I had a feeling in yesterday’s blog entry that I was missing something so on I emailed the young computation-wizard Scott Aaronson. Scott has a number of interesting avatars on the Web, such as his blog, and his “Complexity Zoo” now in wiki format. Scott was actually helpful enough to reach through the second-to-last draft of my Mathematicians in Love to find logical holes in it, by the way. His articles can be a bit abstruse, but I’m planing to study “Quantum Computing for High-School Students” next time I feel really smart!

Anyway, yesterday I asked Scott about his thoughts on the Turing Oracle, as I half-remembered a conversation I’d had with him about it in San Jose last year.

Scott answered:

It looks like you've covered the “stoner” implications of a halting oracle about as well as I could have. (“Sure, you could instantly find any mathematical proof, create an AI model of a human being that best matches his or her observed behavior, and indeed, simulate the entire physics of the known universe, but what could you REALLY do?” )

Unless you had a more specific question, I'll confine myself to one remark, which is that you could already get plenty of zany implications with an oracle for NP-complete problems (forget about the halting problem!). See my paper “NP-complete Problems and Physical Reality” for more about this point.

I answered:

“Stoner” implications! Harrumph. Possibly the fact that my previous blog entry was about Wm. Burroughs fosters this impression…

What I REALLY want is a way to finish my new novel without having to write it.

You you give me hope in your remark that with a Turing Oracle, I could create an AI model of myself that best matches my observed behavior. Aha!

Mulling this over today, I get the following line of thought. The weakest kind of Turing Oracle form it tells me in some finite but unbounded-in-advance amount of time whether or not a given computation C will halt. In a stronger form, there is some fixed finite amount of time such that the oracle always returns its answer within that amount of time.

Now let’s postulate a still stronger magic tool, a Turing Evaluator or TE. There is a fixed finite amount of time such that within that amount of time TE me (a) whether a given computation C will halt and, (b) what was the final output of C, in the case that C does halts.

A Turing Evaluator tells me more than whether the computation C halts, it gives me a short-cut for finding out what C does.

Another way to express what a Turing Evaluator does: Whenever I want to search through the integers for a special integer Special_N having some property, then TE will quickly tell me the value of the smallest such Special_N, and if there is no such integer it’ll tell me that as well.

There’s a well-known method for coding up pairs or triples or n-tuples of integers as single integers, so I can in fact be searching for several integers at once.

Suppose I’m given finite string of integer variables u, v, … z and a property Good(u, v, … z). I want to find if there are any specific values Nu, Nv, … Nz which satisfy Good. I can use my Turing Evaluator to discover in some fixed amount of time whether or not this is the case, and if it is the case, my Turing Evaluator will return examples in the form of Special_Nu, Special_Nv, … , Special_Nz.

So now I see how to use my Turing Evaluator to write my seventeenth novel Ru_17 (also called Postsingular) as follows.

(i) Code up my first sixteen novels as constant numbers cRu_1, … , cRu_16.

(ii) Establish a system for listing possible neural-net-based AI programs for simulating my writing a novel, list the variable code numbers as FakeRu_1, FakeRu_2, … FakeRu_x, …

(ii) Let y be a variable integer that might code up my next novel.

Define a predicate Good such that Good(Ru_1, …, Ru_16, FakeRu_x, y) means that FakeRu_x codes an algorithm such that, FakeRu_x generates the known novels Ru_1, …, Ru_16, as its first sixteen “novels,” and FakeRu_x generates y as its seventeenth “novel.”

So I apply my Turing Evaluator and get specialFakeRu_x and Special_y, which I can then mail in to David Hartwell at Tor as Ru_17, a.k.a. Postsingular.

Sure, Rudy, sure.

Meanwhile, I’ve finally, sob, finally finished revising Chapters 1-3, and figuring out the outline for Chapters 4 and 5, so now I can continue generating Ru_17 the hard way.

Um … write today? Hell with that. It’s 100 degrees here. I’m heading for Cruz.

Suppose the eighth dimension is normally curled around into a Planck-length circle, but that some perturbation or magic spell unrolls it to infinite length. And suppose as well that it’s psychically possible to overview the whole infinite expanse of the eighth dimension in a finite amount of time. Also suppose that all the eighth-dimensional lines meet at a point.

I will use the phrase “lazy eight” to speak of this change. It combines: eighth dimension, infinity as ∞, and the fact that infinity is “right here” in the eighth dimension as an ubiquitous lazy-man’s enlightenment. So we have an infinite extra dimension at every point. Yet the infinite expanse is accessible; you can reach any location along it in some fixed time.

It’s like you took the vanishing point of a painting and made it be at every point in space. The point at infinity is present everywhere. It’s like being with God. The accessible point at infinity acts as an entanglement channel that connects every point with every other point in synchronicity.

New topic.

