Nova Spivack - Minding the Planet » Cellular Automata

Good Article on Loop Quantum Gravity — New Approach to Physics

Nova — Tue, 22 Aug 2006 19:37:59 +0000

The New Scientist published a nice overview of the emerging theory of Loop Quantum Gravity. I’ve been following this for a number of years, ever since my friend Bram turned me onto it. It’s related in some ways to other models of discrete space-time, such as cellular automata and digital physics.

LEE SMOLIN is no magician. Yet he and his colleagues have pulled off
one of the greatest tricks imaginable. Starting from nothing more than
Einstein’s general theory of relativity, they have conjured up the
universe. Everything from the fabric of space to the matter that makes
up wands and rabbits emerges as if out of an empty hat.

It
is an impressive feat. Not only does it tell us about the origins of
space and matter, it might help us understand where the laws of the
universe come from. Not surprisingly, Smolin, who is a theoretical
physicist at the Perimeter Institute in Waterloo, Ontario, is very
excited. "I’ve been jumping up and down about these ideas," he says.

This
promising approach to understanding the cosmos is based on a collection
of theories called loop quantum gravity, an attempt to merge general
relativity and quantum mechanics into a single consistent theory.

The
origins of loop quantum gravity can be traced back to the 1980s, when
Abhay Ashtekar, now at Pennsylvania State University in University
Park, rewrote Einstein’s equations of general relativity in a quantum
framework. Smolin and Carlo Rovelli of the University of the
Mediterranean in Marseille, France, later developed Ashtekar’s ideas
and discovered that in the new framework, space is not smooth and
continuous but instead comprises indivisible chunks just 10^-35
metres in diameter. Loop quantum gravity then defines space-time as a
network of abstract links that connect these volumes of space, rather
like nodes linked on an airline route map.

From
the start, physicists noticed that these links could wrap around one
another to form braid-like structures. Curious as these braids were,
however, no one understood their meaning. "We knew about braiding in
1987," says Smolin, "but we didn’t know if it corresponded to anything
physical." Read More

A Possible Future of Physics

Nova — Tue, 27 Sep 2005 16:51:34 +0000

Today I read this nice article which provides a short consumer-friendly overview of the history of the Digital Physics paradigm. Digital Physics is not mainstream physics — but it is growing and someday could become huge. It brings together computer scientists and physicists in an interdisciplinary approach to physics. While many advocates simply take the position that some physical processes resemble computations, the most extreme would go so far as to posit that the universe is actually a giant computation taking place on some sort of primordial computing fabric.

I’ve been involved with this field since the 1980’s when, as a college student at Oberlin, I got interested in cellular automata as a tool for modeling both the brain and the universe. This led to summer research on cellular automata simulations of physical systems on the CAM-6 parallel processor at the lab of Tomasso Toffoli and Norman Margolus at MIT. They were among the first experimentalists in the digital physics field — running massive cellular automata simulations of fluid dynamics, population biology, optics, and spin glasses, among other things. Since then I’ve had the opportunity to spend some time with both Ed Fredkin and Stephen Wolfram, discussing the future of digital physics and the quest for a Theory of Everything.

I think that the Digital Physics is the The Next Revolution in physics. But it may still be another 50 to 100 years before it really takes root. But it’s just the beginning of what I think may be an ongoing process of future physical models. Below, I speculate about where this trend will lead us (disclaimer: Wild Speculation ahead: Read at your own risk!)

Humans have always used their most advanced technologies as metaphors for the physical universe — a process which can be seen in the history of physics itself. For example, Newtonian physics and Einstein’s Relativity were largely based on the metaphor of clocks –which were for a long-time the most sophisticated “computers” on earth. Whereas Newton’s vision was mainly influenced by the mechanics of clocks, Einstein’s’ vision was more influenced by the dynamics of clocks. Thanks to clocks we have been able to develop sophisticated computers. And now, with the advent of the computer era, we have begun to model our universe using computers, and even to think of it as a computer.

This emerging Computer Model of physics (aka “Digital Physics”) takes the computer metaphor to its fullest extent by viewing the universe itself as a computer program running on a vast cosmic computer of some sort. The next step in this emerging model will be enabled as quantum computing and the theory of quantum computation begin to be applied to physics. Quantum computers will revolutionize both theoretical and experimental physics by enabling the simulation and testing of infinitely complex physical systems in finite time, using finite computing resources. This will naturally evolve the digital physics paradigm such that the universe is conceived of as aquantum computer.

After the Computer Model of the universe, the next model will come when we start to view our universe not as a single computer, but rather as a vast network of computers. This shift mirrors the evolution of computers and networks, which has led us to the Internet. We will start to view our universe as something like a vast computer network in which countless computations interact, move around, compete, reproduce and evolve higher levels of fitness in an almost Darwinian manner –instead of a single isolated Perfect Computer In Space.

Out of this Network Model of the universe, we will begin to view the cosmos as something that resembles a nervous system. The human nervous system is a computing network that is conditioned by countless internal and external factors at every level of scale, all at once. Feedback is essential to how it functions. It is neither a bottom-up nor a top-down system — rather it is an all-directions system. The universe is also like this — we cannot adequately explain it with a reductionist model– ultimately, the only way to understand it is from all directions at once, as a network. The Network Model will have three phases of development — the first will focus on the inner-workings of the nodes, the second on the functioning of the links, and the third on the interactions that take place via nodes and links.

What’s beyond the Network Model? My hunch is that it will have something to do with a realization that the universal computer networks capable of self-modification such that the output of the programs that run on it affects the very structure of the computing nodes and links that comprise it. When we cross that bridge we will realize that it is not precisely correct to conceive of a division between the computing fabric that comprises the network, the software programs that run on that network, and the output of those programs — instead we will see this as a single self-modifying system. Rather than a static primordial computing fabric on which various programs run like so many experiments in a lab, we will view the entire system as a recursive loop in which each output is taken as an input for the next step in time. In the earlier Computer Model and Network Model, the physical laws were conceived of as being somehow “hard coded” into the computer, but in the model beyond these — what might be called the Evolutionary Model– we will see that the physical laws themselves are evolving. In other words, we will see that there is a feedback loop between the output of the universal computation, the structure of the underlying computing fabric, and the definition of the programs that run on it. These three layers will come to be seen a single evolving, self-reproducing, self-modifying, system. The activity that takes place in the universe will be understood to directly affect the underlying physical laws themselves, and vice-versa.

Next we will begin a phase which could be called the Organic Model of the universe, in which we will begin to view the cosmos as a kind of meta-organism — a creative, evolving, living thing. Our knowledge of the Network Model will enable us to map what takes place on different levels of scale to familiar physical processes that take place within the human organism. Our understanding of the universe will start to take on a distinctly biological character. We will begin to look at computational pathways and the equivalent of organs on a cosmic scale just as we do within the chemical and biological systems of the human body. We will begin to view the functioning of the cosmos as intelligent and creative and even capable of rudimentary adaptive learning on both the smallest and vastest scales. We will begin to become open to the possibility that there are forms of intelligence and life that are vastly smaller as well as vastly larger than what we experience on our human-centric measurement perspective.

Beyond this phase, we will begin to look at our evolving cosmos as a kind of meta-organism in a community of other similar meta-organisms. We might call this the Social Model. Beyond just focusing on our individual universe in isolation, we will begin to look at it as a member of a community of similarly evolving universes — an infinite array of interacting generations of universes that are subject to a process of cosmic natural selection of universes. These different universes will be understood to be capable of communicating, and even reproducing to form new universes. We might call this the Metaverse. Physicists have already glimpsed this level of reality from a theoretical perspective, but we lack the tools to really describe its mechanics, let alone dynamics. But we’ll get there eventually, if our species doesn’t destroy itself first.

Brain Has Particular Neurons for Recognizing Celebrities and Other Concepts

Nova — Wed, 22 Jun 2005 20:22:47 +0000

In a very interesting new finding, researchers have discovered the people’s brains contain individual neurons, or small groups of neurons, that seem exist only to recognize particular people or concepts. This would imply that there is one neuron, or at least a small group of neurons, in our brains for every unique thing that we know. However, that raises certain questions — for example, if this is true, then the brain should be a lot larger since there wouldn’t be room to represent everything a typical adult knows with unique neurons in that amount of space. On the other hand, perhaps the memories are not stored on the neuronal level at all, but instead are stored and computed on the sub-neuronal tubulin "quantum computing" level, which is the subject of much research these days. For more on that check out this book on research into quantum computing in the brain (found by: Josh).

Simulated Universes and the Nature of Consciousness

Nova — Sat, 04 Jun 2005 20:31:43 +0000

Researchers in Europe have completed the first phase of what may be the largest computational physics experiment in history: They built and ran a simulated universe through 14 billion years of development. The experiment used up 25 million megabytes of memory, and the biggest supercomputer in Europe for a month. The result was a “Cube of Creation” of 20 billion light years per side, containing 20 million simulated galaxies. Now they’re studying it to see what evolved. They hope to gain insights into the function of black holes, and other cosmological principles. This is an amazing piece of work — definitely the future of cosmology research.

