Based on what the archaeologists have dug up and analyzed, people used to think nothing didn’t exist.
That was admittedly an awkward sentence.
What I meant to say was, the concept of ‘nothing’ didn’t exist, back in the day. And since ‘nothing’ didn’t exist, people also didn’t have to bother with the concept of ‘zero’. Based on what the archaeologists have dug up and analyzed, that is.
Certain scientists have been searching for archaeological evidence of nothing, and have been unable to find it. For all intents and purposes, people living back in those ancient times never used the digit ‘zero’ when they did math. In ancient Sumeria, for example, if you asked someone, “What is zero times zero?” they would probably just look at you like you were crazy. (That still happens nowadays, but for a different reason.)
Not that archaic people were stupid. We’re talking here about advanced ancient civilizations — people who had indoor plumbing.
We note that there are still people here in Archuleta County who don’t have indoor plumbing.
The question that rises up before us, like an elderly math teacher with a chip on his shoulder: if we modern Americans find it so obvious that zero (that is, ‘nothing’) exists, how can it be that these advanced civilizations (with indoor plumbing) did not bow down to the ‘zero’ as a meaningful number?
We thoroughly modern folks not only recognize ‘zero’ as a valid idea, we also embrace ‘less than zero’ as such an important concept that our civilization would crumble into dust without it. More about that in a moment.
To reach some understanding of this (admittedly abstract) problem, we will take an imaginary trip back to ancient Sumeria (or any other ancient seat of civilization we might feel comfortable visiting) and picture ourselves as a master mathematician in, say, 4000 BC.
Our job, as a royal mathematician, is to explain, using numbers, the operations of society and of the world in general.
Everywhere we look, we see ‘things’. Cows, for example. Beggars. Trees. Houses. The sun, moon, and stars. Sand. Miles and miles of sand.
Try as we might, we cannot see ‘nothing’. Everything around us appears to be… ‘something’.
Then some hot-shot university graduate student comes along and says, “But Professor — may Allah protect you — if we simply add the number ‘zero’ to our counting system, we can create algebraic equations… and eventually predict the dangers of climate change, very soon after the discovery the billions of barrels of petroleum buried beneath the soils of Sumeria.”
We give our precocious young student a fatherly look, and shake our head. “Young man with little understanding of worldly matters, everything you see around you is something. There’s not a single thing that you can find or imagine that is ‘nothing’. But you want to suggest we base our whole number system on the idea that ‘nothing’ actually exists? Such a ridiculous idea would utterly corrupt the sacred art of mathematics. The next thing you know, mathematicians would begin purveying fanciful theories about millions of other things that don’t exist. Have you heard of the Big Bang, for instance?”
“No, Professor, may Allah protect you. What is the Big Bang?”
“The Big Bang is an unforgivable blasphemy… that people hopefully won’t have to deal with for at least another 6000 years… a crazy idea that everything in the universe came into existence in less than the blink of an eye, out of absolutely ‘nothing’… 13.8 billion years ago. It’s exactly the type of meaningless nonsense humanity will have to struggle with, if we allow ‘zero’ into our number system. In fact, our Sumerian language doesn’t even have a word for ‘nothing’, so I had to put it into parentheses to even talk about it.”
“I had no idea what I was suggesting,” the young student confesses, beating his chest and rending his garments. “I pray that Allah will forgive my unspeakable sin.”
“That’s okay, kid, don’t be too hard on yourself. You’re going to make even worse mistakes than this one. Now go home and put on a clean shirt.”
The Professor would be correct, of course. Not only did the fantasy of ‘zero’ eventually come true — 6000 years later — but governments have taken things a step further into the Twilight Zone. Our leaders realized that, if the taxpayers could be convinced to accept the idea of ‘zero dollars’, they could also, with a bit of persuasion, accept the idea of ‘less than zero dollars’. At that point, governments could put the taxpayers trillions of dollars in debt, with the ridiculous promise that future generations would pay for our current extravagance.
We will note, at this point, that the Sumerian civilization lasted about 2500 years.
Just saying.