On the Subject of Infinity · 1:41am Nov 21st, 2019
Somewhat often, people come to me and ask me about infinity. Specifically, how it related to SotS and why I made it explicitly clear that true infinity doesn't exist in the SotS multiverse. I give my reasons, but I get the impression people always walk away without truly understanding what Absolute Infinity of Everything would mean for the themes of SotS...
This absolutely amazing story will, I think, help with that. It's from another author I had no idea existed prior to today. But everything within is extremely pertinent and... it's an emotional ride.
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A reminder that while collapse leads to limitation and danger, preservation ultimately leads to infinity. I think it's one of the lesser thought-of comments in the whole conflict...
-GM, master of near infinity.
True infinity in a multiverse makes for a poor setting for a big, epic story. It renders basically anything and everything anyone ever accomplishes more or less pointless. You killed the Big Bad threatening all of existence? Too bad, there's infinite of them. Nothing you ever do matters, so why bother.
I'll be honest I never really understood the issue, well okay no I do get the problem of an infinite multiverse the whole nothing matters argument. When I think multiverse I think an infinite number of universes that account for every possible eventuality. I guess I don't understand how a multiverse can exist if it isn't infinite. Especially in SoS where every universe is created by someone writing a story, unless there is a point where people just stop writing stories it would have to be infinite.
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Immediately thought of this:
Do give Coyote's other works a look if you have the time. He's one of the tragically underappreciated authors on the site.
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I wonder if there are any others on the LSB list...
-GM, master of lists.
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There's a difference between practical infinity and true infinity. You wouldn't just have ONE of every possible universe, you would have an infinite number of every universe. And not only that, an infinite number of every interaction between universes too. So you would have infinite SETS of infinity.
I've finally understood your claims about "true infinity", GM. (I still don't quite agree, but that's a different debate, and one that's highly based in subjective morality judgements.)
It took me a while to figure it out, as I'm coming from a heavy math background, where "infinite" is just a property and it's trivial to go well beyond the basic kinds. (For anyone interested, look up "transfinite numbers", or even "surreal numbers".)
One rather simple proof is that there is no largest infinity; it's always possible to make a larger infinity than what you have.
One big issue I saw was the claim that "everything would happen infinitely many times in each possible variant", which to me sounded patently absurd; there's an infinite numbet of integers, but none of them are 0.5, so why must "infinity" on the multiversal scale contain everything?
I've realized, now, though, that by "true infinity", you meant something closer to "a summation of every possible world, repeated forever in every possible combination, tiled out unendingly across an unbound multiversal 'area'". This isn't "infinte" so much as "everything": something so beyond mathematical infinities that it is utterly uncomparable. (For all my ZF(C) friends out there, I was thinking of sets while GM was talking of a Proper Class.)
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Every universe comes from a story, but not every story makes a universe. Not all writers are Prophets, and not all writings of Prophets are "Prophetic" works.
To give an example: There's a good chance a (or even multiple) Cupcakes world(s) has(/have) been found. There's no chance such a world will "feature" the/a MU Pinkie, since she, specifically, would not do such a thing. Any Prophet that wrote such a story would find it had no power, as it broke the "believability" criteria.
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That wouldn't really matter unless time isn't infinite and there is a point where existence just kind of stops otherwise eventually every possible story would have to come to exist at one point of time or another.
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That's not really different from how I was thinking of things and again I personally don't see the issue. But I totally understand why others would find it to be an issue.
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As a mathematician myself, this sums up one of my main problems with the common misconception that an infinite multiverse must have the property that everything that could happen, will happen. And that idea doesn't just appear here in the sense of "true infinity". I've seen it many other places.
It is very conceivable to have an infinite universe or an infinite multiverse where most conceivable things don't happen, even if we avoid repeating things. Just because a multiverse is infinite doesn't mean there is some universe that is an exact copy of [insert favourite franchise here]. Nor is there necessarily some universe that approximates said franchise, but differs in certain specific ways. An infinite multiverse just means there is always something more to explore, not that every possible thing exists.
Honestly, this fallacy is my only real issue with the premises of SotS. The false dichotomy between a finite multiverse, and an everything multiverse. There is plenty of room in between for multiverses that are both infinite, yet do not contain everything conceivable. Whether an infinite multiverse would make things meaningless is another question altogether, but the reason wouldn't necessarily be that the same events are being played out in infinitely many variations with all possible results somewhere else, as that need not be the case even in an infinite multiverse.