In previous articles, I’ve speculated that our own universe might also be such a simulation, perhaps run by a much more advanced civilization in a meta-universe outside ours. But in fact, I think our universe is probably quite different from a mere computer simulation (despite how cool it would be if it were a computer simulation!) — because I don’t believe we can explain everything there is in terms of information and computation: I think consciousness doesn’t fit in that model. After exploring this issue for more than 20 years from the perspectives of computer science and physics, philosophy and religion, I’ve come to believe that consciousness cannot be reduce to, or emerge from, information or computation. As far as I can tell, it’s something at least as or more fundamental than space, time, matter and energy. I would even go so far as to say that we won’t ever really understand what the universe is or how it develops or functions without first understanding consciousness much more deeply.

There are basically two fundamental, mutually exclusive camps on the issue of consciousness that have been sparring for millennia. Either you are in the camp that believes consciousness is something that emerges from the physical universe, or you are in the camp that believes that the physical universe is something that emerges from consciousness. (Note: Even the Buddhist theory of interdependent origination, which says that physical phenomena and consciousness arise in co-dependence at the same time, rather than one from the other, can still be reduced to a version of Camp #2 because in that theory, interdependent events take place by virtue of a primordial unification of mind and phenomena that is equivalent to what I mean when I say “everything emerges from consciousness” — in other words, nothing is truly separate from consciousness)

I am a Camp 2 person. I believe that consciousness is more fundamental than anything else. The example of a dream can be used to illustrate my view on consciousness: Although everything in a dream is a projection of consciousness, nothing in a dream is conscious. For example if you dream of Sue that is not really Sue: that dream-image of Sue is not a really a conscious person, it’s just a projection of your consciousness. Similarly, in a dream, if you find yourself interacting with a dream-image of Sue, your dream body in that dream is also not conscious, it is equally just a projection of your consciousness.

Even if you experience your dream from the perspective of being a particular character, looking through their eyes, thinking their thoughts, etc., that which is actually having that experience — the consciousness that is dreaming the dream — is outside the dream. It doesn’t appear anywhere within it, it cannot be measured within it, and it has no form or location. But still, as the one having the dream, it is undeniable that there is a dream appearing and an experience of that appearance. Furthermore, the nature of consciousness itself is self-aware — it can realize its own capacity of cognizance — the fact that it is aware, even though nothing to grasp as “consciousness” can actually be located anywhere. This self-awareness, in my view, is not a function of the brain or the body, or any physical system, rather it is completely beyond material phenomena — beyond all possible universes in fact.

So who or what is projecting the universe in a manner of a dream? Is the universe nothing more than a dream in fact? This question cannot be answered by physics — it can neither be disproved or proved. Even various religions disagree about how to answer it — some label consciousness as soul, or universal or eternal Self or as God, while other systems, such as Buddhism instead argue that it is in fact so completely transcendental that it is entirely empty of self-nature and therefore cannot be reified as one or many, something or nothing, self or other, or truly-existent or non-existent.

Please note that when claiming that everything comes from consciousness, and using the example of a dream to illustrate that, I am not suggesting the philosophical view of solipsism, which posits that everything is just in my own mind, or some cosmic mind perhaps. Nor am I proposing an eternalistic argument that claims that “all is one” or that there is an ultimate, truly-existing soul, or that there are or are not really other beings. From my perspective, which comes largely from my studies of the Buddhist theory of dependent-arising and emptiness, what I am calling “consciousness” cannot really be conceived of — because it is literally beyond thoughts, and even beyond the universe; is not a thing. Therefore, there is no way within this universe to frame or express the nature of consciousness. All we can do is use analogies, which are just shadows of the real thing, not the real thing itself. However, although we cannot describe consciousness, we can directly experience it as it really is, without using concepts or analogies, because we are it.

There are a number of difficult subtleties that have to be carefully sorted out when you really go deeply into this view of consciousness. In particular, regarding the question of whether other beings exist, or whether there is really a universe “out there” apart from your own mind (whether there is actually a sound when a tree falls and there is nobody there to hear it, for example). My opinion is that it is certainly possible for there to be multiple beings with their own experiences — and furthermore that is certainly what appears to be taking place. Yet to be precise, we cannot prove that what appear to be other beings are truly-existent “out there” nor can we prove that there are no other beings apart from ourselves — in fact, we really cannot decide one way or the other about this question, at least if we want to be hairsplittingly precise. Therefore, from a philosophical perspective, the best thing to do is to simply not take a position on that question.

There is no way to prove that “everything is a dream” or that “everything is not a dream,” and so we simply have to avoid forgetting that we really don’t know which position is correct. Most people err on the side of thinking “everything is not a dream” and so they get totally absorbed in the intricacies of of daily life and the material world — they become mindless materialists. On the other hand, those who err on the opposite side of thinking that “everything is just a dream” tend to fall into the extreme of being spaced-out spiritualists. So our task, as rational observers of reality is to try to be as true to what we really can observe for ourselves as possible — meaning we have to avoid becoming either mindless materialists or spaced-out spiritualists. To be most true to what we can observe, we have to take the “middle road” and avoid falling into any extreme philosophical viewpoints. This means, in particular, that we should not fall into a an overly materialistic view of thinking that everything that seems to be “out there” really truly exists apart from our own minds, nor should we fall into a nihilistic view of thinking that there is only ourselves or that there is nothing at all.

From the philosophical view of Tibetan Buddhism (which happens to be my favorite), the most accurate way to portray consciousness might be to say that it, and in fact anything else we can label, is neither nothing, one, nor many — and so therefore we avoid falling into the extremes of eternalism and nihilism. Eternalism is materialism — it is the belief that phenomena truly-exist on their own — that they can be decomposed to irreducible particles. Western science is basically materialism. Nihilism is the extreme opposite of materialism — it posits that nothing exists at all. Nihilism leads to all sorts of delusions and bad behavior but is fortunately quite easy to refute: indeed, the very fact that anyone is able to hold the belief that they are a nihilist refutes their belief in nothingness.

I should also mention that while I am definitely a Camp 2 person, I don’t discount the utility of science for explaining how the material world appears to function, I just don’t think that it can explain what the material world really is, nor what consciousness is. I think that science is ideally suited to explaining the dynamics of matter and energy in time and space — the various physical patterns that we observe. But at the same time, I think that to really explain everything — a theory also has to explain consciousness, and I don’t think there is a material, scientific explanation for that because consciousness is not simply a pattern in the physical world — it is completely transcendental.

Some scientists try to use the fact that consciousness cannot be located or measured like physical phenomena to be proof that it doesn’t exist at all, but that argument is fallacious. Just because no scientist has ever isolated consciousness or measured it doesn’t mean it’s not there, it just means it’s beyond the scope of their measurement tools. For example, if our only measurement tool is a microscope we cannot prove that galaxies don’t exist simply because we cannot see them through it; for if we later have a telescope we definitely can see galaxies. In the case of consciousness the situation is even simpler: no material measurement tool can measure consciousness, but that doesn’t mean it doesn’t exist because everyone, including every scientist, directly knows that they are conscious. So in a sense we could say that the only “measurement tool” that can detect consciousness is consciousness itself. There’s another interesting fact that is worth mentioning here: no scientist has ever directly seen or measured space, energy, or time (all measurements of these are in fact indirect and inferential) — but for some reason they are willing to believe in those phenomena. Why are scientists willing to believe in their inferences about the nature of space, time and energy but not consciousness? I find this puzzling.

Science began as what was called “natural philosophy” — it wasn’t confined to the material domain but actually was a much broader undertaking, an attempt to explain everything. Natural philosophers, such as Sir Isaac Newton, for example, were interested in all the dimensions of experience, including the mind, soul and even the possibility of God. They truly wanted to understand the world, and they considered anything observable to be within the scope of science. Gradually, however, this open-mindedness was lost and science became increasingly limited in focus. Today science is incredibly myopic and close-minded — it has in fact become institutionalized to the point where, to succeed and be respected by their peers, scientists must specialize and conform to the point of losing almost all originality and intellectual freedom. A side-effect of this is that scientists have gotten so focused on trying to observe what everyone else observes, that they no longer notice what they themselves observe — they no longer consider their own minds, consciousness, or their own experiences to be valid subjects of observation, nor do they consider themselves to be qualified observers of their own minds, consciousness and experience.

