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July 31

I think I have a complex

Complexity theory, complex systems theory, systems theory, dynamical systems theory. Perhaps I'm forgetting some. How do these map? Are any of these not a real field? What is subsidiary to what? Temerarius (talk) 01:49, 31 July 2023 (UTC)[reply]

Systems theory appears to be an overarching topic, so spend some time reading our article, which links in those other topics. Graeme Bartlett (talk) 02:42, 31 July 2023 (UTC)[reply]

H'oh-boy, you're really asking a whopper here: these are all deeply complex (ironic phrasing incidental but unavoidable) and at least semi-interdisciplinary concepts with nebulously defined borders, varied applications and sometimes difficult to articulate implications. But I'll give it a try. I was just about to be out the door, so I may need to stage this response. Here goes though.

I'll start with systems theory because it is the paradigm I am most familiar with and I believe can fairly said to be the broadest topic of the lot. Though saying that, I also note that none of the terms you employed refers to a field of thought that is necessarily a formal subdomain of that of one of the other terms, if that makes sense. They all just use similar terminology for semi-convergent purposes.

That caveat done, systems theory is all about understanding phenomena on the basis of their interaction with larger collectives of phenomena. It can be considered (and this is not necessarily the formal definition, but one which I think is helpful at understanding it's boundaries at first blush) as an effort to nest all naturalistic processes and mechanisms within countlessly recursive layers of scale and complexity). In the broad strokes, it is a highly ambitious and holistic method for trying to relate all phenomena. But also, on a less macro-level, it is a way of thinking about even discrete systems, interactions, and pathways as being better understood by their borders and feedback with other phenomenalistic systems. In other words (and I know this is getting highly abstract, ontologicaly dense, and maybe even a little unwieldy sounding, but a thing is best understood by what it does and what is done to it, not just a description of it's parts.

With regard to theories of complexity (to reorder 'complexity theory' into something more workable and consistent with how those terms are often related, for our purposes here), I don't think there's one standard definition of the way the nomenclature is used across the fields in which the concept (of understanding phenomena by virtue of their complexity) arises, but there are some commonalities: complexity models mostly concern how many subparts of a given system there are, how dynamic (that is, generally how reliably defined they are) each component is in its own right, and the computational implications for predicting the behaviour of the holistic systems. That said, on this topic it is too bad SemanticMantis seems to be on hiatus, because I am certain they could give you a more accessible and robust definition. "Complex systems theory" is somewhat more a neologism than either of the other above terms, but I interpret the phrase as meaning just as what you might assume from combining the above two foci of the individual terms: it is about understanding systems comprised of larger numbers of and/or highly dynamic systems.

Which brings us to dynamical systems theory, where I am most out of my depth. This is a good place to note that all of these models have both more analytical and computational components, and more theoretical/broad framework applications, but some lean more to one than the other. You're going to get more broad philosophical generalizations from (at least some) big systems theory thinkers, but dynamical systems theory is almost incidentally using a similar label. It's a purely mathematical approach to crunching data relating to complicated systems by way of functions related by complex equations. And if that is a bit of an earful, I apologize, but I barely possess the vocabulary to conceptualize the broad strokes of these mathematics, let alone find novel ways to express them. Suffice it to say, I would categorize this field as much more discrete than the others, and much more bounded by strict analytical rules, expressly defined inputs, and straight-forward (if highly complex, obviously!) transformative operations.

Was any bit of that helpful?? I hope so, but I'm not sure it will be! SnowRise ^{let's rap} 03:01, 31 July 2023 (UTC)[reply]

Yes, that was a wonderful response! I'll need a minute to digest it, and I hope the robustness of your reply doesn't prevent others from pitching in. Thank you! Temerarius (talk) 03:33, 31 July 2023 (UTC)[reply]

Very happy to help Temerarius! And happier still that what I wrote was basically decipherable. :) I found myself thinking about examples earlier that might further clarify the distinctions here and better emphasize the the applications/raison d'etre of a couple of these fields, and came up with a couple of good ones, but I'm running around putting out fires at the moment, so you'll have to be patient with me in getting them down in paragraphs here.

In the meantime, it also occurred to me that I should mention that there is a movie called Mindwalk that you might be interested in: it's a fairly accessible (indeed, if anything, oversimplified maybe) primer to systems theory based on the writings of Fritjof Capra, one of the academics/public intellectuals who helped popularize systems theory. It's pretty slow: it's just a dialogue between three people (a scientist, a poet, and a politician), discussing the philosophical underpinnings of what was at the time a somewhat novel way of relating naturalistic phenomena, physical and otherwise; it borrows this structure from Galileo's Dialogue Concerning the Two Chief World Systems. It won't set your world on fire with new ideas, I don't think, but you can definitely get a sense of (at least Capra's idea of) how systems theory tries to address describing the physical universe. Plus it must be said that Sam Waterston plays "Simplicio" to perfection therein. ;).

If I recall correctly, Mindwalk is mostly based on Capra's The Turning Point, which is also highly accessible for a book in this area--but also a little preachy and proselytizing as I recall it: Capra also wrote the much better known The Tao of Physics, so if you're familiar with that book you'll have an idea of what I mean. It's constructed on top of hard science, but also contains lot about social philosophy, ideology, and policy. I read all of Capra's work (at the time) a couple of decades back and I think my overall impression was that he was somewhere between brilliant and very heavy-handed as a writer and psuedo-policy thinker. But you can definitely do worse for an entry point on systems theory. SnowRise ^{let's rap} 23:43, 31 July 2023 (UTC)[reply]

My attempt, as I understand these terms. Complexity theory is an ambiguous term, but one meaning is complex systems theory, that is, the field of study of complex systems. In this context the term system usually refers to a dynamical system, a collection of components that evolve in time while interacting with each other – the behaviour of one component can have an effect on other components. For example, the system could be a deliberating jury, and the components are the jurors. For a mathematical treatment, when modelling a system, the relevant aspects are modelled as numeric values – perhaps the strength of a juror's conviction that the alleged facts have been proved beyond a reasonable doubt. Some dynamical systems are very simple, which is generally the case for systems with fewer than three components; such systems are never chaotic. A system is called chaotic when its collective behaviour is chaotic, which means that it is impossible to predict the long-term future evolution on the basis of past observations. Weather is a prime example; no one can reliably predict whether it will rain in Amsterdam on the first of August of next year. Chaos theory is about understanding when systems become chaotic, as well as determining what can be said about the evolution in spite of the chaos. Chaotic systems can be reasonably simple (just three components), while some very complex systems are nevertheless not chaotic. --Lambiam 08:19, 31 July 2023 (UTC)[reply]

There once lived a man named Oedipus Rex / You may have heard about his odd complex --47.155.41.201 (talk) 18:39, 3 August 2023 (UTC)[reply]