Aside, in January 2012: “Of the Pontiffs and Magistrinae and their Wailing”


So I was working on a tetrachloradic divinity device in response to the way that an omnibenevolent omnipotent omniscient God should really be intervening a lot more often, and, apropos of nothing, found myself wondering if it is in fact true that God does not talk to people in dramatic, externally observable and trackable events all the time. Oh, sure, there’s no evidence for it, and there would be such evidence by definition, but

You can totes build a perfect mapping between the real world and a world where that happens. It is easily space-time isomorphic.

Now, that mapping? It isn’t a simplification. It’s got to be practically a complication. And I’d even go so far as to say that that is why we do not experience it. That we tend not to experience things that add that much Kolmogorov complexity to our experiential world unless we’re schizophrenic (or human) or whatever. but

I’d also guess, using my way undernourished computer science intuition, that the additional complexity of an active interventionist God is less than logarithmic in world-size, and possibly even constant. So what does it even mean to say that that world isn’t so?

Now that may make me seem like I’m all apologetic for the Lord and stuff, that I’m being a good theodicist, but OK, that’s not quite true, because look, this bit here? This bit is where I go off the rails of apologetics and crash right into a brain controlling a trolley.

My instinct is also that getting from here to a perfect world is quadratic.

And that is so much worse than merely bad apologetics that it will probably actually be described by future archaeologists as a crude biologically-prototyped example of the computational heresies that would later tear apart the allegiances of the pontiffs and magistrinae of the First Artificial Church.

20 thoughts on “Aside, in January 2012: “Of the Pontiffs and Magistrinae and their Wailing”

  1. It’s an omnipotent, omniscient, omnibenevolent deific compound with four chlorine atoms and one unspecifiable spark of the divine fire. It’s used for theological investigations!

  2. I disagree. In the first place, assuming an active omniscient diety clearly increases complexity by a non-logarithmic factor – Such a being must not only have awareness that scales in linear fashion with the size of the universe, it must also be capable of contemplating the results of its actions, which probably scales in exponential fashion with the size of the universe and the set of actions avaliable to the diety.

    While I’ll concede that the universes may be isomorphic, but an inverventionalist deity is not isomorpic to an inactive God.

    To the second point, If I may be excuded a diversion from Kolmogorov complexity into computational complexity, I’m yet to be convinced that the perfect-world problem is even in NP – I’ve never seen a polynomial method of checking the world for suffering. Indeed, my computational intuition is that properly defining a perfect world requres using a universal quantifer, so it’s not in the existential fragment of second-order logic.

    On the other hand, I suspect a perfect world is rather easier to compress than the one we observe.

  3. Also, I’m not sure if there are many non-Asian sources for tetrachloradic divinity devices – Western chemists prefer safer reactions. There are a great many ways for combinations of chlorine and divine fire to go horribly wrong. You might be able to find a dimethyl divinity device, if you look hard enough.

  4. If the universes are isomorphic but the deities are not then we have a problem, because it means that the best explanation for an active, interventionist God is not an active interventionist God! Which is problematic.

    … and ****, you’re right, aren’t you? I mean, in seeing the edge of a PSPACE or EXPTIME complete problem in defining a perfect world.

    But I think …


    So, an example game that would go along with your picture of perfection is that one player proposes a candidate perfect world that has free-willed general computing sentiences in it. Then the other player proposes a measure or constraint that an entity within the world is capable of conceptualizing and valuing. The first player revises the world to match that constraint. If there’s a cycle, the second player wins; if the second player cannot find such a constraint, then the first player wins.

    This is a particularly brutal game on the first player, but—

    Hm, actually, no, that doesn’t get into PSPACE/EXPTIME-style games, because if the first player can win they can just win. I need a better way for the second player to challenge even hypothetically winning scenarios or something.

    But the point is, I think that may be too hard a way to go to define perfection. I’d think that if each entity in the universe has some level of functional harmony with each other element, that’d suffice, wouldn’t it?

    Though, hm, there’s the matter of what an entity is, too.


    I think that a whole universe’s worth of data dedicated to making my life good should suffice, making it more or less quadratic, but I can see the argument that it doesn’t!

