Thursday, December 25, 2008

God exists (with probability one)

Bonjour Gab. Joyeux Noël. C'est un jour tout particulier pour toi, alors profites-en.

Tu n'aimes pas quand, à la messe de minuit, les imposteurs envahissent ton église pour prier maladroitement à tes côtés, alors je ne prétendrai pas partager ton enthousiasme. Par contre, je voulais te rappeler que moi aussi je crois en dieu — juste pas en Dieu, avec une majuscule. Tu dois te dire que je dis ça pour te faire plaisir. Qu'à mes amis athéistes, je dis le contraire avec autant de conviction. Eh bien en fait... ouain, ça ressemble pas mal à ça.

Et c'est pourquoi ce post est, en quelque sorte, un cadeau de Noël. Pour toi, je fais l'effort de choisir un camp officiel et de l'afficher clairement. Bon, peut-être pas aussi clairement que si je l'avais mis sur Facebook, mais en tout cas c'est là où on arrive quand on tape mon nom sur Google ces temps-ci.

Le reste du post est mon argument "anthropique" que tu connais déjà. Alors, si tu préfères profiter du reste de la journée pour penser au petit Jésus et profiter de Noël, c'est un moment idéal pour fermer cette fenêtre.


The above French comment isn't necessary to understand the following argument. Feel free to disagree violently with my hypotheses or with my reasoning.

The first of these wild hypotheses is that mathematical truths actually exist, in some parallel Platonic world of ideas. My actual belief is stronger: in a twisted interpretation of modal logic, I believe that necessary truths, such as mathematical tautologies, necessarily exist; whereas the facts about our universe are merely ordinarily true, and therefore physical things only happen to exist. I have been led to these unusual beliefs by a convincing argument using the anthropic principle, which I will not repeat here.

Now that we accept the hypothesis, we have to accept a very, very large number of existing things. True statements about numbers. True statements about sets. True statements about true statements. True statements about programs. True statements about programs running games. True statements about a program running an extremely realistic simulation of our physical universe. True statements, one for each instant, describing the entire contents of the simulated universe at that instant. Oh, did I mention that I also assume that our universe is both computable and indistinguishable from a simulation of itself?

At this point I usually picture the statements in the sequence of universe contents to be shown true one after the other, unfolding the story of the universe at the rate at which we feel it happening. But I have come to realize that time is a universe-specific concept, making it implausible to imagine time flowing by in the world of ideas. Because of this, I must admit that I'm not sure how consciousness should enter the picture, but at this point I am at least reasonably sure that (a possibly consciousness-less version of) our universe exists (what a relief!), and even necessarily exists.

An atheist would stop here and point out that since the universe necessarily exists, there is no need to postulate a god powerful enough to bring it into existence. And I totally agree. Nothing so far has argued for or against the existence of a god. Against the lack of evidence, some people (like me!) prefer to assume a god-less model by default, while others prefer to stick to their own favorite meme. But some of us reason one step further.

My next guest in this series of implausible hypotheses is that some humble universe inhabitants are so powerful that they count as gods in their own right. In my book a god is an entity which creates, maintains, and possibly interacts with one or more universe(s). And since I've already assumed that our universe could be nothing more than a simulation, a god could be little more than a programmer with infinite time on his hands. One can certainly imagine a universe similar to ours in which this was true, a universe which would also necessarily exist. In fact, some of us claim that our universe is itself suitable for setting up the kind of infinite computation which running sub-universes require.

With infinite time on his hands, it's not at all a waste for him to run all finite universes, one after the other, until the non-existing end of time. Surprisingly, it's also possible to run all infinite universes, if he interleaves them cleverly. And while you can't assume that god's unsearchable ways will involve enumerating all programs, we've got so many gods in our collection of necessarily existing universes that I'm sure we can find one who likes to do just that.

Running every possibility, god will eventually create a sub-universe looking just like ours and one just like his, in which a sub-god will be running sub-sub-universes including one like ours and one like his, and so on. We end up with infinitely many identical copies of god, and most importantly, infinitely many identical copies of universes indistinguishable from ours.

