Idle Musings | Divide By Zero

Ever tried to divide by zero? If you have, you've likely discovered it's not possible. We don't know what happens when you try to divide an absolute absence by an absolute absence, even if it is in terms of the pure logic of mathematics. Our model of effective calculations breaks down so easily when you take the first number we learn and divide it by itself.

Some will point to this as a flaw in the model, and they may be right, but rather I think it's a paradox of sorts. We know what happens when you divide any other number by zero, it equates to zero. But what happens when we divide zero, a logical absence by a logical number? We get zero. All roads lead to zero. Should, then, zero divided by itself be zero?

I don't think so, though I can see some of the reasoning behind that supposition. Zero is more than a number, and many mathematicians may disagree, but it is beyond a simple value. Beyond the functional utility of numbers as markers for data, and beyond the eleven figured markers of points which range from 0-10 and beyond, we see zero as something completely different, or at least, we should.

Zero is an absence of data. It is a calibration point for which without all other data may be mismatched. Thus zero acts as a reference marker, it tells us where positive number lie and negative ones. 'beyond this point, values are inverse and are not what they seem' it can be summed up as. But once again, it's not quite all that zero is.

Zero serves as an absolute. One could argue that numbers all serve as absolutes when they themselves are representatively absolute, but without zero, one would not exist. Without the existence of the number or marker zero, there would be an infinite number of ones before one with a positive integer. The number line may go like this: '1, 1, 1, 1, 1, 1, 1, 1, 1, 1 1, 1, 1, 1, 1, 1...... 2, 3, 4, 5, 6, 7...

Then, it may repeat every time a 1 is presented. Since our mathematical model is based on the concepts, not the integers of the number 1 and the marker 0, without both, the model would completely fall apart very rapidly and descend into madness.

So yes, our mathematical model is without an answer for the question 'what happens when we divide by zero?' but for good reason: you are trying to divide by an entity that in mathematics, represents a complete logical absence, a calibration point for all other data and the basis for the idea of mathematics itself.

Let me ask you: What happens when you divide a pear by a pear? That's the thing, it makes no sense to divide by zero or a pear, and that's why calculators spit out the below/above response, it knows what you're trying to do and it stands as a strict defiance against would-be opportunistic Plato followers and Nihilists who would state that mathematics isn't real, therefore it is useless and produces no predictable models of reality.

The fact is mathematics produces repeatable and reliable results beyond that of even science, for mathematics does not have reality to contend with, only the comfort of and the simultaneous razor blade of logic: what does not work must be discarded, what does must be kept, and all results must conform to the laws of logical thought.

It is this logic that is the reason calculators are so much better at mathematics than we are: it is simply instructions that can be followed to a logical end. But calculators are limited to work in numbers, and can't explain to you why it makes no sense to divide by zero.

So keep in mind that mathematics was born of philosophical investigations, but the division of zero serves as a physical wall to stop mathematics from ever returning to its ancient past. So, the question 'what happens when you divide by zero?' makes as much sense as a philosopher asking 'how many angels can you fit on the tip of a pin?'

Science informed by mathematics would respond 'well, show me the size, shape or indeed the existence of said angels.' And pure mathematics would say 'As many as can fit given the data we know, and if they have any zero-values, the answer is none.'

Inevitably it was this that led to the death of that old question or adage, logic that is sound really tends to piss people off and subsequently a new line of apologia rises, but we won't get into that.

To sum up, no you can't divide by zero and that's for a very good reason, this isn't philosophy and to divide the absolute marker by the absolute marker is to try to destroy logical mathematics itself and descend back into the realm of proto-science, tribal faith and banging sticks on rocks while screaming at the sky.

Logic is immutable, but it isn't everything, and this universe exists in a state of chaos. The mathematical universe, however, is cold, sterile and only has a few demons which if you don't bother them, will not bother you, such as infinity and the multiple factors of infinity that exist and infinite recurrence: What is the final digit of pi? 1? 7? Who knows; and 0/0 isn't one of them.

Rather, it is a barrier to illogical thought that maintains the usability of mathematics.

Thanks for listening.