    Also, seriously, there are a lot of things like mayonnaise and dimethyl divinity devices that are actually really hard to get your hands on in Asia. It is freaky.

  5. (I am probably pretty goofy on this stuff, though. Every time I try to do a good extension to or even refresher on my technical knowledge my living situation collapses.)

  6. This is why we love you.

    Mind, this isn’t the only reason why we love you. We love you for lots of other reasons, too. But this is one!

    As an aside, if you have the right equipment you can isolate carbamate divinity from a mixture of soy sauce and offering incense, both of which should be readily available in your area.

  7. Warning: Carbamate Divinity is useful for experiments, but care should be taken not to ingest it! The combination of apotheotic and carcinogenic qualities can be problematic, though realistically this is only a problem in large doses.

  8. It’s probably computationally simpler but much more complex in Kolmogorov terms to make a universe that iteratively asymptotically approaches perfection. Also, doesn’t omniscience instantly make the informational complexity of your universe infinite, or do you save yourself from that by also allowing for omnipotence?

    I have a slight quibble with Michael’s assertions, though, since a perfect universe doesn’t need to contain self-checking for its own perfection, probably only analytical proof of such. (Given that a perfect universe begins perfectly, continues perfectly, and ends perfectly (unless continuing indefinitely is somehow defined as being more perfect), there would be no need for continuous verification.)

    Also, I tried making a homecast tetrabromic divinity device, but I tried to use a specified spark of the divine fire. Unfortunately, the axiom of choice seems to not apply in practice to omnipresent objects, and my apparatus was instantly filled with an infinite quantity of both fire and divinity. You wouldn’t believe what the waste company charges to dispose of that.

  9. Yay I am loved! And by THEOCHEMISTS!

    Ever since Eliezer Yudkowsky mentioned axiom of choice skepticism in the context of the two envelopes problem, I’ve been increasingly convinced that it is in fact an incorrect assumption in general, even when speaking of mortal infinities. (That is, any |N, Z, |R, etc. created after 0 and 1 tasted of the apple of knowledge of good and evil, and the mortal sets onto which they map.) As noted I can’t keep my head above water long enough to become suitably confident in the relevant mathematics—OK, not strictly mentioned, but it’s one of the fields I start striving towards when things are good enough that I have spare brain and time for nightly study—but in terms of casual eyeballing, that was when it struck me that in the fallen world as well as the supernal one the axiom of choice might be an unwarranted trick of language and cognition.

  10. For those who aren’t following at all, btw, let me take a moment to cover the very basic ideas here.

    Casually speaking, Kolmogorov complexity is “how simply can you explain this?”

    For instance, as wikipedia says, you can describe the really long string:


    with the shorter string ” ‘ab’ repeated 32 times.”

    Some of this is because we have English and numbers already. Sure. There’s that! But some of it is because fundamentally alternating a and b for a long time is less complex—is more elegant, or redundant, or less meaningful, or less random, or whatever—than just picking a new letter out of a hat every time you have to write a new character.

    I think that when we “understand” something, what that means is that we’re boiling it down to a certain level of descriptive complexity. Well, OK, here is more precisely what I think we’re doing:

    We’re boiling down _our thinking process + that thing + a reason to consider certain parts of that thing contingent or random facts – (the parts of the thing we think of as contingent or random)_ to a certain level of descriptive complexity.

    For instance, I’ve come to the theory that a story’s beginning and ending match. This isn’t because it’s “true” in any absolute and abstract sense. It’s because I find it easier to explain to myself how to make a good story when I have this condition around—it’s easier to find the symmetry in an inexplicably good ending that doesn’t fit this model than to understand good endings without the concept of symmetry. The end result is that, after some internal adjustments to my brain’s map of symmetry and stories—that step, incidentally, is why it’s possible for people to disagree with me on this without it necessarily making one of us “wrong”—my understanding of what makes a good story became, in some sense, a smaller bit string.

    The laws of physics turn an awful lot of phenomena into very short descriptive strings—so short that even if it takes a teenage+ human mind to understand even Newton’s laws, and years and years of study to really understand quantum mechanics, that they’re *still* simpler than the underlying phenomena.

