Is there room for God in digital physics?
In my post: Why is there something rather than nothing, I suggested that the same kind of logic used to determine that reality was mathematical could be applied to the question of whether there was a god. I received a very nice comment from someone of a theistic bent, and so, in the name of encouraging transparent, refutable dialog that’s hopefully more fun than it is upsetting, I’ve decided to come back and expand on that remark.
Given the picture of a mathematical universe, I see two ways in which you might potentially squeeze God in.
The first is to assert that God, or the reason to believe in God, literally exists outside of rationality. This is fine so long as one notices that it’s the same as saying that there isn’t a rational reason to believe in God. One also has to admit that the statement ‘God exists outside of reason‘ makes exactly as much sense as ‘Hand me My Toast Racket, Throgmorton, for Yesterday I go Crystals Hoverport Ukelele Bat-Gammon needle-brisket!‘
The second route is to assert that the existence of a God can be reached as a rational conclusion, and that the God in question exists as part of the mathematical description of the universe. If you go that route, you have to ask the question of whether adding God to your description of nature makes it simpler or more complicated. We already know that a simpler rule for describing the universe is vastly more likely to be true than a complex one.
Thus, if we believe that the complete programmatic description of God can be captured in less space than the rules necessary to encode physical laws, then having God in the picture is fine. Otherwise, he doesn’t figure. So as long as we can demonstrate that having God around is a more mechanistic, less animate, less choice-driven alternative, it’s okay.
In short, exactly the same logic that makes us prefer a discrete model of nature rules out theism. If anyone thinks they see a flaw in this reasoning, I heartily encourage them to share it with me.
How to Build A Universe 
The term ‘God’, with or without the capitalization, is so loaded as to be almost meaningless. I think there’s a related, but somewhat better defined question that can be asked and perhaps one day answered: is this universe an artifact, the creation of some intelligent entity — a simulation within another universe? Nick Bostrom, for instance, gives a plausible (if not totally credible) argument here: http://en.wikipedia.org/wiki/Nick_Bostrom#Simulation_hypothesis
There are other ways to look at the question, such as by noting the rather ad-hoc nature of the apparent ‘initial conditions’ (in our case, the supposed Big Bang). Of all the dodgy ideas in physics, the inflationary hypothesis seems to me like a graunch of a higher order. One might perhaps plausibly assert that if the initial conditions are vanishingly improbable, the idea that this is a simulation inside another universe (one where perhaps this issue doesn’t apply) is in fact an acceptable application of Occam’s razor.
While the whole simulation notion is a fascinating idea, and one I’m glad people are exploring, my personal take is that it’s ruled out by exactly the same logic that makes discrete spacetime likely. If we accept that reality is, at root, mathematical, we have to ask whether adding this extra layer simplifies or complicates the picture. My take is that it complicates matters, and therefore needs to be left out. The reason for our observes universal constants will need to come from elsewhere.
I’m not necessarily pushing simulation. (OK I admit, I’m a simulationist at heart, but for the purposes of this discussion I agree it’s merely a hypothesis, and your point is well taken that it needs to make itself necessary to be anything more than a fleeting fancy).
What I mean to propose is that at heart the theory “God made it” is experimentally indistinguishable from the theory “this is a simulation”. Without further God-stuff (like special books, god-in-the-flesh, etc), both propositions boil down to “some intelligent entity had something to do with this”. At least us simulationists admit that which should be obvious — if the universe is indeed an artifact, that does not in any way immediately give us much information about the proposed creator(s). They could be good, bad, indifferent, singular, multiple, intelligent (or not — they could be acting on instinct, like some lower life form). In fact, the whole idea of a ‘built universe’ (to cop a phrase) is that the universe you build is separate from you (unless you are one of those annoying ‘interferentist’ type creators). Just as we have layers of abstraction in software to insulate components, the act of building a universe is one of separation, creation of something autonomous and independent from the world in which the creator operates.
I believe that this hypothesis is at least somewhat scientific, and open to some degree of falsification, and I don’t want it to be junked in with the “my ancestor’s creation myth, thought up in a cave around a fire, is, incomprehensibly, the absolute truth!” sort of argument. They have similarities, and one might conceivably be used to attempt to support the other, but they are fundamentally different arguments.
Sure. I definitely see a difference. It’s one thing to propose that the universe is a simulation. It’s another to impute a specific moral agenda to the act of simulation design. I would even go as far as to say that if the settings of the universe do turn out to be eerily specific, that the idea of a purposeful simulation might be more appealing than ascribing reality to a very large number of possible universes, of which no others are interesting.
What I’d add, though, is that while the idea of an eerily well-tuned universe has been well popularized, I think it’s a huge way from being shown to be true. A universe in which we know that life has appeared on one tiny blue dot in an indescribably vast expanse is not one that’s ‘ideal for life’, to my mind. One that was ideal for life should certainly be able to do better than one out of eight for our solar system. If our universe is really good at calculating something, it’s probably the movement of bits of dust.
Consequently, I suspect that what we currently refer to as ‘physical constants’ will turn out to be emergent artifacts of an underlying simple algorithm. Or, at least, until we know for certain otherwise, I think that’s the tidiest assumption to make.
Firstly, assuming that the universe is rational, is in itself an irrational assumption. Secondly, if you believe you are conscious and have free will, then the universe cannot be purely mechanistic. Both of these together leave plenty of space for a God of some kind.
If you believe the universe is rational and mechanistic, then your belief in the non-existence of God is part of the mechanics of the universe, and has no bearing on what actually is the case. You wouldn’t be able to perceive God even if it did exist, and the question becomes meaningless.
Zen Master Unmon said: “The world is vast and wide. Why do you put on your robes at the sound of a bell?”
A marvelous reply! Hooray! I will try to address some of your points.
I would propose that assuming that the universe is rational is the *only* rational thing to do. After all, science rests on the assumption that the universe exhibits regular behavior that is amenable to analysis. If we do not assume this at every turn, then we will not explore the full extent to which this hypothesis is true. Where we abandon the assumption, we either insist on randomness, or permit mysticism. And if we say that some amount of the universe is mystically driven, then we can never rule out its influence, as, by definition, it is not well defined.
Therefore, if we are applying reason to the world, the only way to proceed is to assume an ordered deterministic system at *every* level. Where we are forced to deviate from this, we use the notion of randomness as a temporary placeholder until we find a way to reveal determinism at another level.
I would propose that this logic applies universally. And that you’re forced to either take God out of the picture, or you accept mysticism and abandon the process of arguing logically for God’s existence altogether.
As for my lack of belief being part of the structure of the universe, sure. But to propose that this constitutes a viable workaround for his existence doesn’t work. If God exists but doesn’t exhibit influence, then he’s irrelevant. If he exhibits influence, he’s amenable to analysis.
The Cheese Master Alex replies: “Dude, you may be sitting there in your underpants claiming you’re not cold, but I’m putting my robes on because I think cause and effect is awesome.”