The Concept of Infinity — Explained by Bhaskaracharya!

Re Sanskrit
Dec 2, 2018 · 2 min read

What is Infinity (अनंत)?

Infinity, as we hear this word our brain instantaneously thinks of something very big and enormous which we can’t visualize. And indeed, infinity is limitless (अनंत). Mathematically, it is represented by the symbol ‘ꝏ’, sometimes called as a lemniscate.

If you open Mathematical Books of today, you will find the idea of infinity mentioned in somewhat higher level courses. You won’t, however, find either the infinite or the infinitesimal in an elementary book on algebra, let alone arithmetic! The only thing you may find in an algebra book is a very stern warning about not ever dividing by zero! (Because if you divide any number by zero, you get infinity).

On the other hand, in the algebra books of ancient times in India, we find both the infinite and the infinitesimal treated routinely. One such example is Bhaskaracharya Bijaganita (his book on Algebra) and Lilavati (his book on Arithmetic). Bhaskaracharya was a twelfth-century Indian mathematician and astronomer. He was born in Bijapur in Karnataka.

While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskaracharya was a pioneer in some of the principles of differential calculus.

Definition of Inifinity — Bhaskaracharya’s Bijaganita 2.18

In Bijaganita, we find the following shlok

वधादौ वियत् खस्य खं खेन घाते खहारो भवेत् खेन भक्तश्च राशिः॥
vadhādau viyat khasya khaṃ khena ghāte khahāro bhavet khena bhaktaśca rāśiḥ॥
A zero results when multiplied by zero, a “khahara’’ (zero-divided, or infinity) results when a number is divided by zero.

Infinity further explained — Bhaskaracharya’s Bijaganita 2.20

For Khahara, he explicitly adds a colorful description

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अस्मिन् विकारः खहरे न
राशावपि प्रविष्टेष्वपि निःसृतेषु।
बहुष्वपि स्यात् लय-सृष्टिकाले
अनन्ते अच्युतेभूतगणेषु यद्वत्॥

asmin vikāraḥ khahare na
rāśāvapi praviṣṭeṣvapi niḥsṛteṣu
bahuṣvapi syāt laya — sṛṣṭikāle
anante acyute bhūtagaṇeṣu yadvat
There is no change in the Khahara (infinity) by adding or subtracting,
just like infinite immutable (Brahma or Viṣnu)
which does not have any effect by the living beings entering or leaving it
at the time of dissolution or creation of the world.
मात्रा को जोड़ने या घटाने से “खहर” (अनंत) में कोई परिवर्तन नहीं होता,
जैसे अनंत अपरिवर्तनीय(ब्रह्म) का ये दुनिया के निर्माण तथा
विघटन के समय जीवित प्राणियों के मृत्यु या जन्म से कोई प्रभाव नहीं पड़ता।

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