From desert cliff and mountaintop we trace the wide design,
Strike-slip fault and overthrust and syn and anticline…
We gaze upon creation where erosion makes it known,
And count the countless aeons in the banding of the stone.
Odd, long-vanished creatures and their tracks & shells are found;
Where truth has left its sketches on the slate below the ground.
The patient stone can speak, if we but listen when it talks.
Humans wrote the Bible; God wrote the rocks.
There are those who name the stars, who watch the sky by night,
Seeking out the darkest place, to better see the light.
Long ago, when torture broke the remnant of his will,
Galileo recanted, but the Earth is moving still.
High above the mountaintops, where only distance bars,
The truth has left its footprints in the dust between the stars.
We may watch and study or may shudder and deny,
Humans wrote the Bible; God wrote the sky.
By stem and root and branch we trace, by feather, fang and fur,
How the living things that are descend from things that were.
The moss, the kelp, the zebrafish, the very mice and flies,
These tiny, humble, wordless things–how shall they tell us lies?
We are kin to beasts; no other answer can we bring.
The truth has left its fingerprints on every living thing.
Remember, should you have to choose between them in the strife,
Humans wrote the Bible; God wrote life.
And we who listen to the stars, or walk the dusty grade,
Or break the very atoms down to see how they are made,
Or study cells, or living things, seek truth with open hand.
The profoundest act of worship is to try to understand.
Deep in flower and in flesh, in star and soil and seed,
The truth has left its living word for anyone to read.
So turn and look where best you think the story is unfurled.
Humans wrote the Bible; God wrote the world.
-Catherine Faber, The Word of God
I shut my eyes — I opened them. Then I saw the Aleph.
I arrive now at the ineffable core of my story. And here begins my despair as a writer. All language is a set of symbols whose use among its speakers assumes a shared past. How, then, can I translate into words the limitless Aleph, which my floundering mind can scarcely encompass? Mystics, faced with the same problem, fall back on symbols: to signify the godhead, one Persian speaks of a bird that somehow is all birds; Alanus de Insulis, of a sphere whose center is everywhere and circumference is nowhere; Ezekiel, of a four-faced angel who at one and the same time moves east and west, north and south. (Not in vain do I recall these inconceivable analogies; they bear some relation to the Aleph.) Perhaps the gods might grant me a similar metaphor, but then this account would become contaminated by literature, by fiction. Really, what I want to do is impossible, for any listing of an endless series is doomed to be infinitesimal. In that single gigantic instant I saw millions of acts both delightful and awful; not one of them occupied the same point in space, without overlapping or transparency. What my eyes beheld was simultaneous, but what I shall now write down will be successive, because language is successive. Nonetheless, I’ll try to recollect what I can.
On the back part of the step, toward the right, I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realised that this movement was an illusion created by the dizzying world it bounded. The Aleph’s diameter was probably little more than an inch, but all space was there, actual and undiminished. Each thing (a mirror’s face, let us say) was infinite things, since I distinctly saw it from every angle of the universe. I saw the teeming sea; I saw daybreak and nightfall; I saw the multitudes of America; I saw a silvery cobweb in the center of a black pyramid; I saw a splintered labyrinth (it was London); I saw, close up, unending eyes watching themselves in me as in a mirror; I saw all the mirrors on earth and none of them reflected me; I saw in a backyard of Soler Street the same tiles that thirty years before I’d seen in the entrance of a house in Fray Bentos; I saw bunches of grapes, snow, tobacco, lodes of metal, steam; I saw convex equatorial deserts and each one of their grains of sand; I saw a woman in Inverness whom I shall never forget; I saw her tangled hair, her tall figure, I saw the cancer in her breast; I saw a ring of baked mud in a sidewalk, where before there had been a tree; I saw a summer house in Adrogué and a copy of the first English translation of Pliny — Philemon Holland’s — and all at the same time saw each letter on each page (as a boy, I used to marvel that the letters in a closed book did not get scrambled and lost overnight); I saw a sunset in Querétaro that seemed to reflect the colour of a rose in Bengal; I saw my empty bedroom; I saw in a closet in Alkmaar a terrestrial globe between two mirrors that multiplied it endlessly; I saw horses with flowing manes on a shore of the Caspian Sea at dawn; I saw the delicate bone structure of a hand; I saw the survivors of a battle sending out picture postcards; I saw in a showcase in Mirzapur a pack of Spanish playing cards; I saw the slanting shadows of ferns on a greenhouse floor; I saw tigers, pistons, bison, tides, and armies; I saw all the ants on the planet; I saw a Persian astrolabe; I saw in the drawer of a writing table (and the handwriting made me tremble) unbelievable, obscene, detailed letters, which Beatriz had written to Carlos Argentino; I saw a monument I worshipped in the Chacarita cemetery; I saw the rotted dust and bones that had once deliciously been Beatriz Viterbo; I saw the circulation of my own dark blood; I saw the coupling of love and the modification of death; I saw the Aleph from every point and angle, and in the Aleph I saw the earth and in the earth the Aleph and in the Aleph the earth; I saw my own face and my own bowels; I saw your face; and I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon — the unimaginable universe.
