DNA, APOCALYPSE, & THE END OF THE MYSTERY

The New Jerusalem Diagram and the Missing Circle.

J. Michell has reconstructed the geometric pattern of the ‘heavenly city’ which is the template of the New Jerusalem of Revelation 21, St. Mary’s Chapel at Glastonbury, Stonehenge, and the City of Magnesia in Plato’s The Laws.1 The present writer distinguishes the mathematical and historical value of Michell’s work from the latters avowed antagonism to modern science, his traditionalist disdain for the metric system, and his fundamental perennialism none of which attitudes are shared by the present writer. Indeed, it will be made clear in what follows that the mathematical pattern of the esoteric and perennial tradition presented by Michell is radically incomplete, and is, for the first time in history, made complete by the mathematics of an essentially new thinking which in fact is the transcendence in essence of the difference between modern and ancient systems, at once the absolute and final closure of any aspiration whatsoever to ‘re-enter the primeval paradise’. With that stipulation, Michells New Jerusalem diagram, which is the reconstruction of the ‘heavenly city’, is as here illustrated:2

Beginning with the Pythagorean triangle of sides 3, 4, and 5, the large square (11 × 11) in this diagram is constructed such that the circumference of the circle cutting across its sides (the circle of Michells ‘heavenly city’) is, if π = 22/7, a length (44 = 14 × 22/7) identically the length of the perimeter of the square (44).3 The diameter of the outermost circle (the circle enclosing the 12 ‘lunar circles’) is 17. The diameter of the circle inscribed in the square (the ‘earth circle’) is 11. The diameter of the circle inscribed in the four triangles is 5.5. The diameter of the circle nearest the center of the diagram (the ‘thirteenth moon’) is 3. The point at the center of the diagram is taken to be a ‘central dot’ (relative value = ) surrounded by a ‘circular space’ (relative value = .2), either of which is understood to represent the ‘pole of the universe, passing vertically through’ the center of the diagram, as here illustrated:4

The whole figure is enclosed by a 12-sided polygon, corresponding to the sum of the sides of the Pythagorean triangle, 3 + 4 + 5 = 12. The product of 3 × 4 × 5 = 60. 12 + 60 = 72, while 12 × 60 = 720.5 The original dimensions of the diameters, , .2, 3, 5.5, 11, 14, and 17,6 multiplied by 720 yield 24, 144, 2160, 3960, 7920, 10080, and 12240, where 7920 corresponds, on an adjusted scale, to the 12(000 furlongs) × 660 ft. side of the New Jerusalem square.7

This New Jerusalem diagram fits neatly into the plan of the ‘heavenly whorls as revealed to Er’ in Plato’s Republic, ‘in the order given by Plato and proportioned in accordance with’ the values of the musical sequence, 6, 8, 9, 12, 18, 24, 27, and 36, as here illustrated:8

where the total diameter = 10368/36 = 288. The total diameter of the first three rings (34 × 2 = 68) times 180 = 12240, the total diameter of the New Jerusalem diagram, while that of first two rings (22 × 2 = 44) times 180 = 7920, the diameter of the circle inscribed in the large square of the New Jerusalem diagram.

Now the truly remarkable fact is that in the whole of Michell’s analysis of the geometrical pattern of the ‘heavenly city’, indeed, no doubt because of the fact that in the whole history of the appearance of the pattern from Stonehenge to Glastonbury there is no appearance of such an element, nowhere is it noticed that there is one fundamental element missing from the pattern these thousands of years, viz., the unmarked circle in which the 11 × 11 (or multiplied by 720, 7920 × 7920) square is implicitly inscribed, as here illustrated (where the green circle is the ‘missing circle’):

