By Charles E. Kunkle Jr. (aka fraterchaos)
We all know the symbol for infinity... a simple figure that looks like the number 8, yet on its side... two interlocking loops, or perhaps a Mobius Strip. But how often have you contemplated the actual concept of infinity?
We tend as humans to think of infinity as something like eternity; forever. Or perhaps as something so huge that it cannot be measured, like the boundaries of the universe. But in all mathematical fact, that's not really what infinity is at all. Yes, indeed, eternity is infinite time, and the universe is infinite space, or perhaps infinite space-time, but saying that infinity is eternity would be the same as saying all fruits are apples, you would be confusing the specific with the general. Mistaking one example for the entire category.
So then what is infinity, in the mathematical sense, that makes it more general or less specific than eternity, or the universe? In point of fact, nobody, not a mathematician, nor a physicist, nor a chemist, not the most amazing genius the world has ever produced, can actually tell you what infinity IS. But we can understand some things about it by analyzing what we DO know about it.
Let us first step backwards from the actual "stuff" of infinity, and instead take a closer look at the word itself, and how it relates to the underlying concept it names.
Infinity is a variation of the word "finite". Finite means basically, able to be measured, or fitting within some specific boundaries. The "in" part of infinity is a prefix which is meant to signify a reversal or negation of the term it modifies, therefore, in-finite would mean "unable to be measured, not possible to be fit within boundaries" but that does NOT mean it has to be large! There is infinitely small, just as there is infinitely large.
This is a very important point, and one which he habitually overlook. Yes, some physicists and mathematicians understand that there is "infinitely small", but they tend to forget on a regular basis as well... only really remembering it when they are actually working with infinitely small things. Infinitely small is not really an archetypical image within our make up, although infinitely large seems to be. Now, if you pin down that mathematician, you may be able to get him or her to admit that, as far as math is concerned, there is no difference between the infinitely large and the infinitely small... and if you can actually comprehend this, then you will quickly agree. Because, by definition, "infinite" means "unmeasurable", it stands to reason that you cannot measure one infinite and say this is infinitely large, and then measure another infinite and say this is infinitely small, they are identical BECAUSE they are each unmeasurable!
So what then does that tell us about anything real, anything we actually have to deal with? Well, in some ways, it could be the basis of everything, and it could also be why we as humans are having such a difficult time deciphering the mysteries of the universe.
If you cannot distinguish between infinitely large and infinitely small, then who is to say that the smallest things, those infinitely small packets of whatever it is that we call "light", is not in reality infinitely large? How do we actually know that the infinitely large universe isn't, in reality, balanced on the head of a pin? The answer... frankly, we don't!
A photon, a single unit (I avoid the term particle for obvious reasons) of light energy, is massless... ie: infinitely small... according to relativity, if anything attempts to exceed the speed of light, it would take "infinite energy" and increase to "infinite mass"... but what does that mean? It only means that the objects mass would continue to increase until it became "unmeasurable" and therefore infinite, but is it really infinitely large? Just because it kept increasing until it passed a barrier beyond we can no longer measure, does not necessarily make it "infinitely large" it only makes it "infinite".
Perhaps, one reason we are having such trouble understanding these things at this level is because we are confusing "infinite" with "infinitely large". Perhaps every photon is actually a faster-than-light spaceship traveling through the universe. We simply cannot know.
Its possible that because of this, we will never truly find the "Higgs Boson" that gives all other particles their mass... perhaps, when it boils right down to it... mass is an illusion and has been all along...