Scientific Natural Philosophy

The novelty of our methodology calls for this general introduction to initiate the reader to the grand unified theory (GUT), the core of scientific natural philosophy. The conventional methodology of physics, quantitative modeling, has left long-standing problems unsolved, e.g., the turbulence and gravitational n-body problems, and fundamental questions unresolved, e.g., what the basic constituent of matter and the structure of the electron are, an inadequacy that prompted the author to introduce an alternative methodology - qualitative modeling - that digs deeper into nature beyond appearances to find out how it works. It explains not only the appearances of nature revealed by natural phenomena but also their dynamics including natural forces, interactions and behavior in terms of the laws of nature. Natural laws are discovered by observing patterns and regularity in nature and articulating them as natural laws upon which a physical theory such as GUT is built to express scientific knowledge as a deductive system subject to the most updated standards of mathematical rigor and precision. Thus, qualitative modeling gave birth to theoretical physics where there was only mathematical physics. The validity of a physical theory rests on its ability to explain natural phenomena and make verifiable predictions including invention of technology that works. Anytime a contradiction arises in a physical theory within its own structure or from experimental results it goes down the drain unless it is fixed by suitable modification or discovery of natural law that resolves it.

Just as all concepts of a mathematical space are defined by its axioms and conclusions derived from them, all physical concepts and structures, properties and interactions are determined and defined by the laws of nature and conclusions and predictions derived from them. For example, the structure and properties of the superstring are derived from natural laws. In other words, this new methodology axiomatizes physics as a deductive system where the axioms are laws of nature. In effect, it alters the primary task of the physicist from computation and measurement to the search for the laws of nature.

The boundaries between dark and visible matter and semi-and non-agitated superstrings are based on the finest arc length of visible light which may be refined in the future but our analysis will prevail as long as it is based on the laws of nature.

This chapter stands on the major rectification of foundations by David Hilbert in the early 20th Century and more. Recognizing the ambiguity of an individual thought being inaccessible to others Hilbert proposed that mathematics should be concerned not only with individual thought but with its representation by objects that can be studied collectively, including symbols, subject to consistent axioms. We stand on Hilbert’s rectification and avoid other sources of ambiguity, where contradiction usually hides, such as infinity, large and small numbers and vacuous concepts and propositions. Turning on the real number system we find the field axioms inconsistent and rectification paves the way for its reconstruction into the new real number system under new set of axioms.

In physics we wonder why there are long-standing unsolved problems such as the gravitational n-body and turbulence problems and unanswered fundamental questions like what are the basic constituents of matter and the structure of the electrons. We conclude that its present methodology of quantitative modeling that describes nature’s appearances mathematically is quite inadequate, and proceed to complement it with qualitative modeling that explains not only its appearances but also how it works in terms of its laws. Either methodology is indispensable to the other. Using qualitative modeling we proceed to participate in the 5,000-year search for the basic constituent of matter and succeed in pinning it down to the last detail of its structure called generalized nested fractal sequence. The superstring was the crucial factor in the solution of the 200-year-old gravitational n-body problem.

This chapter surveys conventional and new mathematics involved in the development of GUT. The most important conventional mathematics includes the theories of generalized curves and surfaces and the integrated version of Pontrjagin maximum principle developed by L. C. Young. We summarize their original development here because they are quantitative models of many important physical concepts. The boundary year for the new mathematics is 1998, the year of publication of the counterexamples to Fermat’s last theorem that proves the false conjecture and catalyzed the development of new mathematics such as (a) the new real number system, (b) generalized integral, derivative and fractal and (c) the complex vector plane (fully developed here except (c)). The introduction to the complex vector plane that rectifies the complex number system is presented but its full development requires re-writing of the rectified complex number system as the basis for rectification of complex analysis. The introduction of qualitative mathematics paved the way for qualitative modeling, the crucial factor for the discovery of the superstring and the 11 initial laws of nature required for the solution of the gravitational n-body problem by serving as foundations of GUT. The d-sequence of a dark number qualitatively models the superstring, the generalized curve quantitatively models its path and that of an elementary particle and the new real number system quantitatively models time and distance of ordinary space. The generalized surface quantitatively models the expanding Cosmic Sphere before its burst at t = 1.5 billion years from the start of the Big Bang.

We provide a detailed account of the successful 5,000-year-old search for the superstring, basic constituent of matter, capped by its capture in 1997, and highlights what particle physics have accomplished as a vital link in the capture of the superstring. The latter was the key to the solution of the unsolved problems and resolution of fundamental questions of physics, particularly, the 200-year-old gravitational n-body and turbulence problems and about the structures of the superstring, electron, proton, neutron and atom. Most of all, it laid the foundations of the grand unified theory that binds the forces and interactions of nature in this single theory. Naturally, it advances and unifies the natural sciences and strengthens multidisciplinary research as well. As a matter of fact, its theoretical applications have opened up new fields in biology, geology and oceanography, atmospheric science, physical psychology, astronomy, cosmology and medicine.