This belief comes from the mistaken idea that it is impossible objectively to observe one’s own experience. Modern science is built on the notion that only observations which can be demonstrated to, and repeated by, other scientists are considered valid. The problem is that all observations, whether of one’s own mind or of some external experimental result are ultimately subjective. So in fact, although scientists like to think that their methods are not subjective, in fact, to be precise they are subjective. Because ultimately all observations are subjective, observing one’s own mind directly is really no more subjective than observing any external physical experiment or phenomena: We cannot really demonstrate anything objectively, whether internal or external, to anyone because ultimately we all sense things subjectively.

If this isn’t enough to hammer in the point that self-observation of the mind is a valid pursuit of science, there is another argument: If consciousness is truly fundamental, then it is not conditioned by anything it observes and so it is perfectly objective in nature. Of course, here we have to be very careful to make a clear distinction between consciousness itself and the many layers of thoughts that may obscure it (thoughts are not consciousness). Using consciousness (without thoughts) to look directly at consciousness is perhaps the most objective scientific experiment possible!

Therefore, just because nobody can demonstrate their consciousness to anyone else doesn’t mean that consciousness doesn’t exist or that it is unscientific to study it by direct self-observation. In fact, the only way to directly study consciousness is by direct self-observation — that is the best measuring device for the job, so to speak. Furthermore, it is indeed possible to “demonstrate” one’s own observations of consciousness to others in a repeatable manner — simply: if they follow the same steps and end up observing the same things about their own consciousness, then your experiment has been repeated successfully. So in fact the direct study of consciousness is valid, objective and repeatable. In short, it is and should be within the scope of scientific study.

Until scientists discover this fact and look inwards at their own minds, they are never going to make real progress in the scientific study of consciousness, because this is the only way to actually study consciousness. (Note for the brain scientists in the audience: merely studying the physical brain is not really studying consciousness itself — consciousness is not a brainstate but is rather that which is capable of knowing or being. In fact, consciousness itself has no content — it is not a set of thoughts or sensations. Brainstates may represent the content of consciousness at a given moment just as a frame on a movie film print represents the content of that particular moment of the movie, but in this analogy consciousness is the light in the movie projector, not the film or the patterns on the film. Don’t mistake the content of a given frame for the light of the movie projector!).

So, I hope I’ve made the point by now that from the perspective of what we can directly observe, for ourselves, it actually makes more sense to start with the hypothesis that consciousness is fundamental — since nobody has ever directly experienced any phenomena outside the scope of their own consciousness. As far as anyone can directly observe, wherever phenomena are found there is also an observer of those phenomena at that very moment. Furthermore, as far as anyone can measure, there is no way to establish that phenomena actually exist “out there” when they are not observed. So from a truly rational, scientific point-of-view, consciousness appears to be fundamental in that it is ever-present in our experience of the universe, and as or more necessary to having that experience, as are space, time and energy.

It is in fact more rational and scientific to hold that consciousness is fundamental until proven otherwise than to hold the reverse hypothesis. After all, as far as we ourselves can observe, our experience of the universe is mediated by consciousness and there is no way to establish that the universe we perceive is separate from our consciousness. All the evidence seems to indicate the contrary: that the universe is not separate from our consciousness. Many scientists who pride themselves on their rationality in all other areas, seem to overlook this fact (are they literally “blinded by science?”). They think of consciousness as some kind of process within the physical brain. Some even attempt to “explain away” consciousness as some sort of epiphenomenon (e.g. an illusion that can be reduced to something physical), or worse, as a mathemagical result of “complex enough” computation (the absurd but oft cited, “someday the computer just gets sooooooo complex that it suddenly wakes up” argument). But none of these approaches to consciousness can account for the actual experience (what the philosopher, John Searle calls “qualia”) of being conscious — an experience which each of has direct and undeniable access to.

I am skeptical that any computer will ever be able to simulate, let alone embody, the actual experience of consciousness. Since our universe and everything material, is in my opinion, emergent from consciousness, not vice-versa, it is not possible to cause consciousness to emerge from physical things: I don’t think you can build a machine that will become conscious. I don’t think we can synthesize consciousness — it’s already there and we don’t create it. We might be able to build very smart machines, but they still won’t be conscious in the same way that truly conscious beings are. In fact, I think the best and fastest way to make something conscious, if that’s what you want to do, is to just have a baby.

Consciousness is not a material thing, nor is it a result of a material process. It can neither be created nor destroyed and it never actually “inhabits” physical matter, which is why we cannot find consciousness anywhere in the brain or body when we try to measure it (i.e. the brain and body are within consciousness — they can be found within consciousness, but consciousness cannot be found within them). And if that’s the case, then no computer simulation will ever really contain actual consciousness — at best it will be merely a projection in the consciousness of whomever makes the simulation. Now why does this matter? Well for one thing it means that we will never succeed in creating artificial intelligence simulations that are conscious, and furthermore, that no simulation of any kind will be conscious. And it follows then that no simulated universe will truly be like our universe — because there won’t be any real conscious beings in the simulation.

My point here is that to really simulate our universe completely we would have to be able to make a simulation that contains conscious beings, but we can’t do that because we cannot make consciousness. And this is important because consciousness is not just some minor force in our universe — in fact it may have a vastly larger role in shaping our universe than we can presently see or understand. Some physicists even go so far as to postulate that if it weren’t for consciousness our universe wouldn’t exist, or alternatively, that our universe has evolved specifically to support conscious life (what is called the anthropic principle). But although we cannot prove or disprove such views at present, we can certainly see the effect that conscious life has had on our home planet: If consciousness can transform our planet from a jungle to a teeming metropolis in a matter of a few million years, then by extension it could do the same thing to entire solar systems, and perhaps over billions of years, interstellar civilizations of consciousness beings could literally transform galaxies. No simulated universe will be able to truly model or account for such effects.

Research into quantum mechanics is also arriving at the fact that consciousness plays an important, but not yet understood, role in shaping physical reality. It is clear that consciousness has a major impact on the outcome of certain types of experiments, for example. Whether you observe a particle or not determines how it seems to behave. Whether you observe a system, determines whether or not it is in one of various possible states. The act of observation seems to be the catalyst which collapses infinite possibility into a particular event. This can actually be measured experimentally on very small scales, but there is speculation that it operates similarly at larger scales too, in some circumstances. But even if merely at the very smallest scales, consciousness — “the act of observation” – is built-in to how physics works, then it follows that it has a emergent effect on the largest scale — the whole universe. But who knows, maybe the effects of consciousness on the whole are direct, not merely emergent? We don’t know yet.

There’s another reason that consciousness may throw a wrench in computer simulations of the mind and universes alike: Free will. Given that consciousness is totally transcendental, it is not conditioned by anything material. Yet, since everything is a projection of consciousness, consciousness can affect the world. To understand this, we can go back to the dream analogy again: For example, a dreaming consciousness can sense its dream projections, and it is even possible to have a lucid dream in which the dreamer controls the content of the dream, but at no time does the content of the dream ever have the ability to limit or condition the dreaming consciousness. In other words, it’s a one-way interaction. Consciousness can condition what it projects, but projections cannot condition consciousness.

Note here that consciousness is at an entirely different level from thoughts and sensory experiences –they are just mere appearances, not consciousness itself. This means that ultimately conscious beings have free will: They can effect what appears to their consciousness, but what appears to them cannot ultimately effect their consciousness in return — consciousness remains basically free, empty, pure, unconditioned, and untarnished at all times, regardless of what projections currently appear to be taking place. And, if consciousness has free will, then no computer simulation will be able to model it. The reason for this is simple: Computers are logic machines that follow instructions. They don’t have free will, they just follow sequences of logical operations. Nowhere in a computer or computer program is there anything that is truly free. At best we might be able to simulate computer intelligences that act as if they are free, but in fact, their seemingly free behavior is still actually caused by an underlying computer program at some level. Even non-deterministic, “emergent computations” are still reducible to underlying programs. But real free will is irreducible — it is not a result of any programming and cannot be conditioned by any external forces. In other words, consciousness is not a computer program, it is inherently unconditioned and free. No computer program can replicate that freedom.

In conclusion, I think our present civilization is at least several thousand years from really understanding much about consciousness and how it fits into physics, or vice-versa, but if we keep going the way we’re going our civilization probably won’t last that long. So to save time, we could look more deeply into the cosmologies of earlier civilizations that were much more advanced when it comes to consciousness than we are (for example the Buddhist cosmology as represented in the Kalachakra system for example, or the Mayan cosmology, both of which are far more inclusive of consciousness in their explanations of the universe.) I’m not suggesting that those cosmologies are going to help us understand black holes — for that our modern cosmology is probably better — but they certainly could help us understand how consciousness fits in.

