Sunday, October 09, 2005

Emergence

Recently I have posted about such topics as econophysics and the physics of societal and cultural change, as well as similarities in network structures of the Internet and al Qaeda. I am personally fascinated by the relatively new field of study of complexity and emergent behavior, although I am the first to admit I am an absolute beginner in my understanding of what has been done at the cutting edge over the last ten to twenty years. Some of the comments to my posts as well as questions in emails and additional reading I have done (including a book I have just started: check out “A Different Universe” by Robert Laughlin, Nobel laureate in physics…it is a page turner) have only increased my desire to learn more and develop a deeper understanding of what complexity and emergent behavior means, as well as where physics and science in general is headed in the future.

What I want to do in this post is list some examples of what is meant by “emergence,” and in future posts develop a way of explaining what it might mean for the path science takes in this century. A working definition of emergence: refers to the principles of organization for a many-body system. Such systems consist of individual entities that can act/move randomly, but then the system spontaneously exhibits some sort of collective organized behavior. The details of the individual components are not necessary to understand the system’s behavior. In fact, the emergent behavior is typically not predictable with only the rules of the individual components of a larger system. All of the following are examples of emergent behavior I’ve come across in some of the literature devoted to the study of complex systems.

- magnetism: in most materials individual domains are directed randomly but then can spontaneously be redirected by an external magnetic field so they align, causing the emergence of macroscopic fields.
- When you splash water on a surface and those little beads develop: water molecules inside the bead move randomly, but the bead emerges because of surface tension, giving a fixed structure
- Gases in closed systems: molecules move around randomly, but collectively the system follows set statistical rules such as the ideal gas law, PV = nRT
- Synchronization: there are lots of examples of this, such as an audience that begins clapping randomly, but then the clapping organizes into clapping in unison
- Emergent behavior can refer to phase transitions, such as cooling a liquid so the random motion of molecules stops and those molecules then become fixed in some lattice; a solid emerges from the randomness
- Social networks: individuals meet and know others randomly, but what emerges is a network of fixed mathematical structure, such as a scale-free network
- Galaxies: stars begin by moving randomly and are affected most just by other stars in the local neighborhood, but a swirling structured system emerges
- Random motions of vibrated granular materials can spontaneously form structured patterns such as oscillons
- Mix of people with diverse, varying skills emerge as an economy; the individuals can be free to do what they wish with their money, but the collective behavior is a system with fixed mathematical structure and statistical rules
- Art: think of a Monet painting of flowers…look at it closely and the individual brush strokes are imperfect and essentially random, but collectively structures appear and we have a masterpiece. The details of the individual stroke are not necessary in understanding what the emergent behavior, i.e. the global emergence of the form of the flowers, is
- Music: an instrument such as a violin has a continuum of sounds it can make, and played randomly we would recognize as noise. But some random sounds placed in particular order with timing structure emerges as pleasing music
- Radioactivity: individual uranium atoms decay at random. An individual atom can spontaneously decay as easily in a few seconds from now as tens of thousands of years from now. Collectively, however, millions of uranium atoms emerge as a system that follows select statistical rules with well-defined characteristic times such as a half-life. The individual atoms no longer are important, but rather the emergent statistical behavior, which gives predictable results, matters.

What all of these examples show is that the rules for the individual members of each system become less important, and can actually become irrelevant, to understanding the collective behavior of the system. Rather, what is important for the system is the principle of organization that leads to the collective behavior that has emerged. Statistical rules normally dominate to describe the way the system behaves, and predictable results can be obtained for the system, even though the nature of the individual members of the system can act at random. This is the essence of research in complexity and emergence fields of study, and brings about important changes in the way we think about the science of the natural world as well as social sciences. What are the fundamental rules and laws that help describe and explain what we observe? The rules of the individuals (microscopic, local) or of the emergent behaviors of the collective system (macroscopic, global)? Which are more important to understand? Are the rule sets for the local more important than those for the global? Historically most physical science has been geared in a reductionist mindset, breaking problems down further and further to understand the microscopic system of individual components (that is the essence of my days of research in particle physics, for example). Studies of complex systems, however, have been showing the need to step out of the reductionist mindset many scientists have been in and develop an entirely new way of approaching the science. What’s more, the focus needs to be placed on identifying principles and rules of organization, which are more fundamental for the system’s behavior, than the rules of individual components of the system. In addition, what has been observed is that the organizational rules of what are entirely different systems, such as numerous physical systems and numerous models of economics, are nearly identical. This has allowed for unprecedented collaboration between physicists and economists and has lead to new areas of research in econophysics. Most who work in these new areas of study believe we have only scratched the surface in our understanding of emergent behavior of complex systems.

8 Comments:

Blogger mark said...

hey Von,

What they need is a " consilient" mindset.

Let me throw this at you for your consideration...perhaps the rules governing emergent behavior in complex systems has less to do with the *intrinsic* behavior of the system's components than it does with the *extrinsic* characteristics of the environment in which the system is forming ?

Consider the brain and the pruning of neuronal networks that occurs in toddlers - the environment is shaping the network to an extent ( language acqusition certainly, we drop sounds we do not hear).

8:01 AM  
Blogger vonny said...

