Mathematics and Philosophy – Infinity and Zero

In the world we see today, mathematics stands for specific generalisations, absolute truth based on empirical data and testable principles falling in the domain of science while Philosophy deals with abstract theorising, conflicting rational views and contested principles falling in the domain of humanities. Mathematics seems to have grown out of our material needs (how much meat should be hunted given that it turns bad in x days) while Philosophy seems rooted in our morals and conscience trying to give meaning to human existence and its values.

But are these domains so different? One of my friends used to draw concentric circles writing knowledge in the smallest one illustrating how all knowledge started from one common point and then, started branching out in different specialisations (so, the second one might be Science and Humanities with third as its various streams and so on), thus somehow creating his own ‘Big Bang’. He would sit in his pressed kurta in the veranda on a bright sunny day and would be drawing large figures on the floor explaining his point. He wanted to create a knowledge based social media platform based on his idea eventually culminating everything into one but that’s a different story.

Philosophy is considered mother of social sciences like Psychology, Sociology etc. Pure mathematics is foundation of all scientific studies. They seem to be the first branches which sprouted out of the Knowledge tree. But what came first? With no definite answer in place, I would take shelter in philosophical propounding to reach a definite conclusion. Borrowing from Marx who said 

Conscience arises out of materialism, I would say rudimentary mathematics was predecessor of first philosophical principle. Human beings (or Neanderthals or whatever, basic premise is when they started thinking) before they had much idea of their being and society had to fill their stomachs and share the spoils of a successful expedition among the contributors in a civil manner. Differing from the animal world where sharing is mostly done in the most savage way, mathematics helped people to turn more civilised, to empathise with hunger of other human beings, to work in groups and thus, to think about major philosophical questions posing humans.

But mathematics could not have grown alone. It needed sound philosophical principles for its progression. The biggest scientific theorems and principles of our times start with certain beliefs and philosophy in which empirical data is filled later. An example is of the sage Kanada who dreamt of the most elementary particle which made all the matter around us Kana; Anu and Paramanu though no empirical evidence was found to prove his theorem which has been proved today using mathematics by deriving principles of particle physics. The philosophy of Kana Kana mein Bhagvan might have formed the basis of such discovery.  I believe we, modern students, miss out in our curriculum's that there exists strong relationship between philosophy and mathematics, the knowledge of which would help us in understanding the world better and also, understanding the subjects as a whole.

Another example which showcases the strong bond between these two realms of knowledge is the discovery of 0; a discovery, most essential, on which all our modern scientific theories stand. The impetus given to science through this discovery cannot be measured as it is infinite J. Though, I think 0; which has such a strong philosophical foundation could not have been discovered anywhere except India whose philosophical schools, by that time were mature, argumentative and comparable to modern schools. Indian philosophy by that time has already pointed towards existence of such value; or its non-existence (A Shunya is absence of everything measurable). Here, I will try to give away my understanding of Infinite and zero.

In a famous story of Aadishakti, an immense wall of fire appears before Brahma and Vishnu representing the Universe. Both the Gods, intrigued, decide to find its end and go in opposite directions. At the end of quest which went for many cosmic cycles, both come to the conclusion that Universe has no beginning and no end (Na Aadi Na Ant). But then, how do you differentiate between Aadi and Ant? A continuous line has no end. Both its end either lies at the infinite or do not exist (Shunya).

Other example of this analogy is our circle. Draw a square on the ground. Keep on adding 1 corner at a time thus, converting it into a pentagon, hexagon and so on. As you go on doing it, at one point you will reach infinity (Probably though not possibly). What is the closed regular figure with infinite corners will be called – A circle. What is the closed regular figure with 0 corners is called – A circle.

I believe 0 and infinity in mathematics, as in philosophy, stand for the same point; what you see depends only on where you are standing on the number line. Philosophy of numbers helps you understand and use numbers in a much deeper and meaningful way. As a student of mathematics, we should be trying to understand these deeper aspects to make our journey through the subject joyful.

PS: Just wanted to share an extension on the above principle. Since, 0 and infinity are the same point; the number line was never straight as was taught in schools. It was due to our limited perspective that we were made to learn the concept of negative numbers (After all, what can be smaller than a Shunya).

The number line is in-fact, circular with no Aadi or Ant.