THE vmaxwell1/16 ◊ 1 s/m CUBE, HUMAN BODY SURFACE & BSA,
& THE INFINITELY FLAT STRUCTURE OF THE UNIVERSE
Responding to Maxwell's Constant & the Trinary Logic Triple-cube, Dr. SB Hoath wrote on November 8, 2005: "I would wonder whether this logico-mathematical approach might relate to a volumetric method for measuring biological gases in the unstirred boundary layer surrounding the human body." He also wrote further on: "TELEOLOGY. The position of the stratum corneum in the 4-1-2-3 logical order [cf. D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), III.1] is teleological. It begins with the end in mind. This also seems to be the way we perceive the world. The perceived surface is synthetic––it has all the attributes of 'intelligent design'. The requirement that this perception be absolutely NOW [Leahy, Foundation, passim] creates intellectual problems for advocates of a slow evolutionary creation occurring over a vast period of time. On the other hand, if there are ways of visualizing or reading 'deep time' into a logico-mathematical surface; e.g., the 'imaginary' time line linking the origin of the logarithmic spiral with the rectangle of the whirling squares, then the requirement that creation be absolutely now can be identified with the perception of 'deep (evolutionary) time' and the two viewpoints are not at odds with one another. The trick is to discern those objects that best manifest this overlapping organizational principle. Describing and measuring such objects, which are likely to be biological, is a reasonable scientific goal."
Here follows the writer's response.
design": the perceived surface is the conceived surface, as such the very
embodiment of intelligence. In this sense, "design" is redundant. For the
first time the telos is absolutely the means.
Concerning the notion of the time line: from DG Leahy, "Beyond Politics: Lifting the Ban" (2005): ". . . where appearance is immediately absolute substance for the first time, as it is in the thinking now occurring (as distinguished from Hegel, where appearance is absolutely mediated absolute self-relation, modernity’s passivity as dialectical machine), where, in other words, the fundamental presupposition of self-consciousness is no longer operative—that is, where ontological dualism in all its forms is passť—the time/line that is nothing, when distinguished from the Kantian 'self-intuition', is now seen for the first time to correspond to sheer receptivity. Then this time/line, sheer receptivity, so distinguished and raised to the second power or squared, corresponds not to the form of auto-affection, but to the form of alio-affection, viz., sheer receptivity (nothing apart from the subject) experiencing some thing actually not itself for the first time: sheer receptivity for the first time experiencing itself as nothing apart from the subject, but then not experiencing itself as moved by its own passivity. Then this time/line, sheer receptivity, raised to the third power or cubed is sheer receptivity experiencing itself for the first time as nothing but existence. Finally, this time/line, sheer receptivity, raised to the fourth power or hypercubed, corresponds to a sheer receptivity that experiences itself as nothing but itself, sheer receptivity that experiences nothing but transcendence, nothing but the other, a sheer receptivity whose experience—since its experience of itself is as nothing apart from the subject and apart from the subject as nothing but existence—is productive of existence, is nothing but productivity. Here the particular experience of the transcendental ego—for the first time absolutely existent particular experience—is not an alternative to an impossible experience of 'things in general', but rather sheer particular experience identified with universal experience."
