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Transfinite Minds

Good news: the first half of my novel Hylozoic is done, and so, by extension, my projected trilogy is half done as well: Postsingular, Hylozoic, Transfinite.

Bad news: I’m quite vague about what happens in the second half.

I do have what looks like an outline for the second half of Hylozoic, but it’s largely gauze and mist. So I’ll be redoing the outline for a few days now.

And, while I’m in planning mode, it would be great to get more ideas about that third novel, Transfinite.

Today I rode up onto St. Joseph’s Hill in Los Gatos with my trusty Pilot P-700 black fine gel pen and with my outline printed on a few pages of paper folded in four in my back pocket—my favorite form of portable word processing set-up. I marked it up. My handwriting has gotten so free (elderly?) that later I often need to use a magnifying glass to figure out what I wrote.

I need a name for the transfinite beings such as the magic harp. I was calling them “infinites,” though “transfinites” would be better. “Gods” has too much baggage. Maybe “snakes” or “snaaakes,” with the iterated “a” suggesting their (extreme) length. Oh, I know, how about “immortals.” Yeah, that seems to work, at least for now.

Some tough questions:

Q: What is a rune? What is a runemaster?

A: A rune is like a magic spell that directly affects matter. In Hylozoic at present I describe a rune is combination of a telepathic contact, a telekinetic push, and a higher-dimensional flip. And when you lay a rune on something you are “casting” it. And if you can cast runes, you’re a runemaster.

I’ve described three kinds of runes.

* The summoning rune, which linked Jayjay via a subdimensional wormhole to a mind in a distant galaxy.

* The ioneer runes which convert the information in a distant alien’s body into a behavior in a group of Earthly atoms, causing the atoms to emit matter waves that produce a matter-hologram copy of the alien.

* The atomic reset rune which clears the ioneer runes out of the enslaved atoms.

For story purposes, I have it set up so that only Jayjay, of all the people on Earth, can cast runes. He has a dream where the magic harp makes him a runemaster.

Perhaps a rune has something to do with higher infinities. A self-referential loop. But why can only Jayjay cast runes? He’s not really the smartest guy in the world. Maybe it has to do with his (so far latent) painting talent?

Q: When and where is the magic harp located when Jayjay sees her in his dream?.

A: I’d like to just say the harp is dreaming too, and this appearance emerges from the massed moments of her whole life. Except for an immortal like the magic harp, this visionary state is not like dreaming, its like the normal state, and the part where they are embedded in our world is more like the dream.

Q: Why did magic harp make Jayjay a runemaster?

A: Perhaps the magic harp is a future version of my character Thuy Nguyen. Maybe in Transfinite, Thuy goes through an apotheosis and becomes an immortal, in particular, she becomes the magic harp. And then goes back to do what she needs to do. And that’s the end of the trilogy; the snake of history bites its own tail.

Q: Why does the magic harp forget the Lost Chord on her journey from the present-day Lobrane to the Fifteenth Century of the Hibrane?

A: The magic harp is a higher mind that lives in every moment of her Earthly manifestation, yes. But this mind is subject to time flow constraints when embedded in the physical world. If I raise my consciousness to be conscious of my entire lifeworm at each instant of my life, it’s still true that today I don’t know what I’ll do tomorrow. Even though I will in another sense feel the “same” tomorrow, like the same lifeworm.

Q: Where do the immortals live?

A: I will call it Walhalla for now, echoing the Valhalla of Wagnerian myth. I don’t want Walhalla to be pie in the sky, or infinite dimensional Hilbert space. I’d like it to be our actual world, regarded in a different way. We are in Walhalla all the time.

So I’m saying the immortals are physically in our world, but they make the most of what’s available and manage to have infinite minds.

It’s possible that a infinite immortal mind is connected to more than one finite body. In this case, the bodies are like pearls upon an endless golden strand. Two people might separately have infinite souls, and then choose to combine the souls into one; the single soul living in two bodies. A cosmic marriage.

In principle all the silps in an alef-null-sized universe could be bodies of one and the same infinite mind.

Q: Can I see Walhalla?

A: When you dream you are in Walhalla. Time sequence constraints can break down here; you can dream the past and the future. There’s not a problem with a yes-and-no temporal paradox because when you wake up and all quantum states are collapsed, then you aren’t sure what happened in the dream, or you don’t really believe it.

Q: How is our universe infinite?

