It can be, so it is...Continuing from the previous installment, let's restate the premise: the universe is composed of math. By this, I do not mean that the universe is described by math -- I mean that it literally is math, and nothing more. That's not to say that we yet understand all of that math, just that it exists, and may someday be fully discovered.
I'm specifically distinguishing this from the "Cosmic Computer" notion, that the universe "runs" on something larger. Rather, the notion here is that the universe exists simply because it can -- because there is a mathematically consistent description of this state of being which includes us, we perceive it and ourselves as real. That state is wondrously, fabulously, confusingly complex; nonetheless, it exists simply because it is possible.
Yes, this is intuitively ridiculous: it takes the Buddhist notion of reality-as-illusion to something of an extreme. Yet, intuition has historically proven a poor guide to reality -- we are pattern-matching creatures, instinctively ridiculing that which doesn't match the patterns we are used to. And even (perhaps especially) from most modern viewpoints, this is an uncomfortably mystical lens to look through, a metaphysical notion far removed from everyday perception.
But bizarre as it seems, I don't see many concrete counterarguments that aren't self-referential: all of the obvious ones are grounded in assumptions that the manifestations that we perceive as real, either the physical ones or the more ethereal ones such as consciousness, therefore somehow are too real to be so ephemeral. There isn't a lot of concrete evidence for my premise, save that it provides a metaphysical grounding for our increasingly-inexplicable world, but there doesn't seem much evidence against it, either.
Given that, plus the fact that I don't see any other explanations on offer that don't have their own serious philosophical problems, this seems an idea-space worth exploring. So hang on -- I'm going to be wandering into a bunch of tangents over the next few postings.
The inelegant universeContinuing on, we immediately come to a serious question: why this universe? Don't get me wrong -- it's a very nice universe, and I appreciate it. But over the past century, we've come to understand better and better just how *fiddly* it is. To work properly, it requires all sorts of finely-tuned and surprisingly arbitrary constants; current theories indicate that it involves somewhere around ten dimensions; even its history has strange inconsistencies. (For example, current measurements indicate that the rate of cosmic expansion suddenly accelerated about five billion years ago, for no readily obvious reason.)
Combine that with the notion that the universe is simply an emergent property of mathematical potential, and the idea that this messy cosmos is somehow unique begins to look rather strange. I'll admit that my objection here is at least partly aesthetic -- the notion that such an arbitrary universe managed to arise on its own as an isolated phenomenon is just *ugly* to my eyes.
However, given the premise above, there isn't much reason to believe that this universe is unique. Indeed, one of the most interesting correlaries of the cosmos-as-math idea is that the Anthropic Principle arises relatively naturally from it. This principle has been stated many times in many ways in the past few decades, but can be summed up as, "We observe this strange and finely-balanced universe because it is the universe capable of giving rise to us." That is, there isn't anything particularly special about this configuration -- we just can't observe any other universe because we couldn't exist in any other. All of that messiness is necessary for us to exist.
Let me be clear: I like the Anthropic Principle. It makes very deep intuitive sense to me. Specifically, it's the only reasonable alternative I've heard to the notion that our universe was Divinely designed. The fact is that our universe is strange and fiddly, in a way that just happens to make life as we know it possible. Either it was created by design that way, or it happened by accident. And as I've said before, while a part of me does believe in the Divine, I don't really believe that God built the cosmos just so our particular race could exist -- I find that notion both egocentric and (based on everything I know of humanity) implausible. Which implies the likelihood that our universe arose from happenstance.
One of infinite possibilitiesOkay, let's bite the bullet and just say it. The Anthropic Principle makes more sense when there are more alternative universes to choose from. It becomes a certainty if every alternative is available. And in the mathematical multiverse, there is no reason to limit the number of such alternatives.
So here's the next hypothesis, the full expansion of the idea: every possible universe exists, in just as real a sense as we do. If our world arises because of the mathematical potential of such an arising, it seems plausible that any cosmos that can be mathematically described does so as well. Some of these universes are far less likely than others, and one can probably describe an infinity of "non-universes" that don't have the requisite mathematical consistency. But an awful lot is permitted within this concept.
There are several obvious objections to this idea. One is the reductio ad absurdam: does this mean that a "universe" containing, say, nothing more than a perfect two-dimensional triangle exists to the same degree we do? Possibly it does. It isn't a very *interesting* universe, but it might have as much claim to reality. We consider our world to be qualitatively different, but it could just be quantitatively so: our world is complex enough to describe life, which means that it must be fiendishly complex indeed. Note, by the way, the inverse implication: if this is correct, it implies that there are probably other universes that are unimaginably more complex than our own, with life so sophisticated it might regard us as preposterously primitive.
There's also the obvious rejoinder: so what? If these other universes aren't contactable, then this is nothing more than idle speculation. Which is arguably true, but not much different in that regard from most other metaphysics, and doesn't make the notion any less interesting to me. And as we'll see, the notion has many implications for the rest of metaphysics...