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, *m*_{p}/*m*_{e} 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), *l*_{e}/*l*_{p} 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),
*t*_{p
}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),

*m*_{p}/*m*_{e}
×
*l*_{e}/*l*_{p}
× *t*_{p}
× 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 (*m*_{p}/*m*_{e}),
the number of Planck lengths per electron diameter (2*l*_{e}/*l*_{p}),
and Planck time (*t*_{p})
is:

*m*_{p}/*m*_{e}
× 2*l*_{e}/*l*_{p}
× *t*_{p }=
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?"

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 +
(α 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 unification
of the strong, electromagnetic and weak interactions in the Grand Unified
Theory (GUT) takes place at Λ_{GUT} = 1.5 × 10^{16} GeV, where
the unified coupling constant is α_{un} = 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 × 10^{16}
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 *M*_{U}
≈ 10^{16} GeV. In this framework, this is essentially the
explanation of the 'weakness'' of gravity, the smallness of *m*_{proton}/*m*_{Planck}.
Since *m*_{Planck} ≈ 10^{3}
*M*_{U} there are three of the nineteen orders of magnitude still
to be accounted for, presumably by the final unification with gravity."

Where *G*_{D-H2O} =
1000/s^{2} the H_{2}0-resolution of the dimensions of the
gravitational constant (http://dgleahy.com/p26.html),* *Planck
mass *m*_{P} = 1.22089899 × 10^{19} GeV/*c*^{2}
= 2.17645 × 10^{-8} kg, and the GUT mass unification scale *M*_{U}
= 1.22089899 × 10^{16} GeV/*c*^{2},

*G*_{D-H2O}*M*_{U} = 1000/s^{2}
× 1.22089899 × 10^{16} GeV/*c*^{2} = 1.22089899 × 10^{19}
GeV/8.987551787 × 10^{16 }m^{2} = 1.35843333 × 10^{11} eV/m^{2}.

*G*_{D-H2O}*M*_{U}/*c*^{2}_{ }= 1.35843333 × 10^{11} eV/*c*^{2}/m^{2}= 2.42162707 ×
10^{-25} kg/m^{2} = 2.17645 × 10^{-8} kg*/*8.987551787
× 10^{16 }m^{2}.

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 (~ α_{un} = 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},

*m*_{P} ~
(1.170820394^{128})^{ .03847581075} × 10^{-8} kg,

and

*G*_{D-H2O}*M*_{U}
/*c*^{2 }=
*m*_{P}/8.987551787 × 10^{16 }m^{2} ~ (10 × 128 ×
.03847581075/10^{128/4})^{4/128/.03847581075} × 10^{-25} kg/m^{2}.

Where *G*_{H2O} =
6.6739 × 10^{-8 }s^{-2} the H_{2}0-resolution of the
gravitational constant itself (http://dgleahy.com/p26.html),
8.14815777 × 10^{8 }~ 101.8233765 × 8 × 1000^{2} 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* G*_{D-H2O}, 82944 = the area
of the unitary structure of the absolute dead center cube (ibid.), and the GUT mass unification scale *M*_{U}
= 1.22089899 × 10^{16} GeV/*c*^{2},

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, *G*_{H2O}*M*_{U}
= 1.61616979 × 10^{-35} kg/m^{2}, 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),

(*G*_{H2O}*M*_{U}/*c*^{2})^{.0385}
~ (a × 54^{1/.0385})^{-4/128 }
kg/m^{2}.

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

*G*_{H2O}*M*_{U}/*c*^{2}_{ }
~_{ }1.170820394^{2 }× (1.170820394 × .03853)^{1/.03853} kg/m^{2}.

**The **
*G*_{H2O}*M*_{U}/*c*^{2
}__Surface Whose
Edge = 26.29249703 ly__

Where *G*_{H2O}*M*_{U}/*c*^{2}
= 1.61616979 × 10^{-35} kg/m^{2} = 1 kg/6.187468706 ×
10^{34 }m^{2}, (6.187468706 × 10^{34 }m^{2})^{1.5}
= 1.539109514 × 10^{52 }m^{3} 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
× 10^{34 }m^{2})^{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),

^{34
}m^{2})^{1.5}
= 1.539109514 × 10^{52 }m^{3} ~
101.8233765^{1/.03847581075}
m^{3},

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
× 10^{52 }m^{3})/4 ~ 3.847581075 × 10^{51 }m^{3}.

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 × 10^{34 }m^{2})/4 ~
α^{-16} m^{2}.

Where the edge of the
1.539109514 × 10^{52 }m^{3}
embodiment of the universal form
of all logical propositions (ibid.) = 2.487462302 × 10^{17
}m = 26.29249703 ly, the GUT unified coupling constant α_{un}
= 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 × 10^{10} ly,

10(7.827936 × 10^{10})^{.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),

10^{8}(26.29249703/7.827936
× 10^{10}) ~
.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 × 10^{10}
ly, the edge of the *G*_{H2O}*M*_{U}/*c*^{2
}surface = 26.29249703 ly,
and 8 is the number of planes in the unitary structure of the cube
(Leahy, *Foundation*, pp. 434ff),

(7.827936 × 10^{10}
ly)/(26.29249703^{2}
× 10^{8}
ly) ~ 1.13198824.