Gods with numbers, or 3) of numbers with numbers} and is *reflective* of archetypal Number-Gods. That which we call numbers can also be called combinative entities.

58. Reviewing: Every Integer-God arises fundamentally through emanation, but its numerosity relates it to various combinations of Integer-Gods with smaller numerosity. For instance, Integer-God Six arises through emanation from the Integer-God, Five, but has a numerosity which relates it to the interplay or combination of the following Integer-Gods: IG 1 and IG5; IG 2 and IG 4: IG 1, IG 2 and IG3.

**The Astrological Perspective **

59. Every entity which we can *presently* identify as astrologically operative is a *complex entity *(a number)**produced either by 1) varying combinations of Number-Gods, or 2) various combination of *combinative entities *themselves, ultimately produced by combinations of Number-Gods.

60. What I am saying is that Number-Gods can combine to produce composite entities; *and* composite entities can combine (either with themselves or with Number-Gods) to produce even more complex composite entities.

61. By means unknown to the limited mind of man, all beings in cosmos (including those heavenly beings manifesting; throughplanets, stars, constellations, super-constellations, galaxies, etc.)are the results of such combinations, and have their *characteristic numbers* based upon 1) the number of entities which combined to compose them; and 2) the total numerosity of those combining entities.

62. Thus, every entity has its number, and its number will be of two kinds: an *aggregative number,* and a *summation* number.

63. Every entity in cosmos is radiating frequencies which are characteristic of both its aggregative number and its composite number, as well as of the numerosity of its aggregating parts. For instance, for practical the human being has a *superior aggregative number* of *four* because entities from *four* Creative Hierarchies combine to make a human being. The *normal aggregative number* of the human being would depend upon how many representatives from each Creative Hierarchy are involved in the entity manfor instance how many Lunar Lords and how many Solar Angels are involved in making a man. The *summation number* (probably to be related to the number of *cells* or the number of *atoms * in a human being) would depend upon the summing the cellular count within the human system; or even more fundamentally, summing the *atomic count,* and then seeking the complex chord or resultant chord of the sum of all atomic frequencies. The intricacy of such a calculation would be staggering to the mind of man as presently constituted.

64. No matter how complex the combinations and permutations which arise within a given entity, there emerge, finally, perhaps a few numbers (with one number most important) which might be called the Fundamental Resultant Numbers. Simply put, these are the vibratory (hence, radiatory) frequencies *most characteristic* of any given entity.

65. These frequencies radiate into space, and *induce an answering vibration* in those entities which are either exactly resonant or harmoniously resonant to the radiated frequencies.(As a cautionary thought, it is not necessary that only wholes resonate to wholes. Parts of wholes can resonate to other parts of wholes. Few are the relationships in which the parties concerned are *in resonance entirely.*)

66. For instance, according to this scheme, it could be presumed that the numbers emanating from the first ray entity within the Great Bear (still, a very complex being) would find a numerically resonant entity in the Lord of the Constellation Aries, and in the Logos of the planet Mars. (It would not be necessary that these beings be *exactly* resonant to each other, but that they be sufficiently resonant to each other to be called similar in some respects.)

67. If, in astrology, certain beings are said to be related to one another, or to rule or govern one another (and the lower can rule the higher, just as the higher can rule the lower), *these relationships will all be mathematical* and have to do with the interplay between exactly resonant frequencies or with harmonious frequenciesby means of which these related entities have a relatively unobstructed channel of mutual influence between themselves.

68. Astrology is entirely *mathematical,* *Divinely* Mathematical. Mutual influence, mutual augmentations and diminutions or neutralizations are entirely due to the harmonious or inharmonious combinations of frequencies (resulting from the combinative and aggregative numerosities of related entities in the field of Space).

69. When combinative and aggregative numerosities are brought into relationship (i.e., when two entities relate), these numerosities form various *proportions* which are either 1) in unison; 2) harmonious in varying degrees or 3) dissonant.

70. From a vertical perspective, all entities deriving from a given *hyparxis,* or emanating seed point, are members of one vibrational family and are, from an archetypal perspective, always in relatively harmonious relationship. If for instance, I am, monadically, a cell of a particular planetary Logos, and so are you, you and I will always be in harmonious resonance with the planetary Logos of Whom we are an emanation, and with each other (regardless of superficial differences) simply because we came from the *same Source.*

71. Since all beings in cosmos, ultimately came from the same Great Hyparxis (the Universal Logos), it means that, archetypally, at least, all entities are harmonious with the Source and with each otherregardless of more superficial inharmonies and dissonances which arise within the world of combination and numbers.

