At the end of any journey it is always good to reflect back on the experience, acknowledge those who paved the way for the fruitful journey and consolidate what we have learned. In mathematics we thank Pierre de Fermat for his conjecture that set this twin journey into motion. The road was paved by the works of David Hilbert, Felix Brouwer, Bertrand Russell and L. C. Young. In physics it was Isaac Newton who opened the gate and showed the way but we also thank Albert Einstein for setting the agenda for the unification of the forces and interactions of nature called the Grand Unified Theory at a time in the twenties when quantum mechanics was rising to prominence due the great discoveries of Max Planck, Louis de Broglie, Erwin Schrödinger, Werner Heisenberg and Wolfgang Pauli, among others. However, like Fermat who set this twin journey into motion, particularly its mathematical route, it was Simon Marquez de Laplace who did the same in physics by posing the gravitational n-body problem. Neither Fermat nor Laplace solved the problem he posed but we would not be here without them. The main contribution of the physics part of this website is the unification of the natural dynamics and the various forces and interactions of nature. In effect, this website joins the three pillars of GUND macro and quantum gravity and thermodynamics and unifies gravity with the other forces and interactions of nature. Macro gravity is the global dynamics of cosmological vortices of superstrings; quantum gravity is the local dynamics of vortices of superstrings induced by primal toroidal fluxes which are dual to each other and thermodynamics is concerned with generation of visible (kinetic) energy, i.e., conversion of dark (latent) to visible (kinetic) energy, conduction of kinetic energy and its conversion from one form to another.
We sort out the essentials of what we have learned including duality in nature.
(1) Collective behavior and properties are independent and not the sum of individual behavior and properties. This is as true in natural science as in social science. The individual properties of atoms and molecules, for instance, have no bearing on such collective phenomenon as pressure and temperature. In social science, a social organization has more capability than the sum of the capabilities of its members.
(2) Local behavior and properties are independent of their global counterpart. For example, the solution of a differential equation is valid only in a suitable neighborhood of a point where the boundary conditions hold. The seccond law of thermodynamics is valid only at the atomic and molecular scale. It is reversed at the macro scale. For example, our universe has evolved from the chaos of the aftermath of the Big Bang and Cosmic Burst to the present higher order that we enjoy including biological order. Explosion is a point of discontinuity in time and space and destroys order in whatever that exploded. But, by energy conservation, the great release of energy by the Big Bang and Cosmic Burst created a new phenomenon and the latter gave birth to our universe. In the case of the Big Bang it created a super…super depression from where our universe evolved as super…super galaxy and the entire process is subject to the laws of nature. It should be noted that any explosion is a point of discontinuity and deletes any trace of the order of whatever that exploded.
(3) An extension of a mathematical system is not subject to the premises of the latter because it belongs to its complement. Therefore, it requires a separate set of premises to build the former as a mathematical system. However, to avoid contradiction its restriction to the original mathematical system must be consistent with it. As application, the derivative of a function belongs to some higher space, an extension. Therefore, it is independent of the function. Consequently, the behavior of a function is not fully determined by its values; hence, we have to pair it with its derivative to have a full account of its behavior. This is the central idea in the development of generalized curves and surfaces.
(4) Nature changes so does our knowledge. Therefore, we must be alert to changes and engage in periodic reassessment. We have seen lots of those changes during our journey; they reveal the nature of natural laws: they are transitory. No natural phenomena in this part of the Universe existed before the Big Bang and all natural phenomena that exist now and the natural laws they reveal will vanish as our universe reaches its destiny – black holes. In particular, there were neither biological phenomena nor biological laws in our young universe that we now enjoy.
(5) The solution of any physical problem always has two components, the qualitative and the computational. This reflects the complementarity of qualitative and mathematical modeling as a methodology. For example, GUT provided the qualitative solution of the gravitational n-body problem, that each body lies in a rotating spiral at the resultant of the pull of gravity and the centrifugal force of spin. Computation using the integrated Pontrjagin maximum principle determined the position and equation of the trajectory of each body at later time.
(6) Among the symmetries of nature is the existence of dual phenomena such as primal interaction at micro scale and macro interaction of cosmological vortices. Moreover, primum-anti-primum interaction at the micro scale that leads to mutual destruction has its dual in the interaction of two stars of opposite spins and comparable masses that also leads to mutual destruction called supernova. Naturally, this duality of nature is reflected in its language, mathematics, and we have seen them in this journey. Beyond duality we find patterns and regularity in nature some of which we have articulated as laws of nature. We highlight a couple of them.
(a) Cosmic waves are the prime mover of our universe. They are carrier of energy, convert dark to visible matter and vibrate our neurons that triggers and sustains thought.
(b) In the visible region of matter everything has a beginning and an end. Visible matter starts with the agitation of the superstrings to become prima; then the prima form atomic nuclei. The vortex flux around the nucleus draws in the orbital electrons and forms the atom. Since the primum is motion of its toroidal flux which is energy dissipating it gets exhausted and losses energy, its charge. This is the case with the so-called neutron star; it has degenerated into mainly semi-agitated superstrings, the transitional phase towards black hole that builds up in the eye of cosmological vortex. A neutron star has considerably weakened it does not radiate energy anymore.
Albert Einstein set the GUT agenda in the 1920s; this host carried it out and extended it to GUND.
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