EPIDERMAL STRUCTURE: CELL FORMATION
FREQUENCIES & CORNEUM ALPHA-COUPLING


On January 17, 2004, Dr. SB Hoath communicated to the writer the following calculations: where 1 is dimensionless, mp/me the ratio of Planck mass to the mass of an electron, (2.1760 10-8 kg/9.10950 10-31 kg, or, equivalently, the number of electrons in a Planck mass), le/lp the ratio of the radius of an electron to Planck length (2.81790 10-15 m/1.6160 10-35 m, or, equivalently, the number of Planck lengths in the radius of an electron), tp Planck time (5.39060 10-44 s), and 4.454065458 the radius of the circle circumscribing the pentagon containing the entry bowl in the infinite pentagonal series of bowls (http://dgleahy.com/p15.html#infinite pentagonal),  

mp/me le/lp tp 4.454065458 Hz ~ 1,

 

where 4.454065458 Hz corresponds to a cycle time of 0.224513988 s.  

 

He further noted that if the diameter of the electron is substituted for its radius in the above equation, then the product of the number of electrons in a Planck mass (mp/me), the number of Planck lengths per electron diameter (2le/lp), and Planck time (tp) is:

 

mp/me 2le/lp tp = 0.449027977 s,

 

where 0.449027977 s corresponds to 2.227032729 Hz (and where 2.227032729 is the foundational distance separating the bases of the bowls in the infinite pentagonal series of bowls [ibid.]).

 

Then Dr. Hoath wrote: "What is particularly interesting is the solution for a practical time unit; i.e., 0.449027977 s.  Might this time unit be utilized in resolving biologically relevant frequencies?  We might ask, for example, what cycles at multiples of 2.227032729 Hz?"
 

 

Epidermal Cell Formation Frequencies
 

In response to Dr. Hoath's observations and questions, the writer observed the following: where the time required for the replacement of the entire epidermis is 28 days (SB Hoath and DG Leahy, "The Organization of Human Epidermis: Functional Epidermal Units and Phi Proportionality," The Journal of Investigative Dermatology 121, 1440-1446) = 2419200 s, and 5382 is the average number of cells per Functional Epidermal Unit (FEU) Malpighian layer (ibid.),

2.227032729 10-3 Hz 2419200 s ~ 5382.

Where 75346 is the total number of cells in the 14 Malpighian FEU layers (ibid.), and 14 2.227032729 10-3 Hz = 3.117845821 10-2 Hz,

3.117845821 10-2 Hz 2419200 s ~ 75346.

Where 17778 is the total number of cells in the 16 stratum corneum (SC) FEU layers (ibid.), and α is the fine structure constant or square of the EM coupling constant,

α s-1 2419200 s ~ 17778.

Where 93124 is the total of Malpighian and SC FEU cells (ibid.), and 3.117845821 10-2 Hz + s-1) = 3.847581075 10-2 Hz,

3.847581075 10-2 Hz 2419200 s ~ 93124.

With respect to the 16 layers of cells in the FEU SC (ibid.), it is further noted that where 3.117845821 10-2 Hz is the formation frequency of the FEU Malpighian epidermis, 4.454065458 10-4 Hz twice the formation frequency of one layer of cells in the FEU Malpighian epidermis, and 1111 the average number of FEU SC cells per layer (ibid.),

(1 + 3.117845821 10-2) 4.454065458 10-4 Hz 2419200 s ~ 1111.
 
 
The Epidermal and GUT unified coupling constants
 

The unification of the strong, electromagnetic and weak interactions in the Grand Unified Theory (GUT) takes place at ΛGUT = 1.5 1016 GeV, where the unified coupling constant is αun = 0.03853 (H. Fritzsch, "Are the fundamental constants constant?," Cern Courier 43.2, at http://www.cerncourier.com/main/article/43/2/13).

1.5 1016 GeV ~ Planck mass, but is off by three orders of magnitude. C.T. Hogan, "Why the Universe is Just So," at http://nedwww.ipac.caltech.edu/level5/Hogan/Hogan3_4.html (Published in Rev. Mod. Phys. 72, 1149, 2000), writes: "The numerical factors here are just approximate, but are exactly computable within the framework of supersymmetric GUTs and yield a unification scale of MU 1016 GeV.  In this framework, this is essentially the explanation of the 'weakness'' of gravity, the smallness of mproton/mPlanck.  Since mPlanck 103 MU there are three of the nineteen orders of magnitude still to be accounted for, presumably by the final unification with gravity."

Where GD-H2O = 1000/s2 the H20-resolution of the dimensions of the gravitational constant (http://dgleahy.com/p26.html), Planck mass mP = 1.22089899 1019 GeV/c2 = 2.17645 10-8 kg, and the GUT mass unification scale MU = 1.22089899 1016 GeV/c2,

GD-H2OMU = 1000/s2 1.22089899 1016 GeV/c2 = 1.22089899 1019 GeV/8.987551787 1016 m2 = 1.35843333 1011 eV/m2.

GD-H2OMU/c2 = 1.35843333 1011 eV/c2/m2= 2.42162707 10-25 kg/m2 = 2.17645 10-8 kg/8.987551787 1016 m2.

