G.W. Adamson presents an analysis of the extreme and mean ratio right triangle, here illustrated, as the template for the structure of time, where the powers of φ are the proportions of the areas of the subdivisions of the apex when divided as shown at any level:1


However, in the absence of a consideration of the logical underpinning of the mathematical facts, Adamson seems to vacillate between two different understandings of the relation of time and the vacuum state. First he says that the apex of the triangle is the location of Planck time, "the time between 0 and 10-43 sec.," "the first moment of creation." At this point, because the apex is always the "potential to become" and exists in the present and is equal in magnitude to the present, Adamson is led to assert that the "POTENTIAL TO BECOME must exist beyond time itself, beyond and transcendental to the 0 point." But later on he says that "behind time is the apex" and that "'Time'" starts not at zero but at 10-43 Sec.," and that between zero and the first instant of time is the vacuum state (= consciousness itself or being in itself [i. e., the potential to become, but not yet "something"]) which potential to become is the apex.

Now, while the vacuum state,"'something' between zero & the first instant of time," is "transcendental to past, present, and future," it cannot be "beyond and transcendental" to the "first moment of creation," i. e., to the first "present," for the reason that such a being "beyond" presupposes just the differentiated temporality -- past, present, and future -- which in turn presupposes the "first moment." It seems Adamson is led to project the potential to become back beyond the zero point because he has not distinguished the first instant of time from a "present" which has a "past." But the vicious circle or infinite regress or what might be called the fallacy of transposed temporality -- projecting time out from within time -- is eliminated if the vacuum state is simply the "first instant of time" and that first instant of time -- a first sheer now -- is not confused with such a "present," that is, with a time which has a past.

In order to make clear that the first now of creation is a time existing ex nihilo, i. e., neither a time which comes into being out of nothing (as if 'nothing' were a potentiality for time, or, indeed, the potentiality of time), nor a time which is a past time continuous with the act of creation, let the extreme and mean ratio right triangle of time be reduced to the underlying "logic of the beginning."2 First substitute for the -values of the triangle the values of the logic which relate within the triangle in the identical manner as the mathematical values (i. e., as φ-2 + φ-1 = 1, φ-1 + 1 = φ, 1 + φ = φ2, . . ., so 0 u10bl.bmp (170 bytes) = 1, 1 = 0, 1 0 = , . . . [the logical corresponds to the mathematical in this further way (where φ0 has the logical value I[dentity], and takes the place of the signs of division and multiplication as required): φ-2 = (φ2 φ0)-1 = 1 I = 0, φ-1 = (φ1 φ0)-1 = 1 0I = , 1 = (φ1 φ-1)1 = 1 0 = 1, φ = (φ0 φ1)1 = 1 I = 0, φ2 = (φ0 φ2)1 = 1 I0 = , φ3 = (φ1 φ2)1 = 1 0 = 1, φ4 = (φ1 φ3)1 = 1 01 = 0, φ5 = (φ2 φ3)1 = 1 1 = , φ6 = (φ2 φ4)1 = 1 0 = 1, φ7 = (φ3 φ4)1 = 1 10 = 0, φ8 = (φ3 φ5)1 = 1 1 = , φ9 = (φ4 φ5)1 = 1 0 = 1, . . .]), as follows (the logarithmic spiral centered on the diagonal is shown for comparison):3


Let this triangle of time represent the latest state of the universe. Then let the successive contractions of the apex, 0 > > 1 > 0 > , with the corresponding increases in the number of differentiated fields, represent the evolution through time from the earliest state of the universe at which stage there is nothing of time but the apex 0, the beginning, the first instant of time indifferently the potential to become. Then inscribe this series within the structure of the 'cornerstone',4 assigning the elements of the series to their places within the 'essence' of the logical lattice5 in accord with the logical value of the respective apices, as follows:



Here then the logical cornerstone is the template of the creation. The sequence from the first now of time which is indifferently the "potential to become" to the last "present" of the universe is inscribed in the sequence of the logical essence (here in the shape of the golden rectangle). This inscription makes visible the fact that although the internal structure of time is logically continuous -- starting with the first instant of time (lower left 0) and ascending to the differentiation of "potential to become," "past," and "present" (middle left ), thence proceeding to the stage in which the "future" is additionally differentiated (central 1), which stage is the direct logical product of the two preceding states of the universe (0 = 1) just as the next succeeding stage (middle right 0) is the logical product of its two preceding states (1 = 0) and the last stage (upper right ) is likewise a direct logical product (10 = ) -- nevertheless the whole of time is discontinuously continuous with what precedes and follows it, with the sequence in which it is inscribed, that is, lower right 1 and lower middle logically produce the first instant of time, the beginning, indifferently the "potential to become" (1 = 0), but the second of the two (lower middle ) preceding the first instant of time (0) cannot in the same way (directly, i. e., non-deductively) be taken together with that first now (0) to produce the second stage of time (), just as the last stage () together with the next to last (0) does not directly produce the upper middle 0, although the upper left 1 is directly the product of the latter and the last stage of time, the end (0 =1).

