Mathematical method universal constants and important numbers Part-II

Transcendental numbers, universal constants and other important aspects

There are many numbers which occur in nature in the context referred to in the beginning of this piece. Known as "transcendental" numbers, they amaze us with the role they play in the ordered structure of the world around us. Transcendental numbers cannot be expressed as the root of any algebraic equation – examples being s pi, e and the Feigenbaum's number.

The number pi, as we are all aware, represents the ratio between this circumstance of a circle and its diameter – a universal constant so far as two-dimensional planes are concerned. While investigations have determined the value of this number, it is easily seen that that value is irrelevant so far as the natural relationship property between the two figures is concerned.

The number e, called Euler’s number, represents the base of natural logarithms.This Feigenbaum number, as it is called, occurs in the context of the study of the properties of dynamical systems and is associated with a phenomenon called "period – doubling". The ratio of successive differences between period doubling bifurcations parameters approach the Feigenbaum number.

This number, strangely, plays a crucial, and exactly the same, role in understanding complex systems such as clouds, flowing rivers and the pattern of parameters changes in which here present variations in the weather.

The gravitational constant, symbolized G, is a physical constant that appears in the equation for Newton’s law of gravitation. Sir Isaac Newton (1642-1727), the English mathematician, quantified the behavior of the force of gravity. He noticed that the gravitational force between two objects is proportional to the product of their masses, and inversely proportional to the square of the distance between their coentres.

The acceleration observed in any body due to gravity is called acceleration due to gravity. The force due to gravity is given by, Where m = mass of the body and g = gravity.

Among some fifteen numbers which are commonly accepted as the most important transcendental numbers that have a role to play in understanding the physical sciences and the phenomena associated with associated with them, there are numbers such as Krapar’s number, Bell’s number etc.
which, however, one need not concerned with oneself in this context.

Planks constant is fundamental to quantum mechanics, which holds that light behaves as both particles and waves. Max Planck discovery was considered radical for the 18th century and contradicted the classical view of the universe, which holds the events proceed predictably in a clockwise fashion.

Planck's constant showed that the energy of light is proportional to its frequency. This and a modified form of it called Dirac's constant, were used by Einstein in a relatively new field of mathematical physics called Quantum Mechanics.

Quantum Mechanics helped explain the nature of three of the four fundamental forces of nature, electromagnetism, the weak nuclear force and the strong nuclear, – while the theory of General Relativity explained the other remaining force, namely gravity.

The constant lambda was introduced by Einstein artificially to explain how the universe should I been static, rather than in an expanding state. Later, however, upon discovering that the universe was actually expanding, he abandoned that constant, calling his earlier interaction the “biggest blunder” of his life.

Strangely enough, his so called blunder proved to be actually right as and has been revived by scientists subsequently to explain is and represents the “dark energy” that seems to be counteracting the impact of gravity, causing the universe to expand.

Little wonder, then, that the discovery, the description and the study of these numbers and the conclusions drawn there from, have for was constituted the very basis of all effort of philosophers, scientists and mathemations to understand the working of the world around us.

A binary code represents text, computer processor instructions, or other data using any two-symbol system, but often the binary number system's 0 and 1. The binary code assigns a pattern of binary digits (bits) to each character, instruction, etc. For example, a binary string of eight bits can represent any of 256 possible values and can therefore represent a variety of different items.

In computing and telecommunications, binary codes are used for various methods of encoding data, such as character strings, into bit strings.

There are other values especially in the physical sciences, such as watt, volt ohm and ampere beer et cetera which I am referring merely nearly to show that there are many such values.

In the preceding discussion we have noted the role which certain numbers play in the manner in which the universe is organised. As can be seen there is much more than meets the eye in the day to day phenomena that we observe in a routine manner. They are all governed by fundamental and unalterable principles which, however, reveal themselves to us easily through these numbers.