223.80 Energy Has Shape
223.81 I recognize the experimentally derived validity of the coordinate invariant: the result does not depend on the coordinate system used. Planck’s constant is just what it says it is: an experimentally ascertained constant cosmic relationship. Planck’s constant as expressed is inherently an irrational number, and the irrationality relates to the invariant quantum of energy being constantly expressed exclusively in the volume-weight terms of a special-case shape which, in the geometrical shape-variant field of weight-strength and surface-volume ratio limits of local structural science containment of energy, as mass or effort, by energy-as-structure, is neither maximum nor minimum. The special-case geometrical shape chosen arbitrarily by the engineering-structures-eschewing pure scientists for their energy-measurement accommodation, that of the cube, is structurally unstable; so much so as to be too unstable to be classified as a structure. Unwitting of this mensural shortcoming, Planck’s constant inadvertently refers to the cube, implicit to the gram, as originally adopted to provide an integrated unit of weight-to-volume mensuration, as was the “knot” adopted by navigators as a velocity unit which integrates time-space incrementation values. The volume and weight integrate as a gram. The gram was arbitrarily assumed to be constituted by a cubic centimeter of water at a specific temperature, 4 degrees centigrade.
223.82 Relationship constants are always predicated on limits. Only limits are invariable. (This is the very essence of the calcIllus??.) Variation is between limits. Though Planck’s constant is indirectly predicated on a limit condition of physical phenomena, it is directly expressed numerically only as a prefabricated, constantly irrational number-proportionality to that limit, but it is not the inherently rational unit number of that limit condition. This is because the cube was nonstructural as well as occurring structurally between the specific limit cases of surface-to-volume ratio between whose limits of 1, the cube rates as 3.
223.83 Max Planck found a constant energy-value relationship emergent in all the photon-discovery experimental work of others. A great variety of exploratory work with measurements of energy behaviors in the field of radiation disclosed a hitherto unexpected, but persistent, minimum limit in relation to such energy phenomena. Planck expressed the constant, or limit condition, in the scientifically prevailing numerical terms of the physical and metaphysical equipment used to make the measuring. The measuring system included:
the decimal system;
the CGtS and;
XYZ coordinate analysis,
which themselves were procedurally assumed to present the comprehensively constant limit set of mensuration systems’ input factors.
223.84 Let us assume hypothetically that Ponce de Leon did find the well of eternal-youth-sustaining water, and that the well had no “spring” to replenish it, and that social demand occasioned its being bailed out and poured into evaporation-proof containers; and that the scientists who bailed out that precious well of water used a cubically-shaped, fine-tolerance, machined and dimensioned one-inch-thick shelled, stainless steel bucket to do their carefully measured bailing and conserving task. They did so because they knew that cubes close-pack to fill allspace, and because water is a constant substance with a given weight per volume at a given temperature. And having ten fingers each, they decided to enumerate in the metric system without any evidence that meters are whole rational linear increments of a cosmic nature. Thus organized, the Ponce de Leon scientists soon exhausted the well, after taking out only six and two-thirds cubic bucket loadswith a little infinitely unaccountable, plus-or-minus, spillage or overestimate.
223.85 Planck’s constant, h, denotes the minimum energy-as-radiation increment known experimentally by humans to be employed by nature, but the photon’s energy value could and should be expressed in terms of a whole number as referenced directly by physical experiment to nature’s limit-case transforming states.
223.86 Had, for instance, the well-of-youth-measuring scientists happened to be in a hurry and had they impatiently used a cubical container of the same size made of a thin-wall plastic such as the cubically shaped motel waste containers, they would have noticed when they stood their water-filled plastic cube bucket on the ground beside the well that its sides bulged and that the level of the water lowered perceptibly below the container’s rim; though this clearly was not caused by leaking, nor by evaporating, but because its shape was changing, and because its volume-to-container-surface ratio was changing.
223.87 Of all regular polyhedra, the sphere (i.e., the high-frequency, omnitriangulated, geodesic, spheroidal polyhedron) encloses the most volume with the least surface. Whereas the tetrahedron encloses the least volume with the most surface. The contained energy is at minimum in the tetrahedron. The structure capability is at maximum in the tetrahedron.
223.88 Planck did not deliberately start with the cube. He found empirically that the amount of the photon’s energy could be expressed in terms of the CGtS-XYZ decimal-enumeration coordinate system already employed by science as the “frame of reference” [^4] for his photon evaluation which, all inadvertently, was characterized by awkwardness and irrationality.
223.89 Energy has shape. Energy transforms and trans-shapes in an evoluting way. Planck’s contemporary scientists were not paying any attention to that. Science has been thinking shapelessly. The predicament occurred that way. It’s not the size of the bucketsize is special casethey had the wrong shape. If they had had the right shape, they would have found a whole-rational-number constant. And if the whole number found was greater than unity, or a rational fraction of unity, they would simply have had to divide or multiply to find unity itself.
223.90 The multiplier
223.91 If they had taken the same amount of water at the same temperature in the form of a regular tetrahedron, they would have come out with a rational fraction of unity. They happened to be enumerating with congruence in modulo 10, which does not include any prime numbers other than 1, 2, and 5. The rational three-ness of the cube in relation to the tetrahedron is not accommodated by the decimal system; nor is the prime 7 inherent in modulo 10. Therefore, Planck’s constant, while identifying a hitherto undiscovered invariant limit condition of nature, was described in the wrong frame of reference in awkwardalbeit in a constantly awkwardterm, which works, because it is the truth; but at the same time it befogs the otherwise lucid and rational simplicity covering this phenomenon of nature, just as does nature’s whole number of utterly rational atoms exchanging rates in all her chemical combining and separating transactions accounting.