## Zero Is Not Nothing

“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?”
“Nowhere.”
“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.

## Walking with Einstein and Gödel

I picked up the book When Einstein Walked with Gödel this past week at the library because of the title and the photo on the cover of the two mathematicians walking across a campus in Princeton, New Jersey.

I was disappointed that the entire book was not about the two of them, but is instead a collection of essay by Jim Holt. The title essay is one I really like as it deals with one of my favorite topics – our changing notions of time. It comes from a friendship between Albert Einstein and Kurt Gödel when they were both working in Princeton in the 1930s. Einstein had shaken the physical world with his work, and Gödel had shaken mathematics. They ended up taking almost daily walks to their offices at the Institute for Advanced Study.

Gödel would have looked pretty fancy (he liked white linen suits) and Einstein would have looked like the absent-minded genius that we know with his crazy hair and too-big pants.

But what really interests me in reading the essay today was the walking. Today was a very nice spring day that was warmer than it has been. I took the covers of the deck furniture and sat outside with my lunch and coffee. And I went for a walk.

I love walking and I am a firm believer in the power of walking to spark creativity and thought. (More on that tomorrow) Of course, it would be great to have the content of those walking conversations between Al and Kurt. I imagine that the conversations went beyond math and physics, though I’m sure math and science were the main themes.

I have so far only skimmed a few of the other essays in the book, but each could be a walking conversation. Did you know that the word “scientist” was only coined in 1833? It was a philosopher, William Whewell, who used it in his efforts to “professionalize” science and separate it from philosophy. Holt quotes Freeman Dyson (another person at the Institute who I actually got to meet and talk with briefly when he gave a talk at NJIT) as saying that “Science grew to a dominant position in public life, and philosophy shrank. Philosophy shrank even further when it became detached from religion and from literature.”

I certainly couldn’t keep up with Einstein and Godel on the science of time, but I would love to put in my own ideas and get some feedback from the boys.

Some of Holt’s questions that he attempts to answer in the essay are also intriguing ideas for a walking conversation. Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? And the biographical sketches of famous and not-so-famous thinkers makes me want to go on walks with them too – Emmy Noether, Alan Turing, Benoit Mandelbrot, Ada Lovelace and others.