There’s a lot more that could be said about this view of consciousness, but I’m not enough of an expert on Buddhist philosophy to explain it all in detail. I should also add that it is possible that my view is not exactly equivalent to the Buddhist view, and if that is the case, then any differences or mistakes herein are my own. If you’re interested in going directly the source (which is by far superior than anything I could write), I would suggest that you start reading up on the philosophy of dependent-arising and emptiness, for example the work of the ancient Indian philosopher Nagarjuna, and then perhaps start reading about the Buddhist conception of mind. There are lots of good books available on these subjects, although some are quite scholarly and difficult for beginners. Another, more accessible approach is to discuss these issues with a qualified scholar and teacher of Buddhist philosophy.

Cool Visualizations of Electromagnetic Fields

Nova — Mon, 04 Apr 2005 21:51:52 +0000

These visualizations were produced at MIT — they look like modern art but are actually visualizations of electromagnetic fields. Pretty!

Creator of Sim City Previews Amazing New Game

Nova — Sun, 13 Mar 2005 03:42:20 +0000

Many years ago I spoke with Will Wright — one of the most interesting visionaries I’ve met (and who happens to be the creator of Sim City) about his dream of a universe game — one in which the player could evolve life from the simple cellular level all the way up through galactic scale civilizations. Well it seems he has been busy working on this dream, and it sounds fascinating. He previewed it recently at a meeting of game designers, where he discussed the emergent, unpredictable and open-ended nature of the game, which is called Spore. When I spoke to Will about this years ago, I remember that he spoke of wanting to create a game that would enable players to experience the wonder and creative potential of the universe at all levels of scale. It sounds amazing, I can’t wait to try it.

Cell chip coming soon

Nova — Mon, 07 Feb 2005 03:43:10 +0000

Big news coming — a radical high-performance, ultra-miniaturized parallel processing chip is about to go mainstream in a variety of consumer devices, giving Intel some serious competition…

Semiconductor designers from International Business Machines,
Sony and Toshiba will reveal on Monday the inner workings of a
“supercomputer on a chip” they claim could revolutionise
communications, multimedia and consumer electronics.

The Cell microprocessor has been under development by the three companies since 2001 in a laboratory in Austin, Texas.

Its unveiling at the International Solid State Circuits Conference in
San Francisco has been eagerly awaited and products containing Cell
including Sony’s PlayStation 3 games console are expected as early as
next year.

Advance reports suggest the chip is significantly
more powerful and versatile than the next generation of
micro-processors announced by the consortium’s competitors, Intel and
AMD.

The two leading chipmakers are just moving from 32-bit to
64-bit computing and to dual-core processors essentially two “brains”
on a single chip.Cell is understood to have at least four cores and be
significantly faster than Intel and AMD chips.

“This is
probably going to be one of the biggest industry announcements in many
years,” said Richard Doherty, president of the Envisioneering research
firm. “It’s going to breathe new life into the industry and trigger
fresh competition.”

Read the full article here

Artificial War

Nova — Wed, 23 Jun 2004 22:32:04 +0000

Here is a book that readers who are interested in multi-agent systems will find useful. The author, Andrew Ilachinski is also a reader of this blog, by the way — it’s called “Artificial War: Multiagent-Based Simulation of Combat” and provides an examination of the thesis that what happens on a battlefield (though the arena can be much more general of course) is a self-organized emergent phenomenon that can be understood, at least in part, by examining relatively “simple” underlying rules. In essence, mobile cellular automata. The book summarizes work that dates back to 1997 and was sponsored at different times by the US Marine Corps and Office of Naval Research. Among many applications of this research — consider the applications for computer games and simulations, as well as for visual effects (think, even more realistic epic battle scenes and crowds).

Anyway, here’s the link

TOC and index can be downloaded here

Was our Universe Created in a Lab???

Nova — Thu, 20 May 2004 17:35:26 +0000

Here’s an interesting article on another theory that suggests our universe is just an experiment in someone’s lab.

How to Build a Network Automaton

Nova — Wed, 05 May 2004 00:09:41 +0000

Here is a cool new kind of complex system I am thinking about a lot that we might call a “network-automaton” or a “graph automaton” — a system that evolves networks (graphs) over time. This rule is similar to cellular automata rules such as the famous “Life” rule discovered by John Conway, however instead of computing the states of cells on a grid, it computes the shape of a network. In a nutshell this system applies a simple local rule at each node in a network that determines what other nodes it should connect to in the next step of time as a function of the connections each of those nodes had in the previous step of time. This yields complex network structures and interesting dynamical emergent behaviors over time — networks that grow and change as time goes by, networks in which there may even be stable or cyclical topological patterns that move across the network, as well as interactions between such patterns (topological interactions) that resemble the interactions between fundamental particles.

Network automata of the sort I propose here may be useful for modeling the structure and dynamics of a wide range of systems from physical systems, to biological systems, to the growth and development of computer networks, to social networks, business networks, and other types of higher-order networks.

(By the way — I would really like an open-source application — in Java perhaps — for generating and visualizing network automata rules such as those in this article. If you are a good programmer and would like to volunteer to make some software that can simulate the dynamics of the class of systems I propose here, please email me! I think this will be a very interesting avenue of exploration, and such a tool could be extremely useful.)

See the rest of this article for a detailed description of how to build a working network automaton….

Here is how a network automaton works….

We define a “network” as a set of locations called “nodes” that may be connected by “links.” Nodes are represented as black dots, spaced regularly on a white colored plane. Links are black or white lines that connect pairs of dots. A black line corresponds to a link that is “on” and a white line corresponds to a link that is “off.”

We define the state of a given node as the number of “on” (black colored) links it has to its neighbor nodes.

Now at each step in time t, for each node, we draw black or white links from it to each of its neighboring nodes, according to a function of the states of each of its neighboring nodes at time t-1. In other words, we update the link structure around each node as function of its local neighborhood.

For example, we draw either a black or white link between each node and each of its neighbor nodes at time t as a function of the state of each neighbor node at t-1. The state of each neighbor node is the number of “on” links that it has at time t-1. In other words, this rule deterimines the number of links of each node to its neighboring nodes as a function of the number of links of each of the nodes in its neighborhood.

One important note — You may have realized in visualizing this that there will be cases in which “conflicts” occur. For example, for a given pair of nodes A and B, A may compute the link A–>B as “on” but B will compute the link B–>A as “off.” What do we do in such cases? One option is to choose one of these choices randomly, another option is to have them “cancel out” to “off” or to “sum” them to “on.” An even more useful option is to keep both states. We can call this a “superposition” of states. We can represent this “indeterminate” state by a new color of link — not white or black, but perhaps grey. Our rule can be modified such that each node only sees it’s relative state for that link. Over time the network can “collapse” these indeterminate states as nodes come into agreement. For now, let’s just keep both states. So every link has two states, one in each direction but nodes can only “see” the links that correspond to their perspectives. This allows for the measurements that nodes make of one another to be relative to their own perspectives. Another way of viewing this is that there actually exists two links between every pair of nodes, one in each direction. Each link has 1 state. This is equivalent to the previous suggestion.

So now how might this system behave?

Let’s say that we are computing the state of a particular node, K. To do so, we must look at each of the nodes in K’s neighborhood. K has 8 neighbors named N, S, E, W, NE, SE, NW, SW that correspond to the nearest nodes at major points of the compass around K on the plane (Note: other neighborhood structures could also be possible such as just four neighbors N, S, E, W, or even hexagonal neighborhoods but for this example we will just use 8 neighbors). First we look at neighbor N and get its state: N’s state is the number of “on” links it has to other nodes. Our state-function might work as follows: If N’s state is 1 or 2 then we set the link from K to N equal to “off.” If N’s state is 3, 4, or 5 then we set the link from K to N equal to “on.” If N’s state is 6, 7 or 8 we set the link from K to N to ”off.” After we finish this for N, we then do the same thing for the next neighbor, S. (Note: I have not tested this particular state-transition rule, it is just an example, there is a large set of possible rules given that each node can have one of up to 8 states. It would be interesting to try many of them). Once we go through all 8 neighbors of K, we have computed the new state of K (the state of K at time t+1) and so we then move on to the next node K+1. Once we go through all the nodes in the graph, we draw the results of the updated nodes and links. Then we start the cycle again for the next step of time, t+1.

Rules such as those described above result in graphs that evolve and change shape over time, depending on various initial conditions (sets of initial “on” links). Depending on the state-function chosen and the initial conditions we may find “rules” with more or less “interesting” behaviors. It is certain that some of these rules will display interesting emergent dynamics. This is similar to cellular automata rules such John Conway’s game of Life. The difference is that here we are using similar techniques — a set of interacting local rules — to evolve the topology of a network.

But this is just the beginning. We can devise many more intersting state-transition rules than the simple example above.

For example we could use probabilities –
Instead of stating that if K’s neighbor N has z number of links an “on” link is definitely created from K to N, we could instead use a probability P that a link is created. The probability P could in turn be computed as a function the state of N at time t-1, or perhaps as a function of the state of K at t-1, or of the states of both N and the and K at t-1, or perhaps as a function of the states of all of K’s neighbors at t-1, or as a function of the states of the nodes that K is linked to at t-1, or perhaps even as global property such as a function of the states of all nodes at t-1. As you can see there are many interesting variations to explore here.

