Zero may appear to be nothing on the surface — merely an O without a figure, as Shakespeare puts it — but if you take a peep inside its oval window, you’ll see the world in its endless, ever-changing presence. From finger counting to calculus, from abacuses to computers, from interpretations of zero as “nothing” in literature, the number has grown to be a global phenomenon. She — zero — is the one and only that sparked the idea of how nothing may actually be something.
No matter what you make of it, be it diabolic or divine, zero is a very shady number. As I sat in my seventh grade math class, I did not know why the teacher decided to put a diagonal line inside of zero to differ it from the rest of the numbers. I never asked her why she did that, as her answer always remained the same: “because zero is different.” I never dared dwell upon why my teacher singled zero out from the rest of the digits. I did gather enough information to know that zero is abstract, not exactly tangible. Research proves that zero teased and offended the Greeks, settled in India for a while, and suffered in the West. It also made its debut in the fields of literature and science. Zero has proven to have a rich history that dates back to some 7,000 years.
No one can really put their finger on who exactly invented the number zero, but the Sumerians were the first to develop a system of counting. This was made of necessity, as they needed one way or another to keep track of theirgoods: cattle, horses, donkeys. However, the Sumerian system was mostly a positional one because the placement of a symbol, relative to the others, indicated its value. Their positional system was given to the Akkadians, the people of the ancient Semitic empire, around 2500 BC and then to the Babylonians in 2000 BC. The Babylonians were the first to conceive of a mark to signify that a number was missing from a column. Similar to how today in 2014, 0 signifies that there are no hundreds in a number at an end. The lack of positional value (perhaps we can call that “zero”) was suggested by some sort of space between the sexgesmal numbers. Around 300 BC, a symbol (two slanted wedges) was born as a placeholder. It would take another time and people before one could use zero at the end of the number, not wedged in its middle.
Fast forward to the Greeks… you would not be surprised to know they were stumped. They constantly asked themselves, “How can nothing be something?” Always the philosophical ones, of course. The ancient Greeks had neither a name for zero, nor did their system feature a placeholder like the Babylonian’s. Yes, they pondered it, but there seems to be no conclusive evidence to say the symbol existed in their language. This proves how diabolical zero actually is, as it confused so many.
If 0 did exist, it was around 130 AD, when Ptolemy — writer, mathematician, astronomer, geographer — used zero (a small circle with a long overbar) within the sexgesmal numeral system, but not much was done with it because positions were limited to the fractional part of a number (minutes, seconds, thirds, etc.), not the integral part. Perhaps this is because, with few exceptions, most achievements of the renowned mathematicians in ancient Greece were rooted in geometry, where they did not need something as a zero; they worked with numbers as lengths of lines.
Around 650 AD, in what is now present-day India, zero’s utility as an actual number was understood. Brahmagupta, an Indian mathematician and astronomer, used dots underneath numbers to indicate zero. The dots were referred to as sunya, which means empty. Brahmagupta wrote standard rules for reaching zero through additions and subtractions and other mathematical operations that are used in algebra today. However, he had trouble with zero when it came to division. It wasn’t until Isaac Newton and Gottfried Leibniz finally came along to save the day that this changed! But first, zero had to make a pit stop in Europe.
Arabian voyagers brought texts by Brahmagupta and his colleagues back from India along with spices and other exotic items. Once the concept of zero reached Baghdad around 773 AD, it was developed in the Middle East by Arab mathematicians. These mathematicians based their numbers on the Indian system, building off of a previous strategy to unfold the mysteries of zero. In the ninth century, Mohammed ibn-Musa al-Khwarizmi was the first to work on what we now know as algebra. He also developed quick methods for multiplying and dividing numbers known as algorithms, which, by the way, is a corruption of his name. Al-Khwarizmi called zero sifr, or empty, nothing. By 879 AD, zero was written almost as we now know it, an oval, but in this case smaller than the other numbers. With the conquest of Spain by the Moors, zero reached Europe and, by the middle of the twelfth century, translations of Al-Khwarizmi’s work had made their way to England.
In 1202, the abacus was born. The abacus is usually used to perform arithmetic operations and it was noted for its use of zero. The next great mathematician to use zero was René Descartes, the founder of the Cartesian coordinate system. As anyone who has had to graph a triangle or a parabola knows, the origin on the coordinate plane is (0,0). The concept of zero finally reached Europe and spread like an epidemic, but the final step towards understanding the natural history of the recurring, shady zero would be to look at Newton and Gottfried Leibniz’s world.
As previously stated, simple operations came fairly smoothly, but when it came to dividing by zero, people started scratching their heads. How many times does zero go into ten? Or actually, how many non-existent apples go into two apples? The answer is indeterminate. However, one must know that working with this concept is the key to calculus. A common example is the speed of a car, which is ever changing because of stoplights and traffic. If you want to know the speed of a car, this is exactly where zero and calculus enter the picture. And police officers foster and unknowingly celebrate this via speedometers (bad or good, take it as you will). To know your speed, you measure the change in speed that occurs over a set period of time. By making that period smaller and smaller, you could estimate the speed. In effect, as the change in time approaches zero, the ratio of change in speed to the change in time becomes fairly similar to some number over zero — the same problem that stumped Brahmagupta.