The diameter of this ‘missing circle’ is 21/2 × 11 = 15.55634919 (or multiplied by 720, 11200).9  In terms of the original, i.e., unadjusted, scale of 12000 furlongs in Revelation 21, this diameter would be 15556.34919. Now, among the first 1 billion natural numbers there are only eight whose integral products are either the 1st or 3rd parts of themselves, that is, members of the classes to which belong, respectively, the uniquely related numbers, 82944 and 27648. The sum total of these eight numbers is 124451, so that the average value of the eight = 15556.375, with a difference ~ 1.7/1E6, the diameter of the ‘missing circle’ of the New Jerusalem diagram.10 124451 is at once, with a difference ~ 5/1E5, 10 times the circumference of the 1/(81/2 × 1E3) smaller circle (5.5 × 22/7 × 720 = 12445) inscribed in the four triangles which, in turn, are inscribed in the circle twice its size whose circumference (11 × [π = 864/275] × 720 = 24883.2)11 is exactly .3 times 82944, that is, .3 times the ‘absolute dead center’ number,12 and which is in turn inscribed in the New Jerusalem square, which latter is, again, in turn inscribed in the ‘missing circle’.

The radius of the ‘missing circle’ (= 7.778174595, when the diameter is taken to be 15.55634919) is exactly (60501/2)/10, that is, 1/10th the ratio of the side of the New Jerusalem square (taken as 7920) to the side of the square (101.8233765) inscribed in the ‘circular space’ which is the central shaft through which passes the ‘pole of the earth and universe’, which latter square is the side of the ‘absolute dead center’ cube, as here illustrated (the side of the cube the square inscribed in the central shaft): [If your browser does not display this image click here; use back button to return to this place.]

The ‘absolute dead center’ cube, first constructed in 1985 in the context of the elaboration of the logic of the essentially new thinking now actually occurring for the first time in history,13 fits perfectly, organically, and with absolute appropriateness into the place at the very center of the New Jerusalem diagram, the 1/36th part of its side (10368/36 = 288 = √82944 = 3168/11), its central square,14 corresponding precisely to the square (16.97056275 × 16.97056275) inscribed in the ‘central dot’ of the diagram [inset], the area of which ‘dot’ is the fundamental measure of the New Jerusalem diagram, 3168/7 or 452, or 1 New Jerusalem unit.15

The diameter of the earth circle inscribed in the square inscribed in the ‘missing circle’ is 7920, which, divided by 720, is the original 11. This 11 is effectively the value of the diameter (= 11) of the decagon formed by the double helix structure of the DNA molecule, which decagon is visible in the top-down view of the molecule. The ratio of the circumference of the circle in which the DNA decagon is inscribed (≈ the circumference of the earth circledivided by 720) to the circumference of the ‘missing circle’ of the New Jerusalem diagram is effectively 101.8233765, the edge of the ‘absolute dead center’ cube.16

Postscript Concerning Michell and the Missing Circle

In September 1992 the writer wrote to J. Michell to convey to him the essentials of the preceding analysis. No response to this letter has been received to date. But in his 1994 book, At the Center of the World, in a chapter entitled "The Cosmological Prototype," Michell recapitulates his previous analysis of the New Jerusalem diagram, but now adds the following diagram:17

Michell writes: "To complete [the] outline of the [New Jerusalem] diagram, the original circle with radius 5040 is enclosed within a vesica, the first figure of symbolic geometry. The longer axis of the vesica is calculated to be 17460, the previously mentioned number of fusion, and that number is also the side of the square containing it. A circle is constructed to contain the square, and the area of that circle is (if π = 22/7) exactly 12! or the numbers 1 to 12 multiplied together, or 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12."18 While it might appear that the analogue of the ‘missing circle’ is here in the form of this image of completeness, it turns out that this is not the case, as is demonstrated when the ‘missing circle’ is relocated within this completed form of the New Jerusalem diagram:

Indeed, when the ‘missing circle’ is placed within its vesica, the square upon the length of its longer axis is inscribed in the true analogue of the ‘missing circle’, which true analogue transcends the circle of completeness just as the ‘missing circle’ itself transcends the cosmological circle of the original diagram:

Here the circumference of the outermost circle — the circle of transcendent completeness — the true analogue of the ‘missing circle’ (the ratio of the former to the latter ≈ √6 : 1) — divided by 1E5 ~ αz ~ (αy).5, i.e., ~ the product of the fine structure constant and the edge of the cube whose surface area is the sum of the three unique numbers identically their integral products, at once ≈ the square root of the product of the fine structure constant and the edge of the ‘absolute dead center’ cube.19  The original diameter of this circle (the diameter divided by 720) (1E2)/φ2, while the original diameter of the outermost circle of the ‘image of completeness’, the length of whose circumference is now seen to coincide the length of the perimeter of the square constructed upon the length of the vesica’ of the ‘missing circle’, the angstrom circumference of the DNA molecule.20

The Logically Outfitted Triple Absolute Dead Center Cube and the New Jerusalem Diagram.

