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Against Recurrence: #2

May 28th, 2015
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I’m nowhere near finished reading Max Tegmark’s fantastic new book, Our Mathematical Universe, and my thoughts are still evolving. The stuff I’ve been discussing is in Chapters 5 & 6. of Tegmark’s book. Today’s post follows up on my post “Against Recurrence”: #1.” And I’m prompted to say more by the good comments on that post.

What I’m talking about has to do with how we might emotionally “feel” about the idea of an infinite universe that may contain identical copies of ourselves. I don’t like the idea of identical copies of me, it seems wasteful, and in some sense it makes my life seem pointless.

Rather than wholly giving way to emotion, however, I want to reason about the recurrence proposal. So, once again, the idea is to go with the idea that we have an infinite number of stars and planets and see where that takes us.

It’s hard for us to grasp how really big an infinite set is, and how strongly it differs from a finite set. If you get infinitely many tries, you really can expect to flip a googol heads in a row.

If we say the universe is akin to a 3D chessboard made up of minimal spacetime cells, and if we say that each cell can only be in some limited number of states, then our local visible universe volume is akin to an array of numbers, and therefore in the endless number of “hands of cards” that infinity deals out, it’s quite possible that the same pattern could re-emerge, and not just once, but many times or infinitely many times over.

As I say, my (emotional) issue is that it seems like waste to have an infinite universe and then to be cluttering it with repetitions of things. So I’m alternating between (a) looking for a way out and (b) coming to accept this.

One way out, as I already hinted, might be to argue against the cell-grid image of spacetime. I think such a worldview has more to do with our current cultural obsessions than with ultimate reality. A lot of scientists are, after all, geeks. People lacking in empathy, or in a poet’s “negative capability” for tolerating ambiguity, or in a relish for old-fashioned sloppiness. People who want things to be orderly, straight, square, lined up. (And, admittedly, as a mathematician, I myself have tendencies in that direction—counteracted, of course, by being a beatnik SF novelist.)

Even if we suppose there’s a smallest possible space size and a smallest time length — that is, quanta of space and of time — would these quanta really be arranged in a dry, precise grid? Not likely. Nothing in nature is dry and precise. Look at moss on a stone, look at the leaves on a tree, look at the sand on a beach. Nature duplicates herself—but only approximately.

Natural systems are chaotic. A waving leaf, a fluttering flag, a human heartbeat, or one’s flow of thoughts—in the analog idealization, these processes never ever repeat themselves. Even though, in a rough qualitative sense, they’re always doing the same thing. Chaos theory is a great teacher. Always different, yet always the same. That’s a viable option. You’re surrounded by seeming sameness in daily life but yet—ah, but yet—nothing is ever really same. You never step twice into the same river. The world is continually dancing, unfolding, jiving, and coming up with fresh variations.

Temporal sequence is a source of variation as well. It may be that, once in a blue moon, a fluttering flag takes on what seems to be the same configuration. And it may be that, at certain deja-vu-type times you feel like your head is right back where it once was. But then the next tick of time feeds in and, ah yes, the progression is, after all, different than before.

So what about the boring, jive-ass, Lego-like grid of spacetime quanta postulated by our contemporary cult of the mighty Computer? I’m saying that, far from being like 3D or 4D graph paper, we’d be looking at something more like the slightly wonky and irregular units of a honeycomb or knit scarf, with the spatial locations of cells jiggling or moving around as time went on.

How might we express such an irregularity in the spacetime cells? Well, under the current scientific dispensation it wouldn’t be kosher to talk about analog real-number distances between he cells—although I’d like to. We might to turn to something more digital like, say, “adjacency.” This brings us to the mathematical disciplines of “graph theory” or, better, “network theory,” which look at structures made of vertices (spacetime cells) with lines (adjacencies) connecting some of them.

But if we take the network theory route, we’re still stuck with the visible universe being a finite digital pattern. Rather than a 3D graph-paper-like grid, it’s now a heap of dots with lines connecting them. So we’re still stuck in Squaresville. Recurrence Land.

But wait. Let’s go back to the idea that the network is dancing, with connection lines popping in and out of existence. A Big Aha here, a Small Aha there. “Have you met my friend?” “I’m never speaking to you again.” “Let’s do-si-do.”

You might find a finite region within our infinite space that momentarily looks just like our current home region. But then, ah yes, with the next tick of time, our visible universe and the twin visible universe would progress on to different states.

