Zero Destroys the Number Line

Nearly everyone with a high school diploma has been forced to learn at least the basic laws of Algebra that are the foundations for all other mathematics. However, very few people ever really question the underlying theory from which we form our logic. We no longer carry the Renaissance approach to learning in which an individual would study a wide range of liberal arts to acquire a well rounded education. However, most of our early mathematicians were also philosophers and influential figures that shaped politics and religion. As a result, zero brought with it a threat to our understanding of logic. If we imagine the real number line as an elastic rubber band that can stretch and shrink, we are able to visually see how zero can create problems. Multiplication can be thought of as stretching the rubber band by a scalar. But when any integer is multiplied by zero, the entire number line collapses into an infinitely small point. So if multiplication crushes the number line, then division in theory should undue to destruction. This wishful thinking is anything but true. Dividing by zero, even one time, destroys the entire framework of mathematics. It is difficult to show without a simple proof, but by multiplying and then dividing any number by zero one can show that the ratio of zero to zero [0:0] is equal to anything and everything. One can imagine the problem this would have created among philosophers and mathematicians. Eventually, mathematicians came up with a clever solution to the problem by saying that the answer is “undefined”. This in itself is an oxymoron for in the very act of defining the unanswerable as “undefined”, we have in fact given it a definition.

Zero Nothing or Everything?

Zero is by far the most fascinating and misunderstood mathematical concept ever unearthed. It is only now that we are beginning to appreciate the power of such a seemingly innocent number. Looking back throughout history reveals just how feared this abstract concept was to ancient civilizations. Zero was first invented by the Babylonians, as it proved to be not only practical when doing calculations, but necessary to the very framework of logic. The history of zero and its acceptance in the scientific community was anything but stable. Ancient Greece banned the number and Aristotle himself was so threaten by the idea that he strongly lectured against any notion of such a profane conjecture. Because early mathematics and religion were closely correlated, the Catholic Church deemed the concept blasphemous due to it threatening the church’s narrow understanding of God. Few people truly understand and appreciate the existence of zero and how it allows for everything that is and ever will be. Zero is such an exception to all mathematical logic that most people simply learn and accept its unique properties that overpower all other mathematics. For millennium, society had functioned perfectly fine without the use of zero. After all, we don’t need a number to express the lack of something. Most people can respond to the absence of matter by using expressions such as “I don’t have anything” or “There is nothing”. An early farmer would not say “I have zero sheep.” It is for these reasons that zero had been pushed under the rug of everyday thinking and was only brought into existence when conveniently needed for computational purposes. Next posts, I will talk about the unrivaled properties that sets zero apart from all other numbers.