I'm vaguely familiar with the application of the theory to neural networks, genes, etc., but that stuff isn't very interesting to me (since it is open to anthropomorphic bias).

However, it is the application of the theory to humans that's a topic that I find very interesting (since it cannot be 'anthropomorphic').

Could you give me an example of human 'swarm-like' behavior? Obviously the large crowd in panic mode is likely a good example. Do you know of any others?

There you have it. In the face of an overwhelming force, be it a flash flood, wildfire, stampede, attacking neighbor tribe, or whatever else, it often makes more sense to grab infants or any other critical items and run like heck rather than stop and die while discussing the situation. It obviously aids individual survival, and I don't see any counter-balancing group detriment that might weed out such a tendency.

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Panic mode is not an example of this. That is chaotic behaviour and that's a whole field in itself. As M. Mitchell Waldrop puts it, emergent complex behaviour lies on the edge of chaos, i.e. in the transition phase between order and chaos. Mathematically speaking, behaviour as in swarms only emerges at a very precise setting of a general parameter. Putting the parameter lower a jot leads to genuine chaotic behaviour while putting the parameter a jot higher leads to static, uninteresting and unuseful behaviour.

A swarm of birds would turn chaotic e.g. when someone fires a gun at the swarm. The static behaviour would be if all birds kept the same position relative to a virtual coordinate system, but such a swarm structure would not function in nature. Instead of fluently swerving around an obstacle, some birds would simply crash into it.

Similarly, a panicking group of human individuals shows chaotic, random behaviour without emergent complexity (although there are other patterns there called strange attractors, but that is the field of chaos theory).

An example for human behaviour has e.g. been observed in highway traffic where a brusque slowing down, but not to a stop, of cars can be observed as moving through the traffic flow without any relation to the individual cars or the average speed of the cars. This behaviour is also critically dependent on a single parameter, in this case traffic density. If the parameter is somewhat lower, this effect is not observed at all, while a minute increase in traffic leads to static behaviour, i.e. coming to a standstill.

I think there's a slight misunderstanding here. This behaviour is not programmed into the individuals, it is a property of the whole, of the system. It's an organizational aspect. It occurs independently of the componenents of the system. They can be bees, ants, but also software agents, water molecules, brain cells, air molecules, even computer bits of information.

There's no possibility here of anthropomorphism. The exaxt same thing happens, with the exact same chararcteristics in all the aforementioned systems. Even the parameter I mentioned in the previous post is always exactly the same (0.236 or 0.263 IIRC).
It's the key to self-organization of systems. The components are not important.

Okay - a distinction between a 'swarm' and 'chaos'.

So what is 'swarm' behavior then? (human example please)

This doesn't ring true at all. A human crowd in a panic does not operate in a purely chaotic pattern. They do head towards safety/doors/exits, not heading in all random directions.

1. Many people traveling on highways have access to radios and traffic reports. Their actions may appear random to a disinterested observer (in a helicopter for example) yet their actions are influenced by their 'external' knowledge of the traffic conditions.

2. Intelligent or experienced drivers in rush hour are able to eliminate those kind of 'traffic flow slowdown/ripple effect' based entirely upon observation of the occurance.

Such examples of knowledge and planned actions appear to defy the assertion of 'swarm' behavior.

No.

The action cannot occur independent of the components of the system if the 'group action' depends upon that actual actions of individuals. If we remove the individuals from the example, there is no 'group action'. Ergo, that 'group action' is entirely dependent upon the actions of individuals. And the action of individuals can be rationalized.

I think you ought to re-read your statement here. We are not discussing religion. Such a blanket dismissal is precisely why I raise the objection. I suspect a big blind spot here.

You know as well as I do that data can be manipulated to fit the equation.

Any theory that is applied to humans and at the same time dismisses the acts of humans isn't a theory worth considering. My interest in this topic is ths dropping fast. I loath the scientific attempt to ignore human beings (as if the scientists themselves are pretending to be above mere human-ness).

Panic is defined by the OED as 'sudden uncontrolable fear or anxiety'. With the word 'uncontrollable' in there I'd say that those in the panicking crowd that exhibit behaviour with method, i.c. seeking the exits, are not panicking, but are in a state of controllable fear. So, when I use the term panicking crowd, it means a set of people that all show panic, without exception.