Cornered now, the world-numbing advocates of Recurrence might protest, “No, that can’t happen, physics is deterministic, and any two momentarily identical systems have to stay identical forever after.” Not true. For two reasons. (a) Any region of space is going to be receiving inputs from the rest of space. Noodges and jiggles that upset and scramble whatever teetering Cat-in-the-Hat pile of plates you’ve got. (b) Even if there were nothing “outside” of these two seemingly identical regions of space—even if we were talking about two identical pocket universes—we still have the saving fact that Physics is not deterministic.

What? Not deterministic? Live by the sword, die by the sword, quantum mechanics!

Yes, stodgy, boring, spoil-everything, quantum mechanics insists that we can’t have wonderfully smooth and infinitely variously marbled matter with patterns all the way down into gloriously infinites subsubsubsublevel after subtillionlevel. But QM also delights in saying that physics is fundamentally random—in the sense that any observation that chooses between two options produces completely unpredictable outputs. The refer to the built-in randomness as the Measurement Problem. They love to get all ecstatic and mystagogic and woo-woo about it. “The QM universe is stranger than anything we can possibly imagine.”

“Measure this, mofo.” The fickle finger of Fate appears in zombie universe B, stirs the porridge, and, having writ, rocks on.

But…might it not be that, among all the seeming identical copies of our visible region’s Now Moment, there would be some other, particularly dogged, zombie regions that are tracking our moves? And here, ah yes, we’re saved by Mamma Mathematics.

If we accept the digitization of space, the number of possible visible regions in an infinite space is going to alef-null. The lowest level of infinity. But—even accepting the digitization of time—the number of possible future universe-histories is then going to be 2alef-null, which is known to be a transfinite number larger than alef-null.

Georg Cantor, father of our strange transfinite country, thought this higher-order infinite number would be alef-one, but these days, the mathematician hep-cats think it’s more likely to be alef-two. Bigger than alef-null in any case.

And this means that, in fact, the probability of finding another volume of space that behaves just like ours forever is 0. Not absolutely impossible, you understand, but an event so unlikely that the probability is formally 0.000000000… With those no-effin’-way 0’s running out forever. We’re risen from the tomb.

These posts are rhetorical as well as scientific!

By the way, ahem, there can be regions that behave just like us for arbitrarily long finite times—a different region for each specified length of time—wihout there being any region that matches us forever. But any given region eventually divergees from us. I might say more about this somewhat subtle point later.

Math is strange and wonderful. I look forward to reading the rest of Max T.’s book which, after all, has Mathematics right in the title!

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Against Recurrence, #1

May 27th, 2015
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Today I’m returning to a question that’s nagged at me for about fifty years. You might call it the question of recurrence.

Would an infinite universe necessarily contain identical copies of me?

My post today uses some of the material that I wrote for the preface of the 2004 edition of my nonfiction book, Infinity and the Mind.

As is usual for my blog posts, most of images I include will have nothing to do with the text. At least not at the conscious or deliberate level. At the intuitive and synchronistic level, of course, each of them is a sly commentary and a perfect fit.

I’m thinking about the issue of recurrence again because I’m reading Max Tegmark’s wonderful 2014 book, Our Mathematical Universe. It’s the best popular science book I’ve read in ten or twenty years. You can find some of the same ideas in a 2003 article by Tegmark, “Parallel Universes,” in Scientific American.

Right off the bat, let me point out that there’s no mathematical certainty that a supertraveler across endless space with endless galaxies would necessarily find another Earth just like the one right here. Consider for instance an infinite set of integers which has only one odd member, the number 3. Someone who starts at 3 and looks for another odd number is going to be disappointed.

{2, 3, 4, 6, 8, 10, 12, … , 2n, …}

So, as a mathematician, I’ve always bridled at the physicists’ claim that an endless world has to repeat. An infinite set doesn’t have to exhaustive.

As a higher-order rebuttal to the tedious insistence that an infinite world must repeat, I’d also point out that it might be that the objects in our world are in fact infinitely complex—and are not like the Lego-style pixel-by-pixel structures that physicists like to image them to be. If matter is endlessly smooth, then there’s room for endless, non-repeating variety.

But let’s look at Tegmark’s reasoning before I argue about it any more. The thing to keep in mind is that nowadays many cosmologists believe that our space really is truly infinite, with an endless number of stars and planets. The initial Big Bang singularity is to have happened not at any single point, but across an infinite space.


Click for a larger version.

If the old image of the Big Bang was like a white dot appearing in a plane, the new image is like an entire endless plane becoming suddenly illuminated in every part. You might visualize a sheet of light settling down upon the plane.