Hey mark,

Exactly...this is the gist of complex systems, where the principles that govern how the individual components of a system behave normally cannot be used to describe or explain how the collective behavior of the entire system behaves. The environment will have an effect on the system in a different way than it would on individual components. Your brain example shows this beautifully...perhaps 'the whole is different from the sum of its parts' is a good way to think about it, and the trick is to figure out how a many-body system organizes within a particular environment. This is the hard part!

8:20 AM  
Blogger Bob Klapetzky said...

Excellent Post.

The concept of phase is critical.

The physical characteristics of elements vary in their different phases, of gas, liquid, and solid. Response is vastly different to external inputs dependent on what phase it is.

The phase transition is a chaotic, complex event that has been ignored for very practical reasons. Academia’s product is paper. Up until the recent advances in cheap computational power, it was very difficult to produce a lot of paper regarding phase transitions in complex systems. (James Sethna: Cornell)

The affect of the external environment is dependent on which phase the system is.

In the sub-critical state external factors play a small, ineffective role, and the individuals behave in a random manner.

In the critical state, there is a high degree of correlation within the participants/units. The same large external event will have a much larger affect, versus when the system was sub-critical.

To our detriment, in our everyday observations around us, we tend to have short-term memories, and “anchor” to recent events. Recent events being in one phase, and the future holding a large event during another phase with a dramatically different result and we are left standing there wondering why.

Sincerely,
Bob Klapetzky

6:58 PM  
Blogger James said...

Here's a question - what do you do when a system is too big to use simple mechanical laws but too small to apply statistical rules? I know scientists are having trouble applying quantum mechanics to individual molecules.

I guess we can just use really really big computers to crunch approximations, but are there cleverer methods to walk the fine line between the fundamental laws and statistics in this "almost-complex system?"

5:11 PM  
Blogger Matt McIntosh said...

Re: the importance of complexity in economics: as with so many other things, Hayek was there first. Thomas Schelling, too.

2:31 PM  
Blogger Curtis Gale Weeks said...

Most of my limited understanding of emergence comes from reading a collection of essays on literature: Chaos and Order: Complex Dynamics in Literature and Science. It is a fascinating collection exploring the work of literary figures like Jorge Luis Borges, Stanislaw Lem, and the poet H.D. The essay on H.D. is particularly revealing, in the way certain themes and images are reintroduced throughout a poem but through different wording and phrasing: motif becomes a method for the introduction of order, but doesn't work in a linear pattern; motif emerges.

Fascinating work.

6:37 PM  
Blogger Bob Klapetzky said...

Vonny, James, Matt, and Curtis.

You are so right. Isn't the best solution often simple, and elegant.

Vonny, your site quotes Dr. Feynman. Dr. Feynman's is one of my inspirations.

Passionately believing that my topic of study behaved in a manner similar to hysteresis, but unable to prove it, my hypothesis languished. Then I heard a story about Dr. Feynman. In class, he would bring the cascading avalanches within a magnet to life, by attaching the magnet to audio speakers. You could hear the avalanches. Barkhausen noise. Talk about clever and simple.

This simple, clever, elegant exercise was inspiration, in, and for, my search for barkhausen noise within my topic of study. (Yes, I found it. No, I’ve not published, yet;)

Thank your Dr. Feynman! (and Levy, Zipf, Bak, Mandelbrodt, etc..)

Matt: Great point. What a substantive body of work Dr. Hayek produced. You have motivated me to review his works. Thank you. Nobel. “Nuff” said. A giant often overlooked.

As you know, his theory was overpowered by Keynes, for a while. I propose that Hayek was a victim of the times, as Keynes would be later. They are both right part of the time, and wrong part of the time. Again, (if I'm wrong, at least I'm consistent) it depends on what phase the markets are in, as to what is the appropriate metric/model/tool.

Curtis, you should check out: "Human Behavior and the Principle of Least Effort"; G.K. Zipf. 1949 It is right up your alley.

Sincerely,
Bob Klapetzky

8:22 PM  
Blogger vonny said...

Thanks for all the thoughtful comments. I am convinced that studies into complex systems adn emergence will dominate numerous fields in the next few decades, so it is neat to see how these fields actually emerge.

Bob, it sounds like you have been involved in this work, so I appreciate your feedback. You are so correct about the idea of phase, and the fact that our ignorance of what happens during phase transitions is vast. It may take someone with a Feynman level genius to make significant progress in this area, but likely there will be steadily increasing interest and research in the actual transition periods.

Matt, having no background in economics, thanks for the comment about Hayek and Shelling. I'll need to learn more about their work, too.


Curtis, I was equally ignorant of work with emergence in literature. How cool is that?!

James, there is no clear-cut way of knowing where the threshold might exist as far as using straight physical 'law' versus statistics. It depends a lot on the system, intiial conditions, the time evolvement, the environment, and so on. With something like quantum mechanics, you are right that there is great difficulty in applying it to even simple molecules...not because we can't write down something like the proper hamiltonian operator, but rather because when we stick it into the Schrodinger equation the mathematics are simply too hard to solve exactly. Even for atoms except hydrogen, we need to make approximations to solve the differential equations, which means solving them numerically. From your own work with three-body systems, you know how quickly the math blows up in our face and we need to do simulations. It is not easy.

Cheers, everyone.

5:30 AM  

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