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jducoeurIt 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 universe
Continuing 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 possibilities
Okay, 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...
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(no subject)
Date: 2004-06-16 04:58 pm (UTC)Notes
Date: 2004-06-16 07:56 pm (UTC)...the notion here is that the universe exists simply because it can...
To my mind, this is the weakest part of your presentation, if only in terms of word choice.
For one thing, it suggests that potential implies causation. This is not only outside of human experience, but specifically contraindicated by human experience. A stronger statement would be, "the Universe exists because it must exist". Math exists, therefore intricate interactions of mathematical structures exist, therefore things like the Universe exist. Given that math exists, there is no alternative. Of course, such a statement might not match your intent.
For another thing, "because it can" has annoying connotations or sentience - human beings climb Mount Everest because they can.
That state is wondrously, fabulously, confusingly complex...
Note that one of the stronger arguments for your whole image is that, on the level of mathematics, the Universe isn't all that complex. It looks complex due to the fact that even with this minimal configuration we get complex large-scale structures and events.
This also goes to enhance the notion of fiddlyness. The universe is so precisely tuned that four particles - electron, proton, neutron, and photon - can account for pretty much everything in normal human experience.
Some of these universes are far less likely than others.
Uh, given that your premise is that all universes that can exist will exist, this is a contradiction. There is no "likely" or "unlikely" in the common probabilistic sense. All universes that can exist do so with certainty, 100% probability. Universes that cannot exist do not, with certainty. There is no chance whatsoever.
You probably don't need me to mention that you are now on the thin ice of Determinism vs Free Will. Watch where you step...
Re: Notes
Date: 2004-06-17 06:16 am (UTC)Fair points, both. I find that I'm particularly struggling with wording in this case, trying to express pure intuitions verbally (and made worse by my usual rhetorical caution).
There is no chance whatsoever.
That's an oddity I'm finding here, and I'm wrestling with how to resolve it. On the one hand, the math says that some states have a far higher probability of existence than others -- that is, there are many more paths that *lead* to that end state. On the other hand, the argument also implies that all paths are eventually reached.
The question is, is there any qualitative (or, indeed, quantitative) difference between a high-probability state and a low-probability one? My intuitions all say yes, but I'm not finding any particular rational ground for that viewpoint. So I keep finding myself straying back and forth over this particular line.
(Which emphasizes a point that I haven't said explicitly, and probably ought to put into my conclusions -- this is *very* much a work-in-progress philosophically. A bit beyond musing out loud, but I'm a long ways from having mined out these ideas.)
You probably don't need me to mention that you are now on the thin ice of Determinism vs Free Will.
Oh, I am painfully aware of that, and will be getting to that shortly. (Indeed, now that you mention it, this really is intimately related to the probability question. I'll have to put that into my outline; thanks for pointing that out.) That is certainly one of the thornier issues here...
Re: Notes
Date: 2004-06-17 09:25 am (UTC)Okay, here's the thing - if all states that can exist do exist, what do you mean by a "high probability state"?
My guess is this - consider the ensemble of all universes. Assume that many of them are in some way similar. If you were to pick one universe at random from the ensemble, you have a high probability of picking one of this group of similar states. If you have a machine that jumps you into a random universe, you are more likley to end up in a "high probability" universe.
Thus, quantitatively, the difference between high and low probaility universes is simple - there are simply more of them.
Qualitatively - well, that depends upon what subjective measure of similarity you are using - size, shape, complexity, dominant color? I suppose, for example, that there are many more universes that are simple, and fewer that are complicated. The more fiddly bits the universe has, the harder it is to balance all the bits out to a self-sonsitent whole.
Re: Notes
Date: 2004-06-17 04:05 pm (UTC)The issue is complicated by the fact that I'm wrestling with issues of time (and quantum mechanics) along with everything else, so probability keeps intruding into my mental model. I think that's messing me up, and I need to separate the problems of multiple universes with different physical laws from those of probability within a single set of physical laws...
