Welcome to the post-25-word-limitation era of the Parallax Machine. As I write this, the American election is still (not surprisingly) in limbo. So let’s divert ourselves for at least a couple of minutes by completing the countdown, with a post dedicated to the number zero. Back at the turn of the year, which seems like ten years ago, I talked about how we count decades, centuries, and millennia. As part of that discussion, I noted that the Romans had no designation for the number zero, and I threatened to eventually talk more about the number. Let this be proof that my threats are not idle.
We have evidence that the concept of zero dates back to the Sumerians around five thousand years ago. It was not dealt with on its own, but rather to help build up other numbers – for example, the number 504 indicates four ones, zero tens, and five hundreds. So zero’s introduction into the world was strictly a practical matter, and was only dabbled with toward that end for quite some time. The symbol for zero as a placeholder in other numbers was crystallized by the Babylonians around 300 BC. The Mayans did something similar around the same time.
As we approached the BC/AD transition, the Greeks, philosophical nuts as they were, began to debate amongst themselves about how to treat zero. Should it be a number? How can nothing be something? This got tied up with philosophical discussions about the analogous thing in nature: a vacuum – and also with even deeper conversations about how the universe itself came about. If everything had a beginning, then it was preceded by nothing. How can nothing have turned into something? If the answer is God, then there wasn’t a nothing, there was God. But how did God begin? Excuse me for a moment, I need a drink.
Zero has had a lot of different symbols over the ages, but our modern beloved donut originated primarily from the Chinese. The concept of zero as a number, however, we owe to the Indians, somewhere in the middle of the first millennium AD. Europe didn’t get on the zero train until the 12th century AD, but it played a crucial role in the mathematical advances that took place a few centuries later by Isaac Newton and others. Once we devoted a lot of attention to math, and particularly in how to use it to represent the real world (like with Newton’s laws of motion or Kepler’s laws of planetary motion), zero became crucial.
Mathematically, zero is a weird animal indeed. For example, it is the only number that can’t be in the denominator of a fraction. Although if you divide the number one by smaller and smaller numbers, you’ll get a larger and larger number as a result – which makes it look like you would eventually end up with infinity if you actually divided by zero. But infinity isn’t a number, it’s a concept. Yet it too plays a crucial role in mathematics – lots of things end up “approaching infinity” as a means of describing the behavior of the world around us. Calculus (invented independently by Newton and Gottfried Liebniz) doesn’t work without this kind of seemingly nonsensical thinking, yet calculus helped put us on the Moon. Excuse me while I take another swig.
Zero also defines the dividing line between positive and negative numbers. Profit and debt mean nothing without the definition of zero as the break-even point. Zero multiplied by any other number equals zero – no other number can do that. Zero added to or subtracted from any other number equals that number – no other number can do that either. Absolute zero is the coldest that any object in the universe can become – although it’s a little like infinity in that it requires the complete drainage of all energy and motion down to the tiniest of scales, which is practically unachievable. And, perhaps most importantly, zero is usually the number you hit when you want to be transferred to a real live human being at your bank or internet service provider.
I believe I now have zero left to say in this post.