“If you look at zero you see nothing;
but look through it and you will see the world.” – Robert Kaplan
“an O without a figure” – William Shakespeare, King Lear
“Where did you go?”
“Then why are you late?”
– exchange between a father and son
on a Sumerian clay tablet from 5000 years ago
I remember vividly when one of my sons at age 5 realized that zero was very important. He has a mathematical mind (he ended up in the finance world) and it hit him that nothing in math works without zero. He would discover in the years to come that it plays a role in many other things too.
It is a symbol of what is not there. Add a zero with any number and it does not change. Add a zero to the end of any number and it increases. A bit of a paradox.
This concept was invented (or is the proper word “discovered”?) in pre-Arab Sumer. It got a symbolic form in ancient India.
It obviously is mathematical but it figures then into other areas as large as the universe itself. Mathematician Robert Kaplan follows this symbol’s history in his book The Nothing That Is: A Natural History of Zero. It is partially a cultural tale, part scientific discovery, part law of nature and it has a few strokes of Romance.
The Sumerians counted by 1s and 10s but also by 60s. That’s not so foreign to us if you consider our 60 minutes in an hour and that 6 × 60 = 360 for the degrees in a circle. Kaplan reminds us hat we have a bunch of number systems: 12 for months in a year, 7 for days in a week, 24 for hours in a day and 16 for ounces in a pound or a pint. All these systems were our ways of trying to make sense of the universe. and gigantic concepts like Time.
Our ancestors pre-zero were clearly handicapped in dealing with large sums. (Kaplan says to try multiplying CLXIV by XXIV.) The mathematically astute Greeks didn’t really have zero. It was Indian mathematicians who treated zero like any other number, instead of as a symbol.
I find math fascinating but have always been math-phobic and always struggled with math courses once we got past the arithmetic and into algebra and beyond. So, I enjoyed the story of zero. For example, how in the Middle Ages, zero comes to western Europe via Arab traders.
It was considered “dangerous Saracen magic” and associated with the Devil. But those who worked with numbers every day were not only the rare mathematicians but any merchants or money lenders.
All this leads to double-entry bookkeeping, equations, the invention of calculus, and the scientific revolution. Leap into our lifetimes and most people know that computers see everything as zeros and ones.
Kaplan’s other books were on the library shelf besides this one and they are all math-related. The other title that got my attention is The Art of the Infinite. (It has a subtitle that may seem impossible to some of us: “The Pleasures of Mathematics.”) I do recall that for me as a child it wasn’t so much zero that caught me by surprise as it was infinity.
I think I have come to understand zero. I’m not sure I have any greater grasp of infinity than I did as a child. In the same way that I now know much more about the stars and the heavens than I did as a child, I still look up at the night sky with a childlike wonder and know I will never understand it all. Others know far more than me and yet they will never understand all of it. In physics and cosmology, whether the Universe is infinite is still an open question. My lack of knowledge and my wonder are infinite.
I asked earlier if zero is discovered or invented, and it turns out that this was a question famously debated by Kurt Gödel and the Vienna Circle. Kaplan writes, “The disquieting question of whether zero is out there or a fiction will call up the perennial puzzle of whether we invent or discover the way of things, hence the yet deeper issue of where we are in the hierarchy. Are we creatures or creators, less than – or only a little less than — the angels in our power to appraise?”
Other cultures, disconnected from Mesopotamia, Greece, India, or Europe, such as the Mayans, also had to discover zero. (Ah, “discover” – and so I have revealed my answer to that question.) As infinity began as a philosophical concept before it became mathematical, zero moved from math to philosophy.
Nothingness as a philosophical term is a huge topic of its own. Nothingness is the general state/domain/dimension of nonexistence. It is where things pass to when they cease to exist. But it can also be where they come into existence, as in some cultures where God is understood to have created the universe ex nihilo, “out of nothing.”
Nothing is infinite.
Yes, I see the paradox.