I've been disinclined to apply this to humans from the outset for precisely these reasons (see posts #5 and #14). It can be found in human behaviour on the condition that the humans act in a onedimensional fashion. As soon as these humans start to behave like actual humans it's no longer applicable. That was why I rejected the transference to group pshychology in the OP.
Nevertheless, in the right conditions, it does occur. And that in itself is breakthrough observation. It shows that systems have characteristics because they are a system and for no other reason.
I've been thinking of better examples in human behaviour, and although I didn't find any actual studies of it, I'm pretty sure one would at least find some occurences of it in the behaviour of a peloton of cyclists in a race such as the Tour de France. But you could use the same arguments, such as the presence of information from outside the system, and the presence of some hierarchy at least within the teams that make up the peloton, to reject its omnipresence and I would agree.
But again, nevertheless, it does occur in the right circumstances, such as when the entire peloton manages to swerve around an unforeseen obstacle, of which the bigger part of the peloton has no information at all since only the first few rows can actually see the obstacle.

Now I'm sure that there is a misunderstanding. May I ask whether you have read the entire thread ?
Neither of these statements :

were about humans, but about all systems where emergent complexity, such as swarm behaviour, is actually and undeniably present.

Here I should have written 'The nature of the components is not important' instead of 'The components are not important'. That the components have to be there in the first place is of course trivial.

No, sorry, it was quite correct. Nothing gets attributed with human characteristics. What complexity does is finding systems all over the place that have the exact same mathematical representation, regardless of what the components are, all over the place, that is to say, with the exception of systems that are constituted by already complex systems, such as humans. It's in the latter part of the thread that we started exploring if it could be applicable in some very restrictive cases within human behaviour. The answer is, yes, but with very severe restrictions. I would be the first to reject it for all human behaviour.

No. Categorically, no, not in this case. I know these maths. I have them on my computer. I gave a link to them in post #13. They are as trivial as non linearity gets. Nothing in the coding allows to predict the point at which the complex behaviour emerges. And yet, it has been observed that it is always at the same point. This is actually as important a discovery as that of the omnipresence of Π (3.14159...) or e (2.71828...).

I'm afraid humans will continue to be ignored in this subject as it is only applicable in extreme cases as explained higher.

That seems reasonable. And quite unlikely for actual human beings. Those last two words seem to imply a 'categorical' rejection of the theory's application to the actions of (conscious) human beings.

Sorry, I skipped over the first page of the thread. I began at the point I arrived.

I certainly agree that application of this theory to humans is problematic. That's what interested me to question your post.

Example please.

Yes it would - if one can show that it occurs with humans. I don't think it does.

Anything else but humans, sure, no problem - you can argue the math till the cows come home about neural pathways or electronic data movements, or even herds of cattle and that's fine by me. I have no objection to the theory itself, only an assumption of application to human behavior.

Exactly. Humans can't act non-human.

Even then, that application would be of a very limited in duration since the rest of the riders, besides the immediate leaders immediately affected, have additional information from the noise/reaction of the spectators to assist in their own individual response decision/reactions.

P.S. Are you familiar with a book called Blink by Malcolm Gladwell? It is about the remarkable human ability to make rational decisions in a blink of a eye. Highly recommended.

As I mentioned in my post above, I began at the point I arrived. I didn't read the first page. Sorry.

Okay, then I have no objection. I categorically reject the application upon human behaviour as unsound - on any macro or micro level application.

If some algorithym spots this mathematical pattern in some instance of human group action, I would suspect random coincidence.

Like I said above, my argument here only applies to potential application to human group actions, not the theory or your precious mathematics.

Good, though I have a strong skepticism against even these alleged extreme cases as well.

Thanks for the clarifications.

As I read this I imagine a pigeon saying to another pigeon, "You know, I flew into the old owl the other day and he told me that we are only able to fly because the math fits" And the other pigeon replies, "What do you mean? I don't know what math is so please tell the old owl that I'm quite able to fly without it. I fly because I want to fly."

You sound as if it's hard to accept that humans are governed by the same laws as every other living organisms. Is that what would bring your suspicion about?

Kinda reminds me of the bumble bee - it is alleged that according our theory of flying, bumble bees can't fly.

No. I have no objection to the laws of gravity for example.

My argument in this thread is entirely predicated upon my objection to a theory that is based upon the actions of non-conscious objects being applied to humans. Humans are conscious beings and don't act like inanimate objects.

I see this could turn into yet a 'free will' discussion and potential thread hijack so I'll just thank you for replying and leave it at that

I've been thinking to find other examples. Some candidates I contemplated are the behaviour of people leaving a crowded train and moving out of the station, European style mass demonstrations, mass sport events such as marathons, but they all suffer from the same issue. There always is information external to the system, the components are always complex systems themselves and so on, precisely as with the previous ones.

To find an example, it seems obvious that basic human traits would have to be temporarily disconnected. A mass of sleepwalkers could be usable, but that of course is farfetched Stupefied drug or alcohol users could do the trick but they do not generally operate in masses.

Certainly, it could not have the extended duration a swarm has.

No, I don't know it. And, alas, if I allow my bibliomania to add yet another one to the pile, there is a statistically significant risk of a poleshift.
Would it give sufficient ca