Zero isn’t nothing.
Well, it’s nothing, but it’s far from insignificant in the world of mathematics, science, and technology. And, it hasn’t always been around.
For thousands of years, mathematicians in diverse civilizations developed ways of understanding numbers. From the basic counting systems that have been a part of human society since its inception, to more complex operations like quadratic equations developed in different cultures, the mathematical world was rich and varied.
But still: no zero.
The idea of zero as a number—that is, not just a concept but a mathematical entity you could add to, subtract from, or even divide by—was an intellectual leap that didn't happen overnight. It evolved from its roots as an abstract idea pondered by ancient philosophers to its practical application as a placeholder in early number systems.
I want to bring you through a little bit of this journey today.
The Many Faces of Zero
Zero is a paradox: it represents nothing but kind of means everything. Without the modern zero, we wouldn’t have computers, GPS, or telephones. Spending and receiving money would be incredibly challenging and complicated. Doing any sort of advanced math would be out of the question.
Not all zeros are equal, though. There are different types.
Philosophical Zero comes from the ancient world, where the concept of "nothingness" has frequently been a subject of profound contemplation. Greek philosophers like Parmenides presented some of the earliest Western philosophic ideas about the nature of "nothing." For Parmenides, even to discuss "nothing" was paradoxical. If you can think or speak about "nothing," then it isn't really "nothing" at all.
This paradox troubled many early Greek thinkers and influenced debates on the nature of the void and the cosmos.
In ancient India, Nagarjuna, a foundational figure in Mahayana Buddhism, took a different view. He introduced the concept of "śūnyatā," or emptiness, not as a nihilistic absence but as an essential quality that allows for change and transformation. In contrast to Parmenides' paradox, Nagarjuna's concept embraced the ambiguities and contradictions, positioning "nothingness" as a pivotal element in understanding the interconnectedness of all things.
Placeholder Zero burst onto the scene much later. While nothingness as a concept probably predates history by a long time, we have some records of when we think zero as a placeholder first rears its head, around 2300 years ago in Babylon.
And: this is how zero has been used for most of our history, as a way to distinguish between numbers like 10 and 100, or 55 and 505. Its primary function was not calculation but an indication of absence, a space-filler that allowed more complex number systems to flourish.
This wasn’t our modern zero, though.
The Number Zero requires us to revisit India once again. In the year 628, Indian mathematician Brahmagupta took a groundbreaking step by defining zero as a number with its own set of rules. His Brahmasphutasiddhanta discusses how to add zero, subtract zero, and recognize it as a distinct point on the number line. The notion of zero as a number opened doors for advancements in algebra, calculus, and beyond.
Naturally, this concept made its way to Europe by way of the Italian peninsula, just like coffee, silk, gunpowder, medicine, and so many astronomical and physics concepts. It was Fibonacci who ultimately popularized the number zero, but prior to that, the Arabic world had been familiar with the concept, ultimately working them into their numerical system, now ranging all the way from zero to 9.
The stage was set in Europe for all of these ideas to intersect during the Enlightenment, and so we think about Descartes crafting a zero on his coordinate system, and Isaac Newton’s calculus, and so on. But the history of zero goes back a lot further than that, and I wanted to share just a touch of that with you today.
The next time you look at a zero, whether it's on your digital clock, your bank statement, or in an equation, take a moment to appreciate its complex and storied history. Far from being "nothing," zero is a symbol that holds the world as we know it together.
From ancient philosophies to cutting-edge technologies, zero has been the unsung hero that's enabled us to progress as a civilization. It’s worth considering what else we might be missing—what other fundamental concept that we might one day take for granted, just as we do with the number zero?
"The next time you look at a zero [...] on [...] your bank statement."
Oooof, right in the feels, man. Right in the feels.
That was a fun post!
This reminds me of a conversation I have each time I’m teaching coding to beginners and discuss the concept of `None` (in Python, or similar in other languages).
We can’t have nothing, so we need an object that represents nothingness. But that object is not nothing. It’s something.
Of course, in programming, this is very different from zero, but I digress
Great post!