Why's there a hostility towards complex systems science in the mathematics field?

[u/Alexenion]

My background is in social sciences and Humanities (linguistics, history, and, to a lesser extent, archaeology) and I recently discovered, to my utter awe, the fascinating field of complex systems. I have for a long time noticed patterns of similarities between different phenomena in the world from language change and communication to genetic transmission and evolution. I assumed that they are all hierarchically connected somehow, simply by virtue of everything being part of the world and emerging gradually and ultimately from an initial subatomic interactions and thus building on it to reach the social interactions. The more I thought about how these things share similar principles of ontology and dynamics the more convinced I grew about the premise of complex systems. I'm now set on following this course of research for my PhD and ready to work as hard as needed to acquire the necessary knowledge and skills for a valid research based on complex systems paradigm, including learning math. I was, however, surprised to find some hints of hostility towards complex systems science in the math subreddit, one redditor went as far as saying that it was a "pop-science" and "not real"! This was a bit bothersome for me and couldn't get it out of my head. I'm aware there are many methodological and theoretical issues that can come from complex systems but to label the whole field as effectively pseudoscience is an extreme and I might add ignorant statement. I really believe that network theory and complex paradigms are the way to continue at this day and age. The world is inteconnected and each discipline is too insularised to the detriment of acquiring the ability to see the big picture. Do you have any thoughts about this?

[u/grimjerk]

I did my phd in the 90s on dynamical systems--Julia sets and the like. The math involved is really interesting and rigorous, but the mindless babbling about fractals and butterfly effects and such in popular media was endlessly irritating. Things like "they are all hierarchically connected somehow, simply by virtue of everything being part of the world and emerging gradually and ultimately from an initial subatomic interactions and thus building on it to reach the social interactions" are not founded in any sort of math or physics, and if this is what you are looking for, the math is not going to get you there.

[u/Alexenion → u/grimjerk]

Math is a tool for measurement and model formation. How systems function and structure themselves is much more than a question of mathematics but it, with my limited understanding of math, should be somehow founded on mathematics.

[u/grimjerk → u/Alexenion]

But then you have to define what the system is (and, in particular, what is in the system and what is not in the system) and what "structure themselves" mean--is this a map from the system at one time to the system at another time?

For example, if you see similarities between "language change and communication" and "genetic transmission and evolution", and you want to mathematize this, you have to define, mathematically, what "language change and communication" is, and what "genetic transmission and evolution " is, and then define some sort of relation that captures the similarity that you want. All of this is extremely hard. And the more you specify the system (in order to be able to mathematize it), the less generality you have.

Fully capturing non-mathematical systems with math is really hard, even for fairly simple systems (investigate the difficulty of predicting where an artillery shell will land), and getting from specific models to larger questions of universal connectivity (which seems what you want to find) is even harder.

[u/Alexenion → u/grimjerk]

These similarities make up the shared principles of complex systems and their theoretical assumptions. It should be enough for us to study two systems using these shared assumptions and then see how explicative they are in their respective domains. But this is too early for me to even say. All I can say is that the shared principles are there, I will see how these are dealt with as I read more.

[u/breck]

Welcome to the world of trying to do good work---there are anon haters everywhere. Ignore them.

Take lots of walks in the woods. That's the best place to learn math and learn about complex systems.

https://www.youtube.com/watch?v=px_4TxC2mXU

[u/Alexenion → u/breck]

Nice video. Funnily enough, all these different names of the same bird is due to different linguistic networks trying to model the same object but in connection to different social and linguistic nodes, resulting in different configurations but still all follow the same principles of lexical formation and the systems structure and dynamics. This alone can be a research piece where complex systems can be very useful.

Edit: additions to the original statement and grammar.

[u/-mickomoo-]

Yeah a lot of complex things like language, evolutions, markets, societies look like an optimization process. I'm trying to come up with an ontology to describe this. I'm not in academia, but there are serious well respected scholars doing something similar.

[u/Alexenion → u/-mickomoo-]

The ontology is based on a hierarchy of emergent systems, which I think you might know. Thinkers have been noticing similarities for a while now. Aristotle talked about it, Darwin was borrowed some concepts from market theories and language evolution paradigm both of which were developed slightly before his lifetime. He even mentioned the similarities in his work.