Let's recapitulate. We have now established the existence of many, many worlds, some of them like ours, some of them different. At the top level are infinitely many of them, all distinct. One of them is indistinguishable from ours. Infinitely many are extremely close to ours, like the many-worlds of quantum mechanics, but not exactly the same. Those top-level worlds exist by virtue of the first hypothesis, the existence of the world of ideas. Again, nothing so far encourages or precludes a pre-top-level god who created that world, so I default to a god-less model. In addition to the single top-level world which is like ours, infinitely many others exist as sub-universes, created by something in a higher-level universe. Those universes do have some sort of god, namely, that thing which created them. It could very well be a machine without a programmer, or a programmer without a machine.

Many-world models are suitable for probabilistic arguments. For example, if a many-world theory postulates a particular distribution of worlds, it should be possible to calculate the conditional probability of an universe having such and such property given that intelligent beings inhabit it. This could be used to make observable predictions about our universe, and test the theory. Today, however, I'm going to be lame and make a non-observable prediction: the conditional probability of an universe being god-less, given that it is indistinguishable from ours, is zero. After all, there is only one such god-less universe, the one at the top level, divided by infinitely many equally probable indistinguishable universes. Hence, god exists with probability one.


gelisam said...

The above probabilistic argument assumes that all worlds are equiprobable. An alternative probability distribution would assign equal probabilities to each top-level world, with the sub-universes each receiving a small share of their parent's probability. My argument breaks down in this setting.

Anonymous said...

Quel est le tag HTML pour envoyer un plein seau de tendresse au bloggeur ?

Merci Sam. Cette démo et le mot qui l'accompagnent sont le cadeau le plus étrange, le plus dévoué et le plus touchant que j'ai eu cette année.

Je vais retourner à ma contemplation du petit Jésus emmailloté dans sa crèche avec un sourire aux lèvres et la pensée surréaliste très douce que quelqu'un, sur le web, m'a offert une démonstration de l'existence de Dieu. Voilà qui va te garder à mes côtés toute la journée.


P. S. This blog is great, by the way.

Anonymous said...

Basically, infinite probability has been used to deny god an existence in our universe (by people like Dawkins), by rendering his creative act as unneeded. Yet infinite probability also ensures that god does exist in some form (or all forms), assuming there is no ultmate law of physics that would limit consciousness, and we have no reason to assume there is a limit.

Nice to see people share my view.

It is also my view that Dawkin's use of the illogical nature of particles to try and make the illogical an everyday event is self contradictory. In fact the illogical is everyday, and allows for such mad things as gods (which I would class as any consciousness greater than any found on this planet)


gelisam said...

Infinite probability? The probabilities I have considered in my post are finite, since (like all probabilities) they lie firmly between zero and one. But I think you're using this to refer to the zoo of all probable and improbable universes which I am postulating at the beginning of my argument.

I happen to be a big fan of Dawkins. I am not aware of him relying on the idea of multiverses to support the thesis that god is unneeded, but indeed the existence of the zoo implies the existence of our universe, so postulating a universe-creating god is at best superfluous.

But as we both observed, if the zoo is generous enough, it will also contain universes with gods in them. You might be interested in Gödel's ontological proof, which uses a zoo generous enough that in addition to the ordinary gods who rule over sub-universes, it also contains gods who rule over all of the universes. Personally, I think that's a bit far-fetched.

Regarding Dawkins' use of the illogical nature of particles, I believe you are referring to his enlightening "queerer than we can suppose" talk, according to which human brains are adapted to understanding rocks, not particles. But the corollary of this talk isn't that illogical things are allowed, merely that humans are biased toward so-called logical things.

For what it's worth, from the point of view of rock reasoning, it is the idea of god which is more logical than the alternative. From the point of view of long time scale reasoning, complexity ramps are much more logical. Multiverse reasoning unifies the two point of views by allowing complexity ramps to create gods and gods to create sub-universes.

gelisam said...

By the way, my definition of god is "which has created, or has the ability to create, one or more universes". For example, game writers are the gods of their little universes.

I'm not familiar enough with consciousness to comment on your choice of definition, but in any case, what is this "greater-than" relationship which you are referring to? I think you're equating "infinite probability" with "infinite consciousness", none of which currently make sense to me, sorry.

I might be back with more intuition after I'm done reading what Susan Blackmore has written on the subject.

thecod said...

You might be interested in Gödel's ontological proof, which uses a zoo generous enough that in addition to the ordinary gods who rule over sub-universes, it also contains gods who rule over all of the universes. Personally, I think that's a bit far-fetched.


Your god(s) does seem to have very little influence on the poor mortals he helped create....