Basically, while I get the logic as to why Preservation may eventually lead to Infinity, although the mechanism that would lead from finiteness to Infinity is somewhat fuzzy, I can conceive of certain limiting processes that could cause it, or the infinite progression of time could be the Infinity referred to. However, I do not accept the premise that Infinity would cause Everything possible to occur somewhere or somewhen. To bring the analogy back to math, (my personal specialty), you could keep counting 1,2,3,4,5,6,7,... for infinity, and while you would reach inconceivably large numbers, you would never reach 0.5, or -2, or anything other than a positive integer. Infinity and Everything are two VERY different concepts, yet often confused by many people...
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When I say "true infinity". it's shorthand for a concept that, if taken to it's ultimate conclusion, is basically "Here is a Multiverse that contains every possible combinations of atomic/sub-atomic/whatever configuration per Planck time/whatever the smallest unit of time is." It's kind of difficult to explain, but assume a "universe" as series of particle patterns that change every Planck Time, or even faster. Imagine each "configuration" as a slide in a slideshow, and the slides change every Planck Time/shortest possible unit of time. Therefore, a "truly infinite" multiverse in this instance would contain every possible slideshow. Of course, this means 99.9999999% of universe would not be subject to any laws of physics, since all the particles would be moving around with no rhyme or reason and be Chaos of the rawest kind. Not only that, but there would also be an infinite number of each "slideshow". This is completely ludicrous and not really just "infinity", and it also makes for a pretty terrible setting for a story, but, eh, that's how I see it.
Yeah, to echo the Real Mathematicians above, infinity isn't a number, it's the concept of the largest number. And the fact that that doesn't really make any sense is why it's only used in the vein of "as X approaches infinity" by people who aren't children or morons (which was originally a medical term for those whose mental handicaps lock them into functional childhood; my choice of words was very deliberate).
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Tagging said mathematicians and giving them a hard descriptivist Truth Bomb: people can be assumed to mean things when they talk, and those things aren't always what their words normally mean. Nobody uses formal definitions unless they're writing a proof. GMBlackjack was using "infinity" to mean something that doesn't have much to do with "actual" infinity except being confused for it by the layman, but the layman is the target audience so the distinction is irrelevant.
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I'm replying to everyone even if I'm only really addressing the mathematician's claim.
If you've noticed in SotS, pseudo-infinites have been mentioned. There are vector-defined universes that can zoom in forever and never find a resolution. There are iterative situations that generate themselves on algorithms as required, creating more and more rooms as the inhabitants need there. There's also recursive definition, where one universe leads to another etc.
True Infinity has, and always will, mean the idea of the Omniverse. All things existing. Now, some don't find that terrible, and that's fine. But True Infinity has always meant Omniverse. And one of the craziest things is you don't even NEED an actual, physical multiverse to have that happen. While mathematically you are right, you can never have a largest infinity and you can never count the same number twice, our PHYSICS adds an unfortunate implication.
Let's say our universe is infinite (which it might just be, as far as we can tell the curvature of space-time is zero, meaning there would have to be infinite amounts of space.) Let's count the number of cubic meters of space. You count 1, 2, 3... etc. You will never count cube '1' again. However, if you go far enough, you will find an exact copy of it. In fact, you will eventually find every possible arrangement of matter and energy. Not just for a cubic meter, but in a truly infinite space, every cubic kilometer, light year, you name it. Eventually, you will find duplicates for every state of matter.
Now, most might think "okay, that just means 'worlds' exist where we have our physics, but that every combination of humanity and every other alien exists. There's no "magic" or "time travel" or "faster than light." And to which I'd say, you're right, if the universe didn't have the capacity to lie to people.
Quantum Mechanics tells us that everywhere in space there is a nonzero chance of everything just re-arranging itself spontaneously into any arrangement. This is why particles sometimes pop into existence for seemingly no reason, this is why black holes radiate away hawking radiation, and this is why quantum tunneling happens (and, in essence, why the memory in your smartphone works). We take the probabilities of these events and exploit them. Most spontaneous arrangements are on the scale of single atomic nuclei with single subatomic particles, and even then those probabilities are pretty small, though we do have to deal with them at the microchip level.