The volume of the triple ‘absolute dead center’ cube is, with a difference ~ 3/1E4, 3168000, 100 times the ‘squared circle’ of the New Jerusalem diagram.  The ratio of the body diagonal of the triple New Jerusalem cube (26267.66834, with a difference ~ 6/1E5, 1E4 × 82944/31680, or, with a difference less than 1/1E2, 1E4 × φ2) to that of the triple ‘absolute dead center’ cube (337.7099347, the square root of Plato’s ‘World Soul’ number, 114048)21 is exactly 60501/2 or 10r, 10 times the radius of the ‘missing circle’ in the New Jerusalem diagram.22  The ratio of surface areas of the two structures is 6050 or (10r)2, the square of 10 times the radius of the ‘missing circle’, while the ratio of their volumes is 60501.5 or (10r)3, the cube of 10 times the radius of the ‘missing circle’.

The Integration of The New Jerusalem Diagram, The Triple Absolute Dead Center Cube, The Universal Form of All Logical Propositions, and the Logical Proportion, 1 : 2 :: 4 : 3.

Let the four overlapping triangles whose twelve vertices support the twelve ‘lunar circles’ of the New Jerusalem diagram23 be the four alternating triangles of 1’s and ’s (alternating, green, yellow, green, yellow) each of which has one side which is the diagonal of one of the four parallel planes of the triple absolute dead center cube,24 and let each of the three members of the four sets of ‘lunar circles’ be identified by the triangle supporting it as either or 1, yellow or green, as here illustrated: [If your browser does not display this image click here; use back button to return to this place.]

Then the four sets of ‘lunar circles’ are, clockwise from the top, 1 (2 yellows, 1 green), 1 (1 green, 2 yellows), 11 (2 greens, 1 yellow), and 11 (1 yellow, 2 greens), where the logical relationship of these four sets is indicated by the set of 0’s (blues) composed of the two diagonals which parallel the 1 and diagonals of the four parallel planes of the triple cube and the two diagonals connecting these two,25 so that the most direct path along the lines of reflection represented by the four diagonals of 0’s (blues) transforms the immediate clockwise 1-2-3-4 order of the four sets of ‘lunar circles’ to the 1-2-4-3 reflective order of the ‘logical’ proportion,26 that is, to the order of the proportion, 1 (yyg) : 1 (gyy) :: 11 (ygg) : 11 (ggy), which, when p = " (y) is the first ‘lunar circle’," and q = " (y) is the second ‘lunar circle’," is in the form of the universal form of all logical propositions, .27

