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August 26, 2007

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Hmm, interesting. I've never actually realized that people used "emergent behavior" as a model or an explanation for anything. In that context, I'd always treated it as just a description, with the meaning that an "emergent phenomenon" is a "complex or seemingly complex phenomenon arising from interactions of a large number of very simple subparts," or something of the sort. Never thought of it as a model or an explanation, but just as a reasonable descriptive word. But if it is used as an attempted explanation to end discussion, then it's just functioning as a curiosity-stopper and should be questioned further.

What are phenomena that aren't "emergent"? I guess Eliezer is right when he says "a single quark". I think Eliezer makes a good case that the word is overused, and doesn't enlighten the discourse.

It might be more useful to describe things in reverse " X are the components of phenomenon Y". Such as "Neurons firing are the known components of intelligence". Because when we observe something, it can be useful to ask "what are its components"?

It contrast, everything observed IS the component of some bigger system, but it can be also useful to ask, what is the next biggest ordered system it is a part of, etc. That's where "emergent phenomena" might legitmately come in. Because an ant colony might be the next biggest ordered system that an individual ant is a part of, and that does seem like useful information.

Okay, but that's really not how I have understood emergence. It delineates a subject matter, and does so in an abstract way that includes many specific examples which are purportedly alike in some important way. But I don't think this use necessarily implies that the explanation has thereby been given. It is, rather, usually an attempt to delineate a subject matter which can be further investigated. I believe that the hope is that a general theory of emergence is possible, though my impression is that there isn't even a generally agreed-upon definition of it, let alone a commonly accepted theory.

One common element that I have sometimes noticed is that an emergent phenomenon can be idealized and a simplified mathematical model constructed of it, which is not precisely correct but which is a very good approximation. The existence of such simple and very good models is remarkable and extremely lucky for us.

For example, an actual fluid such as water is really made up of molecules that interact, but there is a simple mathematical model for fluids which treats fluids as absolutely continuous and smooth all the way down, not composed of atoms but fluid at every scale. As I vaguely recall, this simple mathematical model can be adjusted by plugging in values for viscosity, compressibility, and so forth. It is not exactly the same as actual fluids (the resemblance breaks down completely on the scale of molecules) but it is very close at the macroscopic scale.

Similarly, we have the concept of the "ideal gas", which is only an approximation to real gases but on a macroscopic scale a very close and useful one.

That we can vastly simplify and idealize something without losing all that much predictive power seems to be a characteristic of many so-called emergent phenomena.

In line with previous comments, I'd always understood the idea of emergence to have real content: "systems whose high-level behaviors arise or 'emerge' from the interaction of many low-level elements" as opposed to being centrally determined or consciously designed (basically "bottom-up" rather than "top-down"). It's not a specific explanation in and of itself, but it does characterise a class of explanations, and, more importantly, excludes certain other types of explanation.

I would think that something like "life/intelligence is an emergent phenomenon" means "you don't need intelligent design to explain life/intelligence".

I remember when Warren Spector & Harvey Smith were going on about emergence in videogames. I think their definition was something like "a non-obvious [it may even surprise the designers] outcome of a system of rules rather than something scripted". That's a rather subjective definition but it seems to fit as well for the things that are described as "emergent" in real life. Since life is not actually a videogame but has universally valid rules, it would not be a very useful concept for that domain. I think Wolfram has written a lot about that sort of thing, but I don't actually know much about what it is he says other than that its an important idea.

I'm getting the feeling that Eliezer is starting to get overly eager to attack semantic stopsigns. I recommend magic oil in the evening and emergent phenomena in the morning.

My impression of "emergence" was that it's closely related to pattern recognition. You have atoms A, B..ZZZZZZZZZZ, and you recognize that these atoms form a certain pattern. So you say that a supercluster of galaxies/bar stool/intelligence "emerges" from a bunch of atoms.