A: I can think of three senses:

(a) Upward infinity. Infinite spatial extent, with infinitely many stars, and infinitely many degrees of higher level structures, that is, ultra-k-clusters of galaxies for every number k.

(b) Downward infinity. Infinitely divisible matter. The Planck barrier is simply an illusion. By renormalizing, we can in fact flip our view of things, and see the “big” stuff as being below the Planck scale and us as being the “small” stuff. A flip-flop. The endlessly many ultra-k-clusters below the Planck scale would then represent lower and lower levels of matter.

(c) Infinite dimensionality. There may be endlessly many dimensions.

Q: How big is the infinity of our universe?

A: In the previous answer I was coy about the range of k and the meaning of “infinity”. But if I say our physical world is infinite, which level of infinity do I mean? As a set theorist I know of lots of options. Here are four that come to mind:

(i) Alef-null, the smallest infinite number, the cardinality of the set of natural numbers.

(ii) c, the power of the continuum, that is, the cardinality of the set of real numbers. Note that the size of c is at least as big as alef-one, which is the first infinity after alef-null. So far as we know, c may be very high up in the alef hierarchy, indeed it could even be as big as . But some present-day set theorists like Hugh Woodin feel c is alef-two. As I recall, in White Light, I espoused this belief, which was also advocated by Kurt Gödel.

(iii) , the class of all ordinals, which Georg Cantor calls Absolute Infinity.

(iv) The size ηΩ of the Absolute Continuum, where I use the terminology of Felix Hausdorff . This would be at least as big as . I discuss the Absolute Continuum in my book, Mind Tools, it is a class of points in which you can find another point between any two sets of points. An Absolute Continuum is a proper class which contains embedded into it every possible set-sized order type. It’s moot whether or not you can well-order the Absolute Continuum as a whole, so it’s not necessarily true that it can be mapped one-to-one onto Ω.

Q: So which infinity is the size of our space?

A: A cautious idea is to settle for alef-null stars, alef-null levels, alef-null divisibility, and alef-null dimensions. In this case, however, the infinite overminds are not really transfinite; they have size alef-null. If they like, they can arrange themselves into countable transfinite order types such as ω + ω and get a weak kind of transfinitism, but even so, it would be questionable in this case whether I could justify calling the third novel Transfinite as I would like to.

Or I can rush to the higher extremes and say that I’m after Absolute Infinity, or ; after all, this is SF, why hold back. In White Light, my character went out to .

Perhaps this time around I’ll require even more. I’d like the higher infinities to be immanent, embedded in our immediate surroundings, in my finger tips. And I can do this by saying that our physical space is Absolutely Continuous, at least in the small, that is, in terms of divisibility.

Given that I would prefer a symmetry between large and small, this also entails that the physical world is Absolutely Infinite, and that it extends past alef-null, alef-one, and so on, star upon star. A principle of plenitude is in operation here.

The following issue comes up in this case. If I say our space is a proper class, then I have to wonder if the immortals proper classes or merely transfinite sets? I suppose I’d have them be merely transfinite sets, so that they, like us, still have higher levels to aspire to. Alef-null’s ceiling is alef-two’s floor…

And we could then have a higher Divine which is a proper class. This would lie over and above the transfinite immortals; akin to Meister Eckhart’s Godhead beyond God.

Q: How do the two branes of Postsingular fit in?

A: I have set it up so that reality has two (and only two) parallel branes: the Lobrane and the Hibrane. Perhaps the immortals are transfinite minds based upon the Lobrane, and the less pleasant subbies are minds based upon the Hibrane. Each brane can be an Absolute Continuum.

The paired branes are the underlying dyad that drives creation. Yin and yang.

10 Responses to “Transfinite Minds”

  1. Kelson Philo Says:

    I must ask, what is that delightful looking rectangle beneath the first photo? It’s swirl (gnarl?) is stunning.

    Your thought process on the immortals is intriguing, what is the name of the snake that eats it’s tail, ouruboros(sp?)? Not to call them ‘ouruborians’ or anything, but for some reason, i thought, add an ‘ell apostrophe’ to it, “French-ify” it if you will. Because it just seemed right that such a creature would be able to speak in beautiful flowing tones…And once that was done, it suddenly seemed very close to ‘Lobrane’…

    Downward Infinity certainly sounds a bit like a cosmic looking glass of sorts. Very peculiar indeed…

  2. glenn branca Says:

    Can there really be a direct correlation between mathematics as we know it and human conciousness?
    Can the infinite in fact exist? Or is it just a product of our imaginations?
    Is it not possible that our world (universe) is a dying lifeless desert that we are stranded on?
    Is every moment of our lives a manifestation of some “magic” that we are far from understanding?
    Could the dim light of our lifeforce ever illuminate a whole universe?
    Are these animals that populate our planet under the name homo sapien anything more than murderous thugs and theives?

