by Rucker, Rudy
My antithesis in the book’s dialectic triad, expressed by the word “soul,” is the existential observation that consciousness doesn’t feel like a computation. We have an innate sense of awareness that we express by the phrase, “I am.” One has a feeling that being conscious involves merging into the world, which doesn’t seem like something a computation would easily do. Our experiences with sensual qualia give us a sense that consciousness has a texture not captured by computation. Dreams and religious visions also give us a feeling of having a higher consciousness that’s not captured by computations.
My synthesis in this dialectic triad is to claim that naturally occurring computations can in fact have the richness of consciousness, for the reason that they are gnarly computations. Furthermore, I argue that all naturally occurring processes are in fact complex enough to be gnarly computations.
I’ll say more about gnarly computations in the next section, but for now suffice it to say they are complex and unpredictable. In my book’s title, I use the word “seashell” to represent the notion of gnarly computations because certain seashell patterns are believed to be naturally occurring computations of this complex sort. (See Figure 21.)
Rudy holding a cone shell with a gnarly cellular automata pattern
To summarize, my original dialectic argument says:
Thesis: Everything is a computation.
Antithesis: Human consciousness doesn’t feel like a computation.
Synthesis: Everything is a gnarly computation.
And this argument takes us from my statement (1) to my statement (2).
What is Gnarl?
By way of explaining more precisely what I meant by a gnarly computation, I’ll point out that computations lie on a spectrum of complexity. My analysis follows that of Stephen Wolfram in his book, A New Kind of Science, [Wolfram 2002].
The spectrum of computational complexity
Suppose that we focus on some particular category of computations such as Turing machines or cellular automata rules. No matter what the category, we always find four basic kinds of behaviors: comes to a halt; goes into a repeating loop; produces unpredictable but somewhat orderly output, produces random-looking output.
We view the first two types of behavior as simple, and the second two types as complex. In chaos theory, both of the complex classes are regarded as chaotic. The reason I have introduced the word “gnarly” for the third class is so as to have a more convenient phrase than “somewhat orderly chaos.” Christopher Langton refers to this zone as the edge of chaos.
In this context, we aren’t very interested in the distinction between the terminating and repeating computations, so we lump those two simple classes together. Thus we arrive at three general classes: simple, gnarly, and random-looking. And just as in the fairy tale about Goldilocks and the Three Bears, we can view the behaviors as too cold, just right, and too hot.
Simple (Too Cold): Dies Out or Repeats.
Gnarly (Just Right): Complex, moving, unpredictable. Life. Natural processes.
Random-looking (Too Hot): Seething.
Most of my own taxonomic research on computations has centered on two-dimensional cellular automata. We can think of these computations as taking place on a computer screen. Each pixel acts as a tiny independent computer, each pixel updates its state on the basis of the states of its neighboring pixels, and the states are depicted as colors.
At the end of his life, the computer science pioneer Alan Turing was beginning to use these kinds of rules to show how the patterns on animal coats and butterfly wings might emerge from cellular automata rules based on two competing chemicals, an activator and an inhibitor. The “Turing patterns” that emerge from these rules can look like spots or filigrees.
Nine gnarly cellular automata
We can create computer simulations of these rules by supposing that the state of each pixel includes two real numbers representing the intensities of activator and inhibitor. Figure 23 shows some of the patterns generated by these rules. In these images we see the spontaneously generated scrolls that biochemists call Belousov-Zhabotinsky scrolls. The dynamics of these patterns are lovely. The spirals are constantly turning, and the scrolls expand, swallow each other, and spawn off new scrolls—almost like living creatures.
Getting back to my main line of argument, let me say a bit more in my support of my statement (2): Every object or process is a gnarly computation. In many cases it’s intuitively clear that nature is performing a gnarly computation: think of swaying trees, a flickering fire, the cracks in drying mud, flowing water, or even a rock. A rock? To the human eye, a rock appears not to be doing much. But viewed as a quantum computation, the rock is as lively and seething as, say, a small star. At the atomic level, a rock is like a zillion balls connected by force springs, and we know this kind of compound oscillatory system behaves chaotically.
Panpsychism
For the next stage of my argument, I want to argue for a form of what Wolfram calls the Principle of Computational Equivalence. This is my statement (3): Every naturally occurring gnarly computation is a universal computation.
Computer scientists define universal computers as systems capable of emulating the behavior of every other computing system. The complexity threshold for universal computation is in fact very low. Any desktop computer is a universal computer. A cell phone is a universal computer. A Tinkertoy set or a billiard table can be a universal computer. And very many gnarly computations such as Conway’s Game of Life have been proved to be universal computations as well.
One difficulty here is that in 1956, Richard Friedberg and Albert Muchnik, working independently, showed that one can in construct computations which are gnarly but not computation universal. This is why in my version of the Principle of Computational Equivalence, I restrict the focus to “naturally occurring computations”—the supposition being that the Friedberg and Muchnik computations are in fact so artificial as not to occur in the wild.
