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Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef

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2.13  Corpuscular Philosophy

On the other hand, there has been a long philosophical debate about the structure of matter and whether it is infinitely divisible. Atomists posited that matter consists of two fundamental principles: atom and void, but these philosophical atoms are not like the atoms we now known in science, whose internal structure is identified down to the levels of elementary particles and fields, whereas the philosophical atoms are absolutely indivisible. Conversely, the substance theory is based on a prime material continuum that remains qualitatively invariant under division.

This philosophical debate between the continuum and discretuum views of matter lead eventually to the development of calculus by both Isaac Newton and Gottfried Leibniz in the 17th century. As we will discuss further in section 16, Newton became most famous because his pioneering work on gravity and mechanics, that is essentially built on the concept of an absolute and continuous space and time, was exceptionally successful in explaining the various phenomena of motion, and was eventually developed by Einstein into the Theory of Relativity. On the other hand, Desecrate and Leibniz built their philosophies on the atomic theory, which was developed into the Corpuscular Mechanical Philosophy, but unlike Newton’s Mechanics which quickly found many industrial and practical applications, this line of thinking had not been given adequate consideration, otherwise it would have been developed faster into Quantum Mechanics that eventually came out with new terminology, although the Standard Model of Quantum Field Theory is essentially based on the same concepts because the elementary particles, that are the quanta of field excitations, are nothing but the monads advocated by Leibniz, as we shall discuss in section 14 below and further in chapters V and VI.

After the early development of heliocentric astronomy, many philosophers believed that the Aristotelian conceptions, which are based on the geocentric model, could no longer provide adequate foundations for natural philosophy. In the early 17th century, various European philosophers, including Galileo Galilei (1564-1642 AD), Isaac Beeckman (1588-1637), Pierre Gassendi (1592-1655 AD) and Rene Descartes (1596-1650 AD), adopted the corpuscular mechanical philosophy which was based on the atomistic theory of Democritus (460-370 BC), but unlike the philosophical atoms, corpuscles can be geometrically divided although they are physically indivisible.

Gassendi tried to explain all the qualities of matter and all the phenomena in the universe in terms of atoms and the void. He gave an account of the entire creation, including the heavens, the inanimate and the animate worlds, and the human soul, and he argued for the existence of an incorporeal, immortal soul, and also believed in the existence of incorporeal angels and demons.

Descartes also articulated his mechanical philosophy in his Principia philosophiae that he published in 1644, but his ideas were quite different from Gasendi’s. He wanted to develop a mathematical approach to the mechanical philosophy, and he was a plenist, claiming that matter fills all space, thus denying the existence of void. He believed that geometrical extension is the only one primary quality of matter, which provided the foundations for his attempted mathematization. He also drew a sharp distinction between matter and mind, considering thinking to be the essential characteristic of the mind. His concept of mind, as immortal, established the boundaries of mechanization.

Descartes attempted to deduce the mathematical laws of motion and impact. Although these laws were inadequate, their prominent place in his system reflects their importance in the mechanical philosophy where contact and impact are the only causes in the physical world. Having established the physics that he considered fundamental to his system, Descartes proceeded to give mechanical explanations of all the phenomena in the world, including cosmology, light, the qualities of material objects, and even the human body.

Gassendi and Descartes set the agenda for the next generation of natural philosophers, who accepted mechanical principles in general, believing that they had to choose between Gassendi’s atomism and Descartes’s plenism. Robert Boyle (1627-1691), Christiaan Huygens (1629-1695), and Isaac Newton (1642-1727), among the most prominent natural philosophers of the second half of the 17th century, developed their philosophies of nature in this context. Boyle is best known for his attempt to incorporate chemistry within a mechanical framework, while Huygens followed Descartes in attempting to mathematize physics and the mechanical philosophy. He applied this approach to create a wave theory of light, a mathematical analysis of centrifugal force, and an improved theory of impact.

Newton, however, first accepted the mechanical philosophy in his early years at Cambridge University, and he used it in his attempts to explain a number of phenomena, including gravitation, reflection and refraction of light, surface tension, capillary action, and certain chemical reactions. When he failed in explaining these phenomena using corpuscular mechanics, Newton was led to the view that there exist attractive and repulsive forces between the particles composing bodies. This concept of force came to him from his alchemical studies. The concept of force brought back the older theories of action at a distance that had been banished by the mechanical philosophy, but it enabled Newton to accomplish the mathematization of physics, which is what made the classical mechanics eventually prevails over the corpuscular mechanical philosophy.

Nevertheless, Newton himself argued that the geometric nature of reflection and refraction of light could only be explained if light was made of corpuscles, because waves do not tend to travel in straight lines. We will discuss Newton’s Mechanics in section 16, and the nature of light in section 18

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I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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