EPITOME OR FOOD FOR THOUGHT

Where (x/6)4/x3 and 8x3/x4 are the two ratios whose relation defines the rational constitution of any cube, 0, U, and 1 the elements of a dyadic ternary logic, and 0,  , and 1 the elements of real trinary logic,

0U = 0 = 1 = (x/6)4/x3 × 8x3/x4 = 162−1,

true for both logics and all cubes.

00 =  = 11 = 1 = [(x/6)4/x3]2 = (8x3/x4)2 = [(8x1/x2)2 = (8x2/x3)2 = (8x4/x5)2 = . . .] = 162−1,

uniquely true for real trinary logic and the absolute dead center cube.1

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Compare the Poynting vector rate of change of energy per unit area S when a plane electromagnetic wave passes through a volume element:2

likewise the intensity of the wave I defined as the time average of S:3

where the unique properties of real trinary logic and the absolute dead center cube can be seen to underlie the Poynting vector dynamic structure E2 = B2 = EB:

00 =   = 11 = [(x/6)4/x3]2 = (8x3/x4)2 = [(8x1/x2)2 = (8x2/x3)2 = (8x4/x5)2 = . . .] (x/6)4/x3 × 8x3/x4.

In the case of the absolute dead center cube [(x/6)4/x3]−1 = (8x3/x4)−1 = the Volume/Surface ratio of the absolute dead center hypercube.4  Where there is a parallel-plate charging capacitor with circular plates of radius R with a circular path between the plates whose radius r < R,5

the Poynting vector is

and where R = √10368 mm with R4 = 1.07495424e8 mm4, the Volume/Surface ratio of R4 is

[(R/6)4/R3]−1 = (8R3/R4)−1.6

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This unique identity of logical and numerical relations in the case of the operations of real trinary logic7 and the unique mathematics of the absolute dead center cube8 coincides the agreement of integral product identities in the transdecimal calculation9 of the respectively relevant Greek and Hebrew terms.

Λγος κα ριθμς (‘absolute’ ‘Logos At Once Number’) = 8.2944e22,

נקדת האפס של תנופה (‘absolute’ ‘Dead Center’) = 8.2944e22.10

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In the equation unique to the absolute dead center cube, (x/6)4/x3 = 8x3/x4 = √162−1, on the left side of the equation (x/6)4 = the unvisualizable 4th dimension volume 82944, and, on the right side, x4 = the unvisualizable 4th dimension volume 107495424.

The integral product of the Hebrew for ‘the volume will not be visualized', הנפח לא יהיו להיות דמיינו,k= 8.2944e28 = the integral product of the Greek for ‘Jesus Christ', Ιησοῦς Χριστός.11

The integral product of the Hebrew for ‘the volume not able to be visualized’, הנפח לא המסוגלת להיות דמיינו,= 1.07495424e36.12

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The circumference of the circle intersecting the unique (x/6)4/x3 = 8x3/x4 absolute dead center cube hyperbola

equals 8π = Gμν/Tμν the ratio of the curvature of spacetime to matter/energy when Einstein’s field equations are expressed in geometrized units.13

Notes

1 See, on this web, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube.  Cf. D.G. Leahy, The Cube Unlike All Others (CreateSpace, 2010), Section I.1.  The operation here described uniquely shared by real trinary logic and the absolute dead center cube at once logically differentiates the dead body and the living body.  Cf. D.G. Leahy, Beyond Sovereignty: A New Global Ethics and Morality (Aurora, 2010), pp. 63f., n. 14: “What is required [to understand the logic of ‘the body qua living’] is that the mediated identification be qua actual an existing root of the whole. The members of the living body qua actual β = {{}{00}} and qua actual reciprocal interrelatedness γ = {{01}{01}} and δ = {{1}{1}} are embodied members of the body immediately qua actual the whole and an existing root of the whole α = {{}{00}} = {{{01}{01}}{{1}{1}}} = {11} = {1} that is the body. Each embodied member of the living body qua actual and qua actual reciprocal constitutional interrelatedness is identically the set of logical elements that are their square roots α = {1}.”  The integral product of τ σῶμα τῆς ζωῆς, ‘the body of life’, = 6.5028096e25 (where 65028096 = 1 × 784 × 82944 the product of the three natural numbers uniquely equal to their integral products.  See, below, n. 4), the rational product = 112.5 (= 1.13−1 × 27), and the linear product = 5.7802752e23.  5.7802752e23.125 ≈ 3.2e5/343 the rational product, the ‘identity’, of Λγος κα ἀριθμς, ‘logos at once number’.  So, also, (5.7802752e23.125)17/37 [≈ (3.2e5/343)17/37] ≈ eπ = (−1)-i.  See, below, n. 10.