Another interesting type of rule would be to have more than just “off” and “on” links. Instead, color the links as a function of the states of the nodes they point to at t-1, or of the states of both nodes they connect at t-1. This enables the formation of rules that treat the link-states as factors to amplify or dampen the measured states of the nodes they point to. Thus when K measures the state of its neighbor N, the result of that measurement might be a function not only of the number of links N has at t-1, but also a function of the state of the link from K to N at t-1.

We can also go another step further in our explorations. Rather than have purely local neighborhoods, we could combine the above concepts to allow for non-local neighborhoods. In this case, at each step in time, each node computes the state of the link between it and every other node. To accomplish this, each node considers every other node to be in its neighborhood. It looks at the state of the link connecting it to each other node at t-1 as well as the state each other node, and possibly of its own state at t-1 as well, and based on these it computes a state for the link from it to that node at time t. By configuring the rule carefully such as system can be made to evolve various network topologies and dynamics over time.

Another interesting potential modification of the above non-local rule is to compute the state of each node at time t as a function of the link-states and/or node-states of only those nodes to which it has links above a certain threshold (or of a certain value or range) at time t-1.

A final note. We can represent all the information in this system in an array. Let U be the number of nodes. This array therefore has U * U cells in it. Cells are named by their x,y coordinates in the array. So for example, cell(1,5) refers to the cell at location x=1, y=5 in the array. Now we adopt the convention that the “nodes” are represented by the cells where x=y, for example, (1,1), (2,2), (3,3) and so on. Cell (1,1) represents “node 1″ and cell (2,2) represents “node 2″ and so on. The “links” are all the other cells. So for example, cell (1,2) is the link “from node 1 to node 2,” and cell (2,1) is the link “from node 2 to node 1.” In each cell we will also store a number representing the state of that cell. So we will add another dimension, s, to this array, for the states. So each cell has values (x,y,s) — it’s xy coordinates in the array and its state. This 3 dimensional array is sufficient to represent all the information in the system.

It is important to realize that this array contains a link from each node to each other node. If that link has a value of zero it can be considered to be “off” and thus the nodes it connects may be considered to be non-local to one another. If that link is non-zero however, then the nodes it connects are local to one another. Depending on what the state of each such link is, any desired topology can be modeled. This in turn depends on the functions we use to compute states. We can choose to have a fixed “Euclidean neighborhood” in which every node has 8 nearest neighbors that never change, or we can use a rule such as the final rule above in which every node is in the neighborhood of every node. In the latter case, using a probability function or other more subtle functions the states of the links connecting nodes to all other nodes can change such that various local neighborhood structures can emerge over time in feedback with the node states. This is ultimately a more general model, but probably not a good starting point due to the complexity of visualizing it (it may require more dimensions — 3D, 4D or more).

NOTES:

- Andy Ilachinski, e-mailed a very helpful response to this article in which he provided a number of links to related research on what are called Structurally Dynamic Cellular Automata or SDCA’s. What I have proposed above is an approach to making SDCA’s in which the neighborhood topologies are the states of the nodes in the network. In other words, each node’s state is its local topology. Andy gave me some references to very interesting papers on the subject, including:
* There are some wonderful illustrations of the output of SDCA’s in Andy’s book “Cellular Automata: A Discrete Universe”. These illustrations are exactly what I have been visualizing — essentially beautiful sequences of the evolution of various topologies based on local rules. They vary from simple geometric symmetries to fascinating complex and chaotic networks. If you are interested in this I can’t recommend enough that you take a look at this book. Anyone working on the physics of networks should know about this.
* Steve Majercik wrote a Manfred Requardt

- The rules I am interested in compute the topology of each neighborhood as a function of the topologies of neighborhoods it is connected to. In the most general case (the last rule above), every neighborhood is connected to every other neighborhood, but the links have states as well. By having both node states and link states we can generate very sophisticated rules in which the way that any two nodes interact is a function of their link states (one in each direction). Thus the topologies of neighborhoods are functions of the states of nodes and links that comprise them. As these states change over time the topology of the network evolves. This effectively links the “energy in space” to the “shape of space” — unifying them at a fundamental level. Everything reduces to topology.

- In the final model that I came to in my thinking on this subject I realized that in the general case every node should have 2 directed links with every other node (on in each direction “to” and “from”). The state of a node is a function of the state of all its links. The state of each link is a function of the state of the node it comes from (or alternatively, of the states of both nodes it connects). I believe this model is capable of containing any topology, including systems in which the topology and geometry of space from the perspective of any location is relative (this is the value of having 2 directed links connecting each pair of nodes — it enables each node to measure the other independently of the other’s measurement of it — the link can can have a different state in each direction). This is basically a superset of the SDCA concept — any SDCA can emerge within such a network.

9 Block Pattern Generator — Try it

Nova — Tue, 04 May 2004 19:26:50 +0000

This is a really nice visual pattern generator based on quilt patterns. Try it out.

The Physics of the Web

Nova — Tue, 04 May 2004 18:23:29 +0000

This is a very good article on the physics of scale-free networks such as the Web.

Lately I have been getting increasingly interested in graph theory and also in knot theory. There is a similarity between networks and knots and it should be possible to do a mapping such that the theorems and algorithms of knot theory could be translated to apply to network topologies. I’m sure someone is already working on this, but it’s worth pointing out. For example, many networks could be viewed as planar projections of knots (the shadows that knots cast on a plane). I have also been thinking about the subject of loop quantum gravity which I learned about from my friend Bram Boroson.

All of this connects to an idea that I’ve been thinking about lately for a new kind of discrete system for evolving topologies that I call a “loop automata” — basically the idea is to use networks of interlinked loops as the fundamental building blocks for evolving spaces, and the dynamics within them. In my conception of a “loop automaton” the points at which loops intersect (“crossings,” to use knot theory terminology) are “nodes” and the segments of loops between intersections are “arcs.” So using a single construct we can have both nodes and arcs in our model. In other words we can construct graphs out of systems of interlinked loops.

Loops can have various states (a simple model might have a single valued state for the “energy” of the loop, while more complex models might deal with oscillation frequencies or even shapes of loops) The next step is to design functions on such networks of loops that modify the state of each loop based on the states of loops it intersects with (it’s neighborhood). This function should govern the creation, destruction, linking and unlinking of loops, as well as the states of loops. By specifying either that all loops are fixed diameter (regardless of what other loops they intersect with) or that loops can only intersect other loops in a single point (in other words that intersecting loops are never on the same plane) then we can interpret the resulting network of loops as a space that must have one of a set of certain dimensions and shapes. This enables such a system to represent any potential space. Information propagates along such spaces as the states of loops interact, causing feedback between the topology and the energy state of space.

In such models, every pair of directly connected nodes have two arcs connecting them — one in each direction (I assume that all loops are directed arcs that circle back on themselves endlessly). This enables information to propagate along different paths in different directions, enabling a form of “social interaction” between nodes. For example, imagine that every loop is a little clock around which a single pulse of energy is circling at some frequency. Whenever the pulse passes through an intersection point with another loop (ie. through a node) an interaction takes place between the two loops. This has the effect of modifying the state of the loop we are looking at such that as the pulse continues from that point onwards around the circumference of the loop it may have a different frequency. In other words, as the pulse goes “to” a node it has some state, and as it returns back “from” that node it may have a different state. This “back and forth message passing” takes place between directly connect loops as well as along transitive chains of loops.

Unless you spend a lot of time thinking about networks, graphs, knots, cellular automata and digital physics all of the above is probably incomprehensible. I apologize for the “rough” sketch but these are preliminary ideas at this stage. Still, from my reading on knot theory, graph theory and other related subjects I am starting to see a pattern here. Perhaps using loops as the fundamental building blocks of networks is not such a bad idea.

Chaotic Computing – Alternative to Quantum Computing?

Nova — Wed, 28 Apr 2004 09:16:33 +0000

A new approach to computing called Chaotic Computing has been proposed. It uses chaotic elements to simulate logical operations. The benefits are that such systems may be dynamically reconfigurable in real-time, and may be able to perform multiple operations at the same time. This may be an alternative to quantum computing. It may also be how our brains work.

Finding Primes Using Cellular Automata

Nova — Tue, 30 Mar 2004 03:49:29 +0000

It just occurred to me that distribution of primes looks VERY much like the output of a cellular automaton rule. This makes me wonder whether it might be possible to use a cellular automaton to generate prime numbers. If we can find the rule that generates the prime numbers, perhaps this rule has other important properties. Just a hunch. In any event, it would help to explain the distribution of primes. Below I discuss some approaches to doing exhaustive searches for CA rules that generate the primes.