I once had a prolonged debate with an anticognitivist. He, as usual, argued that no matter what kind of AI you build, if you take it apart, it's just "switches flipping". In that debate, I maintained that intelligence does not require anything else - it emerges from switches flipping the same way that Firefox emerges from switches flipping. Both are just human names for patterns that arise in a sea of subatomic particles.

[That was one frustrating debate... Both of us were equally bewildered that the other refuses to get it.]

Aren't superconductivity and ferromagnetism perfect examples of emergent phenomena? I'm not saying that calling something an emergent phenomenon adds any deeper understanding of it. But I think there certainly are phenomena that can be fairly called as emergent.

Aren't superconductivity and ferromagnetism perfect examples of emergent phenomena?

Yes. So are non-superconductivity and non-ferromagnetism. That's the problem.

I don't buy the analogy between emergence and phlogiston or vitalism. Offering up "emergence!" as an explanation of a phenomenon is a category mistake, to be sure, and is a semantic stopsign when misunderstood this way.

As other commenters have noted, however, there is a proper understanding of emergence that is useful. (In philosophy, for instance, it's an admittedly sloppy but still useful term to classify different kinds of explanations of consciousness). This doesn't seem true of explanations that appeal to phlogiston or vitalism. Vitalist explanations aren't category mistakes. They're simply vacuous explanations, full stop.

Creeping into his soul, he felt the first faint tinges of despair.

After all these posts on how the strength of an idea is what it excludes, forbids, prohibits, people are still citing positive examples as proof of the power of emergence? Tell me what it isn't!

Black holes, dark matter and dark energy seem to pretty much fit this description. They are, after all, inventions tacked on to calculations, in order to make theory and calculation fit observations.

Here is David Chalmer's short philosophical stab at what emergence is and ain't.

Hmmm...

What isn't emergence? Well, on a trivial level, everything observable is a consequence of physics. So, is there anything observable that does not fall into the category of "physics", and does that make the category meaningless?

I think I can come up with some things that "emergence" is not.

If X is not "emergent", then:
a) X does not have a cellular automata-like model; there are no readily identifiable components of X that follow relatively simple, computable rules which generate the observed behavior of the system. (The game of tennis doesn't look like an emergent property of any of its obvious components, unless you decide that tennis emerges from human brains.)
OR
b) X does not have a high-level model that describes the overall behavior of X without modeling the behavior of each individual component of X separately. (A list of telephone numbers is not emergent.)

People probably do use "emergent property" as a placeholder for "something caused by something else, but I don't understand how" far too often, though.

"Black holes, dark matter and dark energy seem to pretty much fit this description. They are, after all, inventions tacked on to calculations, in order to make theory and calculation fit observations."

See http://en.wikipedia.org/wiki/Bullet_cluster for dark matter.

There are a few examples of non-emergence. For example, if we tessellate many small equilateral triangles to create a larger equilateral triangle, the resulting figure will not show any emergent properties.

Outside of mathematics, though, the concept is vague and I can't see much use for it as applied to specific phenomena.

For example, if we tessellate many small equilateral triangles to create a larger equilateral triangle, the resulting figure will not show any emergent properties.

On the contrary - the large shape emerges from all the small shapes! Isn't it wonderful? You can even get the same behavior on the higher level as on the lower level, only this time, it's emergent!

...is what an emergence advocate would say, if they wanted to claim yet more territory for their ever-growing kingdom.

If we take EY's example of a market crash, the non-emergent hypothesis is that of a random process. In other words, price action is like the action of gas molecules, or Brownian motion. To say that a market crash is an emergent phenomenon is to say that it displays more order than gas molecules bouncing off one another, which do not display emergent properties. That is not an empty distinction, as far as I can see.

Eliezer: I generally like your posts, but I disagree with you here. I think that there's at least one really useful definition of the word emergence (and possibly several useless ones).

It's true, of course (at least to a materialist like me), that every phenomenon emerges from subatomic physics, and so can be called 'emergent' in that sense. But if I ask you why you made this post, your answer isn't going to be, "That's how the quarks interacted!" Our causal models of the world have many layers between subatomic particles and perceived phenomena. Emergence refers to the relationship between a phenomenon and its immediate cause.

