MEASURE OF SUPERCONDUCTIVE YBa_{2}Cu_{3}O_{6+x }

The 1987 breakthrough in the work on High Temperature Superconductivity
was achieved with the production and determination of the structure of the synthetic
stone, YBa_{2}Cu_{3}O_{6+x}
("1-2-3"), here illustrated:^{1}

a triple cuboid unit cell the middle center of which is occupied by an yttrium metal atom, the top and bottom centers each by a barium metal atom, while the corners of the cuboid sub-units are occupied by copper atoms, between which are located oxygen atoms in sites, as illustrated, either fully or partially occupied (the last in the case of the topmost and bottommost planes of the tetragonal phase), or unoccupied (as in the case of the ends of the front-to-back axis of the topmost and bottommost planes of the orthorhombic phase, as well as in the central planes of both orthorhombic and tetragonal phases).

If the relationship of the *metal* elements constituting this
superconductive ‘synthetic rock’ is set out in the following proportion (the
atomic weights proportional to the number of atoms of each metal in the "1-2-3"
crystal):

Y (88.9059) : Cu

_{3}(190.638) :: Cu_{3}(190.638) : Ba_{2}(274.68),

then, the rational product of this proportion
2φ/10 (= [5^{1/2} + 1]/10), the tenth part of the rational product of the proportion of the
elements of the first smallest subsquare of the 100-square grid of the unum-founded
Fibonacci sequence (composed of its diagonal poles, **F*_{1} [= 1] **F*_{12} [= 233] and **F*_{2}
[= 2] **F*_{11} [= 144], ordered according to their LAU functions, i.e., according to the order,
0 : 1 :: 1 : ).^{2}

With a difference less than 1 in 10 billion -- if it actually exists at
all -- the rational product of the proportion constituted of *all* the elements of
the compound "1-2-3," where *x* = .24*, *

Y (88.9059)/Ba

_{2}(274.68) × Cu_{3}(190.638)/O_{6+x}(99.8391), = φ^{-1},

while, likewise, that of the ‘minimum’ (4-1-2-3) order^{3}of this proportion,

O

_{6+x}(99.8391)/Y (88.9059) × Ba_{2}(274.68)/Cu_{3}(190.638), = φ.

The rational product of the ‘logical’ (1-2-4-3) order of the elements of this proportion,

Y (88.9059/Ba_{2} (274.68) × O_{6+x}
(99.8391)/Cu_{3} (190.638),
^{φ} = (4/3 × 1/4)^{φ},

the inherent formal prediction of the effective interchangeability here
of oxygen and copper in the last place of the proportion as the base (4th : 3rd :: 1st :
4th) of φ, an interchangeability likewise
formally anticipated in the foundational atomic weight ratio of the former to the latter,
viz., ~.25.^{4} The intelligibility of YBa_{2}Cu_{3}O_{6+x}, and, by inference, of all other superconductive compounds, in terms of
φ-proportionality and the unum-founded Fibonacci
sequence is manifest.^{5}

Let there be the circumscribed regular decagon embodying φ-proportionality:

Inspection shows that the ratio *CD/CB*
the ratio of the height to the diagonal of the triple-cuboid structure of YBa_{2}Cu_{3}O_{6+x}, revealing
that the tenth part of the inscribed regular decagon is the fundamental template of the
"1-2-3" structure, while the ratio *ACB*/(*AB+AE*)
the volume/surface ratio of the breakthrough superconductor. In addition
to these purely rational coincidences of the_{ }φ_{ }section and "1-2-3" structures, there exist ratios of the
elements of the structure of the former which predict the pattern of metric values found
in the latter: for example, the ratio of the circumference of the circle circumscribing
the regular decagon to the line *B*, i.e., 2π*r*/*DB*,
the angstrom-unit length of the six-fold diagonal of the cuboid
sub-unit of the "1-2-3" crystal, while the ratio 2π*r*/*ACB*
the angstrom-unit length of the average linear sub-section of the
total ‘perimeter’ of the structure. Furthermore, the angstrom length of the
‘perimeter’ itself ten times the ratio
2π*r*/*AD*,
while ten times the ratio 2π*r*/*BCDB*
the angstrom surface area of the superconductor’s triple-cuboid
side. (When *n* = 1, *CD* and *CB* ,
respectively, the ‘retrospective’ ‘square’ and ‘linear’
values of **F*_{1},^{6} each, in turn, one-tenth, respectively, the angstrom height and the angstrom
diagonal of the YBa_{2}Cu_{3}O_{6+x} triple-cuboid structure. The notion that the use of the metric system or a base
ten measure is explained by referring it to mere convention, effectively the refusal to
transcend the Copernican principle, is here, as it is in other ways throughout the text,
called radically into question by the significant coincidence of rational and metric
relations which exists in the relationship of YBa_{2}Cu_{3}O_{6+x} and the one-tenth section of the regular decagon embodying
φ-proportionality. The fact that the decagonal
embodiment of the ‘golden section’ predicts the pattern of metric relations in
"1-2-3" is evidence that if, hitherto, all the world had agreed that the
magnitude of the meter was to be either more or less than the distance light travels in
vacuum in 1/299792458th of a second, then, in that case, it would have been necessary now
to redefine the meter to that magnitude which, however, has been in fact agreed upon.
There is high historical irony in the fact that the light measure of the meter is a
refinement of the measure of the 1/10,000,000th part of the polar quadrant of the Earth.
But the transcendent irony is that the substitution of the light-measure of the meter for
its Earth-measure neither is nor can be a fundamental shift, for the simple reason that
the Earth-light-metric itself turns out to be a root function the ‘golden
section’. Let _{} be the mean
square metric radius of Earth divided by a square megameter, ~(6.37E6 m/1E6 m)^{2} ( 40.561349431 [the
megametric value of the average of the polar and equatorial radii of Earth (~6.37)
the base factor of the square-constant of the 10,000-square of the
unum-founded Fibonacci sequence ( 6.37E2089)^{7}]),
then,