Here’s how such a rule might work: Simply adopt the convention that non-primes are cells with state 0 and primes are cells with state 1. Make a 1-dimensional cellular automaton. Next select a given COLUMN (not row) to represent the “output” of our computation — The goal is to come up with a rule and initial conditions that causes the bits in our chosen row to turn on and off such that the output bit at time n indicates whether integer n is prime or not. Interesting huh?

It also occurs to me that we could simply search for this experimentally by analyzing all rows and columns in the output of all 2-state 1D CA rules on all initial conditions (of a given number of cells) to see if any of them match the prime number distribution. We can start our experiment in a simple way — choose a small number of cells initially — say 10 — enumerated 0..9. Between 0 and 9 there are the following primes: 2, 3, 5, 7. So we want to begin our search by looking for CA’s that contain patterns that match 00110101 (cell 0=not prime, cell 1 = not prime, cell 2 = prime, etc.). If we find such a pattern, then we simply have to look at the next 2 cells to see if it generating the prime numbers (if the next two cells are 01, then so far, so good and continue looking at adjacent cells; if the pattern breaks then stop testing this segment and look somewhere else).

In thinking about this a little further I’ve realized that we could use a genetic algorithm to search for the rule and initial conditions. Simply represent the first n integers as a line of cells with states 0 or 1, corresponding to whether integer n is not-prime or prime. We can view this line of cells as horizontal (the state of one step of time in the system), or vertical (the state of a single cell across steps of time). Now we just have to evolve CA rules that generate this sequence of cells. This might be the best way to find our prime generator rule.

This is an easy experiment to do for anyone who is fluent in Mathematica and has some time on their hands. If you happen to do it, I would love to hear the results!

A New Way to Find Patterns in Distributions of Numbers

Nova — Fri, 26 Mar 2004 08:49:02 +0000

This evening I had an interesting idea for a new way to look for patterns in the distribution of numbers such as the prime numbers and the digits of Pi. In a nutshell I propose that there may be patterns in these number sequences that might not be evident to a computer but could be evident to the human eye and human intelligence, which among other things is tuned to find order in chaos, even when that order is “fuzzy.” In this article I propose a new class of rules that are similar in some respects to cellular automata, for generating visualizations of the distribution of numbers, and for leveraging distributed human intelligence to evalute those visualizations for meaningful patterns.

Let’s use the prime numbers as an example for this essay. We can represent the distribution of prime numbers visually as a line of black dots that is interspersed with white dots wherever primes occur. We can also represent primes that belong to various classes with various corresponding colors if we wish. In any event, it’s just a line of pixels. Now let’s define a program that generates rules for displaying this line of pixels in various ways.

(Note: After writing this article, I discovered some software that illustrates one instance of this idea beautifully, based on work by Stanislaw Ulam, one of the originators of cellular automata theory. The “Ulam Spiral” generates interesting visualizations of the distribution of primes that illustrate that they are clearly non-randomly distributed.

For example:

The basic difference between my conception and Ulam’s is that I do away with the constraint that the primes should be arranged in a spiral — that is just one way to pack the primes into a plane and why should it be the one we choose? My approach generates different packings of primes in space in the hopes that one of them will reveal even more interesting hidden structure to the distribution of primes, that structure being expressed by the rule that generates the packing. It’s interesting that I came up with this idea without first knowing about Ulam’s work on this, but it’s not surprising that Ulam was onto this; he was one of my inspirations in the early years of my interest in cellular automata theory).

In my approach the rules for generating layouts are simple — they are based on the analogy of the “Etch-a-Sketch” (a drawing toy in which you make picture by drawing a single line and simply turning it left and right) — a pixel is drawn and then depending on various variables (such as the number of pixels already drawn, the number of pixels drawn before of a single color, the color of the most recent pixel, and the colors of pixels about to be drawn, to name a few possibilities) the next pixel is placed in a certain direction relative to the previous pixel (any direction, depending on the number of dimensions — in a 2D visualization there could be at least 9 directions in which to draw the next pixel — same place, north, northeast, east, southeast, south, southwest, west, northwest).

A more general, and ultimately better, version of my rule for laying out the numbers is to simply say that the location on the screen in which to place the next number in the number sequence, is determined as a function of the number itself and/or preceding numbers (and/or some set of numbers that follow it, if desired). This allows for all types of layouts to be generated, from layouts in which the numbers are arranged contiguously in space to those in which adjacent numbers do not appear in adjacent locations in space.

My hypothesis is that there may be a hidden structure in the distribution of prime numbers that is only evident when they are arranged on the right type of surface, according to the right algorithm. For example, consider arranging the number line on a sphere, then where do the primes appear and does that reveal hidden structure? What about higher-dimensional layouts?

One rule that such a system could generate might wrap the line at every n pixels, in order to fit it in some sort of a rectangular array. Another rule might wrap the line in a much more complex way, making right and left turns to wind it through a complex path in two dimensions. Still other rules could potentially wrap the line to fill a 3D space, or even higher dimensional spaces. Because these rules can also potentially draw pixels on places where pixels were once drawn in the past, they can even appear to be animated over time — for example, suppose a rule draws a square of pixels and then redraws a new square over that square — if this runs fast enough it would appear to be a movie of sorts and this opens up the possibility that the pattern in the primes might be visible as a sequence in time and space — which actually makes sense given that our universe consists of space-time. Who knows, perhaps our universe IS simply the pattern generated by such a rule running on the distribution of primes in a certain number of dimensions.

In any case, using such simple rules, the line displaying the distribution of primes can be displayed according to an infinite variety of geometric visualizations. My hypothesis is that while the vast majority of such visualizations will appear to be random, some perhaps may display unexpected structure — for example, suppose that in some the primes line up in a certain way, or form a complex but recognizable geometric shape or tiling.

The human eye is capable of recognizing even the slightest traces of order in such chaotic fields, and this is key to my approach. There may be patterns in the distributions of primes that are not precise, but are rather “fuzzy” or “nearly precise” in the same chaotic way that Nature is. Computers are not good at recognizing “fuzzy patterns” — but human senses and brains are tuned specifically for this. In fact, a variant on the above visual pattern scheme might be to render these distributions with sound — for example by interpreting a Rule as a specification for a soundwave or rhythm for example. In any case, the key is to leverage the ability of the human brain to find order in chaos, especially when that order is only semi-ordered. So how can we accomplish this, given that the search space of possible patterns is infinite?

One way might be to leverage the minds of millions of people at once — for example by making a distributed screensaver — similar to SETI@home — on which randomly selected visualizations of prime number sequences are rendered according to randomly selected rules. As these visualizations flash across thousands or millions of computer monitors, users can click to rank the ones they see as “more patterned” or “less patterned” and this feedback goes back into the system to affect the rules being used to generate further visualizations. In this manner perhaps we can guide the evolution of rules towards more interesting regions of the search space. We might also just get lucky — perhaps someone sitting at their computer terminal one evening will see a surprisingly ordered pattern flash in front of them — perhaps it will be a complex geometric tiling, or a shape, an animation, or a gradient — and this pattern, may reveal a hidden structure to the primes that could open up incredible new vistas in our understanding of mathematics, science and even perhaps our universe itself.

I often wonder whether there is something potentially cosmic hidden in the distribution of prime numbers — perhaps something related to the deepest structure and dynamics of our universe in fact. Is the key to chaos hiding there — the meta-pattern that explains all natural patterns, including for example, the chaotic fluctuations in the weather, in population dynamics, and in stock markets? Or will it turn out that the pattern we find requires a space with 11 dimensions, for example — and what might that imply about the universe we live in? Or will the pattern by dynamical — a changing sequence that has certain repeating or at least self-similar properties over time and space? And wouldn’t it be interesting if the best way to find that structure was with human (not computer) intelligence, with all its inherent fuzziness and imprecision?

And now for the Big Idea in all of this. I have a hypothesis that there exists a particular manifold on which the prime numbers “line up” perfectly to form some sort of structure, and that this particular manifold is something fundamental — it will tell us something fundamental about the structure and nature of spacetime, number theory and physics — in a sense it will unify them. You might call this Platonic Unification in that it unifies abstract number theory with physical space and time — it bridges the gap between “the Forms” and the world of “shadows” that we live in, to put it in Platonic terms. But as long as we are speculating, let’s not stop there — what if the structure of the primes on this manifold is actually of interest as well — for example, suppose it is a map of something — a map of the universe, or perhaps the key to chaotic system dynamics.