So, for instance, suppose I'm on the interstate and I get caught in a traffic jam. I might wonder why there's a huge jam on the road. It's possible that there's a simple, straightforward explanation: "There's a ten-car pileup a mile further on, and five of the six lanes are shut down. That's why there's a traffic jam." Obviously we could get far more reductionist— both in terms of "why is there a pileup" and "why does a pileup cause a traffic jam"—but for the conceptual level we're operating on, the pileup is a full and complete answer. And thus the traffic jam isn't an 'emergent' phenomenon; it has one major identifiable cause.

In contrast, a lot of traffic jams 'just happen.' The previous sentence is false, strictly speaking; the jams come from somewhere. But you can't point to an individual cause of them; they arise from the local effects of millions of local actions taken by individual drivers. Removing any one of these actions wouldn't eliminate the jam; it's a cumulative product of all of them. So people searching for an explanation of why it takes two hours to dive ten miles in rush hour get really frustrated, because there's no good explanation to give them. And people trying to fix rush hour get even more frustrated, because there's no good angle to attack the problem from.

So emergence, in this sense, means that a phenomenon has many intertwined causes, rather than one or two identifiable and major causes. It turns out, of course, that most interesting phenomena are emergent (non-emergent phenomena are, by definition, boring, since their causes are straightforward). But "emergence" is useful as a shorthand for "the causes are complicated and interconnected, and I can't pick one out and tell you, 'here it is, this is why that happened.'" It's important not to get confused, and not to think an explanation of why we don't understand something is the same as an explanation of that thing. But as long as you remember that, it's a useful thing to remember.

I want to say that I like Jadagul's reply

"Even better: A colony is made of ants. We can successfully predict some aspects of colony behavior using models that include only individual ants, without any global colony variables, showing that we understand how those colony behaviors [emerge] from ant behaviors."

Emerge and arise are synonyms. I'll agree with your desire to quell the potential overuse of "emergent," however as is well outlined above there is a specific testable model being proposed when emergent is used closer to correctly. That is that there is no system-wide variable that leads to the observed outcome. Prove that variable or mechanism and the outcome doesn't emerge or arise - thus disproving that the system has emergent properties.

-Gene

In most of the contexts in which I have seen the word "emergent used", it has signified a lack of understanding of the underlying causes of the phenomenon being described but rather than acting as a semantic stop-sign seemed to be used as its exact oppposite - as a marker for an area sufficiently interesting to be deserving of further research with a view to eventual full explanation. But perhaps I've been misunderstanding the intent of the authors.

"After all these posts on how the strength of an idea is what it excludes, forbids, prohibits, people are still citing positive examples as proof of the power of emergence? Tell me what it isn't!"

I thought I did. (Even if Jadagul expressed what I was grasping towards much better than I did.)

I'm pretty ignorant on this, but I always thought that the phrase related to complex outcomes that result from surprisingly simple systems, so that the complexity is "emergent".

One example is chaos. One can have chaotic non-linear dynamic systems and non-chaotic non-linear dynamic systems.

But, again, I could have misunderstood.

Jadagul's example seems to me to be a clear place where the term emergence is useful. Phil Goetz has given others in the past. OTOH, it still seems that in most of the cases where emergence is used as a synonym for "magic" much too often. 'Emerges from' seems to be less strong evidence for a legitimately useful term than than 'emergent', as 'chaotic' seems to be a perfect synonym for the latter.

Even in the case of 'chaotic', the tendency to use the term as a stop-sign is serious. A great deal of understanding of chaotic systems is possible (they are probably most of what we understand in the world, after all), just not precise long-term prediction of their configurations.

