Re: Future work will be necessary to provide a clear explanation.
> Appearance of complexity for certain parameter values is similarly well known (see the Lorenz system).
The Lorenz System is an example of chaotic behaviour, as is the double pendulum; those show the effects of variations in initial parameters (something that also bedevils LLMs) but their behaviours aren't complex. The closest to complexity you get is the attractor, but that is showing that the system can calm down, can simplify. The wild motions you get otherwise are just a random tangle, complicated to follow, but nothing complex.
> "Flocking" is a trivial consequence of "follow your neighbour" represented by simple differential equations.
"Follow your neighbour" just gives rise to everyone ending up heading off in the same direction, with fluctuations smoothing out over time. The original Boids algorithm has three distinct and separate rules, with priority (so "don't collide" takes precedence...). But the results are not "trivial" - well, except in the rather vapid sense of "We know how to do it, and applying those rules is simple, ergo it is trivial". We know how to do it - because we do go away and do it. Before that demonstration, it was not at all clear, let alone trivially so, that such simple rules, which are only applied locally, would give rise to the global results we see. And they are still not trivial because, except by trial and error, we can not determine - and most certainly not by any trivially simple mean - how to modify the local rules to get a precise global result.
> None of this is "emergence"
Saying something is "emergent" does not give any particular quality, other than (paraphrased) "it is a large global behaviour that arises from applying simple local/micro rules across a large population which results in an apparently coherent and complex behaviour at the global/macro scale." We can see this happening, we can create demonstrations of it happening in our models. It is something that exists.
The fun part of emergence, the reason it does get people all excited (ignoring the hypesters and advertisers who glom onto anything that they think makes their sales pitch exciting - no, that isn't quantum, stop saying that) - is that it does provide a route to explain how complex behaviours we see in Nature come about. How do all these global behaviours come about, when we can clearly see that the bits that make up the whole are individually thick as two short planks? Slime moulds - What? How? All they can do is expel a few simple (!) chemicals into the medium and sense when those same molecules are present. Then we try out a few rules, like "if there are 4 molecules nearby, do X but if there are more, do Y" where X and Y are themselves both very localised and generally simple actions. Tada! If those are followed by lots and lots of tiny cells then we can see waves passing through the combined group and your slime mould is going for a walk!
Then we look to see if this can help explain things more of us are interested in - ourselves! And it does indeed seem to be giving us explanations for all sorts things going on inside us. Of course, as more instances of a mechanism are spotted, they get named individually. For example, "Quorum Sensing".
And as we've had Chaos and Emergence, should one introduce the way that these systems can experience Catastrophe?
Nah, that'd take too much tapping away at this touch screen. But catastrophe, when you see it occur can also be dismissed as "trivial, anyone can see that happens", but what we can do with the concept is anything but.
> it is _alchemy_. The world is going insane
Clarke's Law in effect?
Biting the hand that feeds IT