Notes

1 J. Michell, The Dimensions of Paradise: The Proportions and Symbolic Numbers of Ancient Cosmology (London, 1988). For the New Jerusalem pattern in the larger context of mathematical symmetry and design science, see J. Kappraff, Connections: The Geometric Bridge Between Art and Science (New York, 1991).  For the New Jerusalem cube dimensions in Revelation 21:16, see, on this web, Physical Variables, Placedness, & the Absolute Dead Center Cube, note 1.
2 After Michell, The Dimensions of Paradise, p. 36.
3 Ibid., pp. 68f.
4 Ibid., p. 39.
5 Ibid., pp. 36ff.
6 The product of these original dimensions is, with a difference ~ 7/1E5, the square root of 82944 (cf. D.G. Leahy, Foundation: Matter the Body Itself [Albany, 1996], Sections III and IV, passim), the full significance of which is treated below in the text.
7 Michell, The Dimensions of Paradise, pp. 24f.
8 After Michell, The Dimensions of Paradise, pp. 145ff.
9 If for the diameter 15.55634919 is substituted the L series value 15.5 (cf. Leahy, Foundation, Section IV.2, pp. 519ff.), then the sequence of the diameters of the major circles of the New Jerusalem diagram, including the ‘missing circle’, is 11, 14, 15.5, and 17, and the L series partial sums for these values are: S11 = .75(112 + 11) - 5.5 = 93.5, S14 = .75(142 + 14) = 157.5, S15.5 = .75(152 + 15) + 8 = 188, and S17 = .75(172 + 17) - 8.5 = 221. The sum of this sequence of L series partial sums is exactly 660, the multiple of 12(000) furlongs which produces the 7920(000) unit side of the New Jerusalem square, and exactly ten times the sum of all the whole number diameters of circles within the diagram (3 + 5.5 + 11 + 14 + 15.5 + 17 = 66). 8 (the cubic number) × 15.55634919 × 1832 (this last the transcendental constant, P1.5c [cf. Leahy, Foundation, Section III.5]) = 228096, exactly the total interior and exterior surface area of the triple ‘absolute dead center’ cube (cf., on this web, Logically Outfitted Cube[s]).
10 The sum of all of the first 1 billion natural numbers whose integral products are unit fractions of themselves the denominators of which are primary digits of the number system other than 1 or 3 (excluding 2985984 and 429981696, multiples of 82944 [cf. Leahy, Foundation, Section III.7]), is 47536, which is, with a difference ~ 3/1E4, the sum of all the whole number diameters of circles within the New Jerusalem diagram (see above) multiplied by 720 ([3 + 5.5 + 11 + 14 + 15.5 + 17 = 66] × 720 = 47520).
11 For the use here of this alternate value of p, cf. Michell, The Dimensions of Paradise, p. 24.
12 Cf. above, n. 6.
13 Ibid. The integral product of the Hebrew for dead center, נקדת האפס של תנופה, is 8.2944E22, and its rational product is 1. This is the ‘point zero of momentum’, ‘point zero of swing’, indeed, in effect, still point of the turning.   נקרת האפם של תנוחה, ‘point zero of position’, ‘point zero of rest’, has the identical integral product, 8.2944E22, while its rational product is 1E1.  In their integral product or ‘absolute’ forms, ‘point zero of momentum’ and ‘point zero of position’ are identical.  The rational priority of ‘absolute’ dead center, ‘absolute’ unconditioned position, to ‘absolute’ unconditioned momentum is caught in the priority of its rational product, 1, to the latter’s 10.  