Given the existence of a space fabric as a fluid medium with which matter interacts, it is possible to physically model many physical phenomena at both quantum and galactic levels. Discarding the existence and effect of such a medium is the main reason behind the irreconcilability of some theories and inexplicable behaviour of objects at both quantum and galactic levels.
To develop a conceptual model of a system, the conscious mind begins by linking simple concepts to form mathematical relations. For example, by realizing that the flow rate from a water tap depends on the number of tap turns, a mathematical model is developed. It is then possible to relate the volume of water collected to the duration it takes to collected it, for a given number of tap turns. Relating a system’s variables to each other correctly is all that is needed to develop a mathematical model. This simple water-tap example could be extended to predict the flow rate of water through any pipe. To do that, the model must include all relevant parameters that affect water flow, which include pressure head, pipe diameter, length, and surface roughness. Continue reading “Modelling Supernovae & Black Holes!”
In this post I shall discuss the nature of π as a mathematical constant and reveal its relationship with the fabric of space. As an irrational number π represents the ratio of a circle’s circumference to its diameter. An irrational number is a real number that cannot be expressed as a ratio (a/b), where (a) and (b) are integers and (b≠0).
Returning briefly to the cubical universe, which we considered in a previous post, if the observer there begins to probe his world at the level of the individual cubes defining his space and decides to form different geometries at that level, he could do so only by using those cubes. He would have no other means. Using cubes to define circles, he would soon discover that the geometric properties of his circles vary according to the orientation of the cubes. For example, the number of elements defining the diameter of the same circle could vary depending upon the orientation of the cubes in the circumference. Therefore, in a universe defined by cubical elements π, as the ratio of the units of length of a circle’s circumference to that of its diameter, cannot be constant. Continue reading “π in the sky!”
In mathematics and in physics, complex numbers are considered mysterious. Although they are essential to solving fundamental problems in science and engineering, their true relationship with the physical world remains ambiguous. For example, why do they have two components, which are referred to as real imaginary parts? Why is the imaginary part closely linked to the square root of minus one? And most importantly, what is their relationship with physical reality. This post answers those questions.
In this post, I shall unravel one of the mysteries of mathematics, that is the mystery of complex numbers. In future posts, I shall unravel other mysteries with reference to the basic elements of physical reality. They include infinity and irrational numbers of which (π) is considered most mysterious. Continue reading “Complex Numbers Unravelled”