The Semantics of x/0
Input “5/0” into an TI-83 or older model and the calculator will be quick to point out that your input is “undefined.” It makes sense that it doesn’t make sense. Essentially, what is happening is that the calculator can’t figure out how many zeroes there are in the number “5.” This interpretation, that division is figuring out how much of the denominator is in the numerator, is the most basic mathematical interpretation of the division function.
Zero is fucking weird. While it’s background and implications are vast, zero can be described as a mere variable that is meant to represent nothing. If zero didn’t exist, our mathematical systems would fail to account symbolically when nothing occurs (which makes the invention of zero a bit inevitable). Yet, here we toy with something that represents nothing as though it were something. We’ve gotten pretty damn good at it too.
In this case, we’re trying to figure out how much nothing there is in something. Considering that something and nothing are semantic opposites, that’s impossible.
But let’s pretend that there was no contradiction between something and nothing. Many thinkers have attempted to bridge the gap by saying that even nothing is something, or with other more clever ways. If that were true, then we could divide anything by zero. Since zero is now something, instead of nothing, we can figure out how many zeroes a quantity has. In other words, we can solve the problem of how much nothing there is in something.
Since we can’t directly divide x with any machine, we’ll approximate it.
x/.01 = 10x
x/.0001 = 1000x
x/.000000001 = 100000000x
x/.000000000000000000000001 = 100000000000000000000000x
If we continue this progression, we will continue on to infinity. That means there is an infinite amount nothingness in everything!
Wait, we can make sense of this.
In physics, all elementary particle have a size of zero. With this in mind, we can theoretically have an infinite amount of particles compose of even the most minute of measurements (The argument regarding our universe being finite or infinite comes into play, but I won’t get into it). Alright, so we can avoid getting freaked out by holding an infinite amount of nothing in our hands because it’s really what we’re doing.
Philosophically, it means that nothing has meaning. See, something has to be able to accommodate nothing in it’s definition, which causes a word implosion. It follows that something has no meaning. This is also incredibly difficult to solve, thanks to the confusing nature of meaning, but it can certainly be dealt with. See, it all has to do with where you believe meaning comes from. Is meaning an invention from human nature? Let’s go with yes, and you’re done! Or take whatever theory you feel explains it thoroughly enough.
The point is that there are real questions that continue to pervade regarding something as simple as “x/0.” And while there aren’t any solid answers, as a society, we have learned to deal with this nonexistence very easily. Just ignore it! It may sound negative, but it’s important to realize that the invention of zero has allowed for an amazing amount of productivity in many of the mathematical sciences. Had we remained with a lack of tolerance for this unknown, who knows how much progress we would have failed to make.