The thinking now occurring for the first time in history provides a framework in which it can be immediately seen that the creation of the world is not a matter of understanding differentiated from faith or of faith beyond understanding, nor indeed a matter of "subordinating" "any Personal Deity" to a "God" who is "the ONE LAW."6 The actual situation (now able to be logically and concisely articulated for the first time) is considerably more subtle, but nonetheless perfectly clear and precise. The essence of the above logical inscription of created time is 1 [0 . . . 10 . . . ] 0 1, where Father (lower right 1) and Spirit (lower middle ) create the Beginning of Time (lower left 0 = middle left central 1 middle right 0 upper right ) in the form of the Son (0), that is, 1 = [0], but the Son beyond Time (upper middle 0) together with the One God (upper left 1) creates the End of Time (upper right ), and is together with Father (lower right 1) and Spirit (lower middle ) the One God (upper left 1), that is, 1 = 0 [ . . . 01 . . . 0] 1. Created time is inscribed in the life of the Trinity in such a way that the Trinity is the Alpha and Omega of Time and, as such (1 = [0 . . .], [. . . ]0 = 1), is continuous with time precisely in its discontinuity with the form of temporality which is nevertheless Its image ([0 . . . 10 . . . ] = 1) as doubly reflecting, in the doubly inverted temporal Unity (1), Father (1) and Creator (1).

Thus the newly universal logic definitively explicates the verse at the beginning of John's Gospel,7 'IN THE BEGINNING WAS THE WORD (0): [THE WORD WAS] WITH GOD ([0 1 =] ) AND [THE WORD (IDENTICALLY THE WORD WITH GOD) WAS] GOD ([0 (0 1 =) =] 1)', as follows: the limit to the infinite expansion of the universe is the Absolute First Now, but the Absolute First Now has no Past, and Potentiality ("Potential to Become") is differentiated from the Absolute First Now only as Past, therefore Undifferentiated or Pure Potentiality (the Quantum Vacuum) is the Absolute First Now (the Beginning of Time), effectively the "One Universal Law" which is the limit to the infinite expansion of the universe.

The Undifferentiated End of Time is the Omnipotent God (upper left 1) which together with the Omnipotent Understanding (0) creates the Differentiated Potentiality of Time (10 = = 010), Time (010 = 1) differentiated from the Beginning of Time (0), from the "One Universal Law" which is the first instant of time, as the End of Time (10 = ). This Omnipotent Understanding (0) is the Omnipotent God (upper left 1) and, with the Omnipotent God (0 1), is at once the Spirit (lower middle ) prior to the "One Universal Law" (lower left 0) which is the Beginning of Time and the Spirit (upper right ) which is the End of Time. The Form of the Undifferentiated Potentiality or Undifferentiated Beginning of Time is the Omnipotent Father (lower right 1) and, with the Omnipotent Spirit ( 1), creates the Completely Differentiated Omnipotent Understanding (0 [= 1]). The temporality of the universe therefore recapitulates the intelligible fact of its creation, recapitulates its intelligible inscription within the life of the Trinity as creation ex nihilo.

