PENTAGONAL LIGHT & GRAVITY
& EPIDERMAL STRUCTURE
Mr. J. DePompeo sent the writer the following observation on August 27, 2003. Where G is the gravitational constant, c the speed of light in vacuum, 1/φ + φ = 51/2 the defining intrinsic element of the extreme and mean ratio φ = 1.618033988 . . ., then, taking G as .0000000000667395 m3 kg-1 s-2, and the speed of light in vacuum as 299792458 m s-1, where φ = 2(1/φ + φ)4 = 2(5)2,
φ/(φ2 − 1) = 299792458 × .0000000000667395148 . . . = c × G qua metric values.
This is exact for G to at least thirteen places after the decimal.
Dr. S.B. Hoath, in an email on September 8, 2003 exploring the potential significance of Mr. DePompeo's discovery for our ongoing research on the formation and function of epidermal structure, included, among reasons for pursuing an epidermal-gravitational-light connection, the following statement: "Of interest, lower energy & higher wave length photons (infrared or thermal radiation) pass deep into the skin whereas higher energy & lower wave length photons (ultraviolet) are blocked at the level of the stratum corneum."
Prompted by this comment, the writer noticed that, qua dimensionless numbers, φ2 and φ2 − 1 correspond to certain ratios among the wavelengths of the portions of the electromagnetic spectrum immediately adjacent to visible light. Where the maximum infrared wavelength λir ~ 106 nm (cf. http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c2), and the maximum ultraviolet wavelength λuv ~ 4 × 102 nm (cf. ibid., also http://hypertextbook.com/facts/2002/PavelBorodulin.shtml),
φ2 = λir/λuv,
φ2 − 1 = (λir − λuv)/λuv,
and, where the maximum visible light wavelength λvis ~ 7 × 102 nm (ibid.),
φ2 − 1 ~ (λir − λvis)/λuv,
φ/(φ2 − 1) = (λir × λuv)1/2/(λir − λuv) ~ (λir × λuv)1/2/(λir − λvis).
The writer notes that, where the maximum frequencies are substituted for the corresponding infrared, ultraviolet, and visible light wavelengths, so that the infrared frequency fir ~ 4 × 1014 Hz, the ultraviolet fuv ~ 3 × 1016 Hz, and the visible light fvis ~ 7.5 × 1014 Hz (cf. http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c2), then, on the inverse analogy to λir/λuv (above),
fuv/fir = 75,
and on the inverse analogy to (λir − λvis)/λuv (above),
fuv/( fir − fvis) = −85.
Where 16 is the number of layers of cells in the stratum corneum, 14 the number of layers in the Malpighian epidermis (cf. SB Hoath and DG Leahy, “Formation and Function of the Stratum Corneum,” in The Essential Stratum Corneum, ed. R. Marks, J-C. Lévêque, R. Voegeli (London, 2002), pp. 31-40), and the negative −16 the indication of the ultraviolet barrier function of the stratum corneum,
75 × −16/14 = −85.
Where 75346 is the total number of cells in the Functional Epidermal Unit (FEU) Malpighian epidermis (cf. 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 the total number in the FEU stratum corneum, 2/φ2 (where φ = 1.618033988) the cell reduction ratio governing the difference between the former and the latter (ibid.; cf. also, http://dgleahy.com/p27.html), 5381 the average number of cells/layer in the former, and 1111 the average number of cells/layer in the latter,
fir/75346 × fuv/17778 ~ (5381/1111)32,
1111 /5381 × fuv/fir ~ (75346 × 2/φ2)1/4,
(λir/λuv)/(fuv/fir) = 11111/2.
Where 1, 4, 9, and 16 are the respective numbers of layers of cells in the four epidermal strata (Hoath and Leahy, "Formation and Function of the Stratum Corneum"), and the maximum infrared and ultraviolet quantum energies are eVir ~ 1.65 and eVuv ~ 124,
eVir/75346 × eVuv/17778 ~ (1/4 × 9/16)8.
Where 1/4, 5/9, 14/16, and 30/25 are the respective segmentation ratios associated with the four epidermal strata (ibid.), the maximum x-ray wavelength λxray ~ 10 nm (cf. http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c3), and a is the fine structure constant,
(λxray/λuv × λvis/λir)/[(1/4)/(5/9) × (14/16)/(30/25)] = α2.
With the result that, where the epidermal-phyllotaxis structural ratio is 418 (http://dgleahy.com/p27.html),
α/(λxray/λuv × λvis/λir) ~ 418,
α-1/[(1/4)/(5/9) × (14/16)/(30/25)] ~ 418,
or, canceling α2,
[λxray/λuv × λvis/λir × (1/4)/(5/9) × (14/16)/(30/25)]-1/2 ~ 418.
On September 14, 2003, Mr. DePompeo called attention to the fact that, where 11.70820394 is the diameter of the 'defining bowl' in the "infinite pentagonal arrangement of 'golden bowls' at the φ-level of existence itself" (cf. http://dgleahy.com/p15.html),
(λvis − λuv)(λuv − λxray)/(λir − λvis) × 102 = 11.70820394.