It appears that vmaxwell1/16 ◊ 1 s/m (see, on this web, Maxwell's Constant & the Trinary Logic Triple-cube), where "dimensionlessness" is understood to be really "hypermassiveness" in the sense of the "infinitely flat structure of the universe" and "the absolutely unconditioned body" (Leahy, Foundation, III.3, Part 1, and IV.2, Excursus Circularis), embodies the overcoming of the distinction between 'time' and 'line' (cf. the treatment of time and distance in DG Leahy, Novitas Mundi: Perception of the History of Being [Albany, 1994], Appendix α).1
So, for example, respecting "deep (evolutionary) time": where Planck time tP = 5.39121 ◊ 10-44 s, the minimum unicity (u = mλ) for a given mass b = h0/c = 2.210218631 ◊ 10-42 kg m (J. Cossentino, Spacetime Variation and the Physical Variables: Mass of Photons), the gravitational constant G = 6.67390 ◊ 10-11 m3 kg-1 s-2 (http://www.aip.org/enews/physnews/2000/split/pnu482-1.htm), the velocity of light c = 299792458 m/s, Maxwell's electromagnetic constant vmaxwell = 3 ◊ 108 m/s, the cube of the ratio of the real trinary logic infinite arithmetic value-number and infinite arithmetic value ratios vmaxwell1/16 ◊ 1 s/m ~ 3 = (/)3 (see, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers), the ratio of volume to surface area in the 4D hypersphere = .25 (http://www.mathreference.com/ca-int,hsp.html), the ratio of the average length of the 12 overall edges and 37 diagonals of the logically outfitted triple cube 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 = 3.581255580/(vmaxwell1/16 ◊ 1 s/m) ~ 1.52995422993/3 ~ 829.44/784 (Maxwell's Constant & the Trinary Logic Triple-cube), 1+(829.44/784)-128 ~ vmaxwell/c ◊ .82944-1/4096 accurate to 1 part in 1 million, 1 kg m is a unicity factor, 1/s a frequency factor, and 10-11 the order of magnitude of G,
[tP/([829.44/784] ◊ [1+(829.44/784)-128] s)].25 = 1.50218786895188 ◊ 10-11 ~ ◊ 10-11 kg m ◊ b-1/222 accurate to 1 part in 1 billion,
the edge of a 3D cube whose face is circumscribed by a circle whose dimensionless/hypermassive circumference, where 2π2 is the 4D hypersphere surface area (http://www.mathreference.com/ca-int,hsp.html), and 1 kg m-3 s2 is a density-resistance/conductivity factor, is
1.50218786895188 ◊ 10-11 ◊ (2π2)1/2 = G ◊ 1 kg m-3 s2 = 6.674044849 ◊ 10-11 ~ 6.67390 ◊ 10-11.2
Further, vmaxwell1/16 ◊ 1 s/m = 1.5017812963 may be the quantitative ‘cubic’ framework related "to a volumetric method for measuring biological gases in the unstirred boundary layer surrounding the human body." Supporting this notion is the mathematical (hypermassive/dimensionless) fact that where the human body surface area (BSA) is ~ 1.725983 ◊ 106 [mm2] (cf. http://en.wikipedia.org/wiki/Body_surface_area), the Functional Epidermal Unit (FEU) SC number (SB Hoath and DG Leahy, "The Organization of Human Epidermis: Functional Epidermal Units and Phi Proportionality," The Journal of Investigative Dermatology 121, 1440-1446 ) 17778 [cells], and the BSA of the vmaxwell1/16 ◊ 1 s/m cube 13.53208237,3
17778/13.53208237 = (1.725983 ◊ 106)1/2.
Likewise where the human BSA is ~ 1.737224965 [m2] and the FEU total number 93124 [cells],
93124/13.53208237 = 1.73722496516.
Where φ2/2 is the base factor in the divisor of the epidermal BSA constant (see, on this web, The Langerhans-Epidermal Cell Ratio & the Structure of the Epidermis) and the FEU Malpighian total number 75346 [cells],
75346/13.53208237 ~ (φ2/2)32.
Where the human BSA is ~ 1.724163562 [m2], the volume of the 4D hypersphere 4.9348 (π2/2) (http://www.mathreference.com/ca-int,hsp.html), the edge of the vmaxwell1/16 ◊ 1 s/m cube ~ , and 1.170820393 (see, on this web, The Golden Bowls & the Logarithmic Spiral and Pentagonal Light & Gravity & Epidermal Structure) the logarithmic locus of "deep (evolutionary) time",
Where the volume and surface area of a 4D hypersphere are 4.9348 (π2/2) and 19.7392 (2π2) (http://www.mathreference.com/ca-int,hsp.html), the ratio of the former to the latter is the analogue of a 3D V/BSA resistance ratio (see, on this web, Physical Variables, Placedness, & the Absolute Dead Center Cube). In the case of the 4D hypersphere the ratio is .25 (cf., ibid, the absolute dead center cube V/BSA resistance ratio 82944.25).
vmaxwell1/16 ◊ 1 s/m = 1.5017812963 is the 3D cube whose resistance ratio ~ that of the 4D hypersphere:
V/BSA = (vmaxwell1/16 ◊ 1 s/m)/13.53208237 = 1.501781296/6 = .250296882. ~ .25 ◊ (vmaxwell1/16 ◊ 1 s/m)1/1024.