In other words, what I am suggesting here is that the fact that the distribution of primes is non-random is a “clue” to some Big Secret that we are “supposed to discover” — a clue left for us to find by “God” so to speak, that will lead us to the Ultimate Secret. We can approach this problem iteratively, starting from a small number of dimensions, and trying every packing in spaces of a certain shape and volume. By using a genetic algorithm approach we can tune our search to focus on the packings that yield the most promising structure. It’s like solving a high-dimensional “Rubik’s Cube” problem. But actually it’s really a “Reverse Rubik’s Cube” — that is we start from the assumption that the colors on the Cube already line up and now given a sequence of colors we have to figure out the shape of the “Cube.” Of course it may not be a cube at all — it may be a torus, or hypercube, or some other complex topology.

Social Networks, Physics, Civilizations — Do they All Obey the Same Underlying Rules?

Nova — Thu, 29 Jan 2004 18:40:36 +0000

I am having an interesting conversation with Howard Bloom, author, memeticist, historian, scientist, and social theorist. We have been discussing network models of the universe and the underlying “metapatterns” that seem to unfold at every level of scale. Below is my reply to his recent note, followed by his note which is extremely well written and interesting…

————
From: Nova Spivack
To: Howard Bloom
Subject: Re: Graph Automata — Is the Universe Similar to a Social Network?

Howard, what a great reply!

Indeed the metapattern you point out seems to happen at all levels of scale. I am looking for the underlying Rule that generates this on abstract graphs — networks of nodes and arcs.

In thinking about this further, I think we live in a “Social Universe.” What binds the universe together, and causes all structure and dynamics at every level of scale, is communication along relationships. Communication takes place via relationships. And relationships in turn develop based on the communication that takes place across them.

Relationships and communications take place between locations in the manifold of spacetime, as well as between fundamental particles, cells, people, ideas, network devices, belief systems, organizations, economies, civilizations, ecosystems, heavenly bodies, galaxies, superclusters, or entire universes. Whether you call it “gravitation” and “repulsion” and other forces are really just emergent properties of the dynamics of relationships and communications. It’s really all very self-similar.

I believe that we can make an abstract model of this — just a graph comprised of nodes connected by arcs — where the nodes (and possibly the arcs too) have states, and information may travel across them. Then, at each moment in time, we may apply simple local rules to modify the states of nodes and arcs in this network based on their previous states and the states of their neighbors.

For example, at time t+1, the state of each node is a function of the states of the nodes within some number of arcs from it and states of the arcs along each path to each of those nodes. Also, at time t+1, the state of each arc is a function of the states of the nodes it connects and perhaps also the states of the arcs of those nodes.

A node represents an entity — for example a particle or a person or a stock symbol. The state of a node can be a single number or an array of numbers representing many different variables, depending on our simulation. Arcs represent communications channels, through which nodes measure one another. The state of each arc encodes the strength of the relationship — the communication channel — it represents. Measurements can only happen via relationships — for a measurement to take place some information must travel from the thing being measured to the thing that measures it. In my abstract model I use a directed graph — so each relationship (arc) is only one-way from one node to another node. Thus a “bidirectional relationship” is a case where two nodes, x and y, are connected by two arcs xy and yx.

I also start with a maximally connected graph — every single node has one relationship arc to every other node and one from every other node. This allows for every node to potentially make a relative measurement of every other node according to its “perspective” on the relationship.

At every step in the simulation, every node x measures the state of every other node y via the relationship from that other node y to x — but the measurement is conditioned by the state of the arc along which it takes place such that in some cases it is enahnced dramatically, or dampened to the point where it is simply not strong enough to matter. When a measurement is dampened to that degree it is equivalent to there being “no relationship” between the nodes.

Thus although there are always virtual relationships between all entities, only some relationships are “actual” in the sense that they are strong enough to enable measurement to take place. And this changes over time, based on how the entities interact. Our rule should evolve the strength of relationships based on the measurements that take place across them.

The philosophy of this model is based on the insight that a relationship is in fact the most fundamental thing in the universe — even more fundamental than particles or locations in space-time. This is very much philosophically in the camp of Liebniz as opposed to Newton.

In fact, in my model, both nodes and arcs are actually relationships — a “node” is represented by an arc that loops back on itself — it is something that measures itself — a circular relationship; an arc is a relationship that does not loop back on itself — a relationship that connects one node to another. Therefore there are really just relationships in this model but they are interpreted differently depending on their shape — an “entity” is a node, a self-relationship, a communication channel is an arc — an other-relationship. I mention this only because of its elegance — it makes it possible ultimately to have a single rule that operates only on arcs at each step in the simulation (since nodes are arcs too in this conception), rather than having different rules to compute node states and arc states.

The most basic act in the universe is to measure something via a relationship. A measurement is therefore the most fundamental unit of communication. A series of measurements that take place between two entities is an interaction — a process of communication. Relationships are communication channels (arcs) that affect the measurements that travel across them: strong channels may enhance measurements, weak ones may dampen them. So the measurements that nodes make of each other are conditioned by the arcs that mediate them. Likewise, the state of a relationship, and therefore its effectiveness as a communication channel, may change based on the measurements that take place across it over time.

This model is essentially very similar to a neural network, and in fact a modified neural network algorithm may be just what we are looking for. I would not be surprised if in fact we could empirically discover this rule by looking for a pattern in the way relationships and interactions develop among neurons in the brain, people in social networks, memes in belief systems, services on the Internet, stocks in economies, stars in galaxies, etc. As you point out, gravitation between stars is similar to the attraction between people. And relationships between people are not so different from topological connections between locations in space-time, or the forces that bind particles together.

Using networks to model these various phenomena is not merely interesting, it may be essential to discovering a unified theory of the universe — there may actually be a metapattern to all “social networks” that helps us to discover the key underlying laws of the universe, at every level of scale. And that is something our civilization has not done yet — we have not found a general theory of structure and dynamics that applies equally well at every level of scale, in every context. Quantum mechanics is still not unified with Relativity, let alone with Biology, Society, Ecology, Economics, etc.

I think this “metaunification” will be easier to accomplish if we use the same basic model to represent structure and dynamics at every level of scale. Currently very different models and languages are used by thinkers to represent systems at different levels of scale — and this is one of the reasons we have not achieved much unification to date. We need to get everyone speaking the same language — using the same modelling tools — so it is easier to map between discoveries in different domains. Network models are ideal for this purpose.

I believe that an empirical study of existing social networks on different levels of scale is one route to finding the general pattern we are looking for: All social networks — at all levels of scale — should obey certain laws that we can discover through observation and then generalize into a general theory. Another approach is purely through mathematics — it should be possible to derive an abstract mathematics of social networks. Finally there is also the computational approach — simply generate and test different social network rules, and perhaps even use a genetic algorithm to evolve an optimal one. Perhaps that is the computation that our universe is running?

— Nova Spivack

—–Original Message—–
From: Howard Bloom
To: Nova Spivack
Subject: Re: Graph Automata — Is the Universe Similar to a Social Network?

Nova–Fancy running into you here on paleopsych, The International Paleopsychology Project email list.

Pavel Kurakin and I, curiously enough, are looking at the basic patterns underlying social connections among quantum particles, insects, and, implicitly, humans for an upcoming paper. Pavel is with the Keldysh Institute of Applied Mathematics of the Russian Academy of Science.

Something you’ve said hits a nerve: “the network seeks to help each node optimally balance its connectivity against information overload”. Bear with me while I seem to go way out beyond left field. I’m working on a book called Reinventing Capitalism: Putting Soul In the Machine–A Quick Re-Vision of Western History. One of the chapters is called “Marketing Meaning—Moses And The Slogan”.

It’s about the way in which Moses marketed his new religion…the way in which he drummed it into the head of his Chosen People. If you can believe the Bible and Sigmund Freud’s brilliant analysis of Moses and of the basics of community building in his Moses and Monotheism, Moses boiled his entire system of belief down to a slogan–”Hear, oh Israel, the Lord The God, the Lord is one.” Then the sociologically wise prophet told his followers to hang this bumper-sticker distillation on their doorposts so they would see it in the morning when they walked out of the house and in the evening when they walked back in again. He ordered the men to bind the slogan to their wrists, arms, and foreheads twice a day. And he apparently made darned sure that this catch-phrase was repeated a lot.

Today we call this sort of thing branding. Why is it so necessary to us human beings? Why do we need to have just a small Olympus of stars and leaders we can gossip about? Why do we focus on brands like Coke, Pepsi, and Dr. Pepper, but toss lesser known brands aside? Why do we show interest in only two or three presidential primary candidates–Kerry, Dean, and Clark–much to the consternation of the other five or six?

We have only seven slots for immediate memory in the brain. This limits the information we can handle. It limits the number of choices we can comprehend..or tolerate. (From the description of another Reinventing Capitalism chapter: “A little choice is freedom. Too much choice is agony.”)

So to get through to us, you have to make it simple and you have to make it stick. You have to repeat it over and over again until we get it. Once we’ve gotten it, we can slide it from consciousness to habit (from explicit memory to implicit memory) and concentrate on something else.

