The zero mystique — Why not?

A symbol for what is not there, an emptiness that increases any number it’s added to, an inexhaustible and indispensable paradox…

At home one lunchbreak to nurse my then three-month-old daughter, I found myself watching Kris Aquino’s Pilipinas, Game Ka Na Ba? Always an interesting show, it became extra interesting when a math question came up, something about "the number with no Roman numeral representation." Almost mechanically, I said to myself, "Zero," a second before a contestant got it, too. In my mind I congratulated the contestant for knowing her numbers. Then I wondered, "Does she know why zero has no Roman numeral representation?" Then I wondered more, "How many of those watching or listening know the reason?" And let me wonder now – how many readers of this column, or of this newspaper even know the reason? How many would even bother to find out? Believe me, those who would bother will find the road to discovery very rewarding.

If I were handling a general education math class this semester, that noon break would have given me a very stimulating homework question. In such a class I handled a few semesters ago, I made my students track the history of precisely that number, zero. Zero being zero, it is usually not given much notice, not until it gives students headaches in calculus class when they take up, among others, indeterminate forms and limits of functions.

Surprisingly, such was already the case from the heyday of bigwigs like Pythagoras and Archimedes, and way into and past the glory days of Rome. For the longest time, the brilliant minds of Greek and other early Western civilizations actually refused to acknowledge the existence of zero! Take the Paradox of Zero. The story relates how Achilles will never meet up with a tortoise plodding ahead of him, if he gives that tortoise a head start. It argues that whenever Achilles is about to catch up with the tortoise, the tortoise would have added a new distance between them, no matter how small, and so there will always be some distance, no matter how small, between Achilles and the tortoise! That he would "zero in" on the tortoise, though thoroughly logical, was inconceivable and unacceptable because it was simply unexplainable… to the Western minds, that is. Had they welcomed zero way back then, the Greeks might have been able to discover calculus themselves, and not Newton and Leibniz centuries later.

To borrow from Kris Aquino again, "Why not?" Why did the early Westerners not, nay, refuse to, study zero? Mathematics and philosophy have very close ties. Most early mathematicians were philosophers, and vice versa. For them to consider zero, and consequently infinity, at that time was to go directly against Aristotelian teaching, which was the Bible of that era. Ergo, to consider zero at that time was to invite ridicule, ostracism, ex-communication, things they could not afford.

There was no such fear for the Eastern philosophers. Unlike their Western counterparts, they embraced zero and infinity. Did they not believe in reincarnation and the never-ending circle of life? And so the Egyptians, the Babylonians, the Hindus, etc. had zero well ensconced in their number systems. Enter the Greeks, who under Alexander swept through Egypt and the Babylonian, Assyrian, Persian, Hindu civilizations. Among the precious loot they carried back home was the concept of zero, which finally gained acceptance and earned its proper important place in the West. Its oblate shape is taken from the Hindu system, hence helping form what we now know as the Hindu-Arabic numeration system. Note that the oblate shape connotes the absence of a beginning and an end, as does the symbol for infinity.

Imagine life without zero. Imagine writing thousands and millions using Roman numerals. The number 3,888 is already hideous, MMMDCCCLXXXVIII, what more 3,888,000!

Furthermore, imagine doing arithmetic using Roman numerals. Standing alone zero may mean "nothing," but it makes possible a wide variety of calculations. To begin with, it made arithmetic much easier. Computers actually function through a language using only zeros and ones.

How about financial matters? Do we not measure the significance of one’s salary by the number of zeros in it, and thus one’s financial advancement by declaring "Nadagdagan ng zero ang kita ko!" In which case zero definitely does not mean "nothing."

Indeed, zero also makes for picturesque speech. The urgency of the moment is emphasized by the phrase "zero hour," the closeness to a target by the phrase "zero in," the flattened site of a bomb explosion by the phrase "ground zero."

Zero. I could go on and on about something which ironically is taken to mean "nothing." A paradox? A mystery? So the story of zero goes: it is nothing but it is everything, it is neither positive nor negative, it is empty yet it makes possible the infinite. This is the zero mystique.

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The author is an associate professor of Mathematics in UP Diliman. Her research areas include partial differential equations and operations research. A current interest is General Education Mathematics, which she has been teaching for the past several semesters. E-mail her at [email protected]