More precisely, Tegmark describes a sequence of events before the big bang: a tiny bit of darkly energetic supermatter undergoes an insanely rapid inflation which will last forever. The inflation fills out a finitely wide region of space and an infinite amount of future time. And what we perceive to be the big bang is a long, skinny, infinitely extended U-shaped hypersurface within the inflationary zone.


Click for a larger version.

Very hard to wrap your mind around this, but Tegmark gives a good presentation of the idea in Our Mathematical Universe, using the figure shown above — which is © Max Tegmark, 2014.

So what we call the Big Bang is that bumpy U-shaped line between the light (inflationary) zone and the dark (normal space) zone. And from our perspective that line is one simultaneous moment that happened fourteen billion years ago. And it’s infinitely large.

I’m going to have to talk about some very large finite numbers now. And the way we do that is with exponents. But it’s hard to show an exponent in HTML. So instead we’ll use a caret symbol, like ^, to mean “to the.” That is, we can think of 100 as 10^2, and 1,000,000 as being 10^6. Fine. And now we’re going to go crazy with this.

The region of our endless space that’s presently visible to us is a sphere with a diameter of some 10^27 or one octillion meters. (I should mention that the standard name for a number of the form 10^((k+1)∙3) has the general form k-illion.) This octillion-meter-wide sphere, which we can call our home volume, contains those objects that are close enough so that light from them has had time since the Big Bang moment to travel to us.

Suppose we make the unexceptionable assumption that our home volume has an average temperature of less than a hundred million degrees centigrade (the sun’s surface is a mere five thousand degrees centigrade). In this case, according to Tegmark, the home volume has room for some 10^118 protons. To get a handle on this number it’s useful to use the number googol, which is written as a one followed by a hundred zeroes, that is, a googol is 10^100.

10^118 = 10^(18 + 100) = 10^18 x 10^100 = 10^((5+1)∙3) x 10^100 = quintillion googol.

Now we can wonder how many distinct possible home-volume-sized regions there could be. Okay, this is where Tegmark and his camp “beg the question,” that is, this is where they slip in the conclusion that the want to reach, importing their eventual conclusion as a plausible observation about the state of affairs.

Here it is: “We can think of the home volume as a jungle-gym grid with a quintillion googol slots. One can specify an arbitrary random visible universe by deciding what to put in each slot — one might leave a slot empty, put a proton or neutron in there, or perhaps stick in an electron or some other kind of particle.”

So, okay, I’m going to argue with that. But for now, let’s follow the flow of the Tegmark argument.

To keep things reasonably simple, let’s suppose we have ten alternate ways to fill each of the quintillion googol proton-sized slots. In that case, the number of possible ways to populate a home volume with matter consists of choosing among ten options a quintillion googol times in a row, which is ten to the quintillion googol power. In describing this number, it will be useful to use googol’s big brother, the googolplex, which is a number written as a one followed by a hundred zeroes. If googol is 10^100, then googolplex is 10^googol, or 10^(10^100).

10^(quintillion googol) = 10^(10^118) = 10^((10^100)x(10^18)) = (10^(10^100))^(10^18) = googolplex^quintillion

So now we know that there are at most googolplex-to-the-quintillion possible versions of how our visible universe could appear. A large number, yes, but if our universe is truly infinite, there will be an infinite number of possible home volumes besides ours, and it seems likely that one of them could be an exact match for your own. (Although, again, this is not a certainty.)

How far off might the first copy of our visible universe be? One idea might be to set out in a straight line and whip through the first googolplex-to-the-quintillion home volumes. Just for fun, let’s give this distance a made-up name: one striiide. Given that a home volume has a diameter of a octillion meters, a striiide is an octillion googolplex-to-the-quintillion meters. Would traveling this far guarantee a hit? Not quite.

A little calculating of probabilities indicates that if I travel one striiide, I have a 63% chance of encountering a home volume exactly like the one I started from (the precise probability is very close to 1 – 1/e, where e is the base of the natural logarithm). But as I travel more striiides, the odds go up, and after ten striiides, my chances of having found a visible universe exactly like ours is better than 99.99%.

So, the argument concludes, if the universe really is infinite, then there probably are other people exactly like us somewhere out there. I find this reductive and dispiriting—but I suppose someone might view it as liberating. Like, even if you goof up your life, some other you will get it right?

Nah, to hell with that. It’s like saying nothing I do in my life matters because one of these days I’ll be safe in heaven. Don’t bet on it!

