105400-Relationship-of-Gibbs-to-Euler

1054.00 Relationship of Gibbs to Euler

1054.10 Synergetic Analysis: Euler’s topology and Willard Gibbs’ phase rule give us synergetic-analysis capability. Euler differentiated all physical Universe into lines, crossings, and areas: the fundamental visual aspects of our experiences having to do with our eyes, radiation frequencies, and conceptual images. Gibbs’ phase rule differentiated the physical Universe into liquid, crystalline, and gaseous phases, which are not so much visual as thermal, which is tactile, and which are always characterized by unique wholenumber interattractions, i.e., restraints. Conversely, with successive wholenumber degrees of freedom, thermal, sonic, or viscosity frequencies are differentiated in respect to their condition within their respective states as well as between those states.

1054.11 Euler’s synergetic differentiation and equatingly accomplished reintegration of Universe deals with energy disassociative as radiation; Gibbs deals with energy associative as matter at various thermal stages. Euler’s and Gibbs’ are two different system aspects or behaviors of Universe. Euler deals with the static, geometrical field aspects of Universe. Gibbs deals with energy associative as matter, and what the degrees of energetic freedom may be within a local physical complex, and what amounts of energy would have to be added locally to bring about other states.

1054.20 Relationship of Gibbs to Euler

EULER

GIBBS

Tactile

Energy as matter (associative) Integrated Internal

Visual I

Energy as radiation
(coming apart) L

Differentiated

Locally superficial J 4-* They come together in vertexial bonding

which implies

Mass attraction = which is kinetically active in GIBBS

which is always = potentially directional and descriptive in EULER

1054.30 Synergetic Integration of Topology and Quanta: Synergetics’ “breakthrough” integration of Euler’s topology and Willard Gibbs’ phase rule is explained by the number of intertetrahedral bonds:

Phases:

Bonds: States:

Face I

»4 bond G

Eccentric 3 bonds = Ice

tetra I

^L D

Edge

Concentric 2 bonds = Water bond

(medium phase) (medium phase) tetra

Eccentric

1 bond = Vapor

Point

- bond tetra

Additional bond
energies present in
the eccentric phases

Medium + 2

phase

3+1, 1+3

C O M P R E S S I V E

1054.31 The rigid ice stage is characterized by load concentration, no degrees of freedom, and slow creep. The flexible, fluid stage is characterized by hinge-bonding, load distribution, one degree of freedom, and noncompressibility. The flexible, fluid vapor stage is characterized by universal jointing, load distribution, six degrees of freedom, and compressibility.

1054.32 Median unity is two, therefore unity plus two equals four.

(3 + 1=4; 1+3 = 4; 2 + 2 = 4)

Ice = Median freedom minus one freedom Water = Median freedoms

Vapor = Median freedoms plus one freedom

1054.40 Topology and Phase (see Table 1054.40 )

1054.50 Polyhedral Bonding: Willard Gibbs’ phase rule treats with the states of the environment you can sense with your eyes closed: crystallines, liquids, gases, and vapors. Euler’s points, lines, and areas are visually described, but they too could be tactilely detected (with or without fingers).

1054.51 The mathematicians get along synergetically using Euler’s topology alone. It is the chemists and physicists who cannot predict synergetically without using Gibbs’ phase rule.

1054.52 Euler deals with the superficial aspects of polyhedra: of visual conceptuality. He deals only with the convex surfaces of polyhedral systems. Euler deals with unit, integral, single polyhedra, or with their subaspects. He is not concerned with the modus operandi of the associabilities or disassociabilities of a plurality of polyhedra.

1054.53 But Gibbs unknowingly deals with polyhedra that are composited of many polyhedra, i.e., compounds. He does not think or talk about them as polyhedra, but we find the connection between Euler and Gibbs through the polyhedral bonding in respect to Euler’s aspects. Euler’s lines are double bonds, i.e., hinges. Euler’s vertexes are single bonds. Euler’s areas are triple bonds. Gibbs accommodates the omnidirectional system complementations of the other senses thermal, tactile, aural, and olfactorynot just associatively, but radiationally. Gibbs brings in time. Time is tactile. Time is frequency. Our pulses measure its passing.

