# DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

# 2.12  Complex Numbers

Since we are reviewing the main important concepts in the history that shaped the modern theories of physics and cosmology, which we are going review in chapter III, and because the Duality of Time is deeply related to complex numbers, we want to quickly mention how they were conceived, since this happened at around this same period when all these important observations and theories in physics and astronomy were being established.

Complex numbers first arose in the 16th century when algebraic solutions for the roots of cubic and quartic polynomials were discovered by mathematicians. It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.

This looked first like nonsense, but formal calculations with complex numbers can simplify the solutions of cubic equations with real roots. Furthermore, later mathematicians showed .that the use of complex numbers is unavoidable.

The Italian mathematician Gerolamo Cardano (1501-1576 AD) is the first person known to have introduced complex numbers. He called them “fictitious”, but Rafael Bombelli (1526-1572 AD) was the first to explicitly address the seemingly paradoxical solutions of cubic equations, and he developed the rules for complex arithmetic trying to resolve these issues.

Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex numbercan be then identified with the pointin the complex plane.

A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the complex numbers are a field extension of the ordinary real numbers, in order to solve problems that cannot be solved with real numbers alone. The term “imaginary” was coined by Descartes in 1637, although he was at pains to stress their imaginary nature.

In the 18th century, complex numbers gained wider use, as it was noticed that formal manipulation of complex expressions could be used to simplify calculations involving trigonometric functions. They now have practical applications in many fields, including physics, chemistry, biology, economics, electrical engineering, and statistics.

# Other Pages Related to Search Keywords:

• ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Physicists Call =>:

• ... art in alerting the United States government to the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission. The theory of fission is what PHYSICISTS CALL a non-relativistic theory, meaning that relativistic effects are too small to affect ...

• ## ... Full Symmetry =>:

• ... a comparable ten-parameter group that acts on absolute time and space. Instead of boosts, it features shear mappings to relate co-moving frames of reference. Poincaré symmetry is the FULL SYMMETRY of Special Relativity. It includes: translations, or displacements, in time and space ...

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• ... 00, and later by Einstein in 1905, in his famous paper â€œDoes the inertia of a body depend upon its energy-content?â€, in which he proposed the equivalence of mass and energy as a GENERAL PRINCIPLE and a consequence of the symmetries of space and time. However, in the previous an ...

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• ## ... Called Electromagnetic =>:

• ... otal motionâ€. Additionally, in the end of the 19th century, there were many attempts to understand how the mass of a charged object depends on the electrostatic field. The concept was CALLED ELECTROMAGNETIC mass, and was considered as being dependent on velocity and direction as well ...

• ## ... Light Particle =>:

• ... use this term as energy, but it was later calibrated to include the coefficient of a half: (3.7) Einstein was not the first to have related energy with mass. In 1717, Newton speculated that LIGHT PARTICLE s and matter particles were interconvertible. In 1734, in his own Principia, Emanuel S ...

• ## ... Incorporates Motion =>:

• ... vation of this famous formula. As we already introduced in chapter I, an exact derivation of this experimentally verified relation is not possible without the inner levels of time, since it INCORPORATES MOTION at the speed of light which leads to infinities on the physical level. Hencefort ...

• ## ... Verified Relation =>:

• ... ations in order to reach the final equation. Until now there is no exact derivation of this famous formula. As we already introduced in chapter I, an exact derivation of this experimentally VERIFIED RELATION is not possible without the inner levels of time, since it incorporates motion at ...

• ## ... Famous Paper =>:

• ... lence It is commonly believed that the equivalence between mass and energy arose from the theory of relativity as described by Poincaré in 1900, and later by Einstein in 1905, in his FAMOUS PAPER â€œDoes the inertia of a body depend upon its energy-content?â€, in which he p ...

• ## ... Fifty Years =>:

• ... valence of mass and energy as a general principle and a consequence of the symmetries of space and time. However, in the previous and many other related papers that he published in the next FIFTY YEARS , Einstein gave various heuristic arguments for this relation without ever being able to ...

• ## ... Light Particles =>:

• ... use this term as energy, but it was later calibrated to include the coefficient of a half: (3.7) Einstein was not the first to have related energy with mass. In 1717, Newton speculated that LIGHT PARTICLES and matter particles were interconvertible. In 1734, in his own Principia, Emanuel S ...

The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
Ibn al-Arabi [The Meccan Revelations: Volume I, page 156. - Trns. Mohamed Haj Yousef]

### The Sun from the West:

Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory

### Message from the Author:

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.