In my next post, maybe next week, I’ll say more about how we might evade the dull Lego-block view of our world as being finite in the small. If it’s infinite in the large, why shouldn’t we be enjoying infinity right here and now. Right in our bodies, and in our minds!


Click for a larger version.

Your mind is an infinite Jackson Pollock. Stay tuned.

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Photo Bin: N.Herbert, Occidental, SF, Journals.

May 25th, 2015
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I have a lot of old photos that I never got around to putting into a post. So I thought I’d reduce my inventory in a few long Photo Bin posts.

But first a word from your sponsor.


Click for a larger version of the book cover.

Nice blurbs for my Journals from two of my friends.

“The publication of Rudy Rucker’s Journals beautifully supplements his astonishing autobiography, Nested Scrolls. For anyone who has marveled at Rucker’s gonzo, idea-rich fiction, this behind-the-scene account of his daily inspirations, brainstorms, detours and dead ends will be essential reading. But far more than that, it shows us the essential man behind the keyboard, so to speak: father, husband, citizen of the galaxy.”
—Paul Di Filippo, author of The Steampunk Trilogy.

“Rucker’s Journals are great. I fear he will be famous, long after he’s gone, for providing the best picture of late American society. Out peeps Pepys.”
—Terry Bisson, author of Any Day Now .


Click for a larger version.

Two days ago at midnight I learned how to use the pan function of my Fuji X100S. I like seeing my foot at ease there.

The next five or six photos are lo-fi iPhone 5 photos from yesterday. As they say, the best camera is the one that you have with you that day. But I do feel regret when I’m somewhere interesting with only the iPHone.

A passel of punk stickers on…some technical object. Along Bear Creek Road between Boulder Creek and Los Gatos, where there’s this one pull-out and you can look out across the big basin and see all the way to the open waters of the sea.

A skull in the Boulder Creek sage/hermit cabin of Nick Herbert, a.k.a. Frank Shook.

Saint Nick himself. Nick wrote a brilliant popularization of quantum mechanics: Quantum Reality. And his profound paper, “Holistic Physics: An Introduction to Quantum Tantra” is so important a key to my work that I keep it handily available online on my site.

My novels Frek and the Elixir, Postsingular, Hylozoic and The Big Aha were all profoundly influenced by this epochal paper.

Why isn’t Nick better known? Jorge Luis Borges put it in his essay on Herman Melville: “’Vast populations, towering cities, erroneous and clamorous publicity have conspired to make unknown great men one of America’s traditions.”

A superheterodyne laser collimation unit on Nick’s ceiling.

Two nuts.

And now back to the Fuji x100T.

Me lying on the grass staring lovingly into the lens of the new toy. Like a high-school swain on his first picnic date.

A bottle of Tide with someone’s fingers.

Mandatory calibration shot of Zhabotinsky geranium leaves.

Fuji-seen light through a towering oak.

The rest of the shots in today’s post are from my old Sony RX100, presently laid low by zoom-barrel jam.


“Hell Courtesan” scroll, ~1850, by Utagawa Kuniyoshi ( Click for a larger version of the painting.

Saw this at the Asian Art museum show “Seduction” in SF. Utagawa Kuniyoshi is awesome. He did about six paintings of the “Hell Courtesan,” a legendary geisha who was converted to a higher way by a Zen monk. Here’s a diffuse but interesting post about zen monks and prostitutes. I saw a post somewhere with a giant tattoo of the monk and the courtesan, but I can’t find it now.

Manhole mural inside the Coit Tower.

SF is full of nice ironwork.

Classic EAT sign at Gott diner at the Ferry Building in SF.

Children’s birthday-party hats. Wee wizardry. I always love the reflections of curved surfaces.

Ah, the heart’s nostalgic clutch at the sight of long grass and a motorcycle-tire swing.

This was in the nice AirBnB cottage where Sylvia and I stayed near Occidental, CA. The lady of the estate, Marylu Downing free-hand painted this great star on the wall. Her husband, Roger House, did great proofing work on my Journals.

Heaven for cows around here. I always tell the kids that after I die, I’d like to be reincarnated as a cow on a slope above the Pacific. In Big Sur maybe, or maybe above Bolinas here. That cow is me in twenty years. Another good reincarnation option would be as a pelican. Pelicans as the Hells Angels of the sky. Trundling past in a flying V. Vooden vooden.


Click for a larger version.

Panorama, seen from the road to Bolinas from Occidental, Coleman Valley Road. Cosmic, uplifting, beyond the beyond. And really only a couple of hours from our house.

Big stump at the mouth of the Russian River, where it hits a sandbar island and trickles into the sea.

