reperiendi

Giger’s Alien in Lego

Posted in Fun links by Mike Stay on 2007 June 20

In lego, no one can hear you scream…

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Theocosmology

Posted in Math, Theocosmology by Mike Stay on 2007 June 18

David H. Bailey is an LDS mathematician, perhaps best known for his work on the “spigot algorithm” for pi. He has written rather extensively on the relationship between science and LDS theology.

Theocosmology

Posted in Theocosmology by Mike Stay on 2007 June 15

Agency and intelligence

So much of LDS theology is focused on agency:

  1. the premortal war in heaven over agency in mortality
  2. the purpose of earth life, a probationary state in which we are “free to choose”
  3. the promise of exaltation, being completely free and empowered to do anything

Lehi, during his sermon on opposition to Jacob, spoke of agents:

2 Ne 2:13,16 … There could have been no creation of things, neither to act nor to be acted upon… Wherefore, the Lord God gave unto man that he should act for himself. Wherefore, man could not act for himself save it should be that he was enticed by the one or the other.

as does section 93:

D&C 93:29-30 Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be. All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence.

Elder Nelson treated these verses in the October 1998 General Conference. He follows B. H. Roberts in interpreting the phrase “intelligence… was not created” to imply some portion of our being that God did not create and is the part responsible for our actions; the argument being that if God created the whole of us, then He would be responsible for all the wickedness in the world.

Webster on intelligence:

intelligence \In*tel”li*gence\, n. [F. intelligence, L. intelligentia, intellegentia. See Intelligent.]1. The act or state of knowing; the exercise of the understanding.

2. The capacity to know or understand; readiness of comprehension; the intellect, as a gift or an endowment.
And dimmed with darkness their intelligence.
–Spenser.

3. Information communicated; news; notice; advice.
Intelligence is given where you are hid.
–Shak.

4. Acquaintance; intercourse; familiarity. [Obs.]
He lived rather in a fair intelligence than any friendship with the favorites. –Clarendon.

5. Knowledge imparted or acquired, whether by study, research, or experience; general information.
I write as he that none intelligence Of meters hath, ne flowers of sentence. –Court of Love.

6. An intelligent being or spirit; — generally applied to pure spirits; as, a created intelligence. –Milton.
The great Intelligences fair That range above our mortal state, In circle round the blessed gate, Received and gave him welcome there. — Tennyson.

Intelligence office, an office where information may be obtained, particularly respecting servants to be hired.

Syn: Understanding; intellect; instruction; advice; notice; notification; news; information; report.

Source: Webster’s Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.

With respect to God, then, intelligence is the act or state of knowing God; the capacity to know or understand Him; an endowment; information communicated from God, prophecy (advance notice) and advice; acquaintance, intercourse, and familiarity with God; knowledge imparted to man by God or obtained from Him, whether by study, research, experience, or direct revelation; and finally, an intelligent being or spirit.

The phrase “otherwise there is no existence” is intriguing: what does “existence” mean? My brother Doug takes a stab at it here, but in math there don’t seem to be “things to act,” only “things to be acted upon.” Even Penrose never dares to suggest that our actions aren’t deterministic.

I’m guessing that agents are the root of existence: agents constrained by physical law but free to choose within those constraints is what “existence” actually means. I’m inclined to follow Skousen to a certain extent in allowing intelligences to govern something like an electron. (See also this thread for some related references.)

Bounce a photon off a semisilvered mirror and place a detector on only one of the two paths. If the detector clicks, murder someone. At the judgement day, is your soul in a superposition of heaven and hell? The elegance and simplicity of the many worlds theory is very compelling, but it seems to conflict with what we’d expect here.

Theocosmology

Posted in Theocosmology by Mike Stay on 2007 June 14

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.

I responded,

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).

Given an oracle to the halting probability of a universal Turing machine, one can compute the truth of any particular statement in a finite axiomatic system. Is this related to the white stone?

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.

Theocosmology

Posted in Theocosmology by Mike Stay on 2007 June 14

This is the first in a series of posts on my interpretations of various scriptures relating to the nature of existence.

Spirit and Element

First, we’re materialists:

D&C 131:7-8
There is no such thing as immaterial matter. All spirit is matter, but it is
more fine or pure, and can only be discerned by purer eyes. We cannot see it;
but when our bodies are purified we shall see that it is all matter.

Spirit matter is real stuff, interacting via some physical law with the stuff we see. D&C 93 refers to these two domains as “element” and “spirit.”

D&C 93:33-34 For man is spirit. The elements are eternal, and spirit and element, inseparably connected, receive a fulness of joy; and when separated, man cannot receive a fulness of joy.

That implies there’s some kind of physics governing spirit. I think this verse is relevant:

D&C 29:34 Wherefore, verily I say unto you that all things unto me are spiritual, and not at any time have I given unto you a law which was temporal.

Also, in Satan’s statement,

“Yes, a new world, patterned after the old one where we used to live,”

the phrase “patterned after” suggests the laws of element are homomorphic to the laws of spirit.

In future posts I’ll be examining concepts that appear in both domains.

Life is better

Posted in Journal by Mike Stay on 2007 June 11
  • Talked to my manager, who said his first six months were painful because of not having a clear coding project to work on
  • Got a clear coding project to work on
  • Happy for Jason
  • Miriam and I made some friends at church
  • Will be moving to third floor of 41 instead of second; the view is of trees instead of parking lot.

Exponential growth

Posted in Fun links, Math by Mike Stay on 2007 June 1