72. During the process of Universal Evolution, however, one hierarchy may not get along with another, because of dissonant proportions arising from the interplay of their most characteristic numerosities.

73. Entities are *always* being what they are; thus they are always radiating their complex frequencies, with their few *resultant* frequencies being the most noticeable, characteristic or constant.

74. But entities mathematically affect one another, and thus the intensity and purity of their resultant frequencies may be affected by the frequencies of other entities which, through proximity, influence them.

75. The factor of *ratio* or *proportion* is not the only determinant of resonance or dissonance

76. The factor of geometry is correlated to the augmentation, diminution or disruption of combining frequencies, and thus to their resonance or dissonance.

77. Although, in the subtle worlds, entities are constantly *interpenetrating,* which means that they are present within each others ring-pass-nots, in the world of time and space, boundaries exist, and cyclic motion (rotary and revolutionary) is a characteristic of relationship.

78. Interpenetrating entities will *always* influence each other according to the Principle of Resonance (with the greater entity usually influencing the lesser entity more), but periods of intensification, augmentation, reduction, diminution and disruption are correlated with the geometric relations of the outer more material vehicles of such entities.

79. For instance, if there is an entity qualified by the number 2 and it is in relation with an entity qualified by the number 5, there will be certain geometrically defined periods in the rotary or revolutionary cyclic relationship between these two entities, when 2 and 5 will be more harmonious and mutually augmentative, and periods when they will be less so, and perhaps, even mutually disruptive.

80. The inherent numerosity (i.e., *quantity-as-quality*) and of each entity determines the basic harmony or disharmony of their mutually impacting frequencies, *but* the geometrical relationships of the outer forms of these entities, affects the potential for harmony or disharmony.

81. For instance, Jupiter and Venus may always, let us say for arguments sake, be basically harmonious, but geometrical relationships known as conjunctions, sextiles and trines will further the inherent harmony, whereas squares, semi-squares and oppositions will emphasizes the differences in their mutually interplaying frequencies rather than the harmony of these frequencies.

82. Probably the reason why certain points on a circle (in relation to a point of origin) represent reinforcement and other points disruption, has to do with directionality and attraction in the *micro world of vibration.* A study of micro-vibratory dynamics would be in order to understand why squares and oppositions disrupt an asserted frequency (i.e., a radiating numerosity) and why a trine, sextile (or perhaps a conjunction) reinforces an asserted frequency or radiating numerosity.

83. From the practical point of view, this is simply the case. Such dynamics of harmony and inharmony are the very basis of the Science of Relationships (both micro-cosmic and macrocosmic)

84. So astrology (and all relationships within cosmos) *works* or functions because of

a. The constant radiation by entities of their quantity/qualityi.e., their most characteristic resultant frequencies, and the internal ratios and proportions arising from these most characteristic frequencies.

b. The constant interplay between radiating entities causing relationships characterized by 1) certain aggregative and combinative numerosities and 2) certain mathematical ratios or proportions between the complex frequencies of the interplaying entities.

c. The inherent mathematical similarities between such radiating entities.

d. The inherent mathematical harmonies between such radiating entities.

e. The inherent mathematical neutrality between such radiating entities.

f. The inherent mathematical disharmony or dissonance between such radiating entities

g. Periods of mutual augmentation/reinforcement or of mutual disruption/dissonance dependent upon the geometrical relationship between the such radiating entities within space-time cycles of rotation and/or revolution.

85. More simply, astrology works because

a. All entities are One Entity.

b. All entities are hereSpace being an illusion.

c. All entities affect one another (greatly or minutely) because, ultimately, they are derived from the same Source.

d. All entities, ultimately, are related to each other *vertically;* such relationships are *hierarchical* and based upon the Law of Synthesis.

e. All entities are, ultimately, related to each other *horizontally;* such relationships are *non-hierarchical* and are based upon the Law of Attraction.

f. Further, vertical relationships between entities are based upon the Principle of Unison, and horizontal relationship are based upon the Principle of Harmony and Dissonance.

g. All entities have characteristic resultant frequencies (however simple or complex those frequencies)

h. All entities radiate those characteristic resultant frequencies and thus touch (however powerfully or slightly) all other entities.

i. Frequencies are in relation to each other either reinforcing, harmonious, non-reinforcing or disruptive.

j. Periods of mutual intensification between interplaying entities are related to *proximity* and to *cyclic dynamics.*

86. Ultimately, we (all beings in cosmos) all affect each other and we get along or we dont. Astrology is the science of how and why we affect each other, and how and why we get along or we dont.

87. Further, the Purpose of Astrology is through the intelligent utilization of Time and Space to transform all time-space relationships into *Archetypal Relationship* reflective of the *Fixed Design.*