2 Adapted from S-B. Liao, et al., “Introduction to Electricity and Magnetism”, MIT OpenCourseWare.  Online.  Available at: http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/maxwells-equations/the-displacement-current-and-maxwells-equations/MIT8_02SC_notes26to30.pdf.  February 2013.  For the occurrence of visible electromagnetic light waves in the early universe, see, on this web, .

3  Ibid.

4 See, on this web, Measure Beyond Beyond Reach.

5 For the capacitor illustration and the Poynting vector equation following, cf., above, n. 2, S-B. Liao, et al.  √10368 is the unit dimension of the edge of the absolute dead center cube (cf., above, n. 1).

Where M = mass, M/T = mass flow rate, M/T2 = surface tension, and M/T3 = the Poynting vector, consider the sequence M, M/T, M/T2, M/T3 where the following is true (M × M/T × M/T2)/M/T3 = M2.  Note also that where i(x) is the integral product of x, and i(x) = x, and i[i(x)/3] = i(x)/9, then, uniquely among all natural numbers, x = 82944 (cf. D.G. Leahy, Foundation: Matter the Body Itself [Albany, 1996; eBook, 2009], Sections III.6 and IV.2, et passim; also, ).  Then let there be the sequence [i(x)/9]/i[i(x)/9], i(x)/9, i(x), corresponding by analogy to the first three members of the stipulated M sequence, where [i(x)/9]/i[i(x)/9] = 113.7̅7̅7 = 322 × 9−1 (corresponding to M mass), i(x)/9 = 9216 = 322 × 91 (corresponding to M/T mass flow rate), and i(x) = 82944 = 322 × 92 (corresponding to M/T2 surface tension).  The question arises what/where is the 4th term corresponding to the Poynting vector M/T3 in the stipulated M sequence?  The 4th term turns out to be i[i(x)/9][i(x)] = 6718464 = 322 × 94 (corresponding to the M/T3 Poynting vector), where 6718464 = (36√2)4 = r4 = the inradius (the radius of the inscribed circle) of the face of the absolute dead center cube raised to the 4th power, neatly corresponding geometrically to the 4th power of the radius of the charging capacitor circular parallel plates, R4, in the Poynting vector equation:

.

Note that the rightness of the analogy is further demonstrated in the fact that as (M × M/T × M/T2)/(M/T3) = M2, so ([i(x)/9]/i[i(x)/9] × i(x)/9 × i[x])/(i[i(x)/9][i(x)]) = ([i(x)/9]/i[i(x)/9])2.  For more on the inradius of the absolute dead center cube, cf., below, n. 10; also, on this web, Mathematical & Physical Constants.  Cf., also, on this web, .

7 Cf. Leahy, Foundation, Section III.1, et passim.  See also, on this web, Quantum Gravitational vs. Quantum Logic: Virtually Left-handed Real Trinary Logic.  Cf., also, D.G. Leahy, Faith and Philosophy: The Historical Impact (Aldershot and Burlington, 2003), Chapter 7.

8 Cf., above, note 1, and Leahy, Foundation, Section III.5, et passim.

9

10 The complete transdecimal results for the two terms are as follows.  Λγος κα ἀριθμς: Integral product = 8.2944e22, Rational product = 3.2e5/343, Linear product = 8.89056e19.  נקדת האפס של תנופה: Integral product = 8.2944e22, Rational product = 1, Linear product = 8.2944e22.  With respect to the rational product of Λγος κα ἀριθμς, note that (3.2e5/343)17/37 eπ = (−1)-i Most precisely,

accurate to .037 ppb, where the difference equals precisely

,

where 2880000 = √8.2944e12 the square root of the integral product of מלה מיד אמצע (‘absolute’ ‘Logos At Once Mean’).   Also, where the inradius of the face of the absolute dead center cube = 36√2, the rational product × the linear product of Λγος κα ἀριθμς = (3.2e5/343) × 8.89056e19 = 3.2e19 × (36√2)2 (for more on the role of the inradius of the absolute dead center cube, cf., above, n. 6).  See, also, on this web, The Diagonal Logic of the Triple Absolute Dead Center Cube & Certain Fundamental Mathematical & Physical Constants and Real Trinary Logic, the Imaginary Number i, & the Cyclic Series of Complex Numbers

11 See, on this web, ; also , where it is noted that, compared to the visualizable 8 cubes constituting the hypercubic surface that is Dali’s cross, the Corpus Christi itself is in the place of the 9th hypercubic element — the unimageable hypercube volume.  Concerning this 9th hypercubic element Dali said: "The number nine is identifiable and becomes especially consubstantial with the body of Christ."

12 See, on this web, Measure Beyond Beyond Reach.

13 Cf. http://en.wikipedia.org/wiki/Einstein_field_equations.  See, on this web, The Magnitude of Being.