I felt infinite wonder, infinite pity…
(Jorge Luis Borges, The Aleph)
A finitely-refutable question is one of the form, “Does property X holds for all natural numbers?” Any mathematical question admitting a proof or disproof is in this category. If you believe the ideas of digital physics, then any question about the behavior of some portion of the universe is in this category. We can encode any finitely refutable question as a program that iterates through the natural numbers and checks to see if it’s a counterexample. If so, it halts; if not, it goes to the next number.
The halting probability of a universal Turing machine is a number between zero and one. Given the first bits of this number, there is a program that will compute which -bit programs halt and which don’t. Assuming digital physics, all those things Borges wrote about in the Aleph are in the Omega. There’s a trivial way–the Omega is a normal number, so every sequence of digits appears infinitely often–but there’s a more refined way: ask any finitely-refutable question using an -bit program and the first bits of Omega contain the proper information to compute the answer.
The bits of Omega are pure information; they can’t be computed from a fixed-size program, like the bits of can.
I started a blog to record my Gospel Doctrine lessons. It’s called ankylodoxy, as opposed to orthodoxy.
The brain is an amazing thing; hypnosis can block pain. There are plenty of hypnosis weight-loss clinics for helping people to lose weight and to quit smoking. As we get more detailed knowledge of the brain, it will become a trivial thing to improve one’s willpower. Instead of procrastinating, we’ll be able to tell ourselves to do something and become compulsive about doing it. No more late homework!
NPR’s science Friday has several programs on memory; in one recent one (that I can’t find), they explained that memories are recreated every time we remember them, with an accompanying degradation of the memory. Details we don’t think are important are discarded and filled with plausible reconstructions; the sudden recall of something you haven’t thought of for twenty years is far closer to the actual event than a memory that you think about all the time. It’s also easy to introduce fake memories, because the brain fills in plausible details in exactly the same way.
They know this because of recent experiments using drugs that interfere with the formation of memory: rather than have the patients try to learn something, and watch how they forget it, they had them try to remember something, which they proceeded to forget even after the drug wore off. Humans now have the abillity to selectively erase conscious memories.
There’s another form of memory that’s subconscious, of habits and feelings acquired through repetition. This seems to be a deeper, more protected form of memory. Clive Wearing, who was once a musicologist, contracted encephalitis, which damaged his hippocampus. He has a seven-second memory. He’s constantly feeling as if he’s just awoken from a dream, having no idea where he is or what has happened to him for the past twenty years. But he can still direct his choir perfectly and fills with joy every time he sees his wife.
It’s probable that we’ll be able to erase or modify those memories in the near future, too.
We admire people who do things despite pain. Words like courage, tenacity, and kindness all apply to enduring in the presence of pain. The atonement is the prototype here: love overcoming pain.
The whole concept of mortality in scripture is predicated on the idea that pain is necessary for progression; it separates souls like a chromatograph separates particle sizes. People who are physically strong become so by exercising and enduring pain. Smart people typically work hard to become so. Barbie was right: math is hard–but at the moment there’s no other way to become so.
If we can remove the memory of pain and decide to remove the pain that stands between us and some desired end, will there be any virtue in the accomplishment? Skousen’s argument for the purpose of the pain in the atonement was to work on the compassion of intelligences. Where does compassion go when we can forget the hurt at will?
The View from the Center of the Universe says we’re the first generation that can tell stories about the creation that might actually be true. We should take the mythological imagery we have around us and reinterpret it so that it corresponds to something real instead of something imagined, thus giving people a sence of place in the universe.
Their stories, by most accounts, weren’t very good. But I believe they’re on the right track: stories are how humans understand the world. It’s part of why I like John Baez’ teaching style so much: he tells stories. A search on his site for the word “story” turns up hundreds of occurrences!
Gödel, Escher, Bach talks about string rewrite rules and theorem proving, trying to illustrate the difference between syntax (structure) and semantics (meaning). He states some rules like
xpyqz => sxpyqsz
and then suggests that “sx” is the “successor” of “x”, and thus one interpretation of “p” and “q” is “plus” and “equals,” respectively. But it could just as easily be “equals” and “taken from.” How do we know what a structure “really means?” Does that question even make sense?
Universal algebra is a language for describing simple structures like sets, monoids, groups, rings, and modules (but not fields). Lawvere showed that every algebraic theory corresponds to a cartesian category, and that a functor from the cartesian category to Set gives a model of the theory. The Yoneda lemma says that there’s a one-to-one correspondence between the set of models of a theory and the set of functors out of the theory. So any model has to arise as a functor out of the theory.
