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We are sometimes bothered by the question: 'what happens when you divide by zero?' What really stumps us, though, is not what the result is, it is how one goes about performing the action. How can one slice an apple in zero pieces, for example. Our minds can't get past that conundrum, so often the question is abandoned as absurd.

However, an answer may yet be found.

Mathematics are often used to form a model that describes reality. For example, much of theoretical physics exists in a math-only form. Math is used to develop complex theories long before they can be tested experimentally, and even to make such experiments possible.

Yet, sometimes, the process needs to work the opposite way.

Great advances in mathematics have been made by incorporating the principles of science into the discipline. Cartesian curves, Geometry, and Algebra all arose out of translating elements of reality into mathematical concepts. The entire field of calculus was developed so that existing theories of motion could be described in mathematical terms.

Division by zero is one of the last strongholds of the much-despised term "undefined". Yet, for this too, we might find a reality-based model that can help us apply a definition.

Consider a massive star. When that star reaches the end of its lifespan, it undergoes a gravitational collapse, in keeping with the dictates of Einstein's Relativity and the theories derived from it. If it possesses a mass within certain limits, it collapses beyond all measurable boundaries, beyond even the electromagnetic limits of its sub-atomic particles. It becomes a Black Hole.

By definition, a Black Hole is a massive body of infinite density. Now, bearing in mind that the collapsing star does not automatically become more massive just because it has collapsed in this certain way, how can it be that it has an infinite density?

Well, density is basically mass divided by volume. As the star becomes a Black Hole, it shrinks into a singularity, a point of zero volume. Thus, at that point, there is an infinite density, even though there is only a finite quantity of mass.

Ergo, take any mass, divide it into zero volume, produce a Black Hole. Or, in mathematical terms, M/V=D where V is 0 yields M/0=Infinity. Even if Black Holes don't actually exist, the math is still valid.

Division by zero is possible, if only in extreme circumstances, and it yields a definite, predictable, defined result: infinity.

Not only do we now know that division by zero is possible, but we have an answer too.

Learn more about this author, Bryan Belrad.
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