986.090 The Search for Nature's Coordinate System |
Fig. 986.096 |
986.096 My insights regarding nature's coordinate system were greatly enhanced by two of Milton Academy's greatest teachers: Homer LeSourd in physics and William Lusk Webster Field ("Biology Bill") in biology. During the summer vacation of 1906, at 11 years of age I designed and built my first small but exciting experimental dwelling on our family's small mid-Penobscot Bay island. Living all my youthful summers on that island, with its essential boat-building, boat-modifying, boat-upkeep, and boat-sailing, followed by five years as a line officer in the regular U.S. Navy with some of my own smaller-craft commands, some deck-officering on large craft of the new era's advanced technology ships, together with service involving airplanes, submarines, celestial navigation, ballistics, radio, and radiotelephone; then resignation from the Navy followed by five more private- enterprise years developing a new building system, inventing and installing its production tools, managing the production of the materials, and erecting therewith 240 residences and small commercial buildings^{__}altogether finally transformed my sustained activity into full preoccupation with my early-boyhood determination some day to comprehend and codify nature's omniintertransformative, omnidirectional, cosmic coordination system and its holistic, only-experientially-proven mathematics. In 1928, inspired and fortified by Hubble's Expanding Universe discovery, I gave the name and its symbol 4-D to my mathematical preoccupations and their progressively discovered system codifying. In 1936 I renamed my discipline "Energetic Vectorial Geometry." In 1938 I again renamed it "Energetic-synergetic Geometry," and in 1970 for verbal economy contracted that title to "Synergetics." (See Fig. 986.096.) |
986.100 Sequence of Considerations |
986.110 Consideration 1: Energetic Vectors |
986.120 Consideration 2: Avogadro's Constant Energy Accounting |
986.121 Avogadro discovered that under identical conditions of pressure and heat all elements in their gaseous state always consist of the same number of molecules per given volume. Since the chemical elements are fundamentally different in electron-proton componentation, this concept seemed to me to be the "Grand Central Station" of nature's numerical coordinate system's geometric volume-that numerically exact volumes contain constant, exact numbers of fundamental energy entities. This was the numerical and geometrical constancy for which I was looking. I determined to generalize Avogadro's experimentally proven hypothesis that "under identical conditions of heat and pressure all gases disclose the same number of molecules per given volume." (See Secs. 410.03-04.) |
986.130 Consideration 3: Angular Constancy |
986.140 Consideration 4: Isotropic Vector Model |
986.141 I said, Can you make a vector model of this generalization of Avogadro? And I found that I had already done so in that kindergarten event in 1899 when I was almost inoperative visually and was exploring tactilely for a structural form that would hold its shape. This I could clearly feel was the triangle^{__}with which I could make systems having insides and outsides. This was when I first made the octet truss out of toothpicks and semidried peas, which interstructuring pattern scientists decades later called the "isotropic vector matrix," meaning that the vectorial lengths and interanglings are everywhere the same. (See Sec. 410.06.) |
986.142 This matrix was vectorially modelable since its lines, being vectors, did not lead to infinity. This isotropic vector matrix consists of six-edged tetrahedra plus 12-edged octahedra^{__}multiples of six. Here is an uncontained omniequilibrious condition that not only could be, but spontaneously would be, reverted to anywhen and anywhere as a six- dimensional frame of transformative-evolution reference, and its vector lengths could be discretely tuned by uniform modular subdivisioning to accommodate any desired special case wavelength time-size, most economically interrelated, transmission or reception of physically describable information. (Compare Secs. 639.02 and 1075.10.) |
986.150 Consideration 5: Closest Packing of Spheres |
986.151 I had thus identified the isotropic vector matrix with the uniform linear distances between the centers of unit radius spheres, which aggregates became known later^{__}in 1922^{__}as "closest-packed" unit-radius spheres (Sec. 410.07 ), a condition within which we always have the same optimum number of the same "somethings"^{__}spheres or maybe atoms^{__}per given volume, and an optimally most stable and efficient aggregating arrangement known for past centuries by stackers of unit-radius coconuts or cannonballs and used by nature for all time in the closest packing of unit-radius atoms in crystals. |
986.160 Consideration 6: Diametric Unity |
Fig. 986.161 |
986.161 The installation of the closest-packed unit-radius spheres into their geometrical congruence with the isotropic vector matrix showed that each of the vectors always reaches between the spheric centers of any two tangentially adjacent spheres. This meant that the radius of each of the kissing spheres consists of one-half of the interconnecting vectors. Wherefore, the radius of our closest-packed spheres being half of the system vector, it became obvious that if we wished to consider the radius of the unit sphere as unity, we must assume that the value of the vector inherently interconnecting two unit spheres is two. Unity is plural and at minimum two. Diameter means dia- meter^{__}unit of system measurement is two. |
986.162 Fig. 986.161 shows one vector D whose primitive value is two. Vectors are energy relationships. The phenomenon relationship exists at minimum between two entities, and the word unity means union, which is inherently at minimum two. "Unity is plural and at minimum two" also at the outset became a prime concept of synergetics vectorial geometry. (See Sec. 540.10.) |
986.163
l R + l R = 2 R
2 R = Diameter Diameter is the relative-conceptual-size determinant of a system. A diameter is the prime characteristic of the symmetrical system. The separate single system = unity. Diameter describes unity. Unity = 2. (See Secs. 905.10 and 1013.10.) |
986.164 One by itself is nonexistent. Existence begins with awareness. Awareness begins with observable otherness. (See Secs. 264 and 981.) |
986.165 Understanding means comprehending the interrelationship of the observer and the observed. Definitive understanding of interrelationships is expressed by ratios. |
986.170 Consideration 7: Vector Equilibrium |
986.180 Consideration 8: Concentric Polyhedral Hierarchy |
986.181 Thereafter I set about sorting out the relative numbers and volumes of the most primitive hierarchy of symmetrically structured polyhedral-event "somethings"^{__}all of which are always concentrically congruent and each and all of which are to be discovered as vertexially defined and structurally coexistent within the pre-time-size, pre- frequency-modulated isotropic vector matrix. (See Sec. and Fig. 982.61.) |
986.190 Consideration 9: Synergetics |
Next Section: 986.200 |