But conceived essentially the identity of momentum and position is resistance. The division within identity which is of the essence of modern consciousness is then manifest in physics as the fundamental distinction of momentum and position as alternative conceptions, which duality of concepts essentially precludes the beginning of the perception of resistance itself. But if it is understood that absolute point zero of position is the temporal identity of body and that absolute point zero of momentum is pure displacement, then the temporal identity of body is resistance identified with pure displacement, and for any body the greater its resistance the less is the identification of its temporal identity with pure displacement. The body of perfect resistance is the body whose temporal identity is not identified with pure displacement: the body of the resurrection. The resurrection body, the body of perfect resistance, the body itself now beginning to exist, is the body that experiences no resistance, the body for which the universe is perfectly ordered. Indeed, the body for which the universe is perfectly ordered is in fact the body which perfectly orders the universe. In the first instance this is the body of Jesus Christ the Son of the Father, concerning whom Paul writes in Colossians 1:17, καὶ τὰ πάντα ἐν αὐτῷ συνέστηκεν, ‘and all things hold together in him’.  This is the text which epitomized for Jonathan Edwards his notion that the very essence of body is resistance which is in turn an immediate effect of God’s creative activity (cf. J. Edwards, Scientific and Philosophical Writings [The Works of Jonathan Edwards, Volume 6, ed. W.E. Anderson, New Haven 1980]).  The integral product of this Pauline text is 8.2944E38, while its rational product is 1E1. The body of perfect resistance, the body of the resurrection, is also the body of all who are raised from death, concerning which Paul writes in 1 Corinthians 15:44, ἐγείρεται σῶμα πνευματικόν, ‘what is raised is the spiritual body’, the integral product of which statement is 8.2944E40.  The integral product of ἡ ἐσχάτη ἡμέρα (John 6), ‘the Last Day’, is 8.2944E16.  In the form of the absolute objectivity of the thinking now occurring for the first time in history the body of the resurrection is the very form of thought: the new thought is the beginning of the body of perfect resistance: the beginning of the body which perfectly orders the world.
14 For the conception of the ‘central square’, cf. Leahy, Foundation, Section IV.2.
15 Cf. Michell, The Dimensions of Paradise, p. 39, et passim. The precise, unadjusted, value is 144p, a value uniquely recurring in the ‘dead center cube’ (cf. Leahy, Foundation, Section IV.2, p. 524, n. 98, and p. 525, n. 99). If the value is incorporated in a series of ratios composed of itself together with the natural numbers whose integral products are times themselves, thusly, : 48 :: 147 : 972 :: 11907 : 27648, the rational product of this series is, with a difference ~ 6/1E4, 1 New Jerusalem unit/1E6. The L series partial sum for this sum of elements (neglecting ) is S40722 = .75(407222 + 40722) = 1243741505, with a difference less than 1/1E2, the square of the circumference (720 × 48.89138317 = 35201.79588) of the ‘missing circle’. (For the fact that the inverse 4th root of the 100th part of circumference of the 'missing circle' is the factor common to the weak and strong force exponents of 82944, see, on this web, 82944 & the Four Fundamental Forces & the God Particle.)  The diameter of the ‘missing circle’ (720 × 15.55634919 = 11200) is the base linear measure of the side of the ‘absolute dead center’ cube times the sum of the three separately calculated sequential sums of the 1st three rows of the 10 × 10 grid superimposed on the ‘infinite logical lattice’, where the diagonal of the grid is a ribbon of 1’s descending left to right (cf., for example, Leahy, Foundation, Section III.4), that is, √10368 × 110. (110φ, with a difference ~ 3/1E5, is the square root of the New Jerusalem ‘squared circle’, that is, the square root of 31680 [= 44 × 720 (see above)], while 110φ2, with a difference ~ 6/1E5, is the square root of the ‘absolute dead center’ number, 82944.)  The partial L series sum for the metric value of the velocity of light (S299792458 = .75[2997924582 + 299792458] = 6.74066386301057E16) is, with a difference ~ 2/1E4,