Where the surface area of the 4D hypersphere is 2π2 and the BSA of the vmaxwell1/16 ◊ 1 s/m cube 13.53208237, the ratio of the latter to the former is
13.53208237/2π2 ~ φ4/10,
that is, 1/10
the product of the epidermal segmentation ratios that together
with its reciprocal is the antecedent in the ratio of solutions
of vectorial additions that defines the inextricable functional unity of
the Pinkus-Ryan analytical-synthetic views of epidermal cell
Hoath and DG Leahy, "The Human Stratum Corneum as Extended, Covalently
Cross-linked Biopolymer: Mathematics, Molecules, and Medicine,"
Medical Hypotheses, in press, February 13, 2006;
see also, on this web,
The Langerhans-Epidermal Cell Ratio
& the Structure of the Epidermis).
Where mP/kg = 2.176 ◊ 10-8 kg/kg is the mass fraction whose antecedent is the Planck mass, 1016 the order of magnitude of vmaxwell2, and, transposing the last equation, φ4 ◊ 2π2 ~ 135.3208237, the edge of the cube whose BSA is the last is
(135.3208237/6)1/2 ~ (mP/kg)2 ◊ 1016 ~ (φφ)2.
1 In the thinking now occurring for the first time the universe is essentially conceived as a living body whose structure is infinitely flat. The real trinary logic Creation/Volume metric (see, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers) is
and the V/BSA resistance ratio (see, on this web, Physical Variables, Placedness, & the Absolute Dead Center Cube) is
(V/BSA) = 1/0.
The predicate of the Unity (1) of the Universe is Infinite
Multiplicity/Infinite Particularity (0),
which may be expressed in terms of ordinary mathematics as
where the infinitely flat structure of the universe expands in the ratio of the series of squares of the odd numbers, 12, 32, 52, 72, 92, 112, 132, 152, 172, . . ., the sum of whose inverse = the ratio (π/8)/(1/π) = π2/8 where 82944π/8 ~ (COS G-1)/.01 and 829441/π ~ (COS α-1)/.01 (α = the fine structure constant, π2/8 = at once the square of the ratio of the circumference of a circle to the perimeter of its inscribed square [see also, on this web, 82944 & the Four Fundamental Forces & the God Particle, also, below, n. 3]; for .01, cf. Leahy, Foundation III.5, et passim, also, below, n. 2) (82944π/8/106 ~ 1.170820393, the locus of the logarithmic spiral [see, on this web, The Golden Bowls & the Logarithmic Spiral]), and where successive additions to the previous number of places/particulars expand in the ratio of the series the denominator of whose elements is the relation factor .125 (cf. Leahy, Foundation, IV.2, also, below, n. 2),
The first ninefold of this Universe BSA infinite expansion of places/particulars, beginning with 12 = Unity at the center, is here illustrated
17, the number of interior diagonals in the real trinary logic triple-cube whose end points are logical 0’s (see, on this web, Sorted Diagonals), is the number of places constituting the edge of the ninefold square here illustrated (analogous to the ninefold structure of the real trinary logic Cornerstone that distributes the threefold repetition of the three logical digits, 0, , 1) the area of which ninefold square = 172 = 1 + 829441/2 (cf., on this web, Measure Beyond Beyond Reach).
Analogously to the role of the finite volume/surface ratio in cellular diffusion, the infinite superficiality of the structure of the universe the beginning qua living body surface, at once analogously the beginning qua infinitely flat cell, is absolutely productive receptivity.
Note that when the logical digits in the real trinary logic Creation/Volume metric 1 (V) = 10 are understood to correspond to the arithmetic operations, division (1), addition (0), multiplication (), and subtraction (1) (see also below, this note), and the latter respectively with the rational product (/), linear sum (+), linear product (◊), and integral product (–) (see, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms) of a given number, then the BSA element in the V/BSA resistance/particularity ratio 1/0, read in terms of the analysis that discovers the uniqueness of the natural number 82944 (cf. Leahy, Foundation III.6-7, the number that is its integral product and whose ninth part is the integral product of its third part), is 0 = (+)(◊) = linear sum of 82944 ◊ linear product of 82944 = 27 ◊ 2304 = 62208 the BSA of the absolute dead center cube (ibid., III.5). Where 1 = 1/1 = (–)/(/) = the integral product of 82944/the rational product of 82944 = 82944/36 = 2304, then 1/0 = 2304/62208 = 27-1 the V/BSA resistance ratio of a cube whose BSA ~ 1/[(vmaxwell1/16 ◊ 1 s/m)/(829.44/784)1/16].