On September 27, 2003, Dr. Hoath noted that, where 1.170820394 is the locus of the center of the logarithmic spiral (cf. http://dgleahy.com/p14.html), and where in the third multiplicand the writer has substituted λxray for λxray − 0,
(λvis − λuv) × (λuv − λxray) × (λxray)/(λir − λvis) = 1.170820394,
(fvis − fir)/(λir − λvis)/c = 1.170820394.
The writer notes that 1.170820393 is identically the constant ratio of the diameter of the base of each ‘golden bowl’ to the rim diameter of the bowl next smaller in the infinite pentagonal series of bowls (cf. http://dgleahy.com/p15.html), and at once the ‘retrospective square value’ of the first place in the unum-founded Fibonacci sequence *F1 = *F100/φ99 (cf. DG Leahy, Foundation: Matter the Body Itself [Albany, 1996], Sections III.2 and III.6).
The following is composed of excerpts from a communication from Dr. Hoath on December 31, 2003:
"MKS is the system of units based on measuring lengths in meters, mass in kilograms, and time in seconds. MKS is generally used in engineering and beginning physics, whereas the so-called cgs system (based on the centimeter, gram, and second) is commonly used in theoretical physics. The most familiar units of electricity and magnetism (ohm, farad, coulomb, etc.) are MKS units (http://scienceworld.wolfram.com/physics/MKS.html).
"The Planck quantities are a system of natural units which arise purely from gravity and light (http://www.planck.com/intuitiveplanck.htm).
"Both the Planck quantities [http://dgleahy.com/p30.html] and the structure of the epidermis can be linked to φ proportionality (cf. Hoath and Leahy, 'The Organization of Human Epidermis: Functional Epidermal Units and Phi Proportionality', The Journal of Investigative Dermatology). The epidermis manifests a 'gravitational' structure which can be analyzed in terms of its interaction with the electromagnetic spectrum [see above, passim]. Note the following peculiarities in the definition of electrical charge.
"The MKS unit of charge is the Coulomb. The smallest measurable unit of charge is that carried by the electron, where the elementary charge e = 1.602176462 × 10-19 C. Oddly, in most reference sources, the elementary unit of charge is given not in MKS terms, but is defined in terms of centimeters and grams. Thus, as is typical, if the radius of the electron is 2.8179 × 10-13 cm, the mass of the electron 9.1095 × 10-28 grams, the elementary charge e = 1.602176462 × 10-19 C, then the charge in C is directly proportional to the square root of the product of the resting mass of an electron and its radius [cf. http://dgleahy.com/p26.html#footnote_9] such that:
"This is odd. The MKS unit of charge is the Coulomb but the elementary unit of charge is approximated using centimeters and grams. In light of our recent conversations, however, this is an exceedingly neat relationship. Where 10 is the primary base factor, 1.618034 ~ φ, 20 = the number of surface diagonals of the triple dead center cube [http://dgleahy.com/p04.html], and 1.602176462 × 10-19 is the MKS unit of elementary charge, then,
10 × φ/1020 ~ 1.602176462 × 10-19 = e.
"This is a tidy mathematical relationship which relates some pretty fundamental elements. It seems, however, rather contrived and inconsistent in its utilization of grams, centimeters and base 10 correction factors to derive a fundamental MKS quantity.
"The factor 10 pops up in another related context. Where c is the velocity of light = 2.99792458 × 108 m/s, 1.602176462 × 10-19 C the MKS unit of elementary charge, 4.802 × 1010 the elementary electrostatic unit (esu) charge in the cgs system (http://scienceworld.wolfram.com/physics/Charge.html), then,
(4.802 × 1010) / (1.602176462 × 10-19) × 1/c = 10.
"In contrast, it is easy to stay completely within the MKS system and still demonstrate a connection between φ proportionality and the Planck constants in relation to the form of the elementary charge on an electron. Thus, where, the radius of the electron is given as 2.8179 × 10-15 m, its mass as 9.1095 × 10-31 kg, the square root of the product of the resting mass of an electron and its radius is
[(2.8179 × 10-15) (9.1095 × 10-31)] 1/2 = 5.06652 × 10-23.
"With respect to its form, this number is 1/10th the elementary charge of an electron (see above). In terms of the MKS system, this number should be a better indicator of electronic charge than the derived cgs value. That this MKS value is meaningful can be seen from the following comparison.
"Where, 5.06652 × 10-23 is the square root of the product of the resting mass of an electron and its radius in the MKS system, 5.93089 × 10-22 is the charge form calculated in terms of Planck mass and length [http://dgleahy.com/p30.html], and 11.70820393 is the diameter of the 'defining bowl' in the 'infinite pentagonal arrangement of "golden bowls" at the φ-level of existence itself' [see above], then,
(5.93089 × 10-22) / (5.06652 × 10-23) ~ 11.70820393.
"Where the formal elementary charge of an electron using MKS units is 10 × 5.06652 x 10-23 = 5.06652 × 10-22, the 'Planck charge' is 5.93089 × 10-22 and 1.170820394 is the defining locus of the logarithmic spiral [ibid.], then,
(5.93089 × 10-22) / (5.06652 × 10-22) ~ 1.170820394."