What does this cellular automata-style rule of individual capacity mean when writ large in group behavior? It means that we need to do a lot of quorum sensing. We need to go along with the herd. We need to pay attention to what everyone else is paying attention to. We need to buck it and criticize it if we want, but to fixate on it one way or the other. If George Bush Jr and the Iraq War are the topics of the day, we can hate Bush, love Bush, hate the war, love the war, but not get sidetracked by detailed examinations of who the Chechen rebels are.

We go with the flow of popularity. We follow fads, even if we only come along for the ride and criticize them.

This rule pretty much applies to the cosmos, too. Gas whisps and dust clouds in the early cosmos went where the action was. They congregated around self-forming swirls called galaxies. Then they aggregated even further in suns and planets. The general rule was this: To he who hath it shall be given. From he who hath not, even what he hath shall be taken away.

Why the repetition of this rule on two very different levels–the gravity wars that led to galaxy formation and the popularity wars, the wars of social gravity, that determine who will be the candidates in a presidential election and who will be the hot rock and TV stars of the day? Humans aggregate to limit the flow of information. But do specks of interstellar dust interpret information, too?

Specks of dust do respond to attraction and repulsion cues. If they’re negatively charged they avoid other negatively charged things. They move in the patterns dictated by magnetic waves surrounding stars and furling in galaxies. And, of course, they pick up on the come-hither cues of gravity.

But surely interstellar dust flecks and whisps of gas can’t work to optimize their information flow. They can’t gravitate around stars because of a need to keep their seven slots of memory from radical overflow. Nor can they use those stars to keep them entertained–to assure that they don’t suffer the pain of boredom that comes from information underload.

Whither comes this common pattern that keeps the big getting bigger yet provides a few key choices? Why do embryonic stars in a star nest or cluster compete like starlets in Hollywood to become the next big center of attraction?

There’s a primal pattern, an evolutionarily stable strategy, what I’ve been calling an Ur-pattern, rearing its head here on many levels of emergence. But how does this similarity appear and why?

— Howard

Graph Automata — What Can Social Networks Teach us About Underlying Physical Laws?

Nova — Tue, 27 Jan 2004 18:15:31 +0000

Hello all, I have been thinking about the general problems of social networks on the Internet. It occurs to me that these issues are closely related to digital physics. For more on digital physics see the work of Ed Fredkin, Stephen Wolfram, Norman Margolus, Tomasso Toffoli, and other pioneers of the field of cellular automata.

In the past I have worked informally on cellular automata at MIT in the lab of Fredkin, Margolus and Toffoli — and in particular that led me to get interested in what could be called “graph automata” — rules that operate on arbitrary graphs in a manner that is similar to the way that cellular automata operate on cells in rigidly defined neighborhood topologies. The general concept is that the structure of a graph can be optimized for various parameters in a bottom-up, iterative, emergent fashion by running local rules at each node based on the neighborhood structure around each node (taking into account the number of arcs around each node, the directionality of arcs if any, and the states of nodes if any). There is a general class of rules that we could call “graph automata” that are quite interesting to study because in many ways they are better metaphors for physics than simple CA’s, in my opinion.

In any case, that’s not the point of this note. Instead, I would like to propose that one way to discover the “general laws” of digital physics might be to study social networks. Social networks are an interesting “macro-level” phenomenon that could be considered to be useful analogs for discovering the general properties of physical information networks. They are comprised of nodes connected by arcs in which information flows. We could view all physical systems through this lens and perhaps learn quite a bit from this approach.

Currently social networks on the Internet are either totally informal and decentralized or totally centralized and formal. However in either case they are not being effectively optimized because nobody knows how to optimize them.

To optimize a social network we need to continually evolve the graph as members join, interact and form and end relationships. As the network evolves the paths that information takes between interacting (or frequently interacting) members are therefore evolved (and are hopefully optimized in the process). In other words, if the goal is to optimize the communications between nodes in the network, then the rule we choose should seek to continually optimize the signal to noise ratio of each node. Another way to say this is that the network seeks to help each node optimally balance its connectivity against information overload.

It seems to me that this is a general principle that may apply in many domains — including perhaps digital physics. It reminds me of general relativity in certain respects. Perhaps there are people out there, more mathematical than myself, who are able to take this idea further? I have a strong hunch that this is a clue to a general physical law that might be useful at many levels of scale, and for many purposes. Is there a simple rule that evolves graphs to optimize relationships among interacting nodes? If so, I would not be surprised if this rule generates dynamically changing graphs that obey the principles of Relativity. The rule we discover could be of great value in physics, biology, chip design, communications and network architectures, artificial intelligence and machine learning, information architectures and search, and social network architectures, as well as many other fields, like economics, for example.

While all of this is speculative and I am not a mathematician or a physicist, I have a long history in cellular-automata and AI and I have a strong hunch that there is something here worth looking into further. Keep me posted!

Here is a link to an article about this — I would enjoy hearing your comments!

Optimization of Social Network Architectures Using Tiling Rules

Nova — Tue, 27 Jan 2004 17:10:34 +0000

Here’s an interesting follow-up thought on my suggestion of some Hypothetical Laws of Social Networks.

What if in fact there is an entirely new way to design social networks, based on the mathematics of tilings? A tiling is a method of filling a space with geometric shapes. For example, you can tile a space with squares, hexagons, quasicrystals, spheres, etc. — depending on the dimensions and topology of the space.

We could view a social network as a tiling problem — each “tile” represents a set of nodes and arcs. “Corners” (nodes) are members of the network (such as people or organizations), the edges (arcs) are relationships between members. For this to be meaningful we must require tiles that have at least one node in them (so no circles or spheres or other tiles with only a single arc but no nodes).

Viewed in this way, we can look at particular tilings as designs for optimal social networks. What all this leads to is an insight that if there is an optimal number of relationships per member of a social network, and an optimal number of hops between members of social networks, then given a number of users in a network there is a particular tiling that optimizes those parameters. This tiling could be used as a template for the relationship structure of the social network.

So for example, when a member of a certain network adds a “new friend” in fact the network may not add that friend directly to their node, but rather may reconfigure the tiling structure such that they are optimally connected to that friend, via some number of hops instead of directly.

In other words, if the goal of a social network is to optimize relationship networking and communications — it may require not always directly connecting people when they add one another as friends. And furthermore, it may require continual reconfigurations to optimize the evolving relationship structure as people join the network and form new relationships.

When parties add one another as friends it is essentially placing a constraint on the tiling of the network — it makes the network attempt to optimize the H value (number of hops connecting them) for those parties. I have a hunch that this could be computed recursively and in a distributed fashion — in fact, I think a cellular automaton rule or a tiling rule may be just the way to do this.

Roger Penrose might be a good source of ideas for this. I have a feeling that the best tilings will be highly irregular and chaotic, and ultimately we may be dealing with a high-dimensional manifold (not a simple 2 dimensional plane). But the same principles apply in any number of dimensions. Also I would suggest looking what is going on in the field of “loop quantum gravity” as a source of ideas for this. Of course graph theory, cellular automata, and the theory of geometric tilings are all relevant as well.

The key point I am making is that it should be possible to optimize the structure of the network using local distributed rules — or at least regional neighborhood rules — rather than global rules — computed recursively perhaps — that seek to optimize local tilings around nodes so that they are optimally connected to parties they add to their social networks.

Optimal connectivity is a balance between sparsity and density. The current trend in social networks of directly connecting parties to their friends is actually the very WORST way to structure these networks. A much more intelligent, and adaptive, paradigm would be to continuously reconfigure the network to suit the priorities of the nodes while seeking to provide them with optimal connectivity to their contacts. Direct connectivity is not necessarily optimal connectivity.

We need a way to design a social network such that it self-optimizes as members join and as they form relationships, such that members are optimally connected (not underconnected, not overconnected, and within range of their friends). As the network grows it has to continually retile itself to stay optimal. What this looks like is an evolving, self-optimizing irregular chaotic tiling.

I also have a hunch that this is a hint towards a general physical law — similar to the universe optimizing the shape of space so that light travels most efficiently, I think a discrete universe could be viewed as a big social network of sorts where the relationships are the topology, the nodes are the locations in space, and the messages they exchange are light pulses.

The goal is to optimize the shape of this network around every node such that it does not experience “information overload” and is also optimally connected to other nodes it interacts with. Whenever an interaction takes place between two nodes we should consider them to have a stronger relationship, and this should bring about a perturbation and re-shaping of the network connecting them such that they are optimally connected.

Every interaction therefore brings about topological changes to the network based on the goal of optimizing information flow of further interactions. Seems to me that this could become a general physical law — just has to be expressed in the right mathematical language. The law should be invariant across levels of scale and domains — all networks should basically be optimizable using the same “network physics.” Is this the network-equivalent of general relativitiy? I think there are some very interesting similarities.