As I mentioned in “Against Recurrence #1” contemporary cosmologists are inclined to say that the space of our universe is infinite. The whole infinite space was effectively filled with a giant flash about four billion years ago.

In 2008, I was interested in a fairly simple model for this called the cyclic universe. Invented by Paul Steinhardt and Neil Turok, it basically postulates a pair of “branes” that oscillate back and forth, periodically passing through each other and thereby filling all of infinite space with a revivifying and reseeding flash. I posted about it several times, and I even discussed it on the phone with Steinhardt.

Eventually, Bruce Sterling and I even wrote a story based on this idea, it was called “Colliding Branes,” and you can read it online. I sent the story to Steinhardt, but he never wrote me back. I guess he was like, “That is not what I meant at all. That is not it at all.”

Click for a larger version.

Now, in 2015, the cyclic universe model seems to have lost ground to the eternal inflation model that I mentioned the other day in “Against Recurrence #1“. This is the idea that one speck of supermatter expands forever, and that successive regions of space “boil off” from the expanding speck, creating a diagram like the one I found in Max Tegmark’s book—I’m showing it here again, and I’ve added a drawing below.

We’re looking at a spacetime diagram, with time running up forever. The idea seems to be that the one little scrap of “starter dough” has two regions that last forever, shown on the left and the right. The “steaming off” galaxies from the starter dough keep endlessly appearing, each with its own timeline that in turn bends up and runs toward eternity. The poor saps in these galaxies (us) imagine that all of them arose at the same time. The other tricky angle is that that finite-looking space inside the “U” between the two borderlines—that space is unbounded, and in fact infinite.

Back in the ‘50s and ‘60s some cosmologists used the word ylem to refer to the starter dough, so I might use that word here too.

Really this drawing should be shaped more like a V than like a rectangle, the idea being that the horizontal dimension is tiny and finite at the bottom, and it opens up endlessly as we run up the pseudotimeline of the ylem blobby. But, as I say, we see that whole U-line as being the one moment of universal creation of an endless world.

And it’s the quantum fluctuations and wriggles in the starter dough that are seeding the infinitely many galaxy births. In other words, the starter dough contains an infinite amount of information.

What gets me attention is that the eternal inflation model is in effect ascribing infinite complexity to that finitely large initial glob of ylem. This tends to support a view of mine which is, these days, complete out of favor with scientists. That is, I advocate the doctrine of “infinities in the small.”

The current philosophy of science is dominated by the pernicious and unreasonable doctrine that space and time are quantized into pixels. But why should we believe this? It’s like the situation where, to a hammer, everything looks like a nail. We use computers, so to us everything looks like a computer screen.

Quantum mechanics is only one stage of our ongoing exploration of the world. Inevitably we’ll move beyond it, onwards into the subaether, the subdimensions, the ultra particles, the rootless tree of matter, the absolute continuum, whatever. If the universe is infinitely large, why can’t we have infinities in the small? If the primordial ylem contains infinite information, then why shouldn’t the tip of my finger?

Regarding physical infinities, here are two relevant quotes from Georg Cantor, the founder of set theory, which is the mathematical study of infinity.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.

—-Georg Cantor, writing in the 1880s, passages translated by me for my nonfiction book, Infinity and the Mind.

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Okay, fine. At this point you might wonder why I’m so obsessed with arguing for infinities in the small. Well, my issue, once again, is that, if we are going to have an infinite space with infinitely many planets, I don’t want to frikkin’ squander this endless grandeur on lame-butt wallpaper-like repetitions of the same things over and over and over. I don’t want the cosmos to be sit-com reruns. I want our infinite space to be filled with infinitely many worlds with no two alike! And if each of us is in fact an infinite being, then it’s clear that there’s no need to repeat. QED.

And now we get to my real underlying purpose in these posts. I’m working on a novel called Million Mile Roadtrip. My teen characters are in a car on an alternate universe that has the form of an infinite more-or-less flat plain (albeit with mountains and seas). The plain is divided into basins about ten thousand miles across. Each basin is, in effect, like the surface of a new and different populated planet, no two the same.

My question is this: what is the process that seeds a universe with an endless number of different worlds? Where does all that tasty info come from?

I’m not at all into the defeatist shoulder-shrugging non-explanation along the lines of, “Well, there’s infinitely many planets, and each one is completely random, the product of quantum coin flips so pretty much everything possible has to crop up.” This multiversal line of thought is currently much in favor, but I don’t like it. I want some frikkin’ answers, man!

[Rings from Isabel Jewelry.]

Although it’s not quite relevant, I’ll quote from an 1880s essay by Hermann Schubert, attacking the then popular spiritualist notion that there are ghosts which live in the fourth dimension. Schubert winds up his essay with these stirring words:

The high eminence on which the knowledge and civilization of humanity now stands was not reached by the thoughtless employment of fanciful ideas, nor by recourse to a four-dimensional world, but by hard, serious labor, and slow, unceasing research. Let all men of science, therefore, band themselves together and oppose a solid front to methods that explain everything that is now mysterious to us by the interference of independent spirits.

Great rhetoric. To make it fit what I’m talking about in this post, I’d need to change “independent spirits” to “unseen, endlessly spinning roulette wheels.”

What if we say that there is only one universe, and its infinite, and it’s not random at all, no, it’s filled with lovely, beautiful forms such as might be crafted by an infinite, omnipotent, eternal Mind? What if our universe is a supreme work of art? [Religion alert! Angry buzzers! Flashing red light!]

But wait. What if the supreme mind isn’t some distant, bossy God. What if the Mind is omnipresent, an ocean in which we swim, a great dance in which, by thinking our own thoughts, we participate. What if you’re infinite—and you made the world? Look within yourself. Could it really be otherwise?

Okay, fine, I enjoy writing mystical effusions, they get me high. But then I like to try and tighten it down a little more. What would be a reasonable process by which some great Designer might come up with endlessly many cool planets without having to comb through a superexponential amount of junk?

My Twitter follower R. R. Mutt reminded me of a recent article in the New Yorker about a guy, Sean Murray, who’s using what they call a “procedural algorithm” to generate endless numbers of planets for the artificial world of a forthcoming videogame, No Man’s Sky.

The idea is to come up with an algorithm that accepts some random parameters, and use that for creating your endlessly many populated planets. The desiderata are that (a) the algorithm produces something fairly reasonable-looking no matter what the parameters are, and (b) the algorithm’s parameter space contains many bifurcations—meaning that different parameters can produce totally different-looking worlds, and (c) the parameter space’s basins of attraction have a fractal quality, meaning that, by digging down into more and more precisely specified parameter sets, you can obtain infinitely many interesting and distinct outputs.

The DNA in our cells is, in a way, a parameter set for the procedural algorithm of life on Earth. And the algorithm is very richly sensitive to the parameters.

I once heard the biologist Richard Dawkins talk about the pre-Cambrian explosion of new species being sparked by something that somehow enhanced the “evolvability” of the organisms.

So as universal gods, we’d need something like DNA, but better—for spinning out an endless range of cool worlds.

And that’s all I’ve got today!