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“Simply Gödel,” Phenomonology, and Monads

March 17th, 2017

I recently read an advance copy of a great book by my friend Richard Tieszen. It’s called Simply Gödel. It’ll go on sale in mid-April, but you can pre-order now if you like. The book is a remarkable achievement—a handy guide with the impact of a philosophical tome. It’s all here: elegantly lucid discussions of Kurt Gödel’s epochal discoveries, a sympathetic account of the eccentric genius’s life, focused discussions of his encounters with his astonished peers, and a visionary peek into the future of mathematics, philosophy, and the on-rushing specter of robots with minds. A compact masterpiece, brimming with fresh revelations.

I’ll discuss some of my thoughts sparked by Simply Gödel today, adding some of my paintings to the illos, including two new ones.

As I’ve mentioned in my blog posts “Memories of Kurt Gödel” and “Conversations with Kurt Gödel,” in 1972 I had a couple of long talks with Gödel in his office at the Institute for Advanced Study. He made a huge impression on me. It goes almost without saying that he was the most intelligent person I will ever meet. Even though he was, at some lower levels…eccentric.


“The Wanderer,” acrylic on canvas, 24 ” x 18 “, September, 2008

How so? Gödel had very unusual views on the nature of reality. He firmly believed that there are indeed higher levels and higher beings—things like ghosts or demons. Indeed, he felt that a person is in some sense an extradimensional being that might be called a monad, after Leibniz’s use of the word. A monad affects the physical world, but it’s not embedded in the spacetime framework. A bit like a soul.

At less philosophical levels, Gödel could be paranoid. He worried that poison gases emanated from his refrigerator or from his furnace. He worried that strangers might be assassins who planned to kill him. He worried that his food was poisoned—and he preferred not to eat anything unless his long-suffering wife Adele had tasted it first.

But these aspects of the man weren’t apparent when he was talking about mathematics, science, philosophy, and mysticism. To me, he seemed like a man of knowledge and wisdom, profoundly so.


“Origin of Life” acrylic on canvas, March, 2017, 30” x 20”. Click for a larger version of the painting.

Shown above is a painting of me talking to Gödel in 1972. Well, actually it’s a painting of an abstract image based on a cellular-automaton screen I recently captured, characterized by having double scrolls known as Zhabotinsky patterns. See my previous post, “Still Seeking the Gnarl,” for more about these CAs. These patterns occur naturally in certain chemical mixtures, and they could have played a role in the origin of life within the primordial soup. So I called it “Origin of Life.” But, who knows, maybe it is me and Gödel. Monads in an extradimensional space of phenomenological impressions. But which one is me?

Gödel was Einstein’s best friend during the physicist’s later years in Princeton. Why? Probably Because Gödel was the one person who could readily understand what Einstein was talking about. And perhaps because both of them had made a priori intellectual discoveries that changed humanity’s way of seeing the world. But Einstein wasn’t above teasing his younger friend. Here’s a quote from Ernst Gabor Strauss, taken from Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel.

Reading Tieszen’s great Simply Gödel got me thinking about all these things again. If we have souls and telepathy, maybe Gödel is still talking to me. Helping me understand Tieszen’s book, as far as it goes. Something in the book that strikes me as particularly interesting is the notion that, in his later years, Gödel was looking for a way to justify his belief that we have a direct perception or intuition about mathematical objects. He felt we could “see” even such objects as outré as transfinite sets such as the cardinal alef-one, or the continuum of all real numbers between zero and one. You want to know if these two sets have the same size? Focus. Look harder…

Immanuel Kant famously said that the “real” objects around us are so-called noumena, and we know them only at second-hand, that is, via the phenomena given by our senses…sounds, images, touch sensations, smells, etc. And later the philosopher Husserl started talking about phenomenology, which might mean the practice of taking your sense impressions as in some sense external to you as well. Like, rather than blundering around banging our shins on noumena, we’re spacing around in a cloud of phenomena. Husserl isn’t super clear about any of this. He strikes me as something of a bullshitter, never writing one word when twenty will do. But I feel there’s a fertile acorn sprouting beneath his great load of words. With an oak to emerge.


“Topology of the Afterworld,” acrylic on canvas, 40 ” x 30 “, August, 2009.

Trying to imagine being a phenomenologist, I let go of my ordinary stance of being an object among objects. As Husserl would put it, I bracket this mode of thought, that is, put it on hiatus. (There’s even a short Wikipedia article about phenomenological bracketing!)

So I frikkin’ bracket the whole issue of what is reality. I’m a monadic focus point amid phenomena. I’m not watching things, I’m kicking it back a level, I’m experiencing phenomena. It’s like an exercise in mindfulness. Just focus on the flow of sights and sounds and touch and weight and don’t try to interpret them or see them as objects, just take them for what they are…phenomena.

