Light and truth
The “element” physics of light and truth are interesting. Light (energy) and truth (information) are both conserved quantities (though Hawking had his doubts, he’s recanted). In special relativity, the speed of light is the maximum speed at which information can travel. Rolf Landauer showed in 1961 that forcing a bit to a particular state requires kT ln(2) Joules of energy.
If Maxwell’s demon (James Clerk’s, not Neil A.’s) acquires his information about the particles in the box by looking at them, then something has to be providing the photons; eventually he’ll run out of them and won’t be able to see the balls any more. I think it was Szilard that pointed out that if the demon knew the initial positions and velocities of the particles, he wouldn’t need to observe them, but merely compute when they would pass through the door. As with Landauer’s principle, information can be exchanged for energy.
Algorithmic information theory studies what is computable. The halting probability ΩU of a universal Turing machine U is composed entirely of pure information: any program computing the first m bits of the probability is at least m-c bits long. So except for c bits at the start, every bit of information is a complete surprise, a new bit of truth that can’t be computed from what’s already known. It’s called “algorithmic randomness” because it’s entirely unpredictable, though there’s nothing random in the way the bits are defined. Pure information ahs some nice properties from a religious point of view: it’s not something you can compute from prior information, so it has to be revealed if you’re to know it at all, and there’s no way to prove that they’re right to anyone else once you’ve got them. Truth can be exchanged for light, as explained above. Roger Penrose has famously suggested that the collapse of the wave function is uncomputable (though not necessarily algorithmically random) and is related both to quantum gravity and to human agency. That’s still deterministic, which is a big problem for moral accountability, but has some good properties: behaviors based on uncomputable quantities are self-extant: there’s no prior reason why they should behave that way, if you say a reason is some series of rules applied to previously known axioms (or choices).
Note that uncomputable quantities, by definition, don’t arise through some physical process in time. Perhaps there’s some orthogonal time where infinite computations can run and become instantly available–for example, in Penrose’s toy model, the process of tiling the plane with a given set of tiles has to finish instantly to tell the wavefunction which way to collapse. This sounds rather like Cramer’s transactional model of wave function collapse; I’ll have to look at that more closely.
Doug recently had a post on Chalmer’s argument of perfections:
Consider whether statements (1) and (2) are true: (1) If X is true, then I believe X. If one does not accept this, then one accepts the opposite: one would be willing to state “X is true and I do not believe X.” But that is clearly a contradiction for any particular X. Therefore, we must accept that (1) is true for all X.
(2) If I believe X, then X is true. The negation of this would be saying “I believe X and X is false.” Again, this is impossible to state consistently for any X. So statement (2) is also true for all X.
But (1) means I am omniscient, and (2) means I am omnipotent.
Yes, classical logic assumes an omniscient, omnipotent “I”. Small wonder that there are those who feel it’s not as useful as some other flavors of logic!If your definition of truth includes the possibility that something may be “true” without you knowing it, then you’re working in intuitionistic logic. There, they define truth to be “known truth.” Then the only true things are those that you have a proof for and the law of the excluded middle doesn’t hold: if something is not provable, that doesn’t imply that it’s false. In this context, omniscient means “I know all proven things,” which is hardly surprising.
Statement 2 translates as “If I believe X, then I have a proof for X,” which implies omnipotence, as before. Its negation is “It is not the case that (I do not believe X or I have a proof for X).” For example, I could believe X when X is unproven.
Here’s a verse that defines truth as knowledge:
D&C 93:24 And truth is knowledge of things as they are, and as they were, and as they are to come.
This could apply equally well to an omniscient God or to an intuitionistic mortal; we know we’ll be judged on our actions given our knowledge at the time.
President McKay taught, speaking of the symbol of the compass, that “all truth may be circumscribed into one great whole.” All points in the Mandelbrot set lie within the circle of radius 2, but the converse is not true; in fact, it’s unknown whether the set of points is even computable. The complement of the set is computably enumerable. Similarly, it’s easy to come up with sets that include all true statements and a lot of false ones, and the true statements are computably enumerable (just list all proofs in order of length).
D&C 130:10-11 Then the white stone mentioned in Revelation 2:17, will become a Urim and Thummim to each individual who receives one, whereby things pertaining to a higher order of kingdoms will be made known; and a white stone is given to each of those who come into the celestial kingdom, whereon is a new name written, which no man knoweth save he that receiveth it. The new name is the key word.