But the cornerstone as template of creation is also the entrance to the interior structure of the Trinity. The sequence of the stages from beginning to end of universal time inscribed within the cornerstone, 0, , 1, 0, , when read as overlapping sets of three, (0[(1)0]), recapitulates the three rows of the cornerstone, 01, 10, 10.8 The analysis of the set of five logical digits into three overlapping sets of three is the perfect analogue of the procedure used to predict rationally the number of edge-overlapping triangles needed to rigidly brace any polygon or polyhedron.9 The regular pentagon is the five-vertex polygon whose diagonal is to its side as φ : 1. The square-based pyramid the area of whose triangular faces is each .5 times the area of the base of the pyramid is the five-vertex polyhedron the sum of one of whose ascending edges and .5 times the base of one of whose triangular faces is to the triangular height of each of its faces as φ : 1.10 5.5 is the ascending edge of the smallest square-based pyramid the area of each of whose faces is a whole number not 1 and .5 times the area of the base of the pyramid. The base of this pyramid is the smallest whole number square other than 1 in the infinite structure of existence, the 4-square.11 In the case of this pyramid the ratio mentioned is the defining ratio of φ, .5(5.5 + 1). The cornerstone with the four digits 1, 0, , 1 -- those assigned to the Divine Essence (1) and the Three Persons (0, , 1) -- outside the inscribed temporal 5-digit sequence, 0, , 1, 0, , the cornerstone as above, viz., 1, 0, [, 0, 1, , 0], , 1, is the perfect analogue of this foundational square-based pyramid qua rationally rigid structure. Let there be, then, a pyramid whose vertices are 0, , 1, 0, and . Applying the formula, T = V - 2 = 5 - 2 = 3,12 the base of this pyramid is composed of two of the required three edge-overlapping triangles (EOT's) in the pyramid, here 0 (Blue) and (Yellow), while the third EOT is one face of the pyramid, here 1 (Green), which together with the two EOT's constituting the square base, braces its opposite face, here 1 (Gray), which last is by analysis the underlying triangle (UT) here corresponding to the Divine Essence, while the two remaining faces of the pyramid are empty triangles (ET's), purely the result of the bracing of the UT (1), by the three EOT's (0, , 1):




The areas of the four triangles, 1, 0, , and 1, are identical. Since the base triangles 0 and are halves of the square base qua area, let the area of each of the four triangles be designated .5.13 But since the two triangles 0 and are also halves of the square base qua form, i. e., as elements of the base of the pyramid edge-overlapping with respect to each other, while the two face triangles designated 1 are differently formed, i.e., as faces of the pyramid not edge-overlapping with respect to each other, let the former be additionally designated .5 qua form, but let the latter be designated 1 qua form.14 The forms and areas thus designated, the formal addition of the 3 EOT's, 0 (Blue; Son), (Yellow; Spirit), and 1 (Green; Father), .5 + .5 + 1, = 2, which is identically the area addition of the 3 EOT's and the 1 UT, 1 (Gray; Divine Essence), .5 + .5 + .5 + .5 = 2. The Three Persons of the Trinity, qua distinction of Persons (EOT's), are neither more nor less than the Three Persons of the Trinity, qua indistinction of Essence (Equal Areas), taken together with the Divine Essence (UT). But the Three Persons of the Trinity, qua distinction of Persons, cannot be taken together with the Divine Essence (EOT UT), that is, there is no distinction of Essence. The area addition of the Three Persons, the Three Persons qua indistinction of Essence, but taken apart from the Divine Essence, .5 + .5 + .5, = 1.5, which is identically the area addition of 0 (Blue; Son) and (Yellow; Spirit) taken together with 1 (Gray; Divine Essence), .5 + .5 + .5 = 1.5. The union of Son and Spirit with the Father in the indistinction of Essence apart from the Divine Essence is identically the union of Son and Spirit with the Divine Essence apart from the Father in the indistinction of Essence, indeed, it is the union of any two Persons with the Divine Essence apart from the third in the indistinction of Essence, at once the union of the Father, qua distinction of Person, and either of the other two Persons, either qua distinction of Person or qua indistinction of Essence, 1 + .5 = 1.5. For the Father, qua distinction of Person, to be united with both the Son and the Spirit in any way whatsoever, i. e., whether qua Persons or qua Essence, is neither more nor less than the Three Persons of the Trinity, qua indistinction of Essence, taken together with the Divine Essence, .5 + .5 + 1 = .5 + .5 + .5 + .5 = 2.15

The cornerstone which is creation ex nihilo inscribed within the Unity of the Trinity, turned inside out is the pyramid which, qua rationally organized rigid structure, is the perfect analogue of the essential relations of that Living Unity which is the Trinity. When attention is paid to the specific dimensions of the foundational pyramid formally analyzed in the preceding -- those which exist in such a pyramid as described whose base is the 4-square of the infinite structure of existence and which perfectly embody the defining ratio of φ, .5(5.5 + 1) -- it will be seen that the shortest path about the pyramid, beginning and ending at its apex, multiplied by the length of the diagonal of its base = 82944.25. Since the shortest path about the entire pyramid, beginning and ending at its apex, lies in perpendicular directions, and since the diagonal of the base also has its perpendicular counterpart, those lengths may be multiplied into 82944.25 to give 82944.5. That pyramid embodying -proportionality, marked with these ordinarily unmarked diagonals and shortest paths about the pyramid (which lengths are the factors of the square root of the unique 82944), when projected from directly above the apex onto the plane, is the limit of the Cartesian coordinate system whose absolute value is Unity:




