In the Beginning…
I’ve been thinking about infinity as a concept for most of my life.
As a child, I would wonder about all that space in the night sky as I stared up at it on nights I couldn’t sleep.
When I got into high school and began to deal with infinity as a mathematical concept, things became more interesting. Then in science class—later physics and astronomy—things became positively fascinating. I’ve been an ardent amateur mathematician and physicist ever since.
What Are We Talking About?
Infinity started out as an Iron Age concept for anything too large or numerous to be understood by the minds of the time. ‘Too large’ was more than they could see from the top of a tall hill on a clear day. ‘Too numerous’ was more than a hundred or so. Don’t get me wrong; I’m not dissing the intellects of those of our fellows who lived in the millenia before the Common Era. We can’t do much better ourselves in comprehending the large and the numerous; we just have better math.
Today, there are those who argue, quite persuasively, that Infinity has no real-world meaning; that there are not any actual infinities in nature.
Some argue that not even mathematics has them. Think about that for a minute. In the view of some mathematicians, the series of natural numbers (1, 2, 3,…) has a finite end, a final number. I’m outraged by the notion though, because I’m a layperson, I cannot say my view carries the weight of a professional in the field.
I am not one of those who think infinity is merely a fantasy, though I admit that their arguments have merit (math profs notwithstanding).
Things Get Complicated
To say that something is infinitely large, or that there are infinitely many of some type of thing—and literally mean that—is to invoke an idea that cannot be grasped by our minds. When I say that the universe may be infinite in spatial dimension (as it may well be), I cannot really have any idea what that means in the tangible way I can understand the more modest finite dimensions of the room I’m writing this in.
If I say that there are an infinity stars in this infinite Universe, I run into similar difficulties. I can imagine what a thousand things look like. A thousand glass beads would make a cube 10 x 10 x 10, for example. I can increase that conception to one million if I make a cube of 10 x 10 x 10 of the smaller cubes of marbles. Beyond this, my ability to hold an appreciable idea of large numbers of glass beads quickly diminishes. What would a billion of them look like? I cannot picture it. (You may be better at that.)
It’s worse than that, though. Our minds want to find an end to the universe. We convince ourselves that it can’t really be endless. At some point, there must be an end. And something else beyond.
It’s the same with number. Eventually, the counting (if we’re mad enough to consider counting an infinity of marbles) must end.
We can’t really grasp this ‘infinity’ thing at all. This may be why so many scientists deny it can exist.
Orders of Infinity
The infinite begins to lose definition—to become inadequate, in other words—when we begin to contemplate the existence of other Universes. This is where orders of Infinity come in (see Georg Cantor’s work).
When it comes natural infinities, the work of Dr. Brian Greene, especially The Hidden Reality is a real eye-opener.
I was no stranger to the concept, even as a youth. It has been fodder for science fiction and fantasy for a long time. Michael Moorcock’s Eternal Champion Romances is my personal favorite fictional treatment of the subject; with Robert Heinlein’s work, especially The Number of the Beast, being a close second.
Parenthetically, I prefer the term ‘aion’ to that of ‘universe,’ borrowed from the early Gnostics, largely because—as Dr. Greene points out in the aforementioned book— if our spacetime continuum is infinite in space, it is a defacto multiverse in itself (see Patchwork Multiverse, in Dr. Greene’s book).
An infinite number of Aions means that everything that is possible is real. Given that the laws of nature can differ from Aion to Aion, ‘impossible’ becomes a meaningless word.
What Are We—Really?
If we live in a multiverse, there are infinitely many iterations of ‘me.’ An infinity of them differs from me, slightly. Infinitely many have had different lives than I have. Infinitely many are identical to me in every way and live in aions that are identical to the one I inhabit in every way. Infinitely many are identical and live in aions that are different from mine. I could continue, but you get the idea.
Think about that for a moment.
Mind blown, yet?
Where Are We—Really
Consider this. One of the eight different ways we might be living in a multiverse is called the Many Worlds Interpretation (As opposed to the Copenhagen Interpretation) of Quantum Mechanics.
Briefly, the standard has been the Copenhagen Interpretation put forward and championed by Niels Bohr. The probability that a subatomic particle is is in a specific location is calculated as somewhere between 0% and 100%. An array of such probabilities gives a wave (think of a three dimensional graph that looks like bedsheet flapping in the breeze).
Bohr’s position was that, once the particle is observed in a specific location, the waveform collapsed and the probability shot to 100% at the location it actually was and to 0% everywhere else. This presents a problem. The equations that generate these waveforms—which were developed by Werner Heisenberg—don’t predict its collapse under any circumstances.
The Many World’s Interpretation has been put forward to explain the problem of Quantum Probability Waveform Collapse. It gets a bit technical, but the gist is that for every future event where there is more than one possible outcome (the flipping of a coin, for example), all possibilities are realized the moment the coin lands. In other words, the coin lands heads and tails and even edge-on.
This happens because each possible outcome causes the creation of its own aion, differing only in the outcome of this event from all others. For the coin flip, an aion is born where it lands heads another where it lands tails and yet a third where it lands edge on.
For the massive collection of subatomic particles that makes up our bodies, a virtual infinity (see what I mean about this word’s inadequacy?) of possibilities of motion is realized every 10-43 seconds (called ‘Planck Time‘); that’s every 0.00000000000000000000000000000000000000000001 of a second. That’s a practically uncountable, yet finite number of new Aions created in every interval of Planck Time!