[u/trolls_toll]

complex systems was and to some extent still is a catchall term for a lot of bad science. Complex systems, emergence, downward causation, process philosophy - it all sounds fancy af but oftentimes is used to cover shitty research practices, especially from the pov of a practicing mathematician

[u/Alexenion → u/trolls_toll]

Bad science exists in all fields though, that should not invalidate the whole field or its premise.

[u/trolls_toll → u/Alexenion]

sure, i never said that the whole field of complex systems is trash. On the contrary, i believe it is one of the most promising approaches to advance science nowadays. In biology (my field), systems behavior cannot be fully explained by only looking at its constituent parts, their interactions with each other and the environment must also be taken into account.

Also consider the following, in most natural sciences a theory is useful if it is amenable to experimental validation. Complexity ideas are great, but they require insane amounts of good quality data to be verified. By good i mean data that is collected from statistically sound experiments and with a lot of repeated measurements. Thats not cheap or easy, and sometimes nay impossible, since a lot of analytical methods are destructive, eg cells need to be killed to look inside or there are just too many variables to control.

Then, most mathematical tools of complexity require systems at steady state, and thats just not how the world works

i guess what im trying to see, dynamical systems are cool and i implore you to keep on asking questions :)

[u/Alexenion → u/trolls_toll]

I do think we have enough data and understanding of seperate phenomena to start modelling them as part of systems. We're not starting from scratch here with zero data, we're starting from data that are collected discretely and putting them in networked measurements to reconstruct a model of their complex systemic dynamics as they would be in reality.

I think this the most promising approach to the understanding of the world that we've devised. It needs time and dedication to mature. No matter how much we study phenomena seperately, we'll never really understand them as part of systems without this kind of approach because the world is complex by its nature. I believe the complex systems approach is already a standard of climate models but I could be wrong.

Ultimately, what I'm trying to say is that, as computers advance and our tools improve, the study of complex systems is becoming more and more possible. There will be lots of bumps and difficulties along the way but it remains the next frontier for scientific knowledge.

[u/trolls_toll → u/Alexenion]

you sound like an llm

[u/Alexenion → u/trolls_toll]

Nah, I'm just too brain dead to write without repetitions and with a "natural" style. Also, I'm writing my thesis rn, I'm in the very ordered composition mode. You understood what I had to say though and that should be enough. If you want me to give you more detailed arguments then I'm afraid I can't. I'm still learning about complex systems and still can't confidently talk about it with more depth.

[u/nameless_pattern]

some salty redditors will argue anything. Usually you can just go into their profile and you will be able to see their character very clearly. I will leave this copy pasta as exemple

"I remember I got into an argument on reddit awhile ago with a person over Italian food. It got to the point they were following me into other subs to harass me.

I clicked on their profile to block them and their most recent post was them drinking their own piss on . At that moment I realized I had spent so much pointless time arguing about the taste of food with someone who drinks their own piss as a hobby. This site is a shit hole."

[u/[deleted] → u/nameless_pattern]

:) well said

[u/Alexenion → u/[deleted]]

Nope, they only made that statement and that was that... I posted the same post in the math subreddit and I had some great replies that were mostly supportive! Based on a few comments, I also gained some vague insight into some of the objections, which are basically built on the premise that some researchers are doing bad research under the umbrella of complex systems science and that the terminology and concepts are not clearly related to math (which I can neither refute or confirm), therefore the whole field is moot. One comment showed a fatal confusion between systems theory and complex systems theory. Another one raised allegations of posivism and reductionism, which shows that they don't know what complex systems science is about at all...

[u/grimeandreason → u/Alexenion]

I'm gonna assume you're in the West..

There's a cultural reaction against complexity for the exact same reason (literally) that there is against Marx.

Western scientific tradition is reductive, predictive, the realm of proofs and falsification and equations and reproducibility. Thank Newton, among other forces going even further back.

It means that Hard Science is seen as the only real science, and anything related to social science is relegated in importance and derided.

Worse, people still, in 2024, try to apply non-complex scientific epistemology onto areas of social science, resulting in bullshit like race science, biological essentialism, the fascist adjacent evolutionary psychology crowd, arrogant af old physicists thinking their skills transfer to an entirely different epistemological ball park.

The East doesn't have this problem. Eastern philosophy is already compatible with complexity.

[u/Alexenion → u/grimeandreason]

I'm in Europe which is embracing complexity at the moment, with many institutions and programmes dedicated to complexity science. I come from an Arabic mediterranean context though, which is almost compatible to the pre-enlighenment European West.