in significant agreement with the fact that the integral products (the squares of the products of the mathematical values of the odd-numbered letters16) of the Hebrew terms, נקדת האפס של תנופה ('dead center'/'point zero of energy'), קוד קואורדינטות ('coordinate code'), and קואורדינטות קויות ('line [Cartesian] coordinates'), are respectively, 8.2944E22, 8.2944E22, and 8.2944E28, whose shared base factor is identically that of אלהי אברהם אלהי יעחק ואלהי יעקב ('the God of Abraham, the God of Isaac, and the God of Jacob'), integral product 8.2944E26, of יהוה מלך־ישׂראל ('Yahweh King of Israel'), integral product 8.2944E18, of Ιησους Χριστός ('Jesus Christ'), integral product 8.2944E28, and, finally, of לבן כה אמר אדני יהוה הנני יסד בציון אבן אבן בחן פנת יקרת ([Is. 28:16] 'So the Lord Yahweh says this, "Now I shall lay a stone in Zion, a granite stone, a precious corner-stone"'), integral product 8.2944E60.17




1  G.W. Adamson, "The Golden Right Triangle and the Arrow of Time" (San Diego, 1993).
2  D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), Section III.1.
3  Ibid., and Leahy, Foundation, Section III.2.  For the logarithmic spiral see, on this web, The Golden Bowls & the Logarithmic Spiral.
4  Ibid.
5  Ibid.
6  Cf. Leahy, Foundation, Appendix, "The De Trinitate of Augustine and the Logic," which demonstrates the perfect correspondence between the categorically new logic of the beginning and the Trinitarian relationships in Augustine's text.
7  Cf. Jn. 1:1.
8  The writer is indebted to C. Skliris for calling his attention to this fact.
9  Cf. Leahy, Foundation, Section III.3.
10 The ratio of the diagonal of the base of this pyramid to the vertical height of its apex, 8.5 : 3.5, = 2666b.bmp (378 bytes).5, the square root of the rational product of the minimum proportion, 4 : 1 :: 2 : 3. Cf. Leahy, Foundation, Sections III.1 and III.5.
11 Cf. Leahy, Foundation, Section IV.2.
12 Cf. Leahy, Foundation, Section III.3.
13 In the case where the base of this pyramid is 12, the areas are literally each .5, its face height 1, its altitude .866025404, and its slanted edge [(φ2 + 1)/2]/[(51/2 + 1)/2] = [(φ2 + 1)/2]/φ = 1.118033989.
14 This formal distinction corresponds to the arithmetic values of the logical digits, [0 + = 1] = [.5 + .5 = 1]. Cf. Leahy, Foundation, Sections III.1, III.5, and IV.2.
15 The ratio of the Three Persons, when taken together qua distinction of Persons -- perforce not taken together with the Divine Essence -- (.5 + .5 + 1 = 2), or of its equivalent, the Three Persons taken together qua indistinction of Essence with the Divine Essence (.5 + .5 + .5 + .5 = 2), to the Three Persons taken together qua indistinction of Essence but apart from the Divine Essence (.5 + .5 + .5 = 1.5), or to any of the equivalent relations, is 2/1.5 = .  But is the analytical value of the root proportion of the cross ratio, the elliptical proportion of the constant ratio of the otherwise indefinite lengths of the line in projective geometry.  Cf. Leahy, Foundation, Section III.3, Part 1.  The ratios 1333b.bmp (378 bytes), 1.5, and 2, are precisely the values of the proportions developed in the conic-based analysis of the infinitely flat structure of the universe.  The apparent coincidence is eliminated when one notes that in terms of the completely logical geometry, where the square = 0000 = the circle = 0000 (cf. ibid.), the square-based pyramid is the identical figure to the cone.
16 Cf. Leahy, Foundation, p. 357, n. 13, et passim. For 'integral product', see, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product and Related Terms.
17 For 82944 see Leahy, Foundation, Sections III and IV, passim; also, on this web, Report on a Dream & Related Matters & the God Particle, Real Trinary Logic Geometric Series Infinite Sequential Summing, 82944 & the Four Fundamental Forces & the God Particle, and The Difference.  The integral product of the Creator's final judgment concerning his work, i.e., of the טוב מאר ('very good') of Genesis 1:31, is 8.2944E6. Franz Rosenzweig says in The Star of Redemption, speaking of the 'love better than wine' of Song of Songs 1:2, "This 'better' takes up the thread directly at the point where the final 'very good' of creation had dropped it."  The integral product of the טובים בבין ('better love') of the latter text is 8.2944E8.



Home Page