In the 1660s, both Newton and Gottfried Leibniz solved this problem. By working with numbers as they approach zero, calculus soon became mathematics’ crowning achievement. Without calculus, we would not have physics, engineering, and many important aspects of economics and finance. A friend of mine, Sao Mir of Hunter College, explained in depth: “When you’re doing calculus, which is muuuuuch less scary than it sounds, zero is very important. Limits often involve the concept of zero and infinity. This unworkable number suddenly becomes useful!” He went on to illustrate:
We can assume from this that 1/0 will equal infinity. But it cannot. Because if it does, 1=2=3=4=5, which is not true. So let’s throw away that concept. In calculus, it’s different. Zero becomes integral (pardon the pun) to your understanding. However, it is still a paradox. All the more reason zero is shadier than it once was.
Today, there are many branches of mathematics that feature zero. For example, in set theory, if a person does not have any apples, they do have 0 apples. In certain cases, sometimes 0 is defined by an empty set — by, well, nothing. In propositional logic, 0 is used to denote the truth-value false. However, the ambiguous zero is not only used in math, but in physics and today’s very connected world of — what exactly? — oh yeah, computers. I have been honored to witness those physically working with zero through a few of my friends who work with HTML codes for their GLOBALORIA program. From what I’ve gathered, the basis of the Internet and games is code. These codes allow you and me to browse the Internet and watch videos and e-mail. It’s quite a phenomenon actually. And it is all because of her: zero.
In computer science, zero is the lowest integer value. It is often the basis of all kinds of numerical recursion. Proofs and other sorts of computer science often begin with zero. Perhaps we should start adopting this idea of counting from zero rather one. Kudos to Robert Kaplan’s The Nothing That Is: A Natural History of Zero for doing so and starting at “Chapter 0”!
Zero can sometimes be thought of as “nothing.” In the sciences, specifically physics, “nothing” is not used technically. There is this region of space called a vacuum. The vacuum does not contain any matter, though it certainly does contain physical fields. Even if such a region existed, it can’t really be referred to as merely “nothing,” since it has “measurable existence as part of the quantum-mechanical vacuum.” If there is empty space, there are constant quantum fluctuations with particles continually popping in and out of existence. For those more philosophically inclined, I give you Alan Watts, British-born philosopher, writer, and speaker, who gives his two cents about nothingness:
This entire universe comes from what we comprehend as “nothing” and this entire universe will eventually return to nothingness. Watts wants everyone to know that despite the paradoxical nature of this, it’s all here: “Out of this void comes everything, and you’re it.”
Beyond the technicalities of zero, the number (we can call it that now, can’t we?) expands beyond its realm and spirals towards what we, to quote 1989 film The Dead Poets Society, live for: poetry, beauty, romance, love.
Emily Dickinson, the American poet, illustrates to the reader how she’d rather be a “Nobody” through her poem “I’m Nobody! Who Are You?”
Behold! In biting satire, here is Dickinson’s most famous defense of the kind of privacy she oh-so favored, implying that to be Nobody is a luxury compared to those dull Somebodies who are too busy keeping their names in circulation. The poem is mocking everyone who desperately wants to be a Somebody, especially in the media. The free-thinking Nobodies, both the reader and speaker, choose to be anonymous and don’t want their privacy invaded.
So it is with zero. Zero may as well be perceived as a Nobody because many believe that it is “nothing,” but that is certainly not the case. The number is not pretentious nor does it feel the need to “toot its horn.” It is perfectly content where it is and, when bothered with, allows the other to open its doors and explore it. One may call it a rich, yet modest, number. Words like “nothing” and “none” are often used in the mathematical, while “nought,” “naught,” and “aught” are its poetic forms. In football, “nil” is zero; in tennis, “love” is zero; in cricket, “a duck” is zero. Our fellow Brits call it oh when using it in the context of telephone numbers. Slang words for zero include zip, zilch, nada, scratch, and even duck egg or goose egg (though I’m not exactly sure about the last two).
Nevertheless, although zero’s mother is not known and it may still, after all, be a nobody, one thing is for sure: 0 is not an outcast; it belongs. Zero teaches every human that a thing cannot exist without the other. This balance is essential in life and it isgrounded in zero — the very shape that even Shakespeare teased was O without a figure.
- Kaplan, Robert. The Nothing That Is: A Natural History of Zero. Oxford, 1999.
- “The History of Zero.” Yale Global Online. May, 2014. http://yaleglobal.yale.edu/about/zero.jsp
- O’Conner, J.J., and Robertson, E.F. A History of Zero. November, 2000. http://www.math.harvard.edu/~engelwar/MathE300/A%20history%20of%20Zero.pdf
- Kaplan, Robert. “What Is the Origin of Zero? How Did We Indicate Nothingness Before Zero?.” Scientific American. January, 2007. http://www.scientificamerican.com/article/what-is-the-origin-of-zer/
- Siegel, Ethan. “The Physics of Nothing; The Philosophy of Everything.” ScienceBlogs. August, 2011. http://scienceblogs.com/startswithabang/2011/08/16/the-physics-of-nothing-the-phi/
- Moskowitz, Clara. “What Is Nothing? Physicists Debate.” LiveScience. March, 2013. http://www.livescience.com/28132-what-is-nothing-physicists-debate.html