1054.54 People see things move only relative to other things and feel small vibrations when they cannot see motion. The tactile feels angular promontories or sinuses with the fingers or body. Sinus means “without” “nothing,” invisible, ergo, nonidentified by Euler. The frequencies we call heat are tactilely sensed. We have radiation-frequency tunability range. Our skin structuring is tuned to frequencies beyond the eye-tunable range, i.e., to ultraviolet and infrared.

1054.55 Euler did not anticipate Gibbs. Gibbs complements Euler as does synergetics’ identification of the two excess vertexes as constituting the axis of conceptual observation in respect to all independent, individual orientations of all systems and subsystems; i.e., quantum mechanics’ abstract, nonspinnable “spin.”

1054.56 We find Euler and Gibbs coming together in the vertexial bonds, or polyhedral “corners,” or point convergency of polyhedral lines. The bonds have nothing to do with the “faces” and “edges” they terminally define. Two bonds provide the hinge, which is an edge bonding. One bond gives a universal joint. Triple or areal bonding gives rigidity.

Fig. 1054.40.

image

1054.57 Mass-interattraction is always involved in bonding. You may not have a bond without interattraction, mass or magnetic (integral or induced), all of which are precessional effects. As Sun’s pull on Earth produces Earth orbiting, orbiting electrons produce directional field pulls. This was not considered by Euler because he was dealing only with aspects of a single system.

1054.58 Gibbs requires the mass-interattraction without saying so. Mass-interattraction is necessary to produce a bond. Gases may be tetrahedrally bonded singly, corner to corner, or as a universal joint. Gibbs does not say this. But I do.

1054.60 Orbit as Normal: Ninety-nine point nine-nine plus percent of the bodies in motion in physical Universe are operating orbitally; therefore interyielding normally; i.e., at 90 degrees to the direction of the applied force.

1054.61 The rare special case of critical proximity, where bodies converge due to the extreme disparity of relative mass magnitude, happens also to be the rare special case in Universe wherein humans happen to exist, being thereby conditioned to think of the special-case exceptional as “normal,” thus to misapprehend the normal general behavior. The misapprehension regards the 99.99 percent normal orbital as being strangely perverse. There is much evidence within the critical-proximity environment that demonstrates the normal 90-degree, precessional resultants as, for instance, when a rope is tensed and reacting at 90 degrees to the direction of the tensing and thus becoming tauter.

1054.70 Time as Frequency: The Babylonians tried unsuccessfully to reconcile and coordinate time and space with circular-arc degrees, minutes, and seconds. TheXYZ, c.g_t.s. metric system accounted time as an exponent. Time was not a unique dimension. It was a uniquely qualifying increment of experience, of obvious existence.

1054.71 Synergetics is the first to introduce the time dimension integrally as the frequency of systems, which initially are metaphysically independent of time and size but, when physically realized, have both time and size, which are identified in synergetics as the frequency of the system: the modular subdividing of the primitive, metaphysical, timeless system.

1054.72 You cannot have time without growthability, which implicitly has a nucleus from which to grow. We would not have discovered the frequency or time dimensions had we not explored the expansiveness-contractiveness and radiational-gravitational behavior of nuclei in pure metaphysical sizeless and timeless principle.

1054.73 It follows that the isotropic-vector-matrix field discovery represents the frame of reference through which all the interpulsating transformations of time realizations transit, but which will never be directly witnessable in the eternally instant static state.

1054.74 Synergetics is an integration of the frequency of Gibbs with the timelessness of Euler. In Table 223.64, Columns 7, 8, and 9 represent the metaphysical timelessness of Euler; Columns 13, 14, and 15 represent the physical-in-time of Gibbs, the thermal, acoustical, sensorial characteristics that are expressible only as frequency.