since

*c* = 299792458 m/s_{ }
φ^{40.561349431} m/s
(φ^{6.37E6} ^{m/1E6} ^{m})^{2} m/s,

*c *
φ m/s,

and,

φ m
*c*^{1/} s.

The ‘golden section’ embodied in
the circumscribed regular decagon essentially predicts, then, the micrometric value
pattern of the atomic structure of YBa_{2}Cu_{3}O_{6+x}, and (on a scale 3.2E15 times that of the superconductor) the *f*(φ) radical Earth-light macrometric relation. In the
Earth-light relation the square megametric value of the mean radius of Earth -- a square
on the scale of Earth reduced to *a pure number exponent of the ‘golden
section’ ratio* -- produces the *whole number metric value* of the
velocity of light.^{8} This macrometric relation is at once clear proof of the *whole number
significance* of the micrometric value pattern found in the φ_{ }section "1-2-3" decagonal template (3.125E-16 times
Earth-scale), which real significance finally depends on the fact that

φ m
*c*^{1/} s,

precisely as the definition of the angstrom depends on that of the
meter. Here the φ proportion is perceived
in essence, i.e., *qua* foundation of absolute rational unity, to embody the symmetry
of an absolutely asymmetric nothing: the symmetry of a nothingless existence: the absolute
unity without ‘duality within identity’ which is nothing asymmetric, nothing
irrational, i.e., is not irrational unity: absolute unity without duality without
identity: perfect unity neither without nor within duality, rational symmetry without an
irrational point: in the beginning the absolute asymmetry of unity + nothing (1 + 0 [*ex
nihilo*] = [existence = everything + something]).^{9}

**Notes
**

^{1} Drawing after R.M. Hazen, *The Breakthrough: The Race for the Superconductor*
(New York, 1988), p. 251. Cf.
"The Woodstock of Physics," *Physics News Update*,

^{2} Cf. D.G. Leahy, *Foundation*: *Matter the Body Itself* (Albany,
1996), Sections III.1-2.

^{3} Cf. Leahy,* Foundation*, Section III.1.

^{4} Cf. ibid., also, Sections III.5 and IV.2.

^{
5 }The square-planar arrangement of one copper (63.546) atom to four oxygen
(15.9994) atoms -- an arrangement essentially predicted in the form of the absolute
structure of existence itself (cf. Leahy, *Foundation*, Section IV.2) -- pertains
not only to "1-2-3," but to the superconductivity of the superconductors
discovered following the latter’s discovery. Cf. R.M. Hazen, "Perovskites"
in *Scientific American*, June 1988: "Of particular interest is the finding that
the copper atoms are not surrounded by the usual octohedral cages. Instead they are mostly
in fourfold square-planar or fivefold square-pyramid coordination: they are closely bonded
to the four or five surrounding oxygen atoms, which form a square and a square-based
pyramid respectively. In both arrangements the copper atoms lie in the same plane as the
square. Since 1-2-3 and other high-temperature superconductors are superconducting in
directions parallel to the copper planes, many theorists now believe this unusual planar
arrangement contributes to the remarkable electronic properties of the materials. Exactly
how it does so remains to be clarified, however." Cf. the pyramidal formation of the
Trinitarian structure, on this web, **
Thinking
Creation Ex Nihilo**. Cf. also, on this web,