[1 × 784 × 82944 = (9!/ i) = 6.5028096E7]  × 1.0368E9,

while the partial L series sum for the inverse value of the Planck constant, S1.05457266E-34-1, = 6.74385536519925E67, so that, with a difference ~ 5/1E4, S1/ = Sc × 1E51. Since, with almost the exact difference, 1E51 = (1/c)2, Sc = S1/ × (c)2, with a difference almost exactly equal to 1/c (the difference from 1/c ~ 4/1E8).  Further, cf. Leahy, Foundation, Sections III.5, III.6, and III.7. In Section III.6 it is demonstrated that in the infinite series of natural numbers there are only three numbers identically their integral products. The third is 784, which, however, does not fit together with its third part in the above formula, that is, the integral product of its third part is not its ninth part, as it is in the case of 1 and 82944. In this respect 784 is further removed than 82944 from functional identity with 1.  The product of the three unique numbers,

1 × 784 × 82944 = (9!/ i) = 6.5028096E7,

is a function of relations of the foundational digits of the natural number system.  In addition to 27648 there are four other natural numbers whose integral products are their 1/3rd parts, viz., 48 (where 42 = 16), 147 (where [1 × 7]2 = 49), 972 (where [9 × 2]2 = 324), and 11907 (where [1 × 9 × 7]2 = 3969), whose third parts, however, are not the ninth parts of larger numbers whose integral products are the larger numbers themselves (the relation unique to 27648 and 82944 among natural numbers [cf. the formula above in the text]). But the 1/3rd part of the product of the first two of these numbers multiplied by 27648 is 6.5028096E7, i. e., (48 × 147 × 27648)/3 = 1 × 784 × 82944 = 6.5028096E7.  This last radically foundational number appears linguistically in the integral products of the foundational notions, ἡ καταβολή κόσμου (‘foundation of the universe’ 6.5028096E23]), ἐγώ εἰμι τὸ φῶς τοῦ κόσμου (John 8:12: ‘I am the light of the universe’ [6.5028096E47]), Ἰησοῦς Χριστὸς κόσμου (‘the cosmic Jesus Christ’ [6.5028096E39]), and ἡμεῖς δὲ νοῦν Χριστοῦ ἔχομεν (1 Corinthians 2:16: ‘we have the mind of Christ’ [6.5028096E41]).  The integral product of Euclid’s term (Elements VI, def. 3) for the primary partition of unity, ὁ άκρος καὶ μέσος λόγος (‘the extreme and mean ratio’ [‘the golden section’]) is 6.5028096E37.  Finally, the integral product of Plato’s term in the Timaeus (33a) for the ordered totality of the ordered universe,  ἕνα ὅλον ὅλων (‘one whole of wholes’), approximates — the difference ~ 0.08 pph — (1 + 784 + 82944)1/2 × 1E8 × 784 × 82944.  This, in turn, mirrors the integral product of the larger context of the phrase in Plato’s text, ἕνα ὅλον ὅλων ἐξ ἁπάντων τέλεον καὶ ἀγήρων καὶ ἄνοσον αὐτὸν ἐτεκτήνατο (‘he fashioned it as a single whole consisting of all these wholes, complete and free from age and sickness’ [trans. F.M. Cornford (London, 1941)]), which approximates — the difference ~ 0.08 pph — (1 + 784 + 82944)1/2 × 1E78 × 784 × 82944.  The integral product of the whole sentence in which the phrase appears, διὰ δὴ τὴν ἀιτίαν καὶ τὸν λογισμὸν τόνδε ἕνα ὅλον ὅλων ἐξ ἁπάντων τέλεον καὶ ἀγήρων καὶ ἄνοσον αὐτὸν ἐτεκτήνατο (‘For this reason and so considering. . ..’ [ibid.]), approximates — the difference ~ 0.08 pph — 7.84E138 or 6.5028096E143/(1 × 82944).  The integral products of η καταβολή (‘the foundation’), Ἰησοῦς Χριστὸς (‘Jesus Christ’), and ἐγὼ τὸ ῍Αλφα καὶ τὸ ῎Ω (‘I am the Alpha at once the Omega’) are, respectively, 8.2944E12, 8.2944E28, and 8.2944E32.
16 For the foundational role of the edge of the dead center cube, cf. Leahy, Foundation, Sections III.5 and IV.2.
17 After J. Michell, At the Center of the World: Polar Symbolism Discovered in Celtic, Norse and Other Ritualized Landscapes (London, 1994), p. 171.
18 Ibid.
19 For the complex series the sum of which = αz and y).5, and for the linguistic analogues thereof, see Leahy, Foundation, pp. 524ff.  For the three unique numbers identically their integral products, see above, note 15.
20 For the ‘original’ lengths of the New Jerusalem diagram, and the angstrom length of the DNA molecule, see above, "The New Jerusalem Diagram and the Missing Circle."
21 Cf. Michell, The Dimensions of Paradise, pp. 163ff., for Michell’s analysis in support of his hypothesis that 114048 is what Plato had in mind as the number which reacts ‘to every part of the created universe’. The fact that 1140481/2 is the body diagonal of the triple ‘absolute dead center’ cube is evidence of the truth of this hypothesis.
22 See above.
23 Ibid.
24 See, on this web, Logically Outfitted Cube(s).
25 Ibid.
26 Cf. Leahy, Foundation, Section III.1.
27 If, where the distinction of the two subsets, first and second places, and third place, provides the basis for the calculation, the logical values of the four sets of New Jerusalem ‘lunar circles’are substituted as the elements of this proportion, the proportion reads 1 : 1 :: : 0, which is a transposition of the fourfold minimum proportion of the elements of the trinary logic in which "Identity is unity" (cf. Leahy, Foundation, Section III.1, "Afterword 2").

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