It’s so hard to “keep up” with the onrushing flow sensations, one is continually tempted to dive down into associative chains. But when I can do it for a few minutes, it gets me high, and that is, after all, the end goal of philosophy (at least to this reprobate’s mind). And you can jack up your phenomenological awareness to a “transcendental” level and treat your thoughts as phenomena as well.

Looking at the odd 3/4 moon on the horizon last night, rotten looking, moldy as an overripe cantaloupe that seeps smeely fluid, I advised to Sylvia that we bracket any thought about the Moon’s physical nature, and merely focus on the look of the moldy moon.

I think for the rest of the week I’ll make a habit, of saying I’m bracketing whatever is going on around me at any given time. Kind of a Woody Allen thing to do. He loves joking about higher philosophy.

Speaking of phenomenology, Georg Hegel is my great-great-great-grandfather, and one of his best-known works is Phänomenologie des Geistes, which we call either The Phenomenology of Mind or The Phenomenology of Spirit. Not that, so far as I know, Hegel’s notion of phenomenology has much to do with Husserl’s. I’ve been trying to read this book since I was in high-school, and so far I’ve never gotten beyond the preface. But there is one passage in the preface that I’ve grown to love. Especially the sentence I italicized.

A building is not finished when its foundation is laid; and just as little, is the attainment of a general notion of a whole the whole itself. When we want to see an oak with all its vigour of trunk, its spreading branches, and mass of foliage, we are not satisfied to be shown an acorn instead. In the same way science, the crowning glory of a spiritual world, is not found complete in its initial stages. The beginning of the new spirit is the outcome of a widespread revolution in manifold forms of spiritual culture; it is the reward which comes after a chequered and devious course of development, and after much struggle and effort.

I take this passage to express an idea popularized by Stephen Wolfram in his A New Kind of Science. And this is the notion that, in the realm of computation, we can have incredibly rich and complex patterns that are in fact based on extremely simple little rules. The Mandelbrot set is a classic example of this. And, if you think of biological growth as a type of computation, the tree is indeed the “output” of the tiny acorn program. One of the most interesting places to see small rules making cool patterns is in the world of cellular automata.


“Antarctica” acrylic on canvas, March, 2017, 24” x 20”. Click for a larger version of the painting.

This is another recent painting of mine based on cellular automata. The image also dovetails with my ongoing obsession with “At the Mountains of Madness,” which is H. P. Lovecraft’s story about the lost ancient city in Antarctica. You can see the image in that same recent “Still Seeking the Gnarl” post. I think of this painting as an aerial view of the ruined city. Synchronistically, the Capow pattern happened to have a shape like the head of a penguin. Working the phenomena. But maybe that’s possible. Maybe if you get phenomenological enough you can be dancing with the universe, in synch with reality’s higher cosmic patterns.

But if I’m living in some sense to the side of the so-called physical world, then what am I? As I was hinting at above, Gödel seems to want to say that he’s a monad, in Leibniz’s sense of the word. Gabriella Crocco of the university of Aix/Marseille wrote a great 2013 paper about Gödel, Leibniz, and monads, entitled, Gödel, Leibniz and “Russell’s mathematical logic”. The phrase “Russell’s Mathematical Logic,” refers to one of Gödel’s papers.
As another good philosophical resource see my Paris philosopher friend Mark van Atten’s excellent, “Monads and Sets. On Gödel, Leibniz, and the Reflection Principle” from 2009. Mark was my nearly constant companion when I was a visiting scholar in Brussels.

Tieszen’s Simply Gödel further discusses Gödel’s rationalistic Platonism, and gets into the issue of having direct phenomenological perceptions of transfinite sets, which is something which Gödel hinted at in his essay, “What is Cantor’s Continuum Problem,” and which G also discussed with the philosopher Hao Wang, and mentioned when talking to me. One the appealing things about Tieszen’s book (as well as Crocco and van Atten’s papers) is that, as a computer programmer might say about efficient low-level code, they “stay close to the metal.” Meaning that, rather than launching into overly wispy imaginings of what Gödel might have meant to say, these philosophers stick to actual quotes from the man’s published and unpublished papers, the more fragmentary remarks in his archives, and of others’ records of conversations with him. There’s more than enough here to launch the wildest fantasies.


“Thirteen Worlds,” acrylic on canvas. 24″ by 18″. January, 2009.

Getting back to monads, back in 2004, I read the whole of Leibniz’s short book, The Monadology. It’s pretty close to being incomprehensible. It’s way out there. Leibniz seems to say that our universe is an assemblage of “monads” which reflect each other, and each monad has the whole world inside it. Naturally, it struck me that an idea this crazy ought to be used in an SF story. And—here’s the literary surrealist-in-action part—as soon as I thought of that, I immediately thought that each monad should resemble a knobby giraffe. With brindle patches on it. And in 2016, I wrote an SF tale called “The Knobby Giraffe” for Lightspeed magazine.