Where 1.170820394 is the locus of the center of the logarithmic spiral (http://dgleahy.com/p14.html), .03847581075 the number of cycles/s in the epidermal formation frequency unified coupling constant above (~ αun = 0.03853 the GUT unified coupling constant), 82944 the area of the unitary structure of the absolute dead center cube (D.G. Leahy, Foundation: Matter the Body Itself [Albany, 1996], pp.434ff), and 128 ~ (1/.82944)1/.03853,

mP ~ (1.170820394128) .03847581075 10-8 kg,

and

GD-H2OMU /c2 = mP/8.987551787 1016 m2 ~ (10 128 .03847581075/10128/4)4/128/.03847581075 10-25 kg/m2.

Where GH2O = 6.6739 10-8 s-2 the H20-resolution of the gravitational constant itself (http://dgleahy.com/p26.html), 8.14815777 108 ~ 101.8233765 8 10002 the edge of the absolute dead center cube (Foundation, loc. cit.) times the number of planes in the unitary structure of the cube (ibid.) times the square of the antecedent of GD-H2O, 82944 = the area of the unitary structure of the absolute dead center cube (ibid.), and the GUT mass unification scale MU = 1.22089899 1016 GeV/c2,

GH2OMU = 6.6739 10-8  s-2 1.22089899 1016 GeV/c2 = 8.14815777 108 GeV/8.987551787 1016 m2 = 9.0660482 eV/m2.

GH2OMU/c2 = 9.0660482 eV/c2/m2 = 1.61616979 10-35 kg/m2 ~ (8.2944 108)-2 kg/8.987551787 1016 m2.

Where .0385 is the mean between the GUT mass unification unified constant .03853 and .03847581075 the number of cycles/s in the epidermal formation frequency unified coupling constant, a = the square of the EM coupling constant at once the number of cycles/s in the SC coupling constant, GH2OMU = 1.61616979 10-35 kg/m2, 82944 is the area of the unitary structure of the absolute dead center cube (ibid.), 128 ~ (1/.82944)1/.03853, and 54 is the number of cells in an epidermal Langerhans cells unit (http://dgleahy.com/p24.html),

(GH2OMU/c2).0385 ~ (a 541/.0385)-4/128 kg/m2.

Where 1.170820394 is the locus of the center of the logarithmic spiral (http://dgleahy.com/p14.html),

GH2OMU/c2 ~ 1.1708203942 (1.170820394 .03853)1/.03853 kg/m2.
 

The GH2OMU/c2 Surface Whose Edge = 26.29249703 ly


Where GH2OMU/c2 = 1.61616979 10-35 kg/m2 = 1 kg/6.187468706 1034 m2, (6.187468706 1034 m2)1.5 = 1.539109514 1052 m3 coincides the cubic embodiment of the universal form of all logical propositions (http://dgleahy.com/p20.html) where the coordinate system is x = y = z = (6.187468706 1034 m2)1/2 analogously to x = y = z = 1 (ibid.), 101.8233765 is the edge of the absolute dead center cube (D.G. Leahy, Foundation: Matter the Body Itself [Albany, 1996], pp. 434ff), and .03847581075 the number of cycles/s in the epidermal formation frequency unified coupling constant (above),

(6.187468706 1034 m2)1.5 = 1.539109514 1052 m3 ~ 101.82337651/.03847581075 m3,

and the volume of each of the four square right prisms composing the cube (I, II, III, and IV, illustrated at http://dgleahy.com/p20.html) is

(1.539109514 1052 m3)/4 ~ 3.847581075 1051 m3.

Where α-1 is the inverse of the number of cycles/s in the SC cell formation frequency coupling constant (above), 16 the number of layers of SC cells (http://www.dgleahy.com/p24.html), the surface area of the face of each of the four square right prisms composing the cube (I, II, III, and IV, illustrated at http://dgleahy.com/p20.html) is

(6.187468706 1034 m2)/4 ~ α-16 m2.

Where the edge of the 1.539109514 1052 m3 embodiment of the universal form of all logical propositions (ibid.) = 2.487462302 1017 m = 26.29249703 ly, the GUT unified coupling constant αun = 0.03853 (~ 03847581075 the epidermal formation frequency unified coupling constant), and the minimum topology scale of the universe = 24 Gpc (Physics New Update Number 685 [http://www.aip.org/enews/physnews/2004]) = 7.827936 1010 ly,

10(7.827936 1010).03853 ly ~ 26.29249703 ly.

Where .03327185 is the portion of the logarithmic axis cut off in the rotation of the spiral corresponding to the outermost epidermal layer (http://dgleahy.com/p14.html), and 8 is the number of planes in the unitary structure of the cube (Leahy, Foundation, pp. 434ff),

108(26.29249703/7.827936 1010) ~ .03327185.

Where 1.13198824 is the Viswanath random Fibonacci constant (http://en.wikipedia.org/wiki/Viswanath's_constant), the minimum topology scale of the universe = 24 Gpc = 7.827936 1010 ly, the edge of the GH2OMU/c2 surface = 26.29249703 ly, and 8 is the number of planes in the unitary structure of the cube (Leahy, Foundation, pp. 434ff),

(7.827936 1010 ly)/(26.292497032 108 ly) ~ 1.13198824.
 
 
 

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