The Development of Zero

How many elephants are in the same room as you right now? Most people would answer zero to that question (if you answered something else, we should be friends). The concept of zero is familiar to us. Earlier today, my two-year-old cousin told me that his baby sister is zero years old. I filed sales taxes for my business and typed up countless zeros. Today, zero is part of daily life. Even a two year old understands the concept of zero.

Zero is nothingness — a void. If you think deeper, it’s fairly amazing that we throw around such a profound term. I can see, touch and count the number of teabags left in a box, but I can’t see, touch or count the number of elephants in my bedroom. There are also zero storm troopers, zero cookies and zero dinosaurs in my bedroom. In my bedroom, there are an infinite number of zeros. Our number zero, symbolized by “0,” enables us to do calculus, and it’s even half of the reason my computer works right now. In the early days of math, zero didn’t exist — there wasn’t even a word for it, which made even simple arithmetic a bit complicated. Thankfully, ancient Babylonian, Mayan and Indian mathematicians developed the concept of zero and paved the road for truckloads of discovery and innovation.

Just like ours, the Babylonian number system (2000 BC) was positional. In our base 10 system, having a positional number system simply means you have a position for ones, tens, hundreds, etc. Babylonians used the same concept except their ones position included the numbers 1-59 instead of 1-9. Regardless of base, the problem with having no zero is the numbers ‘11’ and ‘101’ suddenly both look like ‘11’. Most people can’t read minds, so that makes understanding other people’s writings a bit difficult. The Babylonians developed a place holding symbol to solve this dilemma. For example, if we used a period as a placeholder, those numbers would look like ‘11’ and ‘1.1’. It dispersed some confusion, but the placeholder could only be used between numbers, so ‘1’ and ‘100’ both looked like ‘1’. Without a zero, modern mathematics had no chance of developing.

Mayan placeholder symbol. Image: public domain via Wikimedia Commons.

Similarly to the Babylonians, the Mayans developed a placeholder symbol that stood for zero. They developed the notion completely independently of the Babylonians — after all, they were half way around the world and didn’t have texting. Their symbol for zero supposedly looks like a shell. To me, it looks more like a spaceship, but I digress. They had the concept of a placeholder, but like the Babylonians, they didn’t use the symbol on its own. Again, its a start, but you can’t add, subtract or multiply using a placeholder.

Brahmagupta, an Indian mathematician and astronomer. Image: public domain, via Wikimedia Commons.

A 19th century image of Brahmagupta. Image: public domain via. wikimedia commons.

The hero of this story is a Hindu astronomer by the name of Brahmagupta. Around 628 AD, Brahmagupta wrote down rules for getting to zero using addition and subtraction and the results of using zero in equations. There are earlier traces of zeros in Cambodia and various parts of India, but Brahmagupta’s account is primary because it gave the rules behind using zeros. Brahmagupta called zero ‘sunya’ or ‘kha’ which mean ‘empty’ and ‘place’ respectively. His rules included things like ‘the sum of two zeros is zero’, ‘the product of a zero and any other number is zero’, and ‘zero divided by a zero is zero’. These rules were revolutionary. As simple as they seem, this one list of rules effectively changed the entire human world. You may have noticed something wrong with one of those rules — our modern mathematics don’t allow you to divide by zero. Brahmagupta’s rules about dividing by zero may have been flawed, but that just means he left something for G.W. Leibniz and Isaac Newton to work on later!

After zero became a fully formed number, it spread like wildfire. Along with spices and other tradable goods, Arabian voyagers brought zero back from India. A hundred years after Brahmagupta discovered zero, it reached Baghdad. In the 9th century, a man named Mohammed ibn-Musa al-Khwarizmi started to develop algebra by working on equations that equaled zero. He called zero ‘sifr’ which turned directly into our word ‘cipher’ and eventually developed into our word ‘zero’. Come 879 AD, people wrote zero almost exactly like we do today; the only difference between our zero and theirs was size. They used an oval that was smaller than the other numbers — it became ‘1’, ‘1o’ and ‘1oo’. Finally, when the Moors invaded Spain they brought zero to Europe, and by the mid-1900s, Al-Khowarizmi’s work reached England at last.

Zero is universal; it transcends culture, space and time. It is part of our global language and is one of the most fundamental ideas in calculus, physics, engineering, computers, and a lot of financial and economic theory. Our lives are full of zeros. Plus, after traveling around the entire world and changing the course of human history, zero inspired this brilliant little video. Enjoy!


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