Now we come to the question of consciousness. On the surface, being a universal computation seems like very nearly a sufficiently strong condition for being conscious. But there is a sense that one’s consciousness has something more, and one might well suppose this additional ingredient to be self-reflection, where the self-reflection aspect of a system stems from having a feedback process whereby the system has two levels of self-awareness: first, an image of itself reacting to its environment, and second, an image of itself watching its own reactions. (See [Damasio 1999].) Thus we arrive at statement (4): Consciousness = Universal Computation + Self-Reflection.
I have come to believe however that the requirement of self-reflection is otiose. That is, my experience as a computer scientist suggests that one can in fact used fixed-point methods to give any universally computing system this kind of self-reflectivity. This leads to my statement (5): Any complex system can be regarded as having self-reflection.
And thus we can deduce (6): Panpsychism. Every physical entity is conscious.
One problem which remains to be solved is whether we can learn to converse with the conscious objects surrounding us. Possibly we will develop some quantum computational technique so that one can sufficiently entangle oneself with an object so as to able to talk with it.
Hylozoism
My fellow philosopher of computer science, John Walker, makes the point that living beings seem to have memory as well as universal computation. (See [Walker 2004].) Walker points out that humans, for instance, have physical memories at three different levels.
Genetic memory: DNA.
Organic memory: Immune system.
Behavioral memory: Neural patterns.
Even if we don’t expect living entities to have a biological component, one can make a case that memory plays an essential role in such characteristically life-like processes as reproduction, morphogenesis, and homeostasis.
Thus we arrive at (7): Walker’s Thesis. Life = Universal computation + Memory.
So now in order to exten
d my line of thought to reach hylozoism, I need some way of asserting that every physical object already has some kind of memory.
While preparing this paper to present in Kyoto, I started thinking of the Zen koan of the flag. Two monks are looking at a flag fluttering in the wind, and this system is performing a gnarly and therefore universal computation. But what is the system? The first monk says, “The flag is moving.” The second monk says, “The wind is moving.” The third says, “Mind is moving.”
The flag koan is, in its own way, a dialectic triad, and the flag/wind system is a conscious mind.
That is my panpsychic interpretation of the koan; probably the more common interpretation is a pantheistic one, under which the flag/wind motion is viewed as an aspect of a single, overarching mind that imbues all things.
Now suppose we want to say the flag/wind system is alive as well. Does the fluttering flag have a memory so as to satisfy Walker’s thesis? At first it seems the answer must be no. An isolated natural system is dissipative, that is, different past histories can lead to identical present states.
In my novel Hylozoic, I suppose that we might get around this problem by changing the topology of space at scales below the Planck length—that is, below the size scale at which our current notions of physics break down.
The current notion of space at very small scales, taken from string theory, is that we have a lot of extra dimensions down there, and that most of them are curled into tiny circles. But what if we could find a way to change the intrinsic topology of space, uncurling one of these stingily rolled-up dimensions? Of course we’d be careful to pick a dimension that’s not absolutely essential for the string-theoretic Calabi-Yau manifolds that are supporting the existence of matter and spacetime. Just for the sake of discussion, let’s suppose that it’s the eighth dimension that we uncurl.
I see our eighth-dimensional coils as springing loose and unrolling to form infinite eighth-dimensional lines. This unfurling will happen at every point of space. Think of a plane with hog-bristles growing out of it. That’s our enhanced space after the eighth dimension unfurls. And the bristles stretch to infinity.
And now we’ll use this handy extra dimension for our universal memory upgrade! We’ll suppose that atoms can make tick marks on their eighth dimension, as can people, clouds, or stones. In other words, you can store information as bumps upon the eighth-dimensional hog bristles growing out of your body . The ubiquitous hog bristles provide endless memory at every location, thereby giving people endless perfect memories, and giving objects enough memory to make them alive as well. (Do understand here that I’m speaking in a completely speculative and fanciful way.)
Is there any less science-fictional way to achieve the same result? One approach might be to say that there are in fact no isolated natural systems. The effects of the flag/wind system’s state ten minutes ago are still present in the state functions of the myriads of particles that are quantum-entangled with the particles of the air and the flag. Put more simply, the system’s memory is part of the universal state function. In this once again pantheistic view, each limited system can draw upon the entire memory of the universe as a whole.
This notion is anticipated by the Zen koan in which a monk asks the sage, “Does a stone have Buddha-nature?” The sage answers, “The universal rain moistens all creatures.”
Thus we arrive at (8): Every physical entity has memory via its interactions with the universe. And now we have reached our goal of (9): Hylozoism. Every physical object or process is alive.
In closing, I should mention that in an earlier paper [Rucker 2008] I combined statements (4) and (7) to have this statement: Consciousness = universal computation + memory + self-reflection. And moving from there, I argued that to be a conscious physical object of this kind is essentially to be alive—so that in the end, I arrived at the same position as in the present paper: Everything is conscious and alive.
I would like to thank Masatoshi Murase for having organized this interesting conference, and Mark van Atten for his useful comments on an earlier draft of this paper.
References:
[Rucker 2007] Rudy Rucker, Postsingular, Tor Books, New York 2007.
