Wednesday, June 9, 2010

A Monotheism Theorem?

I came across this very interesting paper (unpublished I think): Physical limits of inference by David H. Wolpert ( (Caution: Lots of discrete maths involved.)

Check out page 23 about the "monotheism theorem" using a variant of Godel's incompletness theorem: that there can be at most one omniscient god. If there were two, they're be able to read each others' minds and run into paradoxes of circularity. (Credits to Scientific American for its very helpful summary.)

(The author wrote somewhat tongue-in-cheek, but I think his reasoning and maths is very interesting. Whether sound or not... haha that's what peer reviews are for.)

But yeah! A maths proof that there's at most one God. (Whether there is a God in the first place, that one's for us to consider and chew on.)

PS: Of course I believe in a God. :)

Here's an extract from the paper (p.23):
6.2. Philosophical implications
Return now to the case where U is a set of laws of physics (i.e., the set of all worldlines consistent with a set of such laws). The results of this subsection provide general restrictions that must relate any devices in such a universe, regardless of the detailed nature of the laws of that universe. In particular, these results would have to be obeyed by all universes in a multiverse [27,28,29].

Accordingly, it is interesting to consider these results from an informal philosophical perspective. Say we have a device C in a reality that is outside distinguishable. Such a device can be viewed as having “free will”, in that the way the other devices are set up does not restrict how C can be set up. Under this interpretation, Thm. 1 means that if two devices both have free will, then they cannot predict / recall / observe each other with guaranteed complete accuracy. A reality can have at most one of its devices that has free will and can predict / recall / observe the other devices in that reality with guaranteed complete accuracy. (Similar conclusions hold for whether the devices can “control” each other; see Sec. 7 below.)

Thm. 3 then goes further and considers devices that can emulate each other. It shows that
independent of concerns of free will, no two devices can unerringly emulate each other. (In other words, no reality can have more than one universal device.) Somewhat tongue in cheek, taken together, these results could be called a “monotheism theorem”. [emphasis mine]

Now suppose that the domain of a reality is a set of worldlines extending across time, and
consider “physical” devices that are identified with systems evolving in time. (See discussion
just after Def. 7.) Prop. 5 tells us that any universal device must be infinite (have infinite X(U)) if there are other devices in the reality that are copies of it. Since the time-translation of a physical device is a copy of that device, this means any physical device that is ever universal must be infinite. In addition, the impossibility of multiple universal devices in a reality means that if any physical device is universal, it can only be so at one moment in time. (Its time-translation cannot be universal.) Again somewhat tongue in cheek, taken together this second set of results could be called an “intelligent design theorem”. (See Sec. 7 for related limitations concerning devices that are used to control one another.)

Cool. :D

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