Zero, nothing, zilch, nada? The number zero is a misunderstood enigma. Its place in our number system is relatively recent, appearing much later than the Arabic numerals we use to display number digits.

It might seem logical that zero is nothing. It is that but also much more than that; it is a number. Zero is a nothing that is something, but it might be a stretch to see it as a number.

Until recently the oldest documented use of the zero in our Hindu-Arabic number system was a circle inscribed at a temple in Gwalior, India, dating to the ninth century C.E. (also known as A.D.).

Now we know there is a petroglyph from Angkor Wat, deep in the Cambodian jungle that dates to 683 C.E. It reads like a bill of sale and clearly shows the date as 605 on an ancient calendar.

The ancient Mesopotamians used a placeholder around 5,000 years ago to represent the absence of a digit in a string of numbers or as a placeholder in larger numbers. From there it jumped to Babylonia, India and Greece before the mathematician Fibonacci, who popularized the “Arabic” numeral system, introduced it as a number to Europe in the 1200s.

Numbers are representations of counting. We see one thing so we attach the digit 1 to it; two things, the digit 2; and so on. But how do we count nothings?

In today’s mathematics zero represents a placeholder, but a very specific one with numerical properties. Used in a number such as 402, it indicates an empty place in the 10s column. It is not merely nothing, but rather an empty space that is allotted for something.

Zero is an empty box as opposed to no box at all (nothing). If you have a mailbox, you may or may not have mail, but the box is there whether it is empty or not. There may be more than one countable item in the box (there may even be another empty box, but that’s another column).

It is simple to see zero as the starting point in a measurement. When you use a ruler, you align the end or the zero mark with the edge of the object you are measuring. In the rest of the world outside the U.S., the ground floor of a building is the zeroth floor, the beginning of the measurement. The first floor is one up.

The mathematical properties of zero are straightforward until it comes to division. Adding zero to any number does not change it. Multiplying by zero equals zero. The square root of zero is zero, but the zeroth root of any number is 1. If these latter two are not intuitive, take my word for it that they are easy to prove logically.

Then there is that conundrum of division by zero. We hear it said that it ‘equals’ infinity. That is not true because infinity does not exist as a number. It is correct to say that as the divisor (denominator) of a fraction approaches zero, the value of the fraction approaches infinity, but it never gets there. It is the basis of calculus that finding the slope of a curve at a single point involves getting ever closer and closer but never actually dividing by zero.

Conceptualizing the zero makes our modern world possible. Without it there would be no physics and no computers. After all, those glyphs on your screen are nothing but an organized string of zeros and ones.

Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Friday of the month. Email questions and comments to brill@hawaii.edu.