From the Infinitely Flat Body Structure of the Universe to the Everyday Distinction of Body and Environment
Let the Law of Epidermal Segmentation + (LES+) take the form of the series, 1/4, 5/9, 14/16, 30/25, 55/36, . . . (for LES, see, on this web, The Langerhans-Epidermal Cell Ratio & the Structure of the Epidermis, n. 13), where the first four ratios are associated, respectively, with stratum germinativum, stratum incrementum, stratum congressum, stratum corneum—the consequent of each ratio the number of layers of cells predicated respectively of the cumulative sum of epidermal layers that is its antecedent—and 55/36 is associated with the first "environmental stratum."
Let the Law of Epidermal Organization + (LEO+) take the form of the sequence, φ+1, φ2, φ–1, 1/φ, φ, . . . (LEO and LEO+ were developed with SB Hoath out of a proposal first made by him in correspondence with the writer dated January 26, 2000), where the fundamental arithmetic operations (see also above, this note), addition (+), multiplication (◊), subtraction (–), and division (/), are associated, respectively, with the stratum germinativum (+), stratum incrementum (◊), stratum congressum (–), and stratum corneum (/), and the base factor f with the infinite number of "environmental strata," beginning with the first such.
Let there be a LEO+/LES+ sequence where the elements of the latter are predicated of the elements of the former, (φ+1)/(1/4) = 10.47213595, φ2/(5/9) = 4.71246118, (φ–1)/(14/16) = .706324558, (1/φ)/(30/25) = .515028324, φ/(55/36) = 1.059076793, . . ..
Then, where the LES+ coupling constant is the SC ratio predicated of the first environmental ratio,
(55/36)/(30/25) ~ φ1/2,
the LEO+ coupling constant is analogously
φ/(1/φ) = φ2,
and, where i/.125 = 8, 16, 24, 32 . . . is the series of the differences between successive squares of the odd numbers in the infinite expansion of the number of places in the infinitely flat universe, φ-1/2 the inverse LES+ coupling constant (the [limit of the] Universe predicated of [the limit of] the body), .515028325 the LEO/LES SC ratio, 1.059076793 the LEO+/LES+ first environmental ratio, 82944.125 the fourth root of the area outside the central square Unity = 12 in the first ninefold square of the expansion constituting the infinitely flat structure of the universe, and 2/φ2 the cell reduction ratio whereby the SC is formed as the outermost quantum-qualitative limit of the body (SB Hoath and DG Leahy, "The Organization of Human Epidermis: Functional Epidermal Units and Phi Proportionality," The Journal of Investigative Dermatology 121, 1440-1446 ),
(φ-1/2/.125)1/32 ~ 1.059076793,
82944.125 ◊ .125 ~ .515028325,
(.515028325/1.059076793) ◊ (829.44/784)1/.125 ~ 2/φ2.
Where the LES+ coupling constant φ1/2 is the square root/edge of the shared surface (SB Hoath and DG Leahy, "The Human Stratum Corneum as Extended, Covalently Cross-linked Biopolymer: Mathematics, Molecules, and Medicine," Medical Hypotheses, in press, February 13, 2006) of one body and that of another (= φ), φ1.5 the volume of the cube whose face = φ, and the LEO+ coupling constant φ2 is the 4D hypercube/consciousness (surface ◊ surface = φ ◊ φ),
1.059076793/.515028325 ~ φ1.5,
(φ1/2)4 = φ2.
When the 4D hypercube/consciousness (= the LEO+ coupling constant) whose square root is the shared surface of the body and the environment is predicated of 2 (= the everyday twoness of the one and the other bodies), the ratio = the cell reduction ratio 2/φ2 that accounts for the empirical/everyday relationship of the number of FEU Malpighian cells (75346) to the number of SC cells (17778) (SB Hoath and DG Leahy, "The Organization of Human Epidermis"):
75346 – (75346 ◊ 2/φ2) ~ 17778,
and = at once the reciprocal of the BSA f constant f2/2 (see, on this web, The Langerhans-Epidermal Cell Ratio & the Structure of the Epidermis) ~ the base factor of the total empirical/everyday number of epidermal Malpighian cells in the average human body whose BSA is ◊ 106 mm2:
75346 ◊ ◊ 106 ~ φ2/2 ◊ 1011.
2 6.67390506798842 ◊ 10-11 ◊ vmaxwell/c is a cube whose body surface area (BSA) = ◊ 10-7, the rational product of Genesis 1:1, בראשית ברא אלהים את השמים ואת הארץ, "In the beginning God created the heaven and the earth" (cf. Leahy, Foundation, pp. 505ff. and 527f; see also, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms).
