The Acharya Pingala Who Introduced the Binary Numbers

We all know that the world has gone through Corona Virus and still, everyone is struggling as the disease hasn’t stopped spreading. I know you all must be thinking about why I’m adding this context?

It’s because have you ever thought about how they can predict the number of infections spreading? And how did they know that now it’s time for a lockdown? Well, it’s quite interesting to know how it all happens.

We all must have heard about “Binary numbers” once in our lifetimes while learning mathematics. And these numbers of covid were also predicted by this mathematical principle known as Binary expansion.

Do you also know who discovered these Binary numbers? And let me tell you this discovery of Binary numbers happened quite by an accident. It was “Acharya Pingala” who found these binary numbers.

Let’s see how and when he found these binary numbers which are now being so helpful in predicting numbers and any other situation.

Who was Acharya Pingala?

Acharya Pingala was the earliest author and influential scholar of the “Chandaḥśāstra” also known as (the Pingala-Sutras). Pingala is also known as the early disquisition of prosody. His work has been appreciated to date but the historical knowledge about him isn’t known much as he belonged from the 2nd century BCE.

Discovery of Binary Numbers

Acharya Pingala found out about the possibilities of binary numbers quite by a coincidence while he was working on the meter of Chandah of Vedas. So, the Vedas were being collected either in meters or Chandah’s.

Almost every Indian language had the ‘long swar’ also called ‘dheerga’ and ‘short swar’ also called ‘laghu’. This mixture of long and short swars or sounds was the basis of Sanskrit patterns of sounds or Chandah or meters.

Chhanda Shastra

It is written by the scholars that in the 3rd century BCE Acharya Pingala the Indian mathematician worked on the “Chhanda Shastra ”. Now, firstly let’s understand what is the meaning of Chandahsastra? It means that the science used in meters is just like used in either music or poetry where it is recited. And that’s when Pingala stumbled or tripped on the concept of Binary numbers while working on the Chhanda Shastra.

The Chhanda Shastra is a work of a total of eight chapters in the late Sutra style as it has been dated in the last centuries by historians. This work of Acharya Pingala presents the first time description of binary numbers. Along with this, the debate of the combinatorics of meter or Chandah too had a close similarity towards the binary theorem.

Rather than using 0 and 1, Acharya Pingala used laghu or light and guru or heavy to describe the two syllabi in Chandahsastra. While solving the different possibilities of the algorithm through laghu and guru swar. And unintentionally Pingala found the different patterns of Binary Numbers.

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The Combination of Zero and One

In the Chandahsastra these following combinations of 0 and 1 have been represented by Acharya Pingala which was eventually discovered as the binary numbers. These are very similar to the computer programming procedures at present.

So Pingala started by using four zeros in his system of using binary numbers starting with the number one and not zero. These values of numerals are formulated by adding 1 to the sum of place values.

Below you would see that every time the place value increases to the right.

I know it must be getting a little confusing so let’s understand it by using numericals:

• 0 0 0 0 with the numerical value = 1
• 1 0 0 0 with the numerical value = 2
• 0 1 0 0 with the numerical value = 3
• 1 1 0 0 with the numerical value = 4
• 0 0 1 0 with the numerical value = 5
• 1 0 1 0 with the numerical value = 6
• 0 1 1 0 with the numerical value = 7
• 1 1 1 0 with the numerical value = 8
• 0 0 0 1 with the numerical value = 9
• 1 0 0 1 with the numerical value = 10
• 0 1 0 1 with the numerical value = 11
• 1 1 0 1 with the numerical value = 12
• 0 0 1 1 with the numerical value = 13
• 1 0 1 1 with the numerical value = 14
• 0 1 1 1 with the numerical value = 15
• 1 1 1 1 with the numerical value = 16

And so, all the other numbers have been given zero and one combination like this. The procedure which Acharya Pingala used for the binary numbers is:

• He started by dividing the number by 2. If it was divisible then he wrote 1 otherwise 0.
• If the first division answered 1 as a remainder, then he added 1 and divided it again by 2. If it was divisible then wrote 1 otherwise he wrote 0 to the right side of the first 1.
• If the first division answered 0 as remainder which meant it is fully divisible then he added 1 to the remaining number and then divided it by 2. If it was divisible then he wrote 1 otherwise he wrote 0 to the right side of the first 0.

This way this process was continued until 0 remains as the final remainder.

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Conclusion

Through the work of Chhanda Shastra by Pingala the first known description of binary numbers and this way by using 0 and 1, he was able to discover the proper way of finding out numbers by using Binary numbers. As mentioned above there isn’t much information known about Acharya Pingala’s birth and his life but his works had contributed a lot to the mathematics field.

So, this was all about Acharya Pingala and his work of introducing Binary numbers. I hope this piece of information was helpful for all of you. You can even try using the steps shown in the procedure of how Pingala used the binary numbers. Thank you!