NOTE: The following piece is excerpted from the unpublished essay “A Manifesto on Time, Mathematics, Infinity, and Related Issues” by Fred Blahnik.
If we as humankind cannot grasp the numerical relevance of infinity, then how can we grasp the concept of infinity per se? How can we smugly assign a descriptor to something we do not come close to comprehending? How indeed?? It is one thing to say that something goes on forever, but “forever” is an undefinable concept that we as men and women can never come close to comprehending. What exactly is “forever” anyway? How can we possibly conceive of something that abstract? How can we know there is not a termination point at some undetermined juncture on the number line or at some point in the future? Humans are adept at describing entities with distinct boundaries, but less so—wholly incapable, in fact—at describing entities that do not fit within bounded sets and subsets. Infinity obviously falls within this grouping.
Case in point: We do not even possess names to designate numbers beyond a certain threshold on the number line. If one cannot fathom or ascribe a definitive word to represent a certain quantity, how can we then say such a quantity even exists?! Numbers hold relevance only if they can be suitably pigeonholed and described. You cannot say an impossibly large number exists if you have no way of accurately identifying same. At that point we are little different than toddlers or Tourette sufferers, i.e. people who routinely invent silly words on the fly with no thought to meaning. Short of this absurd juncture, and we are left staring into some amorphous abyss where everything is indescribable and nothing therein has any shape, mass, or texture.
Fred's Soapbox 