[Rucker 2009] Rudy Rucker, Hylozoic, Tor Books, New York 2009.
[Skrbina 2005] David Skrbina, Panpsychism in the West, MIT Press, Cambridge MA 2005.
[Rucker 2005] Rudy Rucker, The Lifebox, The Seashell and the Soul, Thunder’s Mouth Press, New York 2005.
[Wolfram 2002] Stephen Wolfram, A New Kind of Science, Wolfram Media, Champaign IL 2002.
[Langton 1990] Christopher G. Langton, “Computation at the edge of chaos,” Physica D, 42, 1990.
[Damasio 1999] Antonio Damasio, The Feeling of What Happens: Body and Emotion in the Making of Consciousness, Harcourt, New York 1999.
[Walker 2004] John Walker, “Computation, Memory, Nature, and Life,” on his website.
[Rucker 2008] Rudy Rucker, “The Great Awakening,” in Damien Broderick, ed., Year Million: Science at the Far Edge of Knowledge. Atlas Books, New York 2008.
* * *
Note on “Everything Is Alive”
Written in 2009.
Appeared in the Proceedings of the Kyoto “What is Life” Conference.
With friendly schoolgirls in a Kyoto bus, 2007.
In October, 2007, Sylvia and I got a free trip to Kyoto, where I spoke at a conference on the theme, “What is Life.” It was an eccentric mix of talks—a number of them were what most academics would call pseudoscience. Which might help explain my presence! I worked up a “rigorous” proof of the hylozoic hypothesis that every object is not only conscious but literally alive. Note that “hylozoism” is indeed a real word, you can look it up on Wikipedia. And I used this notion in my novel Hylozoic. Note that a crucial step of my proof of my tenet that “Everything is Alive” is based on a SFictional fantasy that appears in my novel. I enjoyed taking advantage of the intellectually loose nature of the conference to write an academic paper that is in some sense a flight of fancy. This said, I really do, when I remember to, believe that all the objects around are in a very real sense alive. Why not think this? It makes the world a cozier place.
An Incompleteness Theorem for the Natural World
Introduction
The philosopher Gottfried Wilhelm von Leibniz is perhaps best known for the fierce controversy that arose between him and Sir Isaac Newton over the invention of calculus. The S-like integral sign that we use to this day is in fact a notation invented by Leibniz.
When Leibniz was a youth of nineteen, he wrote a paper called “De Arte Combinatorica”, in which he tried to formulate a universal algebra for reasoning, in the hope that human thought might some day be reducible to mathematical calculations, with symbols or characters standing for thoughts.
But to return to the expression of thoughts by means of characters, I thus think that controversies can never be resolved, nor sectarian disputes be silenced, unless we renounce complicated chains of reasoning in favor of simple calculations, and vague terms of uncertain meaning in favor of determinate characters. In other words, it must be brought about that every fallacy becomes nothing other than a calculating error, and every sophism expressed in this new type of notation becomes in fact nothing other than a grammatical or linguistic error, easily proved to be such by the very laws of this philosophical grammar. Once this has been achieved, when controversies arise, there will be no more need for a disputation between two philosophers than there would be between two accountants. It would be enough for them to pick up their pens and sit at their abacuses, and say to each other (perhaps having summoned a mutual friend): “Let us calculate.” [Gottfried Leibniz, Die philosophischen Schriften, edited by C. I. Gerhardt. Translation by George MacDonald Ross.]
Let’s refer to this notion as Leibniz’s dream—the dream of finding a logical system to decide all of the things that people might ever disagree about. Could the dream ever work?
Even if the dream were theoretically poss
ible (which it isn’t), as a practical matter it wouldn’t work anyway. If a universal algebra for reasoning had come into existence, would, for instance, Leibniz have been able to avoid his big arguments with Newton? Not likely. People don’t actually care all that much about logic, not even Leibniz. We just pretend to like logic when it happens to be on our side—otherwise we very often abandon logic and turn to emotional appeals.
This said, there’s a powerful attraction to Leibniz’s dream. People like the idea of finding an ultimate set of rules to decide everything. Physicists, for instance, dream of a Theory of Everything. At a less exalted level, newspapers and TV are filled with miracle diets—simple rules for regulating your weight as easily as turning a knob on a radio. On the ethical front, each religion has its own compact set of central teachings. And books meant to help their readers lead happier lives offer a simple list of rules to follow.
But, as I hinted above, achieving Leibniz’s dream is logically impossible.
In order to truly refute Leibniz’s dream, we need to find a precise way to formulate it. As it happens, formal versions of Leibniz’s dream were first developed early in the Twentieth century.
An early milestone occurred in 1910, when the philosophers Bertrand Russell and Alfred North Whitehead published their monumental Principia Mathematica, intended to provide a formal logical system that could account for all of mathematics. And, as we’ll be discussing below, hand in hand with the notion of a formal system came an exact description of what is meant by a logical proof.
There were some problems with the Russell-Whitehead system, but by 1920, the mathematician David Hilbert was confident enough to propose what came to be known as Hilbert’s program.
