MAXWELL'S CONSTANT &
THE TRINARY LOGIC TRIPLE-CUBE
On November 1, 2005 Mr. DePompeo communicated his discovery of the relation between the Omega2 constant (http://mathworld.wolfram.com/Omega-2Constant.html) and the arithmetic mean length of the edges and diagonals of the logically outfitted triple-cube when the area of the face of one of the cubes equals that of the base of the "pyramid as described whose base is the 4-square of the infinite structure of existence" (see, on this web, Thinking Creation Ex Nihilo). The edge of each of the cubes entering into the creation of the logically outfitted triple-cube will have a length of 2, corresponding to the arithmetic sum of the three logic digits of The Cornerstone of the foundation of the logic of the novitas mentis (cf. D.G. Leahy, Novitas Mundi: Perception of the History of Being [Albany, 1994], Foundation: Matter the Body Itself [Albany, 1996], and Faith and Philosophy: The Historical Impact [Aldershot, 2003]), to wit, 1 = 1, 0 = 1/2, = 1/2 (Thinking Creation Ex Nihilo, n. 14). Thus the logical digits of each edge of each square of the triple-cube, which form the base of the logical matrices through which the direction of the vectors of the diagonals of the triple-cube are determined, sum to 2. Then calculate the length of the 37 diagonals and the 12 overall edges of the logically outfitted triple-cube (see, on this web, Logically Outfitted Cube[s]) as here illustrated whose square edge equals 2:
37 diagonals of logically outfitted triple-cube = 135.481523437932080
12 overall edges of the logically outfitted triple-cube = 40
49 overall edges & diagonals = 175.481523437932080
Average length of 12 overall edges & 37 diagonals = 175.481523437/49 = 3.581255580
3.581255580 = 1.52995422993
Omega2 constant = 1.529954037 ~ 1.5299542299 accurate to 1 part in 10 million.
The total length of the 12 overall edges and 37 diagonals of the logically outfitted triple-cube as here calculated raised to the power of the ratio of its volume to the total number of its edges and diagonals, equals the surface area of a sphere whose radius is Unity and whose diameter is the sum of the arithmetic values of 0, , and 1:
175.48152343724/49 = 12.5665 ~ 12.5664 = 4π.
The writer then noted that the ratio of the total length of the 37 diagonals to that of the12 overall edges of the logically outfitted triple-cube calculated on the basis of the arithmetic values of the real trinary logic digits is
135.481523437932080/40 = 3.387038085.
Where the mass of the photon is greater than zero and vmaxwell = 3 × 108 m/s is Maxwell's constant for the velocity at which electromagnetic waves propagate in vacuum (~ c = 299792458 m/s the velocity of light in vacuum; cf. F.O. Bertrand, "The Velocity of Light and Maxwell's Constant") and 1 s/m is a resistance/conductivity factor,
vmaxwell1/16 × 1 s/m = 3.387038072 ~ 3.387038085 accurate to 1 part in 100 million.
1/16 is the ratio of the number of triple-cube non-end-connected interior diagonals to the number of end-connected interior diagonals (see, on this web, Sorted Diagonals) and the diagonal/edge length ratio vmaxwell1/16 × 1 s/m = 3.387038072 is independent of any particular square edge length of the logically outfitted triple-cube.
Note that where 82944 and 784 are the natural numbers that in addition to 1 are uniquely their integral products (Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms) the ratio of the average length of the 12 overall edges and 37 diagonals to the ratio of the respective total lengths of those diagonals and those overall edges calculated on the basis of the arithmetic values of the real trinary logic digits is
3.581255580/(vmaxwell1/16 × 1 s/m) ~ 829.44/784.
Where = / the ratio of the real trinary logic infinite arithmetic value-number and infinite arithmetic value ratios (see, on this web, Real Trinary Logic Geometric Series Infinite Iterative Sequential Summing; also Theorem for a Flat Universe: The ρcrit = 3H02/8πG Building Block 1000.125 and The Langerhans-Epidermal Cell Ratio & the Structure of the Epidermis, n. 9), with a difference ~ (829.44/784)1/64––therefore with a difference ~ (3.581255580/[vmaxwell1/16 × 1 s/m])1/64 and ~ 1+ [(vmaxwell1/16 × 1 s/m)/2π2]4 (for 2π2 see below)––
vmaxwell1/16 × 1 s/m ~ 3.
(See, on this web, The vmaxwell1/16 × 1 s/m Cube, Human Body Surface & BSA, & the Infinitely Flat Structure of the Universe.) Where 2808 (~ vmaxwell1/16 × 829.44) = .36 times 7800, the product of the opposed place numbers on the left-handed diagonal in the final subsquare of the unum-founded Fibonacci sequence (cf. Leahy, Foundation, III.2; see, on this web, Report on a Dream & Related Matters & the God Particle and 82944 & the Four Fundamental Forces & the God Particle),
3.581255580 × 784 ~ 2808,
and where 2π2 is the surface area of the 4D hypersphere whose radius is Unity and whose diameter is the sum of the arithmetic values of 0, , and 1–– at once the square edge length of the real trinary logic triple-cube––
7843.581255580 ~ (2π2vmaxwell/c)8.
Finally, where 1492992 is at once the product of the means and the product of the extremes of the proportion whose elements are the product of the respective elements of the absolute proportion of absolute thought, 16 : 24 :: 24 : 36 (cf. Leahy, Foundation, pp. 366ff.), and the ratio of the volume to the square of the face diagonal of the absolute dead center cube, V/D2 = √2592 (as calculated, ibid., pp. 437ff.; see also, on this web, Sorted Diagonals, Addendum 4), 16√2592 : 24√2592 :: 24√2592 : 36√2592,
28083.581255580 ~ 14929922 = (24√2592)4 = (16√2592 × 36√2592)2.