(no subject)
Date: 2004-06-17 06:18 am (UTC)It's early, so I'm fuzzy. By "every possible universe", are you referring to "the set of all mathematically consistent states of being that correspond to what we perceive as basic laws of a universe", or "the set of all mathematically consistent states of being that correspond to what we perceive as the absolute entirety of a universe, including full state information - particle X in location Y in state Z for all matter and energy and whatever else"?
Or something else?
(no subject)
Date: 2004-06-17 04:10 pm (UTC)(no subject)
Date: 2004-06-18 08:46 am (UTC)Trying to stick to common parlance, you cannot really define a universe only by what we'd normally call "laws". You also need to set some initial conditions. Otherwise, it'd be like calling a collection of machinery a factory before knowing how much of what kind of materials are going to go into it.
Take our own universe. It has electrons, which carry an electric charge. That charge is not a "rule", nor does it fall naturally out of mathematics. It must be inserted into the math by hand. The same rules would operate just fine on elelctrons of a different charge, but the resulting universe would be much different.
Given that mathematics is deterministic, setting the initial conditions is equivalent to setting the full state information.
Thy premise confuses me
Date: 2004-06-18 11:10 am (UTC)Post hoc, ergo propter hoc, dude.
Math, in our world, is purely a descriptive language construct. How does your concept of something being made of description convert to concrete things?
I don't see the ontological requirement, really I don't. It's like saying the universe is made of agreements, or love, or fear or FungFang. Or lust.
In any case, you are dangerously close to the philosophy of Heinlein's "The Number Of The Beast". I think you wish you were an Author. (:-)
Re: Thy premise confuses me
Date: 2004-06-18 03:41 pm (UTC)Putting it another way, "2+2=4" may be a human descriptive construct, but the *principle that it describes* is an underlying reality. Similarly, we may describe the speed of light with a number built around human terms, but the fact that that speed is a constant relative to any frame of reference (as well as the value of that speed) is a basic principle of the universe that we happen to inhabit.
I'm using the term "math" to describe that collection of fundamental principles and constants, mainly because they are most easily described in terms of math and because I don't have a better term for it. I'm open to better terminology.
As for requirement -- hey, if I saw it as a clear requirement, I wouldn't be hedging so much. But the fact is that there are a number of major metaphysical questions that do not have clear answers, for which many systems have been proposed down the ages. Those systems matter, at least because people often build their personal morality and ethics around those metaphysical systems. I'm musing about a system that might work for me, and doing so out loud because it's an excuse for interesting discussion. (And because stating something out loud like this forces me to be more intellectually honest.)
Is it required? No. But neither is religion, or any other system of metaphysics. So far, I don't see any respect in which this model is inferior to the others, which makes it worth exploration in my book. Just because something isn't clearly required, doesn't mean that it's without value as an idea...
And an inverse question: what I'm doing, largely, is refuting the notion that the universe *needs* a cause -- the underlying notion is that it may arise simply from its own possibility. So the inverse question applies as well: why *does* the universe require a cause? This is an exploration of the notion that it might not. So I'll throw the question back at you: why do you think this model is any more implausible than any other?
Re: Thy premise confuses me
Date: 2004-06-19 01:19 pm (UTC)That's my point. The language is not the thing, the map is not the territory. Math is a tool for reasoning about and describing.
You are off by one level, as far as I can tell.
I agree, strongly, that from what little we know it is apparent that the universe and all in it is consistent in properties from one place to another, and that we can often describe those properties, and predict new ones, with the rigorous transformations that mathematics affords.
"I can tell you how to get from your house to my house with
one-sound short words, just those and no more. This does not mean that the world and all it is part of are made of one-sound short words."
The descriptive language describes something. But the map is not the territory.
Re: Thy premise confuses me
Date: 2004-06-21 06:31 am (UTC)As I said before, I'm open to better terminological suggestions if you have them. But please don't tell me that I'm confusing the map for the territory. Just because the word "America" is an arbitrary word used to describe a set of points on a map doesn't mean that it's invalid to use that word when one needs to talk about the landscape of that area in sum...