Vitalism seems to clearly constitute a "stop sign", but I'd want much more expertise before confidently asserting that proto-chemists didn't use Phlogiston to make novel predictions similar to those we would make with Oxygen. It seems to me like Phlogiston is a conflation of Oxygen and Energy similar to Newtonian "mass" as a conflation of gravitational and inertial mass, or pre-Newtonian "weight" as a conflation of weight and mass.

We can successfully predict some aspects of colony behavior using models that include only individual ants, without any global colony variables, showing that we understand how those colony behaviors arise from ant behaviors.

But that is just what is meant to be conveyed by the claim that intelligence emerges from the interaction of neurons. Of course that is trivially true. But, the original AI theory was that neurons were the building blocks of a universal computer (and how the universal computer was built of neurons wasn't particularly interesting). The problem of understanding intelligence was, therefore, the problem of understanding how the mind could be replicated in LISP code (or PROLOG or rule-based systems or etc).

The newer argument was that neurons have particular properties that have to be taken into account rather than ignored when attempting to understand and model intelligent behavior. And this is what is meant by saying intelligence 'emerges' from the interaction of neurons and is an 'emergent phenomenon'.

"Tell me what it isn't!"

I'll go with TGGP's domain (video games), since that is what we blog about at Kill Ten Rats. The gaming blogosphere uses the term "emergent gameplay" more or less as TGGP defines it. Going back to my first online game, Asheron's Call, an example of what is not "emergent" gameplay is characters slaying monsters and leveling up. Monsters have the same code, but rarely win, so they rarely level; an example of emergent play was having characters sacrifice themselves to bunnies, who would gradually level up to a Night of the Lepus situation. Non-emergent was the use of "pyreals" (gold pieces) as currency; emergent was the economy that arose using alternate competing commodities as units of exchange.

As others have stated, I usually see "emergent" used as a shorthand for something like "the whole is not predictable from the parts." No cell in your brain understands Chinese, and neither does any part of Searle's Chinese room, but the system as a whole does. Is there a better term akin to the fallacy of composition or ecological fallacy?

"Tell me what it isn't!"

The examples I gave, superconductivity and ferromagnetism, are example of phase transitions, which only happen when there are large number of components interacting. I wouldn't call phenomena that can be explained by one or few components as emergent. So, I wouldn't call a black hole as emergent. I wouldn't call an electron and a proton making up a hydrogen atom as emergent. I wouldn't call two hydrogen atoms and an oxygen atom forming a water molecule as emergent. But liquid that is formed by a large number of water molecules is an emergent phenomenon to me. Jagadul's example of traffic jam is also a good one.

I'm pretty out of my depth here, but I'll echo what some people have said above. Before people started scientifically doing either one, would it have been obvious that a simple model would be very successful at predicting the behavior of, say, subatomic particles but would be very unsuccessful at predicting the weather? That is, it seems like there really are some phenomena where it is more true and others where it is less true that predictions can be generally and successfully made using straightforward intuitive models. It seems like the label "emergent" is just a (useful) label for the stuff where this can't be done.

Tom McCabe, that is not proof.

http://www.holoscience.com/news.php?article=stb9s0ye

BJK is on to something: the non-emergent description of a market crash is something like "IF the Fed is raising rates and the economy is slowing down and investors are too leveraged and ... ... ... then the market will crash," while the emergence theory might define investor behavior and note that it will result in periodic booms and crashes, without special rules to govern either. That's the essence of emergence: simple universal rules rather than complex specific rules.

It might feel like junk science because it crosses disciplinary borders, but that doesn't make it invalid.

Don't y'all find it a little suspicious that so many people think "emergence" is a useful concept, yet have different definitions of what it is? (Though more important is what it isn't.)

Next stage in the gauntlet: Why is this a useful concept? Why does it increase your understanding of the universe, and your predictive power? Can you force me to talk about emergence or a concept isomorphic to it?

I disagreed Rip's opinion that black holes etc. are examples of emergent phenomena, but other than that I don't really see much disagreement about what emergence is in the comments here.

I like Zubon's description "the whole is not predictable from the parts" and "No cell in your brain understands Chinese,..., but the system as a whole does."

