The Idea of Zero
Mankind’s unrelenting search for knowledge has led to ideas that we find fundamental to modern thought. Such ideas, though commonplace and often regarded to be but simple concepts, are astoundingly deeply rooted in philosophical thought. The concept of zero – the idea of nothingness – is one of these great pillars of modern mathematical science. In mathematics, nothing is just as significant a quantity as a billion, and is just as real. However, it is important to consider just what nothingness means – what ‘zero’ means – in mathematics.
What is nothing?
Zero is the integer that lies between 1 and -1. (It is interesting to note that negative numbers have interesting philosophical implications on their own right!) In order to fix the position of zero, it is necessary to attach some sort of importance – some sort of significance – to the spectrum of numbers itself. For instance, the numbers could represent the temperature of some distant star. In this case, we could say that the number 5 would signify that the star had a surface temperature of 5K. In this case, zero would signify absolute zero; that is, the lowest theoretical temperature, where particles have zero kinetic energy. In another case, we could map the speed of a car in meters per second to the number line, where negative numbers signify that the car is moving backwards, and positive numbers signify that the car is moving forwards. In this case, the number zero would signify zero motion; that is, a state of not moving, or zero velocity. In any case, we have shown that the quantity ‘zero’ has only as much physical, corporeal meaning as the situation to which the number line is mapped.
Mathematical Manipulations
Zero, when used in calculations, has some intriguing properties. For instance, take multiplication: any number multiplied by zero is equal to zero! This is a unique property of this number. For example, we can ,multiply five by zero:
5 x 0 = 0
It can be proven that this holds for any number. You may ask, then, if the same holds for division. To an extent, this is true, as long as the zero term is the numerator of the division operator:
0 / 5 = 0
However, in ordinary circumstances, zero cannot be the denominator; that is to say, that division by zero in elementary contexts is not possible. Once again, this is a unique property of zero.
Finally, it is necessary to consider addition and subtraction. Any number added to zero results in the original number (there is no change). Likewise, zero subtracted from any number is simply the number we started with! The intriguing case is when a number is subtracted from zero:
0 – 5 = -5
Interestingly, when a number is subtracted from zero, the result is the number we started with, but negative! (If we started with a negative number, the result would be the same number, but positive!)
These many startling properties of this curious number are an example of the delicate beauty of mathematics.