    Adding logarithmic complexity to something, like a world—well, the language is a bit ambiguous. In this case, it means that you’re multiplying the complexity of the world by a factor that grows by a little bit every time the complexity of the underlying world doubles.

    So when I talk about assuming an interventionist God adding logarithmic descriptive complexity to a world, what I’m imagining is that fundamentally a world where God parts traffic for the faithful or randomly gives you fashion advice is _more_ complex, because if it were simpler we’d already tend to understand the world that way—if it were Kolmogorov simpler, then people wouldn’t *talk* about God as an ineffable spiritual force moving in mysterious ways, they’d talk about God as active and interventionist because it would be the sensible way to view the world. However, at the same time, it feels like each time you double the complexity or size of the universe, you’re only adding a tiny little bit to that multiplicative complexity factor of adding a God. And I think I feel this way because I think . . . hm. I think I am imagining that if you split the universe into two universes, and define the complexity of an active interventionist God in each, then the necessary corpus callosum dei is only roughly the size of the baseline physical universe—the two halves of God would only have to communicate the underlying conditions, they wouldn’t have to separately explain all of their decisions. Or somesuch.

  11. I’m inclined to believe the computational complexity of the perfect world problem is an issue, since intuitively, the perfect world includeds dynamic processes which might produce a sub-perfect outcome. As such, it is necessary to compute which of the possible outcomes is compatible with a perfect world.

    I’d think that if each entity in the universe has some level of functional harmony with each other element, that’d suffice, wouldn’t it?

    Probably, but I’m not convinced you can formalize that without using universal 2nd order logic, which puts you straight into co-NP.

    And I find your explanation of a divide-and-conquer approach to interventionist God improbable. It seems to me that the logical endpoint of it is to claim that the perfect world problem can be solved by some kind of greedy algorithm, where maximising the perfection of each individual sub-universe is sufficient to perfect the whole, and I believe that you won’t get a perfect world without taking a holistic approach.

    (As an aside, your observation that people prefer to minimize Kolmogorov complexity, combined with the observations of [Tolstoy 1877], that repeated happiness is simpler than repeated misery, would indicate that we have a cognitive bias to not notice the suffering of others. Which would probably explain some of the way the world is today)

    I have sympathy for the idea of abandoning the Axiom of choice, but have you considered the resultant issues for applied theochemisty? To my knowledge, the quickest way to isolate divine fire is to assert that causality is an ordering on space-time, then use Zorn’s Lemma to derive a First Cause.

  12. Surely the dynamical processes of a purely perfect world must also themselves be perfect and preclude the possibility of imperfection? If your perfect world can become no longer perfect, it wasn’t really ever perfect.

  13. I don’t think so. I suspect we’re talking at cross purposes, probably because we never defined perfection. But classical theology tends to conclude that a perfect God created a decidely imperfect humanity, so the idea that it is possibly to perfectly create an imperfect creation has some precedence.

    I think that the interaction of two objects, perfect in themselves, does not inherently imply a perfect result – If I have a perfect car, and a perfect wall, then smashing the perfect car against the perfect wall doesn’t have to mean the perfect crash.

    Besides, perfection is contextual – The perfect wall to hold up my ceiling won’t be the perfect wall to stop barbarian hordes, and asserting that a perfect world cannot have a process that creates an imperfection seems to be asserting a rather large degree of stasis in your perfect world.

  14. Interestingly, this parallels a debate Jane and Meredith are likely to have later in 2004. ^_^

    Jane’s notion of perfection is that there’s no point in a perfect car crashing into a perfect wall _unless_ it can be a perfect crash. Whether this is awesome or creepy will eventually be left to the reader to decide.

  15. This entire page (initial post + comments) is amazing (I’m not going to say perfect because I don’t have the necessary computational resources to test it at the moment…).

    On a related note: Jenna, could you change your main RSS feed so it contains more than just the single latest entry (maybe 5 or 10 of them)? I almost missed this because another entry had already been posted, and that would have been a tragedy.

  16. I tried to fiddle with ComicPress and broke the main site. I _think_ I actually have to talk to Hitherby_Admin who is busy right now to adjust the RSS feed so that was also pointless.

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