Why can it be useful? I can think of two possible reasons. There is a certain reductionist tendency (although I don't think being reductionist per se is bad) to assume that we get better and better understanding of the system just by getting more and more detailed information about its components. But the concept of emergence reminds us that there are certain things that we only understand when we see the system as a whole. Another thing is that it allows us to see something common in very different systems studied in different disciplines. For example, there is similarity between spinglasses in solid-state physics and neural networks. Also, you can see so-called power law in many kinds of systems. (Although power law may be another example of a concept that is overused.)

The concept of emergence is useful as a guard against certain errors, such as, for example, conspiratorial theories which explain phenomena as the product of intentions (malign or benevolent). Order does not always arise from intention. If society is lawful, that is not necessarily because there is some commander dictating that it be lawful. The lawfulness of society may be a phenomenon with a mostly dispersed, decentralized cause (e.g., lawfulness may be in large part enforced by ostracism of transgressors and thus enforced by all members of society rather than by an elite and privileged police apparatus applying the decisions of a legislature). Similarly, a sudden rise in the price of something may not be the product of a secret cartel or of a particular government policy or politician, but may be the result of a non-obvious confluence of disparate causes. When we say that prices emerge from the marketplace rather than being set by some authority, we are denying the idea that there is some person or group who has chosen that the price should be what it is, a person who can be appealed to to change his mind, or blamed for his decision.

"Tom McCabe, that is not proof."

There is no such thing as proof. See http://www.acceleratingfuture.com/tom/?p=11.

Mainstream astronomers' predictive abilities are shoddy at best. It seems as if every new observation is "surprising," or "shocking," or "baffling."

Yet there are still no direct observations of dark matter.

How deep can biases run? Could it have poisoned the very foundation of modern science? I think it's something to investigate, especially considering the vast sums of money that are at stake if some mainstream theories turn out to be wrong or pointless.

"It seems as if every new observation is "surprising," or "shocking," or "baffling." "

Surely the underlying reality of this "seeming" is that a large fraction of new newsworthy observations is "baffling" etc.

I ll try a silly info-theoretic description of emergence:

Let K(.) be Kolmogorov complexity. Assume you have a system M consisting of and fully determined by n small identical parts C. Then M is 'emergent' if M can be well approximated by an object M' such that K(M') << n*K(C).

The particulars of the definition aren't even important. What's important is this is (or can be) a mathematical, rather than a scientific definition, something like the definition of derivative. Mathematical concepts seem more about description, representation, and modeling than about prediction, and falsifiability. Mathematical concepts may not increase our ability to predict directly, but they do indirectly as they form a part in larger scientific predictions. Derivatives don't predict anything themselves, but many physical laws are stated in terms of derivatives.

True.

I don't have any direct quotes or statistics available at hand, but I think however that it is not disputed that our understanding of the universe is nowhere near complete. And with so many newsworthy observations that don't fit mainstream theory, then surely that must suggest a problem with the theory.

The shape of galaxies could not be explained with visible matter. As a result, the theory wasn't scrapped; they instead simply added enough matter to the equation to make it work -- hence dark matter (which has to have much more mass than visible matter).

This doesn't make mainstream science question the validity of gravity being the dominant force in the universe. Instead, they add hypothetical matter to the calculation. I suspect Mr. Yudkowsky's former statement that dark matter might go the route of epicycles will turn out to be correct (he probably doesn't subscribe to that anymore, I don't know).

That doesn't seem very scientific to me, but perhaps it's still legitimate since dark matter is still considered just a hypothesis.

Eliezer: "Don't y'all find it a little suspicious that so many people think "emergence" is a useful concept, yet have different definitions of what it is?"

That's a non sequitur. Different people define intelligence differently, so what? The fact that they don't understand intelligence doesn't mean that it isn't a useful concept.

When people actually can't agree on the meaning of a word, the signnal to noise ratio drops from using it. But in that case, instead of discarding the word, people just need to standardize it.