But I still feel like I’m missing the mark in my conception of monads.

Something more to think about. Anyway, thanks again to Richard Tieszen and Simply Gödel for getting all these wild thoughts churning in my head!

Still Seeking the Gnarl

March 10th, 2017

I finished a new painting, “In the Lost City of Leng.” It goes with a novella of the same title that I’m working with my writer friend Paul di Filippo. It’s kind of a sequel to H. P. Lovecraft’s greatest tale, “At the Mountains of Madness.”

“In the Lost City of Leng” acrylic on canvas, March, 2017, 40” x 30”. Click for a larger version of the painting.

The story is about some adventurers who find their way into a tens-of-thousands of years old city beneath the ice and snow of an obscure plateau in Antarctica. And some of the down-sloping walls of the hallways are adorned with friezes that describe the history, science, art, and culture of the “Elder Ones” or “cukes” who lived there. The cukes were all be exterminated by some train-car-sized slugs known as shoggoth. So in my painting, we see a couple of explorers, totally unaware of the waiting shoggoth below…

The main thing I was doing for that week or ten days was revising an old program of mine called Capow. It shows smoothly changing (or continuous valued) cellular automata (called CAs for short). Shown above is an image that Capow made for me. I like to say this is an aerial photo of the ruins of the lost city of Leng on the high Antarctic plateau by the Mountains of Madness. By a gift from the muse of synchronicity, the image contains a shape like the outline of a penguin head. Yep, I’m firing on all cylinders, bwah.

“Capow showing the “2D Grid – Gnarly Computation (pattern).CA” file. Click for a larger version of the image.

Supposedly Capow was developed for scientific and technological purposes, and I even wrote a formal paper about it, “Continuous-Valued CAs in Two Dimensions,” at the Santa Fe Institute in 1999. But what I really do with it is to create and watch gnarly edge-of-chaos lava-lamp-like realtime tweakable light-shows, based on 1D and 2D continuous valued cellular automata modeled on linear and nonlinear wave equations, on reaction-diffusion rules, and on user programmable rules. Time to get ill.

I have two web pages about Capow. The older Capow home page, with some references and a bit of history. And the new and more streamlined GitHub download page for Capow. I’d always wanted to put something on GitHub, which seems ultrageek and techie.

If you’re a Windows user, download the program, I’d advise you to load up that “2D Grid – Gnarly Computation (pattern).CA” file, and start to play. It’ll eat your brain. Dig the Norwegian (?) art deco quality of the next image.

I’m planning to do a series of CA paintings now—with the “simple” expedient of hand-copying prints of some of my fave CAs with my crude daubing. Should make for some nice abstract paintings. The hard thing about abstracts is to find a sufficiently off-kilter image that isn’t just the first standard scribble I might come up with. So this where my CA friends can come in.

What is a CA anyway? They’re based on so-called CA rules, which have the form of a tiny program which is, in effect placed into each cell of a 2D grid. I show these cells as pixels on your screen. The cell grid updates as fast as it can, maybe a few times a second, depending on the size of the grid. In the update, each cell or pixel looks at the continuous range of colors of the eight nearest pixels (the ones touching the sides and the corners of the pixel). And it applies its “rule” to this info in order to calculate its new color.

The old “game of Life” is a type of cellular automaton, but a kind of limited one, in that each of the grid cells for Life has only one on-or-off bit in it. But in Capow, each of the cells has one or two decimal numbers in it. We call the Capow rules “continuous-valued CAs.” Way gnarly.

What’s my hat doing in here? I’ve been on an oldtime fedora hat kick this winter, I got two new ones.

With the CAs munging my brain.

I still go out in the hills anyway. Had a great ride in Almaden-Quicksilver Park last week. This is a spot I rode to on June 3, 2004, right when I retired from teaching CS at San Jose State, already more than twelve years ago, wow. Lifebox self-archivist that I am, my Journals 1990-2014 book is online, and here’s a sampled quote from it relating to that particular day.

I’m retired, it’s vacation, I’m glad. I’m in Almaden Quicksilver Park, sitting at a picnic table beneath an oak high atop a long ridge that I biked up. Writing these notes on a folded-in-four sheet of paper from my pocket.

Today feels like a turning point, me going off bike-riding alone on a week day. Still processing the fact that I’m retired. Edging into a new phase of my life. Autumnal, ripe, brimming over.

The meadows are dry, summer gold with empty seed cases like pennants on the grass stalks. The oaks are green and vigorous, a bit dusty-looking already. Billions of chaotic oscillations in the grasses and the leaves, indeed this page is sun-dappled with shifting shadows. Quiet.

A woodpecker taps now and then. They’re such slow workers most of the time. You rarely hear the conventional jackhammer rat-a-tat.

