COSMOS: A Mathematical Perspective

Greater Kashmir

The earth is a special entity because of its atmosphere, oceans and continents, animals and vegetable kingdoms.

“In this world, two realities produce inexpressible awe in me. One is the starry heaven and the other is moral conscience in Man. During the night, when I behold star- studded heaven, my mind exclaims: Who thou art playfully creating worlds and keeping them on their path. How supreme Thou art and how trivial I am. When I ponder over the chasm between the Supreme and my insignificant being, I am struck with awe.”thus says Immanuel  Kant

We humans are mostly engaged in petty affairs but, nevertheless, our achievements in the exploration of the Universe are in no way insignificant. The knowledge garnered through centuries has brought home to us that knowledge is power and is indispensable for survival. The dimensions of the Universe are so infinitely vast that units of measurement prevalent on the Earth will serve no purpose. For measuring astronomical distances, our unit is light year. It is the distance travelled by a ray of light in one solar year and its value is 10 trillion kilometers. A ray of light travels 300,000 kilometers in one second. It means that the light of the sun takes about 8 minutes to reach the earth. 

The earth is a special entity because of its atmosphere, oceans and continents, animals and vegetable kingdoms. The sky appears blue because of the atmosphere but the interstellar space is an unimaginably cold and dark vacuum.

An enormous global interest exists in the exploration of the planets and in many mathematically scientific topics- the origin of life, the Earth, and the Cosmos, the concept of ‘I’, the self, and our connection with Universe.  

The infinite space surrounding the earth is abounding in roving galaxies consisting of galactic dust and gas, stars, supernovae, novae, pulsars, quasars and black holes. If we watch the night-sky, we find milky floating patches and faint tendrils of light. Some are solitary wanderers, some are clusters and some appear huddled together, ever wandering in the cosmic space. These are all galaxies.

A galaxy is an immensely vast stretch of billions upon billions of stars and galactic dust and gas. There may be planetary systems somewhere millions or thousands of light-years from us. Some planets may be teeming with life like our Earth. There may be intelligent beings somewhere. For the present we have no possibility to reach them.

There are some hundred billion galaxies each with a swarm of 100 billion stars on the average. Our galaxy is a spiral galaxy having some 400 billion stars. Cosmic space is so vast and the total number of galaxies so insignificant that if we had the power to be somewhere in space to search for a planet the chances will be one in billion trillion trillion. Therefore, the earth on which we live is most precious.

Einstein predicted in the twenties of this century that a ray of light falling on a non-luminous body will not be reflected back if the gravitation of the body increases tremendously. It was experimentally found to be correct. The earth attracts all other bodies towards its centre and this special case of gravitation is called the gravity. Gravity causes acceleration in falling bodies and its value is 10 metres per second. It is denoted by ‘g’. Its value on the Moon is l/4th of ‘g’ on the Earth. Therefore, 1 kg will weigh only 250 gms on the Moon. Consider now on Earth the value of ‘g’ becomes 100,000 times. Everything on Earth will be compacted with tremendous pressure and force towards its centre. Earth will be reduced to a compact small ball and if a ray of light falls on it from outside the universe it will not be reflected back. The Earth will become invisible. If any other body enters the proximity of the Earth, it will also be sucked in. In short, the Earth will become a black hole. Imagine such a thing happening to a star 1000 times bigger than our Sun when it suffers supernova explosion. With value of ‘g’ becoming even 1 billion times, it will become a black hole. A black hole can suck an enormous galaxy into it. Black hole is supposed to be a bottomless pit. Some say that if somehow we are able to fall into it without suffering any change or in an ethereal body such as we have in a dream we may find ourselves in a different universe.

Black holes were first thought of by the English astronomer John Michell in 1783. Some astronomers inferred from the quasars that the universe is expanding. But other facts have come to light which put a question mark on the doctrine of expanding universe. If there is insufficient matter to prevent the Universe from expanding forever, it must have an open shape with a surface extending to infinity in our three dimensional analogy. If there is enough matter, then it has a closed shape curved like a sphere in our three dimensional analogy and light cannot escape from it, then Universe will be described as a black hole. What is inside a black hole, a mystery. 

According to the Sankhya philosophy, man is beyond everything. It means that it will not be possible to investigate into the nature of man with the help of microscope, telescope, and spectroscope. 

Leibniz’s doctrine of individual forces has something in common with the Sankhya philosophy. According to Leibniz, every being is a unit called monad. Every monad is a living mirror of the Universe, a microcosm. God is the supreme monad responsible for maintaining the order and the continuity of the Universe. It appears that Leibnitz might have been influenced by the Sankhya philosophy.

The subject of celestial mechanics evolved into that of dynamical systems, with major advances by mathematicians G.D. Birkhoff, Kolmogorov, Arnold, and Moser. Methods of chaos theory began to play a role, and the theoretical studies were both informed by and applied to the profusion of new discoveries of planets, their moons, asteroids, comets and other objects composing the increasingly complex structure of the solar system. The mathematical study of the cosmos has its roots in antiquity with early attempts to describe the motions of the sun, moon, stars and planets in precise mathematical terms, allowing predictions of future positions. In modern times, many of the greatest mathematical scientists turned their attention to the subject.

A few million years ago there were no humans. Who will be here a few million years hence? But now tiny exploratory spacecrafts from Earth are moving, glistening and elegant through the solar system and at this dangerous moment of technological adolescence we are managing to avoid self- destruction.

(The author is Nodal Officer, J & K Institute of Mathematical Sciences, Jammu )