Emergence is an annoyingly vague concept, but that doesn't mean it's an empty one.

One meaning of emergence is "decentralized control". In a free market economy, prices and other properties are emergent from a large set of transactions among distributed agents, in contrast to a centrally planned and controlled economy. So there's something that is not emergent, or less emergent. Similarly, it used to be thought that a bee colony was controlled by the queen, but now we know that its activity is also the result of the work of distributed agents. It didn't have to be that way, so we have found an instance of emergence where we might have found something else. In AI, there are emergentist approaches like neural nets or genetic algorithms, or the old-school symbolic approach which is top-down and designed.

So it's clear that emergence is not meaningless. But you are right, it is not an explanation for anything. If you've found that a bee colony is decentralized, you still have to tease out the rules and interactions of the various agents involved.

"Let K(.) be Kolmogorov complexity. Assume you have a system M consisting of and fully determined by n small identical parts C. Then M is 'emergent' if M can be well approximated by an object M' such that K(M') << n*K(C)."

That seems to describe what I described earlier:

"One common element that I have sometimes noticed is that an emergent phenomenon can be idealized and a simplified mathematical model constructed of it, which is not precisely correct but which is a very good approximation."

I didn't, by the way, intend this as a definition of emergence, though it or something thereabouts might qualify.

Eliezer: Here's another example similar to ones other people have raised, a story I heard once, that might explain why I think it's an important and useful concept.

Supposedly, in the early nineties when the Russians were trying to transition to a capitalist economy, a delegation from the economic ministry went to visit England, to see how a properly market-based economy would work. The British took them on a tour, among other things, of an open-air fresh foods market. The Russians were shown around the market, and were appropriately impressed. Afterwards, one of the senior delegation members approached one of his escorts: "So, who sets the price for rice in this market?" The escort was puzzled a bit, and responded, "No one sets the price. It's set on the market." And the Russian responded, "Yes, yes, I know, of course that's the official line. But who really sets the price of rice?"

The Russian couldn't conceive that an organization as complex as the open air market could have assembled itself; he was sure someone must have designed it in order for it to work. It had to have been set up. But markets and prices are an emergent phenomenon; the price isn't set by one person and doesn't have any one cause. And yet the markets function.

Similarly, a lot of people seem to have a mental model of democratic institutions that says it's a non-emergent phenomenon: if you write a constitution and hold elections, you get a democracy with the rule of law. Others (including myself) claim that democracy and rule-of-law are emergent phenomena: if they don't exist, there's no specific set of actions a central actor can take that will cause them to exist. They exist because of millions of decentralized and uncoordinated actions of individuals without specific direction. If you hold the first view, projects like the establishment of the new Iraqi government make sense: we set up a government with a constitution and elections, so it should become a free democratic state. If you hold the second view, the project is insane: freedom and democracy require millions of individual and low-level cultural shifts that can't be imposed from above, so there's no way for us to turn the nation into a democracy. My point here isn't that one view is right or wrong, although I have a firm belief. My point is that it's highly relevant to our foreign policy to ask whether democracy is emergent or not.

Usually when you say, "You can't just impose X from above," you're claiming X is an emergent phenomenon; the hallmark of a non-emergent phenomenon is that it's possible for a single actor to take a series of actions that either cause or prevent it.

In line with previous comments, I'd always understood the idea of emergence to have real content: "systems whose high-level behaviors arise or 'emerge' from the interaction of many low-level elements" as opposed to being centrally determined or consciously designed (basically "bottom-up" rather than "top-down"). It's not a specific explanation in and of itself, but it does characterise a class of explanations, and, more importantly, excludes certain other types of explanation.