Drifting down from the north is the muted roar of San Ho. But I’m facing towards a big valley of parkland, including the Guadalupe Reservoir and Mount Umunhum (means “hummingbird” in the Ohlone Indian tongue).

It’s so good for me to get out into nature. Away from the news, which creeps in everywhere now, into Twitter, Facebook, email, nearly every web page, and, of course, the news apps that I can’t quite stop looking at. Feh.

Also especially good to get out if I’ve been programming. I was spurred to do a new Capow release by seeing an interesting GitHub page about a somewhat similar kind of continuous-valued CA program called Ready, written by the Golly Gang, who are also associated with a fast Game of Life program called Golly. But it’s Ready that caught my interest. If you scroll down the Ready page, there’s some good images and great videos. I spark of that familiar competitive drive, and wanted to keep my program still in the game. So I decided to make a 2017 build of Capow, which is originally from 1998, and was last rebuilt in 2007.

The advantage of Capow is that it’s written in C++ for just one specific platform, and it’s optimized to run fast, and it’s interface is designed for clicking and playing. Ready, on the other hand, has the huge plus of being multiplatform, that is, there’s versions of it for Unix, the Mac, and so on. And it has a more scientific interface. But it runs very slow.

Mainly I wanted to up the “resolution” or number of cells that my Capow can run in its 2D CA rules. The thing about CAs is—they can soak up as much computational clout as your computer has. Make your grid twice as big, and you have four times as many cells. Put decimal numbers into your cells instead of little integers, and you’ve got another speed hit.

But in order to rebuild Capow, I needed to download a (surprisingly!) free Microsoft Visual Studio 2015 compiler to rebuild the code. A rusty laser cannon of a tool…or at least when faced with my ancient code. When you use old code there’s the issue of what hackers (old word for programmers) call “bit rot.” That is, the new compiler doesn’t approve of some of your old code and will throw warnings and cryptic error messages your way.

There’s a slot machine quality to trying to building a running program from code. Over and over you click the build button in your so called IDE (integrated development environment), over and over you get errors—and you fix them. Over and over you run the program, see things you don’t like, go back and change the code, push the build button, get new errors and fix them, push the build button and run the program, see new flaws and fix them, push the build button and—and so on. Like a bathrobed geezer with a walker in a Vegas casino working a slot.

Eventually I got to something that seemed good enough to share. Not something perfect by any means—that would require a whole new fresh start. But good enough.

And now I’m logging time, off and on, in the happy land of CAs. The images I’m showing you in this blog post don’t really do the program justice. All those spirals are merging and turning, and you can ding the screen with the “touch cursor” and the patterns shift. In the old days I used to love to look at these images when I was high—and now I find that I don’t even have to be high to look at them, they get me high on their own because, dude, those are images of my actual brain that I’m looking at.

Yeek! As I say, it’s also good to get outside.

But there is one more thing I want to mention about the Capow images, and this is the fact that so many diverse kinds of CA rules end up making swirling spiral scrolls. I call these Zhabotinsky patterns, after the biochemical Belusov-Zhabotinsky reaction-diffusion or activator-inhibitor reactions known to make such patterns in petri dishes or, for that matter, in the skins and hides of animals, and in the shells of invertebrates. Zhabos for short. If you up a Zhabo into three-dimensions, you get something shaped like a mushroom cap. Zhabos are everywhere. In the swirls of water, in the shapes of beans and fetuses, in lichens, in air currents. You can find a discussion of this online in the “Flickercladding” section of my non-fiction book The Lifebox, the Seashell, and the Soul.

Onward up the hill of life!

To meet the cubic-wave-equation bubbles in the sky?

Or no, maybe what I want is the real sky. Hard to decide—but, after all, I don’t have to choose. We can have both. The reality and the dream, the seek and the gnarl.

Podcast #98. Lifebox Immortality Talk with Q&A at UC Santa Cruz

February 14th, 2017

February 13, 2017. A talk on digital immortality, my novel Software, and the concept of a “lifebox.” Presented at Tim Fitzmaurice’s Core class at Crown College at UC Santa Cruz. Includes wide-ranging Q&A with the students also some remarks and quesitons by Tim. I read an as-yet unpublished story called “Fat Stream,” but I’m not including that in this tape. But my recent podcast #97 has me reading my story “Like a Sea Cucumber,” which illustrates the lifebox idea quite well. Press the arrow below to hear the tape of “Lifebox Immortality Talk with Q&A.”

Play

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Podcast #97. “Like a Sea Cucumber” at St. Luke’s

February 14th, 2017

November 9, 2016. A reading of my story “Like a Sea Cumber,” as part of a literary evening at St. Luke’s church in Los Gatos. The story appeared on the Terraform website. Press the arrow below to play the reading.

Play

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