Moebius meat...
Date: 2004-06-21 07:01 am (UTC)Because we all know, it is made of juicy pork. (:-) Now, of course, when I say pork, I mean something else like pork, but you know what I mean. The neat thing about the universe, though, is the marbling, and sometimes I wonder how you can have pork without a pig, or what it would eat, but then again it isn't really a pig, just something large and made of pork, that squeals.
Trying to make some serious progress, now that my sense of humor has been exercised/exorcised - it is your premise that the universe is consistent from end to end, and in the macro and the micro, yes? And that said consistency might be appropriately describable with notations and tools such as math... correct?
Re: Moebius meat...
Date: 2004-06-21 07:24 am (UTC)That particular slant seems to provide nice answers to a number of common metaphysical problems, at the cost of raising some others. And it's very, very *weird* from a typical Western POV, although it feels more compatible with some of the Eastern ones I've been coming across. (I'm sure it's no coincidence that I'm coming up with this six months after taking a short course in Buddhism, which was a fine mind-stretcher.)
*Sigh*. On some level, I'm trying to explain in words a fuzzy intuitive concept that is still new enough to not even be well-refined in my own head. It's *very* hard to impart the slippery mental image of a cosmos that is literally *nothing* underneath save potential, with those potentialities appearing to be expressed to those who exist inside of them. But that's really the crux of the idea here: that there is no *need* for a superior cause to the universe, if one doubts (as, frankly, I do) the absoluteness of the proposition of "Cogito ergo sum". I'm trying to express a notion that "sum" may not be nearly so well-defined...
Re: Moebius meat...
Date: 2004-06-21 08:40 am (UTC)That is a rather inconsistent inconsistency, oui?
Not to mention - we know the "envelope" of the universe in which we are, exists (pace abstruse personal philosophies). We are able to determine that, insofar as we have looked it is consistent...
What makes you think that there are others? And even if there are, what is the distinction between "more than one" and "this one which has multiple localized consistencies, but is not globally consistent"?
I think you haven't read enough of Rudy Rucker's hard SF, yet. (:-)
Re: Moebius meat...
Date: 2004-06-21 03:42 pm (UTC)Intuition, largely, same as drives any metaphysical system. Remember, the point here is not so much to derive certainty, as to posit an idea and see how well it works.
I was actually thinking about it this morning, and concluding that I do have a personal agenda here: to see if I can come up with a metaphysical system that I personally find intuitively satisfying, as well as consistent with what is known about the physical universe. I'm certainly not there yet, but the challenge is proving quite worthwhile in and of itself.
what is the distinction between "more than one" and "this one which has multiple localized consistencies, but is not globally consistent"?
Possibly none; that depends on the extent of the internal inconsistencies. A single "universe" that encapsulates all possible consistencies would seem to be isomorphic to my multiverse concept in all important ways. But I haven't actually seen any such proposed to my understanding -- most of the descriptions of a greater macrocosmos I've seen assume that the *laws* of the universe are essentially consistent, even if the *constants* vary.
(And yes, it's possible that there really is something absolute about that set of laws, moreso than about the set of constants. I'm just questioning that assumption.)
I think you haven't read enough of Rudy Rucker's hard SF, yet.
Undoubtedly, but I think I need to spend the time getting myself better grounded in current cosmology and quantum mechanics instead. Fact is tougher going than fiction, but tends to be more rewarding in the end...
Re: Thy premise confuses me
Date: 2004-06-19 11:12 am (UTC)A mathematician knows that the notation he uses is a construct, akin to a language. But that language was built to describe things that exist, just as English and Japanese were built to express other things in human experience.
Re: Thy premise confuses me
Date: 2004-06-19 01:20 pm (UTC)My point. But you can't make something out of that construct, you can but describe things with that construct. Sometimes that construct describes accurate things, sometimes it describes impossible things, occasionally it teaches us that new things we have not yet looked for might possibly exist.
But it is just a notation - that's a nice way to put it.