I was told as a kid you can’t divide by zero. When I asked why not, I was told because the answer was “undefined” or “indeterminate.”
That’s true, but it’s also true that dividing by zero utterly destroys logic, mathematics, and our entire understanding of…well, everything.
Seriously, it does. And Charles Seife, in Zero: The Biography of a Dangerous Idea, explains not just why this is the case, but why so many people have been so terrified of a number we all take for granted.
If you think I’m being hyperbolic again, I’m not. Seife shows how and why some of the greatest Greek minds, including Pythagoras and Aristotle, were horrified by the (non)existence of zero. In fact, this fear influenced the development of religions, cultures, and entire nations. That influence, incidentally, played a major role in stunting the progress of human thought.
Luckily for everyone, non-Western civilizations weren’t quite so cowardly.
That’s another thing I enjoy so much about this book – I fear I’m generalizing, but most mainstream scientific narratives tend to put Greece at the center of everything, as if everything important was discovered by them. Obviously they were vital to the development of most subjects and invented more than a few, but they made some mistakes, too, and totally missed some ideas entirely. For example, Seife shows how the Greeks’ obsession with geometry made them completely oblivious to the existence and benefits of algebra, which was discovered in the Middle East. Far Eastern nations played a role, too, and overall, Seife shows that the quest to understand zero is and always has been an international one.
But what about Seife’s claim about dividing by zero destroying everything? I’m hesitant to go into too much detail because 1) this is a blog post, and I’m already about 2/3 through my usual length and 2) it would require a proof that might turn off potential readers, and I’m clearly only interested in racking up views, not helping my readers learn anything.
Besides, the strange – but intelligible to even someone like me who has no special background in math – dangers of dividing by zero is just one of the things you’ll learn. You’ll also find out about the bizarre ways infinity and zero are often tied together, how something can come from nothing, the nature of black holes, and much more.
Above all else, though, you’ll gain a newfound appreciation for just how incomplete our understanding of reality really is. On the one hand, you might say that the fact that dividing by zero can demolish everything shows how delicate the foundations of logic are…but I think the deeper truth is that it shows we still have so much to understand.
Because if reality isn’t making sense according to our rules, the problem is with our rules.
Zero: The Biography of a Dangerous Idea is a great book that traces the origin of those rules, the battles of rival versions, and what we might discover in the future, assuming we’re brave enough to break a few rules along the way.
So go read it. Now.