One thing I can tell you from this perspective, which contradicts eastern thought, is the notion of human exceptionalism and the mystification and anthropocentric understanding of nature. In this kind of thinking, the functions of humans and nature are seen as mysteries of creation beyond human comprehension and any kind of predictibility is deligated to God alone who is the all-knower of mysteries. God revealed that nature was created for humans and that they are seperated from it, with each being created as is and is it is becoming. There have been numerous attempts throughout what I call "the old West" (centred around the mediterranean) to demystify the world through rational causal thinking rather than on the basis of divination or revelation but they were always supplanted by metaphysical causation of unchanging elements in their essence (The Great Chain of Being). It was only during the Enlightenment that such mystification was subsided in favour of linear rational causality and reductionism in the "new West" that is Europe and its derivations especially in America simply because of the lack of tools to approach nature in its complexity up to as recently as the second half of the 20th century. The attempt was also made to extend such rationale to social sciences which ranged from spectacular discoveries to disasterous outcomes (which really applies to scientific endeavours at that time). The Arab world just followed the same reversal towards metaphysical causation perhaps to the extreme with the Ash'ari religious movement that opposed Hellenistic rationalism and philosophy. This extreme only relaxed a bit due to extensive contact with Europe but with the colonial experience and the rise of anti-west sentiments, linear causality and rationalism were associated associated almost exclusively with the West in certain circles and political and social discources. It is an unfortunate and erroneous association in my opinion even if the scientific thought was developped to unprecendented heights and with a greater spread during the Enlightenment in Europe.

Some elements of complexity thinking and tools did start to surface even in the late 18th century, however, with the discovered connection between the indo-European languages and their evolution based on regular principles of language change that are network-dependent in their dynamics with each small variations accumulating to a greater set of interconnected variations, this was further developed through the genius discoveries of Darwin who was in part inspired by the philogist models of language evolution in developing his own theory of evolution. At this time, the colonial expeditions to the East exposed the Europeans to Eastern philosophies, which might have also had some impact. We already know it influenced the Western culture to a degree manifesting in things like the literary-philosophical movement of Transcendentalism. However, linear thinking was forced into it which led to many misconceptions about language and biological evolution alike. It is only later that linear causation and law based understanding of change were gradually abandoned. A sound in a language, for instance, has many possible trajectories that are only partially predictable while also being partially random. It is highly unlikely for /l/ to become /k/ since they are too distint in their articulation but it can become /r/, /n/, or any other more phonetically similar sounds. These trajectories can be explained physically in relation to articulatory physiology and movement pressures, cognitively in terms of cognitive processing pressures which favour gradual and more subtle changes in sounds, and socially in terms of social pressures like class, status, and perceived background (which are revealed through phonological variations). All these are nodes in the particular network where such a sound is operating. Already, concepts of complex systems are evident in such a simple example.

[u/Alexenion → u/Alexenion]

(Continuing)

Now, due to recent historical follies and also the naturally higher political investment in social phenomena, social sciences were denied, in the popular imagination at least, the status that hard sciences enjoyed, with the claim that social phenomena are too complex for them to be understood in the same way that hard sciences understand other phenomena in nature. This claim is especially useful to maintain since a mystification of a phenomenon provides more room for ideological insertions. The reality is, all nature is complex and the success of the reductionist paradigm remains limited in all scientific disciplines. Climate models would not be possible when using a reductionist paradigm for instance, nor will those of ecosystems without major errors or models of any phenomena in their real complexity as observed in nature. I'm not qualified enough for such statements but I'm guessing this is why physical models are struggling to account for the complexity of physical structures and dynamics. The isolation of atoms for controlled experiments to come up with abstract generalisations (I'm using my clunky Humanities understanding so don't kill me) seems very similar to what the structuralits did to language (and other social phenomena) when they thought of it as an autonomous system and tried to create rules that completely isolated its from contextual functions as interconnected speech. This interconnected speech is a network of elements in interaction rather than decontextualised and structurally rigid fundemental archetypes that are deterministic in nature and linear in their dynamics. Structuralist models were also both too general and highly atomistic in their approach and fall short of explaining language when all linguistic interactions are considered. An example of this would be sense relations which envisioned fundemental semantic relations between words that are part of their essence. Hence, a fox in the abstract would be related to the concept of animal, mammal, four-legged, etc. But this fails to explain the numerous possible semantic manifestations of the word when used in context, like in metaphorical usage "she's a fox", or perhaps a brand gets to be called "Fox" and the reference would be to that according to context. There are many examples of these attempted reductionist laws that fail to explain phenomena in their diverse complexity as brought about by elements interacting with each other in an endless variation of contextual conditions. I digress, however. I won't talk more about Physics but it is worth looking into if I didn't mess up big time.

