Written by: Anil Banjade - 21103, Grade XII
Posted on: 29 July, 2020
Two things are infinite: The Universe and Human Stupidity. And I’m not sure about the Universe. -Albert Einstein
In our life, we go through one question “Which is the largest number?” We are introduced to the number system at the age of 5. With time, we learn to count to a hundred, thousand, million, billion, and trillion. But the question is “Do the numbers end?” At the School level, we are introduced to the term “infinity” and you might have seen it in Maths and Physics. If I ask you what exactly is infinity you will rather give me a symbol or you might say it’s a number which can’t be counted and many wouldn’t want to hurt your brain. We often see infinity in Maths and subconsciously, we know numbers are taught in Mathematics. So we assume infinity as a number but it’s not exactly a number.
Infinity is a concept. Infinity is an idea. Infinity is a thought. Infinity is endless. In Maths, Zero and infinity don’t have physical significance. Zero means it does not exist and infinity means the concept that is endless, unlimited, and unbound. We often imagine a train traveling on and on and we consider it as infinity but actually it is not infinity. Just imagine something endless or boundless which has no reason to stop. There is a common misconception that infinities are big only but they can be small too. For Eg: Numbers between 1 and 2. So, It’s not necessary that infinity should be big.
Infinity has been a topic to discuss from Ancient Greek. Zeno of Elea who is known for the creation of paradoxes has a paradox named “Zeno paradox of Zeno dichotomy paradox” is one of the mind-bending paradoxes to understand infinity. In his paradox, he has told how a Greek famous Hercules cannot defeat a turtle in a race. It basically says that if there are two points A and B and the distance between them is 1m then you can never travel that distance. Infinite time is required to travel that 1m distance. This paradox has been useful to understand infinity and with the help of it, many people started giving their ideas.
Pythagoras believed in the sequence of whole numbers and later his own theory proved him wrong because when you take height and base 1 in a right-angled triangle its hypotenuse is root 2 which is irrational. Then come Aristotle and Plato who believed in potential infinity rather than actual infinity and in the modern age of Physics and Mathematics Georg Cantor has described infinity in his own way which is widely accepted.
Infinities are used in Mathematics and Physics which are also classified into Mathematical Infinities and Physical Infinities and Metaphysical infinities. Mathematical infinities include irrational numbers whereas Physical infinities include thought like infinite space-time, etc. Infinities are divided into countable and uncountable infinity. The fun fact is countable infinity can’t be counted. They are the set in which elements could be theoretically counted though the end would never reach and uncountable infinities are like irrational numbers like the value of pi.
The challenge for modern physicists to understand this vast UNIVERSE is to discover the infinity-free equations which follow the true law of physics. In this search of GRAND UNIFIED THEORY, We need to first question infinity and figure it out to understand this Elegant Universe.
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