This comment hits the bullseye. The general idea of emergence is primarily useful is in pointing out that when we don't understand something, there are still alternative explanations to those that superstitiously posit a near-omniscience or that pretend to have information or an ability to model complex phenomena that one does not in fact have. So, for example, a highly improbable organism does not imply a creator, a good law does not imply a legislator, a good economy does not require an economic planner, and so on, because such things can be generated by emergent processes. To come to such a conclusion does not require that we have first reasoned out the specific process by which the object in question emerged. Indeed if we had, we wouldn't have to invoke emergence any more but rather some more specific algorithm, such as natural selection to explain the origins of species.

For this reason, I strongly disagree with the following definition

Let K(.) be Kolmogorov complexity. Assume you have a system M consisting of and fully determined by n small identical parts C. Then M is 'emergent' if M can be well approximated by an object M' such that K(M') << n*K(C).

Because it is just in situations where a phenomenon has a not highly reducible complexity -- where M is not fully determined by n small identical particles, or where it is but K(M') is not substantially smaller than n*K(C) -- that the idea that a phenomenon is emergent, rather than the product of a near-omniscient or near-omnipotent creator, is most useful.

I'd add that the belief that any important phenomenon is highly reducible, or that even if it is reduceable that humans are capable of undertaking that reduction, are two other species of superstition. These are just as pernicious as the related superstition of the near-omniscient creator. In many, perhaps most cases of interest we either have to be satisfied with regarding a phenomenon as "emergent" or we have to superstitiously pretend that some being has information or a capability of reduction that it does not in fact have.

"As a result, the theory wasn't scrapped;"

By "the theory" you mean general relativity, which is one of the most well-confirmed theories in all of physics. You can't just come up with a slightly modified version of GR to accommodate weird observations; the Einstein field equation is a unique solution because of all the demands placed on any reasonable theory of gravity. If you assume:

- Spacetime is flat in the absence of matter;
- Spacetime curvature is linear with respect to the density of matter;
- The standard principles of mathematics (eg, two matrices with different dimensions cannot be equal);
- The laws of physics are invariant under coordinate transformations (no preferred coordinate system); and
- Spacetime does not have an a priori curvature not affected by matter;

you are forced to use general relativity.

Eliezer, I wonder whether the reason you think "emergence" isn't a useful concept is just that it seems so obvious to you that every phenomenon must fit the proposed definition that it doesn't exclude anything that's meaningful for you. (This seemed to be implied in your original post.) Even so, it can still be a useful concept as long as some people think that there could be non-emergent phenomena.

And yes, the proposed definitions of emergence are vague, but, as has already been pointed out, that doesn't imply the concept is worthless.

"Don't y'all find it a little suspicious that so many people think "emergence" is a useful concept, yet have different definitions of what it is?"

I think "bias" is a useful concept, despite the tendency for people to disagree over what regions of failurespace count as "bias." (Uh, ahem).

Some other vague concepts people disagree on: 'cause,' 'intelligence,' 'mental state,' and so on.

I am a little suspicious of projects to 'exorcise' vague concepts from scientific discourse. I think scientists are engaged in a healthy enough enterprise that eventually they will be able to sort out the uselessly vague concepts from the 'vague because they haven't been adequately understood and defined yet'.

(Have been off at the beach incommunicado or else would have been in on this earlier)

So, I am one of the guitly parties writing about those vague and overused concepts "emergence" and "comoplexity," which are often linked. Yes, they are overused and often vague, but both can be more narrowly and scientifically defined, in which case they can be useful.

From my perspective a crucial aspect of emergence involves different levels of ontology, with a new, or qualitatively different something appearing at the higher level as a result of processes occurring at the lower level(s). Now, this emergence may in some sense be obvious, or it may not be, with the latter case possibly "looking magical," which can be annoying, whether it is intelligence or multicellular organisms, or whatever.

Regarding phase transitions, all emergence involves phase transitions, but not all phase transitions imply emergence. Ferromagnatism and superconductivity probably fit, but a Hopf bifurcation in a macroeconomic model in which a system that had been converging on a unique equilibrium smoothly begins to oscillate in a harmonic sine wave manner is not such an emergence. In this regard, a market crash may or may not be an example of emergence, depending on the details of how it came about.

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