The Importance of ‘Nothing’

I’m a programmer. When I ask people their impression of what I do, the usual response is a long string of ones and zeros, said in a robot voice. Before I first started my Computer Science degree, I probably would have said the same thing. After my first semester, I would scoff at such binary answers, and feel powerful knowing I know how to write code. Halfway through my degree, I discovered that when you get down to brass tacks, zeros and ones are really all that comes down to. Finally, here at the end of my degree, I’m really happy that I don’t have to work in raw ones and zeros.

And it has always tickled my fancy that there is no Roman numeral representation for the number zero. I usually just pull this out for fun trivia, but after discovering in class that the Egyptians and Babylonians also struggled with the concept, I thought it might warrant a little extra research.

In this day and age, with our modern schooling, it seems as if zero is trivial. It literally means nothing, after all. It might have a few cool properties. For example, zero added to any number will result in the number as one example…but you can get the same behavior by just multiplying by one! For a computer scientist, zero is a boolean value. Zeroes also have a very friendly feel to them. If you see a lot of zeros at the end of a number, you know that number is a nice round one. And we like round numbers.

But being able to use zero is HUGE! Without it, we would either have an ill-defined positional notation for our numbers, or have to resort to an additive system like Roman numerals.  The lovely round number of 100,000 so cleanly represented here (with a little help from a comma) would require 100 M’s in a row using present day Roman Numerals. Even ancient cultures that used a positional notation would just use contextual clues to figure out if 216 meant 2016 or 2160 or what have you. Babylonians started to help with this problem by making two tiny stylus tick marks. So now, 2106 became 21”6. Interestingly enough, there was never any tick marks at the end of numerals, only in the middle. This leads scholars to believe that these tick marks were not an idea of zero; simply punctuation, much like our helpful little comma from before.

Zero is special in that it has two roles. It can be used for positional notation as we have just seen, but that was just as easily solved with punctation. Zero is also, of course, a number in and of itself, which brings on a whole barrel of troubles. Historically, numbers were thought of much more concretely. People used them to solve ‘real’ problems rather than abstract ones. It is a pretty far jump from for a farmer to go from five horses he owns, to five “things” in existence, to an abstract idea of ‘five’. If the farmer is solving the problem of how many more horses he needs, it is going to be “zero more horses.”

For this reason, perhaps it was lucky for earlier civilizations to miss out on zero. Working with zero can get you into a lot of trouble. There are cases of some of the brightest mathematicians of their time struggling with the concept of zero. And Indian mathematician has this to say about division:

“A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.” – Brahmagupta

You can tell he is reaching when he suggests a number divided by zero is N/0.

The first known zero, found in Cambodia. Image: Amir Aczel.

What’s even more mysterious is how there isn’t some clearly defined point in history where zeros are firmly established. There are some hints and teases in the nautical readings of Greeks and odd punctuation marks in Egypt, but nothing concrete. The earliest known writing of zero is famously from a stone tablet found deep in Cambodia, where it has the date of 605 in sanskrit, with a small dot to denote the zero between the six and five.

A clean rendering of the oldest known numeral using zero. Image: Pakse, via Wikimedia Commons.

It seems odd that such a powerful and tricky number wouldn’t have a more auspicious start. Instead, somewhere, someone in India put a dot on a tablet…and the world was changed forever.

I just hope something like this doesn’t happen:

Zach Wiener, SMBC-Comics 08/29/2012.




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