To Infinity, And… A Bit Further

Limitless vs. The Unfixed Limit

Infinity, by definition, is endless. Boundless. The easiest interpretation of that is to take it literally, that the object in question does not have edges or borders. That is fine for intangible things such as love, human potential, God’s mercy and other abstract concepts, but it gets a little trickier when we try and apply the same definition to actual physical measures such as time or space. The idea of anything real within our world already occupying an infinite amount of existence is much harder to conceptualize.

Take the universe, for example. It is often said to be infinite in size, but at the same time it is also claimed to be still expanding from its initial “Big Bang”. This means that, shortly after the Big Bang occurred and the universe was expanding outwards, there was a distinct difference between the area where it had already expanded into and occupied, and the area where it had not yet expanded to, and was not present in. The universe did indeed have a boundary, and edge, but that edge was (and apparently still is) constantly moving outwards. Therefore, any attempts to measure the size of the universe are flawed because no matter how accurately you measure, no matter how precise the instruments or methods you use, at the exact moment you conduct the measure and gain a result the universe is changing size while you do it. Sure, you could say “At the time of measuring the universe was x big”, but that statement is meaningless as it is instantaneously outdated and does not tell you how big the universe actually is.

In effect, this is a kind of cheat-around for the concept of infinity, because while there is an edge it does not definitively mark the point at which the object being measured stops. And if that isn’t enough to confuse you, think about this: that potential space which the universe is expanding into, that is on the “outside” of the universe edge; how big is it? Does it also have an expanding edge, or a fixed size? And if it does have a fixed size, an actual edge, then what is there on the opposite side of that edge to differentiate it from the non-space on our side? And where does that end? Once you start talking about nested infinities, things get tricky.

Just One Pit of a Larger Hole

Let’s look at one of the most common and well-known applications of infinite space; the bottomless pit. We’ve all heard the phrase in some story or other, but how could such a thing ever really come to be?

Let’s assume, for the purpose of this example, that you dig a perfectly circular hole one meter in diameter straight down into the earth. Ignoring the geological factors which would make such a thing impossible, let’s say your hole passes directly through the center of the earth and continues through to the surface of the globe directly opposite to where you started. Strictly speaking now, that’s a bottomless pit. It’s a pit without a bottom. It wouldn’t work, because gravity wouldn’t be consistently pulling in the same direction all the way through it though.

Even if you could somehow nullify the natural gravity within the pit so that anyone falling into it would continue to move in the same direction through the entire length, once they popped out the other end they would succumb to the natural gravity there, falling back into the pit and, effectively, bouncing back and forth that way forever. But if that were the case, could you still claim they were “falling down a bottomless pit”? To be more precise, they’re moving back and forth through the same fixed length of space infinitely, which is not the same thing. Even if we remove local gravity from the equation and have our theoretical victim pop out of the pit and fall “up” into space to drift forever, can they honestly be said to still be falling down the same pit? Are they still “falling” at all?

The fact is, in order for a bottomless pit to exist the way we imagine it, it would have to have an infinite amount of solid matter to penetrate down through. And that infinite matter would require infinite space to occupy, and that infinite space would require infinite potential space to have formed in, and so on. We’re back to those annoying nested infinities again.

Time, Gentlemen, Please

If the concept of infinite space makes your head hurt, then trying to understand infinite time will make it give up and go home to mother. The main difficulty is that, for all intents and purposes, time doesn’t actually exist. We have invented these concepts of “seconds”, “minutes”, and “hours”, but they are just words, they are not actual objects that can be proven to exist.

What gives us the illusion of time is the fact that change occurs over duration. Think about it, you know there was a “before” you started reading this, and there will be an “after” you finish reading it. The metabolic processes occurring in your body will eventually cause you to require sustenance, and there will be a state where you exist before this need is felt, and after you have eaten. No actual new “minutes” have been created or destroyed, but you can recognize both states and can conceive of their beginning and ending. So what if you never got hungry, ever again? You’d remember a time “before” this state, but there would be no “after” since it was permanent. You could still measure the duration of the new state though, by comparing it to other changes in your environment, such as the rotation of the Earth on its own axis or around the sun.

As long as there are changes occurring, there are before and after states for those changes, which means time has passed between them. So what if we remove all change, what if we put all the matter and energy in all existence into a fixed state and render it permanently set this way. Could you still say that time was “passing” then? It’s a re-work of the classic “tree falling in a forest” riddle. With absolutely no change occurring, and no sentience of any form to observe it, is the universe still experiencing a duration of time? And even if we did achieve such a zero-change state of the universe, could we still argue that this constitutes infinite time?

Even though it is, effectively, endless (and thus infinite in one direction, into the future), we still had it change to that state from its current one, meaning there was a before the zero-change state, and thus it is not infinite in the reverse direction i.e., into the past. How’s the head?

My Stars, It’s Full of God!

While I definitely don’t want to get into a theological discussion here, I would like to close with a religion-based example purely as a means to discuss the “bi-directional” infinity I hinted at just above. It is the commonly accepted belief that “God” (and feel free to substitute that word for whatever deity, creator or higher power you choose) is eternal. That He has always been and will always be. In effect, that He exists for an infinite amount of time. The problem with this is that it raises the question: How can something exist if it was never brought into being? If there was no instance of creation, how can anything continue to be?

The easy answer is to just brush it off as “God is capable of things beyond our mortal understanding, if He so chose to always exist then He always existed”, but while that’s a convenient answer, it’s not a satisfying one. We could always try to apply our “expanding limit” theory from earlier, and say that there was a specific event which caused the creation of God, and in so doing, altered time in both directions to place Him in existence. Imagine a “ripple” in the space/time continuum, spreading outwards from that creation event into future and past, pasting over the old, Godless time with the new, God-present one.

That still leaves us with the concepts of a “before” and “after” for our creation event, resulting in us having to admit that there was indeed a time before God existed but His presence altered it to include Him. The general religious consensus is that God didn’t change the time line, He didn’t need to because He was already there, but was He actually already there or was He only already there because He changed history to make it so that He was already there? And for that matter, is there really any difference between the two? Can the occurrence of an event erase the existence of the state which caused it to happen, without then preventing the occurrence from happening at all?

And, just for the cherry on the whipped cream on the icing of the confusion cake, if God did supposedly just pop into reality at a specific chronological point before spreading out to occupy the entire temporal span, what caused the pop and where did He pop from?