Understanding Infinity [ Part-1]

“The only way to comprehend what mathematicians mean by Infinity is to contemplate the extent of human stupidity.”

-Voltaire


Infinity, a concept(?) which has puzzled men for centuries. There is a common notion in philosophy that since human mind(i'm referring to normal people) is limited to 3-Dimensions, something as abstruse as infinity is beyond comprehension. But, along the way people have come up with some really interesting theories.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of Shakespeare. [ For the proof refer to the wiki page under the same name].




Mathematicians seem to treat infinity as a number. There are of course, Aleph numbers which represent the different cardinality of infinite sets like natural numbers, real numbers etc..which is a different approach to the same concept. They seem to say that one infinity differs from another depending on the set they are taken as a part of. Another interesting one is Zeno's paradox. It states that in order for an entity to go from point a to point b, the entity must first travel half the distance, in order to travel half, it must travel one fourth, and to travel this it must travel one sixteenth and so on infinitely. Zeno conludes thus that the whole concept of motion is an illusion!!

So infinity need not be necessarily very large always. It might be even the smallest immeasurable quantity which does not have a finite ending. So the question which arises is what exactly is infinity? Is it a notion? Or is it just a fragment of man's imagination? Or is it a yearning of the human mind by recognizing the need for something higher and non-definable?

Give it a thought.
till next time,
Au Revoir!