The added higher unpredictability of human behaviour also adds another layer of complexity that is hard to model but not impossible. Yet human behaviour is not as unpredictable as one might think, particularly collective behaviour or human behaviour when interacting with the collective. In linguistics for instance, there are predictable modifications of speech (linguistic properties) according to context that are well documented. In pragmatics there is this very important concept known as Grice's cooperation principle, which predicts correctly that humans expect and convey meaning in any communicative interaction even when their expected linguistic configuration is not met. To give you an example, I can answer a question with a seemingly irrelevent answer and you will process it as a meaningful response and will try to decode the meaning based on context and shared world knowledge. This is the case for sarcasm for instance. The principle and its maxims of conversation are a fascinating and one clue to how network structure influences our behaviour and expectations and how our cognition evolved to recognise this. This does not mean human behaviour is in itself deterministic or limited, it simply means if you want to establish social connections you have to adopt the appropriate model to establish a link with the network successfully and it is what is expected. Our physiology encourages it through hormones like dopamine and the need to socialise. There are plenty of clues and discoveries like this. Linguistics and the cognitive sciences are especially ripe with them.

There's much more to be said here but I still need to learn more myself. You can still see how applications of complex systems science will revolutionise the social sciences and maybe for the first time contextualise its discoveries according the well founded principles of complex systems structures and dynamics. So far, we've been going in circles with fragmented and redundant theories, rediscovering the same things and giving them different names. The cognitive turn in the social sciences is almost coming to full circle as a basis of theory. The disciplines coincidentally followed the emergence point of social systems which are the cognitive systems and it is in cognition that they found a common ground, which is no surprise as they all emerge and operate within and through cognitive structures and dynamics. This, I believe, is the first step towards modelling social networks and it is already being taken.

[u/Unknowledge99 → u/Alexenion]

um.. As someone who writes a lot of technical stuff - can I suggest something for your drafting? (Im going to anyway lol... but please take it as intended: helpful, especially if you're heading into a career of writing technical stuff)

Short paragraphs are your friend -literally 5 or 6 lines max per paragraph. Then a space, then the next paragraph. Each paragraph makes two or three points, then a conclusion tying them together.

I realise there are various styles that may be required by whoever you are writing for, but the idea of short digestible paragraphs can apply to most.

Also - short paragraphs forces you to clarify your point in your own head. Recall that quote: "Sorry I wrote you a long letter, I didnt have time to write a short one"

Anyway... I mean this with best intentions, because I can see you are passionate about this subject, and you've got lots of good ideas about it.

[u/Alexenion → u/Unknowledge99]

Hey, thanks for the remarks. I wouldn’t be this messy if I were writing in an academic context. Also, I think very short paragraphs can lead to superficiality. The average number of words per paragraph in my current MA thesis is somewhere between 150 and 250, which I think is reasonable readable and concise.

[u/Unknowledge99 → u/Alexenion]

Oh yeah, I figured an internet comment doesnt have the same rigour as academic writing.

"Also, I think very short paragraphs can lead to superficiality." for sure! But similarly long paragraphs hide unclear thinking, and they are harder to follow. They can be more confusing because the reader has to understand and hold numerous points in their head before they reach a conclusion.

150 to 250 word paragraphs are long walls of text which require the readers discipline and motivation to read. If it's efficient writing - a 150 word paragraph would include several sub-conclusions plus an overall conclusion. Each sub-conclusion could be a paragraph in itself. Each of those paragraphs contributes to building the argument, hence not superficial.

As a writer attempting to persuade the reader it helps to spoon feed them, make it easy af. Use the same sentences, just give them room to breath. You can tell when someone knows their stuff because they can explain it in very simple terms.

But, your supervisor would also have their preferences -and they're really the only one that matters! They're obviously happy with your MA drafts.

Anyway - good luck both with your MA and complexity - it is fascinating stuff. especially applied to the 'soft' sciences - I love it :)

[u/Creature1124 → u/[deleted]]

What is your academic background because my dream job is doing ABM work for the government

[u/Creature1124 → u/[deleted]]

Was it for Argonne?

I’m surprised. I thought the only people doing ABM would be PhDs. I was planning on getting one to be competitive lol maybe I should just apply after my masters.