I’ve been thinking about Alan Turing’s halting problem. The halting problem is this: Find an oracle such that given any arbitrary computation C, the oracle will in a finite amount of time tell you if a computation C is going to halt or run forever. And we can refer to such an oracle as a Turing Oracle. Turing proved that no computation can act as a Turing Oracle. That is, no computation can serve as an oracle that can tell you whether or not an arbitrary computation will run forever.

Perhaps there could be a Turing Oracle, but its operation would have to involve something other than normal computation-like physics. One option I’ve been thinking of is lazy eight, which I mentioned above.

If lazy eight gives you infinite consciousness, then you could in fact solve the halting problem, as all the infinite searches could be done in finite time. We could in fact have a fixed-time Turing Oracle that always gives you that yes or no answer within some fixed time, say one second. Call this a Strong Turing Oracle.

In Accelerando, Charles Stross boldly writes, “New discoveries this decade include … experimental implementations of a Turing Oracle using quantum entanglement circuits: a device that can determine whether a given functional expression can be evaluated in finite time.”

But Stross doesn’t really delve into what the implications would be. So now I ask you, what would it be like to have a Strong Turing Oracle in hand?

Given any mathematical statement S, I could decide whether S is a provable theorem. I fix on a particular axioms system for mathematics and I define a computation ProofSearch(S) that searches through all possible proofs from these axioms, looking for a proof of S. And I’d feed the ProofSearch(S) computation to my Turing Oracle. If the Oracle tells me that ProofSearch(S) halts, I know that S is provable. If the Oracle tells me that ProofSearch(S) runs forever, I know that S isn’t provable.

Given any possible story S, I can decide if this a story I would ever write. I create an AI model of how I think and write. And I define a computation RuWriteSearch(S) that searches through all possible “creative processes” carried out by the AI model, looking for a process that terminates with writing the story S. And I’d feed the RuWriteSearch(S) computation to my Turing Oracle. If the Oracle tells me that RuWriteSearch(S) halts, I know that S is a story I might write. If the Oracle tells me that RuWriteSearch(S) runs forever, I know that S isn’t a story I would write.

Given any possible scientific theory S, I can decide if this a theory we might adopt. Again I create an AI model of human scientific thought, feed a ScienceSearch(S) computation to the Turing Oracle, and discover whether or not S is a possible future theory or is out of the question.

Lazy eight and the ability to do an infinite search in a fixed amount of time leads to a Strong Turing Oracle. Could the implication run the other way? Could the discovery of the Turing Oracle lead to lazy eight? I mean science-fictionally speaking.

New topic.

Note that having a Turing Oracle is much weaker than having a Truth Machine computer TM such that if S is any sentence in number theory TM(S) outputs a True or False to tell us whether S is true. The Turing Oracle only decides provability, not truth.

We can’t solve the truth question with a single infinite search because arbitrary sentences of number theory have alternating quantifiers that set off nested searches within searches. Perhaps if you had a transfinite time line to work with you could do this, that is, if you could fold together infinitely many infinite searches.

Suppose I let the variables x and y range over the integers. If you had infinity times infinity seconds to play in, you could check the truth of “(for all x)(there is a y)P(x,y)”. You set off a fresh infinite search for each value of x. As it nests deeper the ordinals would stack up. Is that what Gentzen was talking about when he spoke of the ordinal epsilon-zero in the context of proof theory? I never really studied that work.

What would it be like, SF-wise to have a truth machine. The War Against the Rull. Our Flooping Federated Galactic Goobs have a Turing Oracle, but the Rull have a Truth Machine! Looks like the home team is in for it! But wait…

William Burroughs’s Junkie came out from Ace Books in 1953. When I later went to publish my first novel, White Light, I sent it to Ace partly because I knew they'd published Burroughs.

Junkie book was bound in a 69-style double edition with a “balancing” book, Narcotic Agent. My book dealer friend Greg Gibson gave me this rare edition a few years back. I actually removed the book from its plastic bag to read Narcotic Agent, told Greg, “It wasn’t all that bad,” and he's like “You touched the book? You took it out of its bag.”

Be that as it may, Junkie has an appendix with a description of various drugs Burroughs had taken at that time, and the prophetic closing sentence is “Yage may be the final fix.”

In 1963, City Lights published The Yage Letters. I first read the book in 1965, when I was a sophomore in college. It struck me then as one of the funniest books I’d ever read — Burroughs’s jaded laconic descriptions of people and scenes are priceless.

Also the book has Allen Ginsberg’s incredibly heavy letter about his yage trip in Peru seven years later, June 10, 1960. For a while he’s filled with this intense fear of death, a sense that he’s dying right now, “…as if in rehearsal of Last Minute Death my head rolling back and forth on the blanket and finally settling in last position of stillness and hopeless resignation to God knows what Fate…”

Some of you will understand that this is in some sense funny. I lifted the vision for a scene where my character Sta Hi Mooney is having an acid trip on the beach in my novel Software and he thinks he’s dying. “A film came to mind, a film of someone dying on a beach. His head rolled slowly to one side. And then he was still. Real death. Slowly to one side. Last motion.”

