Zero and Infinity: from Nothing to Everything

This is the Jain Temple of Gwalior. Unfortunately I was unable to attain photos of the inside. But in the temple, there are what historians believe to be the first known recorded zeros. Image: Tom Maloney, via Flickr.

This is the Jain Temple of Gwalior. Unfortunately I
was unable to attain photos of the inside. But in the temple, there
are what historians believe to be the first known recorded zeros. Image: Tom Maloney, via Flickr.

One of our recent homework assignments that I found interesting was the BBC radio excerpt called Nirvana by Numbers. This was fascinating for a few reasons. First of all, I was astounded to learn that India had contributed so much to mathematics and I had not heard about it until now. That was mind blowing. What is happening in the education world, that so few people know about their remarkable achievements? Secondly, I could really appreciate the idea of math being something spiritual. The view of math as something fluid and moving, rather than something stagnant appeals to me. People tend to have negative opinions about mathematics and it can be hard relating math to other mediums, like art, music, or religion. When in reality, math adds value to these things, and they all have mathematical elements.

If we consider India around the time of 800 CE, we begin to understand what this middle ground of math and religion really is. We also come to learn about all of the phenomenal discoveries they have made. This component of mathematics containing spirituality (and vice versa) inspired the idea of nothingness or what we would today call zero. And what the Ancient Indians would call “Sunya.” According to the BBC article, “sunya” means void. In the ancient Temple of Gwalior, historians and archeologists have found what could be the first recorded zeros. As they began to do more math, zero became an important concept at the time because it made the point that nothing actually is something, and in some cases nothing is everything. What I mean by this, is that in certain religious beliefs like Hinduism, their word for creator, “Brahma” is equivalent to zero. And as our narrator points out, this is very different from Western culture, because our creator would typically be equivalent to infinity. Another initiative they started that we continue today, is to denote zero as a circle. They did this because a circle is symbolic to the sky, a circle of the heavens. The circle is also empty in the middle which is figurative of a void. So in their eyes there was a lot of overlap in terms of their belief system and math.

For instance, one goal in life was to reach nirvana. Nirvana is the highest state a person can achieve where there is no suffering and no desire They would even go as far to say that reaching a state of nirvana is equivalent to zero. This too could have helped establish the concept of zero.  Because of nirvana, they had an idea of “no” suffering, which meant there had to be a way to describe “none.” And thus the tangible idea of zero had blossomed.

One idea that I was interested in exploring more, was the idea of Vedic Mathematics. The Vedas are ancient Hindu texts, that contain spiritual works. They possess instructions on how to do the basic operations like addition, subtraction, multiplication, and division. But not only that, they had processes in which one could determine area of a geometric shapes. Historians have even found early forms of Pythagorean’s Theorem. According to the people interviewed, as well as an expert on Vedic Math Gaurav Tekriwal, who instructs a TED-Talk, Vedic Math can be very easy. For instance in the TED-talk the general idea for multiplying two two-digit numbers is with a vertical and crosswise pattern. First we take the numbers in the one’s place and multiply them together. Then we cross multiply the one’s and ten’s places and add those products together. Lastly we multiply the ten’s place. The example he gives is 31×12, but let’s try our own. Say we have 24×20. Step one is to multiply 0x4, which is 0. This will be the one’s place of our answer. Next we take (0x2)+(2×4), this equals 8. This is the ten’s place of our answer. Finally we multiply 2×2 to get our hundreds place. This yields 480 as our answer.

There is a very special case for multiplying with the number 11. The basic idea for multiplying any number with 11 is such: we separate them, put their sum in the middle and that gives us the answer.  Let me demonstrate with 26×11.

We take 26 and separate it, so that there is a space between the two numbers. We then add 2 and 6 and put the answer to their sum (8) in the space we left when we separated them. This gives our answer to be 286. Multiplying by 11 is a special case, it is just an extension of the general idea for multiplication in the Vedic sense. It uses all of the same ideas we used in the first example. However because 11 is comprised of all one’s, we can skip the cross multiplication and go straight to the addition. So as we can see, multiplying with these rules is quite simple and fairly straightforward.

In the BBC post, there are two men who have differing opinions about Vedic math. One thinks that it makes math more fun, whereas the other thinks that the ideas and concepts of math do not get taught, just the routine does. And based off the TED Talk I watched by Tekriwal, multiplication does seem much easier, but I can see how the notions could get lost on a student.

I read another article that discusses Vedic Math in terms of the Jain religion. According to this article, the Jains had formulas for circles, like circumference and area, and in some cases could determine answers from quadratic formulas/equations. Another great contribution the Jains made was the concept of a positional number system. In other words, putting all the one’s digits in the same place, all the ten’s digits in the same place etc. They also loved large numbers and contrast  to the establishment of zero, this was the start of infinity. One such large number was 10 to the 53rd power! Wow! That’s big! This article states that the Jains had five kinds of infinity. And those were: infinity in one direction, two directions, area, everywhere, and perpetually. The article also talks about how the early Jains were developing permutations, combinations, and had early stages of Pascal’s triangle in the works. It was called the Meru Prastara.

This article unfortunately did not go into the religious aspects I was hoping it would. But nonetheless, from what I learned through the BBC clip, religion in ancient India played a key role in the root of  their mathematics. From zero to infinity, math was being incorporated into their sacred texts and their lives.

This is something we can all bring into our personal life, even if you are a nonreligious person like me. Knowing that math is beautiful, and sacred, and has an element of spirituality to it, makes me much more excited to do my math homework. It seems less dreary, less gloomy. I will start treating math more like a combination of art and science. I think this could not only benefit me, but how we teach kids math. If we start telling them it’s a creative process, maybe more students will be excited about doing tedious algebra problems.

Works

Bellos, Alex. “Nirvana by Numbers.” BBC Radio. British Broadcasting Corporation, 28 Oct. 2013. Web. 1 Sept. 2014. http://www.bbc.co.uk/programmes/b03c2zvr

Boyer, Carl B., and Uta C. Merzbach. A History of Mathematics. 3rd ed. Hoboken, NJ: Jon Wiley and Sons, 2010. Print.

Šafránková, Jana. “Part 1, Ancient Indian Mathematics.” 15th Annual Conference of Doctoral Students, WDS’06 “Week of Doctoral Students 2006”, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic, June 6, 2006 to June 9, 2006:. Praha: Matfyzpress, 2006. 7-12. Web. 4 Sept. 2014. http://www.mff.cuni.cz/veda/konference/wds/proc/pdf06/WDS06_101_m8_Sykorova.pdf

Tekriwal, Gaurav. “The Magic of Vedic Math – Gaurav Tekriwal.” TED-Ed. N.p., n.d. Web. 04 Sept. 2014. http://ed.ted.com/lessons/the-magic-of-vedic-math-gaurav-tekriwal

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