Lone windblown Monterey pine near Bolinas Head.

Photogenic sail off the cliff of the Bolinas Head. So heart lifting to stand there in the wind. We have lots of room, lots of room.

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Art Show. New Paintings. Fujifilm X100T Camera.

May 23rd, 2015
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My art show at Borderlands opened this week. It’ll run through July 6. We’ll have a reception part on Saturday, June 13, at 3 in the afternoon. We’ll hang out, I’ll do a reading from Journals 1990-2014, and give a little tour of the paintings.


Click for a larger version of the poster.

And here’s a panorama shot of one of the walls in the Borderlands cafe.


Click for a larger version of the pan shot.

Many thanks to Rudy, Jr. and fellow Monkeybrainer Devin for helping me set up. No way could I hang all these paintings alone. You can find prices on my Paintings page.


“The Sage and the Messenger” oil on canvas, May, 2015, 28” x 22”. Click for a larger version of the painting.

Over the last couple of weeks, I finished two new paintings for the show. The Sage and the Messenger relates to a short story I’m working on with Bruce Sterling. One of the characters is sage or hermit who lives inside in a hollowed out spot high up in the trunk of a sequoia tree. And a artificial biotweaked organism comes to bring a message to him. Wanting to lure him into a wild and hare-brained adventure. The messenger iss a thing like biological drone, or like a flying jellyfish. I like the interplay of the expressions among the sage, the jellyfish and the squirrel.


“Cells” oil on canvas, May, 2015, 24” x 24”. Click for a larger version of the painting.

About four days before the show I dove into Cells. I had no real idea what I’d paint when I started. First I did an underpainting in acrylic with a heavy gel medium to get some texture, and to have some extra color glowing through. But I don’t like how flat acrylic looks, so I layered an oil painting on top of that. I outlined some blobs in my original painting, and then filled them in to look like living cells. I used a fan brush for the halo effect, and I flicked the bristles of the fan brush to add some life with splattered dots.

A big push.

My old Sony RX100 camera died this month. The telescoping zoom lens seized up and won’t properly go in and out. I’ve had thee or four pocket digital cameras die in this same way. The lens is a definite weak point. When it breaks, it costs almost $200 to fix, so it’s questionable if that’s worth doing. So I decided to get a small “prime lens” camera, that is, a camera with a non-zooming lens. So there’s not the telescoping crap to break.

I sold a couple of paintings this month, so I splurged and went for a Fujifilm X100T. It’s a compact digital camera (despite being called Fujifilm), solid, great lens, solid metal frame, and with a nice old-school look, kind of like a vintage Leica M-Series camera, but at relatively reasonable price. Not a pocket camera, but it’s small and light.

So I’m going around taking lots of pictures. Some reviewers like to gush that the camera is so good that they use the X100T images just as they came out of the camera. Me, I pretty much run every single shot though Lightroom and/or Photoshop. That’s my work flow. That way I can crop, possibly lighten the shadows, maybe sharpen the image or warm the tone. But this particular shot is right out of the camera. A sweet shop.

I call this terrifying “hand puppet” Cousin Millie. I’ve been showing her to my kids and the grandkids for years.

And the camera is automatic enough that you can hand it to someone that the shot comes out good. I’m till learning the ins and outs of fine points of the controls. The (online PDF) manual is well over two hundred pages long.

The thing about walking around looking for shots is that I dig below the smooth familiar reality to find little bits of oddness. A dial with numbers. What might this mean?

You can never go wrong photographing street-workers’ markings on the asphalt.

Midnight in the china closet. The X100T really fills out the three-dimensional space.

Exultant in son Rudy’s car, riding through the Mission after my paintings…with my new shooter in hand.

I’ve photographed these phone/electric/cable lines a dozen or more times over the years. I think this one is better than usual. Thank you Fujifilm!

My grad-school friend Jim Carrig’s son Eamon showed up the other day. I took him to San Jose’s finest fast food stand, named simply Falafel. It’s on Stevens Creek Blvd near Bascom Ave. They’ve been there since 1966. Wonderful, wonderful falafel. Green inside, freshly cooked and mashed beans, crisp on the outside, hot.

Eamon Carrig himself. He’s started a company that’s designing small robotic sail boats. Sailing drones for the high seas.

Weirdly enough a woman reporter named Leona was at Falafel. She’s from LA, but is writing an article on falafel restaurants in California for Brownbook magazine, published in Dubai! Once the sheiks hear about Falafal of San Jose they’ll be jetting in no doubt.

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