  3. Rudy Says:

    Glenn, my goal in SF is to what-if about ways the world could be more fun. Like having infinity be real. Could be. Why not? I’ll write the story just to see how it might work out. Thought experiment!

    As for humans being murderous—hey, we’re omnivorous terratorial animals, whaddaya want. I saw some Humboldt squid on the news last night who looked every bit as ruthless as us. I could watch them for hours.

    Kelso, the swirl is a Borneo door. In general, you can find out the origin of any of my images by typing its name into the blog Search box to find the first time I posted it, when it’s usually explained. Get the image’s name by right-clicking on the image, selecting Properties… and then dragging the corner of the Properties box so it’s big enough to show the image name. You only need to search for the file name, you don’t need the “” prefix or the “jpg”. So in the case of that swirly image you’d be searching for ngdoor. And you’d get this page:

    And on this page you’d click the earliest entry and find the source.

    I reuse my images a lot. My personal deck of Tarot cards.

  4. Kelson Philo Says:

    Haha! Thanks!

  5. rs Says:

    Now that is some rich sh-t to think about.

  6. Element 5 Says:

    Are you keeping up with what’s happening with the “drones” that have been spotted lately, along with the corresponding “Isaac” documents? The documents show a very odd looking text which is supposed to act as self-actuating software when paired with the incredibly detailed material that the drones are made of, a very curious form of sophisticated computing that finds a parallel in your “runes”. You might want to look into (and lock onto) this.

  7. Mac Tonnies Says:

    The “drones” are fakes — but *interesting* fakes with some appealing backstory. Someone put some time into this.

  8. mike3 Says:

    “Can there really be a direct correlation between mathematics as we know it and human conciousness?”

    Don’t know.

    “Can the infinite in fact exist? ”

    I think so. Although one might not be able to prove it,
    it still seems *possible*. Who’s to say the physical universe
    is the whole story?

    “Is every moment of our lives a manifestation of some “magic” that we are far from understanding?”

    Wouldn’t call it magic, but there could be a force that
    runs things that is far beyond our ability to grasp.

    “Could the dim light of our lifeforce ever illuminate a whole universe?”


    “Are these animals that populate our planet under the name homo sapien anything more than murderous thugs and theives?”

    Considering that not every single human being out there goes out
    and murders his fellow human being, I’d have to say yes, they
    are something more.

  9. John Snazelle Says:

    -Can the infinite exist? Yes. It may be in only a mathematical sense that it exists, but this mathematical sense must be taken as one of the proper, if qualified, senses of “existence”. Otherwise we would not be able to make sense of our mathematical propositions. When we say that there is no largest prime number, we are saying that a certain kind of prime number cannot exist. But what would it mean to say a certain kind of number does not exist unless we already presupposed that other kinds of numbers do exist? It is not only the existential quantifications and singular terms that carry some kind of ontological committment in mathematics, but also the assertions of non-existence. Being is contrast, which means that without some contrast there can be no Being. But the same is true of non-Being. Without some Being with which to contrast, what would we mean when we signified non-Being? Likewise, without an existence with which to contrast, what would we mean when we tried to talk about mathematical objects that cannot or do not exist? But we clearly can and do talk about things in mathematics that cannot exist, such as the set of all sets, or the set of all propositions. And we meaningfully contrast these things with other things that do exist, like the set of all natural numbers or an equilateral triangle. One could respond by saying that such things exist only in the mathematical sense, but that’s fine. Other than some relative, restricted sense of existence, what else could there be? World-indexed properties and world-indexed existence is all even concrete, physical beings like us can aspire to. There is only one Absolute, and of It it cannot meaningfully be said either that it exists or does not exist. At any rate, the direction of contemporary physics seems to be asymptotically approaching an ontology every bit as bloated as plenitudinous platonism, which in my opinion is great. If the physics of information is correct, we are justified in the kind of “patternism” Rudy was already proposing more than thirty years ago: even physical objects are ultimately patterns, and every pattern is a mathematical object.

  10. Derek Says:

    John kills the dialogue once more 😉

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