The History: Finding a 0

A zero itself is nothing, but without a zero you cannot count anything; therefore, a zero is something, yet zero.

(a) Dalai Lama

“Zero began its career as two wedges pressed into a wet lump of clay, in the days when a superb piece of mental engineering gave us the art of counting. For we count, after all, by giving different number-names and symbols to different sized heaps of things: one, two, three …”

“Whoever it was, in the latter days of Babylon, that first gave to airy nothing a local habitation and a name, has left none himself. Perhaps that double wedge fittingly commemorates his place in history.”

Robert Kaplan, The Nothing That Is: A Natural History of Zero

Welcome back! We are continuing our journey towards finding a worthy zero.

In part 1, we’ve uncovered a numerical system developed by the Sumerians and improved by Babylonians around 3-6000 BCE containing something resembling a concept of 1. However, that system was lacking a crucial element: the element of 0 in a numerical and positioning sense.

A More Familiar Representation for 0

Greeks under Alexander the Great (331 BCE) took us one step closer to the 0 we know today, if only in notation. They carried over a zero with the rest of the booty after invading what remained of the Babylonian Empire. Following that, some astronomical papyri began using ‘O’ to denote “nothing.”

In Almagest (150 AD), Ptolemy used Ō to represent “nothing,” with some evidence of positional intent. Still, his use and the need to decorate the symbol to distinguish it from other numbers, denotes that this symbol was still treated as punctuation rather than a digit or a number. Sadly, the symbol did not surface in ancient Greece ouside of writings on astronomy, and the further development of a concept of zero stopped in its tracks.

Robert Kaplan, in his book The Nothing That Is: A Natural History of Zero, includes an interesting quote and additional insight into the Greek’s lack of zero:

The courtiers who surround kings are exactly like counters on the lines of a counting board, for, depending on the will of the reckoner, they may be valued either at no more than a mere chalkos, or else a whole talent (Polybius, 2nd century BC)

The author brings to our attention the fact that the quote did not State “valued at nothing” because the counting boards did not contain a column for zero. A chalkos was the lowest known financial value and a talent was of a much larger value. So instead of “no value” or “valued at nothing” Polybius used the lowest known value: a chalkos.

So far, no sign of a true zero being used in ancient Greece, Babylon, Egypt. Not even the mighty Romans had a symbol for or an understanding of zero.

A Worthy Zero

Between the 3rd to the 10th history AD, when developments started to emerge towards the concept we know today, zero’s history becomes blurred, possibly doctored, and heavily contested between Greek and Indian origins. To summarize, it took a lot of physical traveling of the concept to many parts of the world for people to further refine the concept.

I recommend reading the above-mentioned book if you are interested in the subject and want to find more details. It’s very interesting and I do want to develop the subject further in the future, even if the sources are hard to trace and blurry.

Here, we’ll focus on the most “widely believed fact” on the emergence of a true 0. The earliest writing that proves an understanding of zero close to our definition today is Brahmagupta’s Brahmasphuṭasiddhānta (628 AD):

(Extract from Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascala translated by Henry Thomas Colebrooke, 1817)

I believe we’ve found our zero. This is the first documented use of zero as a mathematical concept with functioning as a full-blown number and digit rather than just a placeholder or punctuation.

But as I gaze upon this discovery, still humbled by the amount of understanding present in this 7th-century mathematics book, I find my plan of gradual discovery towards the bit was flawed. We were looking for ones and zeroes, but now I realize that a bit is conceptually closer to a light switch than to ones and zeroes. A bit is something that is either on or off (true or false). I can continue the dig through history, probably having to take a step back towards logicians or multiple steps forward towards George Boole’s time, but I feel that would take more than the allocated number of posts, either way.

I don’t think going down the historic roots benefits the target audience for this series, which is supposed to be people starting out with programming. If there is feedback towards continuing this history-driven approach, let me know and I’ll be pleased to oblige. I will continue that series at some point, but building the Dojo remains a priority.

I’ll switch to a more practical approach starting from my next post.