On January 1, 2006, Mr. DePompeo called the writer's
attention to the fact that where
is the fine structure constant,
the square root of the ratio of the gravitational and
electromagnetic exponents of 82944 at
once the ratio of the circumference of a circle to the
perimeter of its inscribed square
(see, above, n. 1), and
◊ 10-11 ◊ vmaxwell/c/
◊ 105) = 2187 = 37 (~
1/1000 the atomic unit of velocity cα
2.1876912633 ◊ 106 [m/s]; cf.,
below, this note),
[π/81/2 ◊ 10( ◊ 10-7)2/(6.67390506798842 ◊ 10-11 ◊ vmaxwell/c ◊ 37)]3 = (102α)-1
= Kinoshita (102α)-1 (http://www.eurekalert.org/pub_releases/1996-09/CTC-DATR-180996.php) accurate to one part in 10 billion and = NIST 2002 (102α)-1 (http://physics.nist.gov/cuu/Constants/index.html) accurate to six parts in 1 billion. The writer notes that where 1.170820393 is the locus of the logarithmic spiral (see, above, text, passim; also n. 1), 37 ~ 2186.9565077687 = [c/(100 ◊ 1.170820393)2]/10.
On December 9, 2005, Mr. DePompeo called the writer's attention to the fact that where Cossentino’s variable GEARTH-SUN = 6.6705104 ◊ 10-11 m3 kg-1 s-2 (J. Cossentino, "Spacetime Variation and the Physical Variables"), the V/BSA resistance ratio of the cube whose volume is GEARTH-SUN ◊ 1 kg m-3 s2 = 6.75930066 ◊ 10-5, the rational product of ברא "to create" = .01 (Leahy, Foundation, p. 368, et passim), and the atomic unit of velocity cα (c = velocity of light, α = fine structure constant) = 2.1876912633 ◊ 106 [m/s],
(V/BSA)-2/.01-1 = 2.1887515015 ◊ 106 ~ 2.1876912633 ◊ 106.
The writer notes that where the ratio of the average length of the 12 overall edges and 37 diagonals of the logically outfitted triple-cube 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 (Maxwell's Constant & the Trinary Logic Triple-cube),
(2.1876912633 ◊ 106)1/256/(vmaxwell/c) ~ 829.44/784.
Where the volume of the gravitational constant (m3) is VG = 6.67390506798842 ◊ 10-11, the volume of the absolute dead center cube Vdc = 1.055704767 ◊ 106 (Leahy, Foundation, III.5), and .125 the rational product of יחוס "relation," the constant base power of the denominators of the infinitely alternating sequence of the infinite series of natural numbers and that of the odd numbers which produces the infinite lattice composed of the natural numbers, the differences of their squares, the differences of the squares of those differences, the differences of the squares of those differences, ad infinitum (ibid., IV.2),
(Vdc/VG ).125/(vmaxwell/c) ~ 829.44/784 ◊ .01-1 .
Further for .125, see, above, n. 1; cf. also, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers, the sequential summing of the arithmetic transcription of the double series of 1's and , 0's in the infinitely expanding triangle created by the infinite sequential summing of the real trinary logic geometric series.
The factors of 82944 are powers of the first primes, 210 and 34. 829442-14 = vmaxwell/c accurate to one part in 1 million.
3 Where 144π = the circumference in which the face of the absolute dead center cube is inscribed and at once in a manner unique to that cube = the area of the circumference circumscribing each of the 36 equal subsquares of that face (cf., Leahy, Foundation, IV.2, p. 524, n. 98, and p. 525, n. 99), and 82944 = the total surface area of the unitary structure of that cube (ibid., III.5, pp. 434ff.),
144π(13.53208237 ◊ vmaxwell/c)2 ~ 82944.
Where 82944π/8 ~ (COS G-1)/.01 and 829441/π ~ (COS α-1)/.01 and the ratio of the exponents (π/8)/(1/π) = π2/8 and at once = the square of the ratio of the circumference of a circle to the perimeter of its inscribed square (see, above, n. 1),
(829441/13.53208237)1/4 ◊ vmaxwell/c ~ π2/8.
Further for 144π, see, on this web, Sorted Diagonals (Addenda, passim) and DNA, Apocalypse, & the End of the Mystery, note 15.