The concept of zero is something I took for granted most of my life. After all, it’s just a number, so how important can it be? However, one day I found myself face to face with what seemed like an interesting conundrum. Although the number itself represents ‘nothingness’, the shape represents the polar opposite; namely, the idea of eternity. And what is eternity if not the time equivalent of infinity? Thus, the number zero could be seen as representing both nothing and everything, and this created an interesting paradox in my mind. That’s when I began searching for the solution.
Two Sides of a Coin
At first glance, the ideas of nothing and infinity seem like opposing concepts, values that lie on opposite ends of an immeasurable spectrum. When viewing them from this perspective it stands to reason that they would have nothing to do with one another. However, when you really take the time to contemplate nothing and infinity a relationship begins to reveal itself, one that brings them a lot closer together than most imagine possible.
The best way to see this relationship is to define infinity itself. In short, infinity is the collective whole of all things, otherwise known as ‘everything’. Now we can look at two terms that at least sound like they have more in common; nothing and everything. The next step is to try to define what, if anything, serves as a common denominator between these two extreme values.
In order to find this common denominator, we need to contemplate the idea of infinity once again. What is infinity? Or perhaps a better question to ask is, how else can you express the idea of infinity? The simple answer is as a non-finite value. Infinity is the expression of a non-finite condition. And that is where the connection reveals itself at last. Just as infinity is a non-finite condition, so too is nothing. There is no finite value to nothing. If nothing exists, then no thing is there to be considered. Thus, no thing and every thing are two sides of a coin, a coin that represents non-finite reality.
Crunching the Numbers
Since zero is a number, then the notion of it representing both nothing and infinity must stand up to the ultimate test, mathematics. Does this idea ring true when you consider the impact of zero on whole, or finite numbers? As we all know, whenever zero is added to or subtracted from a number the number remains the same. Up until now the reason for this has always been that zero has no value, and thus doesn’t change the other number.
Whenever a number is divided by zero the equation is seen as false, and thus the number remains the same. This is because a whole number contains no zero value, and so cannot be divided as such. However, things change when it comes to multiplication. Whenever a number is multiplied by zero the answer becomes zero. But how does this work, if zero simply represents ‘nothing’?
Trying to explain this in terms of zero holding no value can be a bit tricky. But, if you try to explain this in terms of finite value as opposed to infinite value, that’s when things begin to make a lot more sense. Nothing is more than a numeric value, it’s a state of being. Nothingness can neither be added to nor subtracted from without ceasing to exist. The moment you add anything to zero it’s the zero that disappears, not the number being added. This is because nothing has become something, therefore changing the very fabric of reality itself. The infinite condition of nothingness has become the finite value of the other number involved.
This very same thing holds true in the case of infinity. Nothing can be added to infinity, as that undermines the very definition of infinity itself. Alternatively, if you subtract something from infinity then the infinite condition ceases to exist, which is why the zero disappears from the equation, leaving only the number on its own. And, in the case of division, since a finite number cannot hold infinite value, then it cannot be divided by infinity. It’s that simple.
Multiplication, however, is a different story. Any time a number is multiplied by zero it’s the number that disappears, leaving zero to remain. This is because multiplication is about two entities becoming as one. More than simply adding to or taking from, multiplication is about transformation on a very different level. And in this case, it’s the larger of the values that prevails, as they are the dominant force at hand. No finite value is greater than infinity, and that includes the infinite value of nothing. Thus, whenever a finite value is multiplied by the infinite value of zero, it’s the zero that remains, transforming the finite value into the infinite condition.
Perhaps the best way to picture this is to consider the shape of zero itself, the circle. Think of everything within the circle as the finite condition, neatly contained in the physical boundary of the thin, round line. Everything beyond that line is the realm of infinite value, expressed both as infinity and as nothingness. Since both realms are separate, finite numbers cannot be divided by that which they do not possess, specifically an infinite value, and vise versa. Whenever the line is crossed, as in the case of addition or subtraction, then the infinite value becomes finite, and infinity is no more, causing the circle to disappear. However, when both realms are multiplied, that is when the finite realm is shattered, leaving only infinite space where the finite realm once existed, and thus the zero is all that remains.
In the end, the fact that a circle represents both zero and eternity is not a paradox at all. Instead, it points to a much deeper reality, one that shows zero as the numeric representation of non-finite value. When you understand zero in this way, it paints things in a very different light. Rather than simply signifying no value, this enigmatic number represents infinite value in both its positive (infinity) and negative (nothing) forms. It is the perfect representation of the two sides of existence as we know it, infinity and oblivion.