However, if you scale this up. Say, if you gave the universe an infinite amount of space to work with, these probabilities will add up. If you really can count cubic meters of space forever, you will find one that has spontaneously arranged itself to create absolutely nothing in the middle of a star. Granted, the chances of this are astronomical. The chance of a marble quantum tunneling through a cardboard box are somewhere on the order of 1 in 2^10^1600000000000000000000000000000 (no, I don't remember if this is exact, but yes, I did have to calculate this for Modern Physics). But if you have a infinite number of tries, every event, no matter how ridiculous, will happen.
Stars could just vanish inexplicably. Galaxies could turn sideways. Intelligence could pop out of nowhere (a concept called the Helmholtz Brain). Atoms in the perfect shape of Twilight Sparkle in deep space. Naturally, most of these arrangements are unstable and would spontaneously decay into nothing.
but there is a nonzero chance the quantum randomness allows them to persist. There is a nonzero chance the spontaneous reactions create entire expansive worlds that THINK time travel is real, or that FTL is real, when in reality it is just the super-improbable universe recreating things, or making space smaller than it looks, or any number of things.
By this, the universe can create a system of 'magic' through pure randomness that only operates as long as the ridiculous probability keeps happening. Every Planck second it has to spontaneously pas a 1 in 1^10^10^10000000000000 chance of continuing to exist (or arranging itself in the next form.) BUT IN AN INFINITE SINGLE UNIVERSE IT WILL HAPPEN, and it will happen an INFINITE NUMBER OF TIMES.
You don't even need a multiverse. You just need the physics of OUR universe played out over a countably infinite amount of space. And everything, everything, will exist, or at least appear to exist and, as far as Twilight Sparkle in cubic light-year 3,234,673,235,346,347,853,239 is concerned, magic is real and so is the power of friendship. It would never occur to her that physics is lying: why would it? It seems to follow rules of its own.
So that's my pushback to the 'mathematical infinity' claim with 'infinity in physics'. There's a reason we spend so much time trying to prove the curvature of the universe. We want a finite universe. Not an infinite one where physics can lie to us.
-GM, master of physics.
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This is the second time I've seen the concept of the Helmholtz Brain recently. So either it's the Baader-Meinhof effect in full force, or the universe is trying to tell me something...
On the topic of the Omniverse, it's a concept I personally use mostly as an excuse to allow conflicting Mutliverses to exist simultaneously. I picture as a endlessly "upwards" series of multiverses, where each multiverse is only one in a "multiverse of multiverses" and that "multiverse of multiverses" is only one in it's OWN set, and so on infinitely.
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I concede that you make a good point. In an infinite universe (or multiverse), that is infinite in both spacetime and matter/energy, and is determined by probablistic laws, such as our current understanding of quantum physics suggests, and such that for a given finite area of space, only a finite number of configurations are possible, then every possible configuration will appear infinitely many times. It's the same idea as knowing that every possible combinations of digits, of any finite length, appears infinitely many times, somewhere in the decimal expansion of pi. It's just that I've seen a lot of misconceptions about the concept of infinity in general, that it's become a bit of a pet peeve of mine.
However, and this is my subjective philosophical point of view, I don't think living in an Omniverse, as opposed to a finite universe should change our trust in physics, or on a deeper philosophical sense, our sense of purpose or meaning in life. While it is certain that physics is lying to someone an Ominverse, even infinitely many people, there are enough other people who are not being fooled by wildly improbable quantum effects that the probability that we, in particular, are being lied to is the same in both cases. That's just what probability means. For me, that means we can have the same trust in our experiments in either an Omniverse or a Finiteverse. (although that trust is never absolute in either case) Why I think that an Omniverse need not lead to nihilism is another story altogether, but I don't really want to get into that here.
As an interesting aside, the curvature of the universe is actually a different question as to the finiteness, or closedness, or the universe. For example, the classic arcade game Asteroids takes place in a flat, but finite, 2D universe. (It would look like a torus, if you were to try and embed it in 3D) On the other hand, there exist geometries with constant positive curvature, but are still infinite, like how a helix wraps around but never connects to itself. I haven't really looked into the cosmology of it, but I don't know why (or even if) physicists generally assume that the universe is "simply connected". That's the assumption that would imply that a flat universe is infinite. Maybe there's a solid reason, or maybe it's just a simplifying assumption, as theoretical physicists tend to make.