GUT explains some previously puzzling phenomena, e.g., superconductivity, matter-anti-matter interaction and metal fatigue, and corrects misinterpretation of natural phenomena, e.g., thermonuclear reaction, magnetic levitation and supernova. Most of all, it brings us to the threshold of a new technological epoch that utilizes the clean, inexhaustible and free dark matter, one of the two fundamental states of matter, that is abundant everywhere in the Cosmos.

The crucial element for all these discoveries are qualitative mathematics and modeling; the latter explains not only the appearances of nature but also how nature works in terms of its laws. Qualitative mathematics is the only route towards the discovery of natural laws.

GUT and its methodology (qualitative modeling) opens up new fields in physical psychology, biology, geological and atmospheric sciences, oceanography and medicine, and brings the science community to the threshold of the new epoch of GUT Technology. The summary of the solution of the gravitational n-body problem brings us to a full circle since the journey into theoretical physics, cosmology, philosophy and applications were started with this problem.

Its theoretical application to physical psychology is the underlying physics of the mind and here are its findings: (a) brain waves are the common medium for carrying out the brain’s and gene’s functions; (b) the brain controls entire body functions and processes, its principal function, and the cortex, the thin layer that wraps around the upper lobe of the brain, is the center of thought, its secondary function; (c) the main function of the gene is to produce body tissues in the cellular membrane and ensure that every part of the body grows in the right place. (d) the principal factor in evolution is the gene.

The theory of chaos and turbulence is developed in the geological and atmospheric sciences and applications, while wave motion and water current are explained in oceanography. The theory of genetic composition is developed towards the generation of technology for the treatment of genetic diseases.

An overview of the technological applications of GUT is provided and the common thread is the utilization of the clean, free and inexhaustible dark matter that is abundant everywhere in the Cosmos.

Having laid down the mathematical and physical foundations of thought through the theory of intelligence we have presented scientific natural philosophy and its mathematics briefly but comprehensively. Since knowledge is dependent on methodology, we have given methodology and epistemology the same importance although the latter is the core of philosophy by tradition. Being materialist, scientific natural philosophy relies on rational thought. Therefore, we undertook critique-rectification of mathematics and its foundations and the methodology of natural science to minimize the inherent uncertainty of thought.

Unlike previous philosophies scientific natural philosophy is far from being speculative based on the most advanced findings of natural science, particularly, the discovery of the basic constituent of matter, superstring. Its discovery was the key to our knowledge of the other inhabitants of our universe from micro/quantum through macro/galactic scales, and from dark through visible matter. For the first time, we know what a black hole and a big bang are. We are now able to explain wave-particle duality, metal fatigue, elasticity and superconductivity. We know the evolution of our universe from its birth at Cosmic Burst through its destiny as a cluster of black holes back in dark matter and the place of our universe in the timeless and boundless Universe – one of the bubbles in it. Moreover, natural laws are transitory which is quite contrary to traditional thinking. There was no natural law in this part of the Universe before the Big Bang, and all natural laws will vanish as our universe reaches its destiny.

There is much wisdom in what this author’s best academic friend, Professor V. Lakshmikantham, says on the subject of research: do it! Some researchers rely on the serendipity of science, others on sharpening their tools and reading the work of others leaving no time to think and ending up nowhere. Perhaps, this author’s experience can offer some insights.

His academic career was interrupted 15 years straight during the political turmoil in the Philippines capped by the imposition of martial law by President Ferdinand Marcos, 1972 – 1986. The situation was the least this researcher needed at the time especially when he found himself not really in immediate danger but in a wide field in the general direction of the business end of the barrel of the gun. He left for the United States in 1971 and found a new imperative: build a support movement for the end of martial rule during which time he shelved his mathematical career completely.

When people’s power ousted President Marcos in 1986 the author returned to the Philippines but faced a daunting challenge: he found himself at ground level while his international colleagues were up on the fifteenth floor of the Tower of Academe. Retracing their steps would have been impossible and historical precedence was not in his favor either. The closest to his experience was Bertrand Russell’s when he was removed from his post as professor of mathematics at Cambridge University, England, for his pacifist activity during the First World War. When he got his post back 26 years later through the effort of British mathematician Paul Hardy, he went around mathematics and remained a philosopher.....

Basic Cosmic or Electromagnetic Waves. Waves generated by the normal vibration of the atomic nuclei that induces suitable synchronized vibration of dark matter (superstrings) that propagates across it.

Black Hole. Massive concentration of non-agitated superstrings in the eye of a cosmological vortex, e.g., galaxy or planet. Since black hole is dark matter, it does not suck matter. It is the eye of the cosmological vortex that nurtures and accumulates it that does; that suction is gravity.

Chaos. Indistinguishable mixture of orders or patterns of behavior. For example, at the onset of a hurricane where air molecules are rushing by the trillions towards tropical depression, one cannot monitor or predict the direction of motion of any molecule due to the immensity of their collisions. However, every molecule is subject to the laws of nature.

Cosmological Vortex. Vortex fluxes of superstrings in the Cosmos, e.g., planet, star, galaxy, a grain of cosmic dust....

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