There’s a nice new (fourth) edition of the book called The Yage Letters Redux. I bought it at City Lights last week with Lawrence Ferlinghetti himself behind the counter.

I introduced myself and said I'd been thinking of him on Bixby Bridge coming back from Big Sur last week (after having reread some of Kerouac's Big Sur). Ferlinghetti said he still has his cabin there, was going down for the weekend, and still doesn't have electricity.

I read the new edition of Yage with joy in a couple of days. And today, additional joy, I found that editor Oliver Harris( an American Lit prof at Keele Univesity in England ) has published a fascinating essay that overlaps with his great new introduction. The essay is in a literary magazine called Postmodern Culture; you can find ”Not Burroughs' Final Fix: Materializing The Yage Letters” online. I gather that it won’t be there indefinitely.

The essay includes some interesting images of original appearances of sections of the novel; which Burroughs published in various small magazines. Turns out The Yage Letters, wasn’t really a direct transcription of actual letters; it’s more that Bill combined letters, journal notes, and essay material to create the illusion of an epistolary novel.

This image is present as a link to an image from the essay, where it’s labeled: “Figure 1: Image from Black Mountain Review 7 [1958]. Image used by permission of William S. Burroughs Trust and Estate.”

This particular “July 10, 1953,” yage letter is important in the Burroughs canon; it’s the last of his 1953 “letters” in the later editions The Yage Letters. Actually it didn’t appear in the first edition (1963) of Yage Letters, probably because by then Burroughs had lifted this passage to use as part of Naked Lunch (1959) called “the market.” But, as Bill wrote the letter one morning while coming down off a night of yage it makes sense to have it in theThe Yage Letters.

Two great lines from the July 10, 1953, letter:

“Yage is space time travel.”

“A place where the unknown past and the emergent future meet in a vibrating soundless hum.”

That second line uses a phrase from his February 28, 1953 yage letter, describing the upper Amazon jungle near Mocoa, Colombia. “The trees are tremendous, some of them 200 feet tall. Walking under these trees I felt a special silence, a vibrating soundless hum.” What a wonderful image for how telepathy might feel.

I’ve always thought of science fiction as an extension of Beat literature.

Speaking of telepathy, Allen’s yage letter of June 10, 1960, talks about “radiotelepathy,” which was a phrase I used in my novel Saucer Wisdom.

One of the nice things in The Yage Letters Redux is that it includes a longer journal note of Allen’s about the same yage trip. Here he writes of beginning “to sense a strange Presence in the hut — or a Being I am blind to habitually — like a science fiction Radiotelepathy Beast from another Universe — but from the series of universes in which I do temporarily exist …”

Allen’s letter and journal note have really wonderful musings upon the psychedelic experience; he has great flashes like, “I was a vomiting snake … the Serpent of Allen, covered with aureole of spiky snakeheads miniatured radiant & many colored around my hands & throat …”

But heavier than the flashes are his repeated expressions of a core mystical revelation: God/the universe/everything/everyone is a One/Many mind accessible to all, and there is nothing arcane or unusual about this fact, it’s staring us in the face all the time, and there’s no secret, nothing to know, this is all there is, divinity is here and now.

“…the realization that we are set there to live and Die, and all man set here together in different bodies in a web of realization of the same fate…”

“… we, here, are it, the great Presence we are the great Presence of the Universe … God himself knows no more than we or I why he was born or where he is going…”

“…this same ancient and familiar mystery Universe…”

“The familiar creepy sexy nosey personal intimate old-known, special re-realization of the Joke sweetness of Illusion fading into the Great Black A**hole of on-Mind one-Love cat-faced snake-faced dog-faced man-faced Mandalic Universal Newspaper Busybody Gossip God. All mine, all everybody’s, all everything’s. And what else could He be but He Himself?”

This is all pure gold in terms of my current work on my novel Postsingular where I’m imagining life in a telepathic parallel world called The Mirrorbrane.

The vibrating soundless hum.

What a week, two covers! I saw a draft version of the cover for my collection Mad Professor coming out from Thunder's Mouth Press in January, 2007. (I'll check with Thunder's Mouth before posting it here; meanwhile here's a Goldsworthy-like rock construction I saw by Big Sur River.)

By the way, the cover draft was by no less a figure than the estimable and inimitable Georgia Rucker!

Here's the table of contents.

I think only one of these stories is currently on line, this would be “Jenna and Me”, which commits the CrimeThink of satirizing the First Family as of 2003 or so.