Is Infinity Real?

The short answer is, “Yes but.”  The longer answer is, it depends.

If that seems confusing or noncommittal, well, what can one expect from a discussion about infinity?  One might wryly say, it’s a big subject.

Mathematically, the answer is, “Yes.”  Infinity is a mathematical value, so therefore it is real.  On the other hand, one might mathematically calculate the length of a table as minus five feet.  There are no tables of negative length in the furniture store—therefore, one can say that just because something is mathematically real, does not necessarily mean that it is physically real.

Geometry recognizes that infinity is real.  Any given line segment has, along its length, an infinite number of locations called “points,” or geometric points.  However, each of those points has dimensions of zero.  Zero, by the way, is considered to be infinitely small.

In the physical world, however, we do not deal with these types of infinity.  Indeed, it seems that space and time are composed of units that are larger than zero, not infinitely small points.  This is why space and time are considered by some physical scientists to be “grainy,” not smooth.

Perhaps the biggest cosmological question concerns the size of the physical universe.  It is either of limited size, or of infinite size.  If it is of limited size, then it is most likely curved inward on itself, somewhat in the way that the surface of the earth is curved.  If instead, the universe is of infinite size, then it is either not curved at all, or curved in a way that is difficult to imagine, curved outward, somewhat as a saddle is.

The idea of an infinitely large, uncurved universe boggles the mind.  It means that someone (or, some thing) could travel forever in a straight line, always with an infinite distance lying before it.

In such a universe, there could be infinite numbers of galaxies and planets, and perhaps infinite numbers of living creatures, even beings much like us.  Perhaps more strangely, there could be an infinite expanse of empty space beyond the part of the universe that contains galaxies and planets.

To completely boggle the mind, there could even be infinite numbers of infinitely large universes, each containing infinite numbers of more universes, a mega-multi-verse.

The answers to the questions posed by these thoughts, would depend on the nature of reality itself, something which we can never know.