This lets us separate syntax from semantics, structure from meaning. The theory is a Platonic ideal that has models in the “real world” of sets and functions. Of course, now that the “real world” has been revealed to be quantum, we should consider functors into other categories, too: a functor into Hilb assigns quantum meaning to the structure. This is how Feynman diagrams are used for quantum field theory: every line represents a Hilbert space of states instead of a set, and each vertex represents a linear operator instead of a function.
Usually, what a structure “means” can only really be answered by considering all of the possible meanings together and looking at the relationships among them. But that’s a very hard task in most cases. It’s easier to have a single, typical instance in mind: what do you think of when I say “undirected graph?” It’s probably an image of a not-so-special graph, not the mathematical definition.
Choosing some example is essential to the way we learn. Adam and Christ, the “last Adam,” are the prototypes used by the Gospel. But there are a lot of details left out.
I’m trying, in these Theocosmology posts, to build up a backstory for my existence, which is the story I’m most interested in; I’m choosing details that may or may not be true, but are as true-to-life, as typical as I know how to make them.
Joy, glory, and knowledge
Here’s the passage that refers to 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.
In the Book of Mormon, joy is used almost interchangeably with glory. Nephi says
2 Ne 33:6 I glory in plainness; I glory in truth; I glory in my Jesus, for he hath redeemed my soul from hell.
C.S. Lewis’ sermon The Weight of Glory discussed an apparent paradox:
I turn next to the idea of glory. There is no getting away from the fact that this idea is very prominent in the New Testament and in early Christian writings. Salvation is constantly associated with palms, crowns, white robes, thrones, and splendour like the sun and stars. All this makes no immediate appeal to me at all, and in that respect I fancy I am a typical modern. Glory suggests two ideas to me, of which one seems wicked and the other ridiculous. Either glory means to me fame, or it means luminosity. As for the first, since to be famous means to be better known than other people, the desire for fame appears to me as a competitive passion and therefore of hell rather than heaven. As for the second, who wishes to become a kind of living electric light bulb? (ibid., p. 5)
He concludes that it is the joy of a child in finding favor with his father, being “famous with God.” Being known of God as opposed to the opposite:
In some sense, as dark to the intellect as it is unendurable to the feelings, we can be both banished from the presence of Him who is present everywhere and erased from the knowledge of Him who knows all. We can be left utterly and absolutely outside—repelled, exiled, estranged, finally and unspeakably ignored. (ibid., p. 7)
Spencer W. Kimball said, “Real intelligence is the creative use of knowledge” (CR, Oct. 1968, p. 130. Emphasis mine.)
Hofstadter examined creativity in his book Metamagical Themas (
). He talks about Knuth’s Metafont package: in that program, a font has lots of different properties that can be adjusted. There’s an enormous space of letters that can be expressed by these parameters, but they are nowhere close to encapsulating all the forms we recognize as, say, the letter ‘A.’ Coming up with a new parameter, for Hofstadter, is creativity–and yet, ironically, such creation must arise exclusively as the result of some deterministic process. He implies he could not have written any other book than the one he did–but within the book, a few pages away from this claim, he talks about how we continually conceive of worlds slightly different than our own, such as one where the state line between Illinois and Indiana is a few miles to the west of where it is here.
In the section on parquet deformations, he mentions the “flickering” effect of looking at a Necker cube. My brother Doug suggests that agency and qualia are part of the same mystery. We have no idea how perception of shape or color arises in the mind, nor how independent action arises: but we can choose to see the cube with its top toward us or away from us.
In Moses, God says that
Moses 1:39 …This is my work and my glory—to bring to pass the immortality and eternal life of man.
In other words, what God prefers to spend his time on is creating more gods. Even Richard Dawkins couldn’t take offense at that doctrine. God is an adult of the species, a father in the literal sense. What can we guess about producing minds that last forever?
Greg Egan has treated artificial minds and immortality in several of his stories. In Orphanogenesis, artificial minds are run on a computer, and when they become self-aware, the computer revokes all authority for the mind to be modified from the outside; the consequence is that some minds descend into eternal madness. A rejection of truth is a rejection of reality. My guess is that a faulty view of the universe leads to eternal madness–outer darkness–if left unchecked, so in mercy, God checks it.
Was there ever a time or a place where an atonement couldn’t reach? Where all the minds were destroyed? Nephi writes about how we’d share Satan’s fate if not for the atonement in 2 Ne 9. There was clearly fear among the premortal spirits contemplating mortality (Rev. 5:3).
Agency and intelligence
So much of LDS theology is focused on agency:
- the premortal war in heaven over agency in mortality
- the purpose of earth life, a probationary state in which we are “free to choose”
- 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.
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.
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:
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.