What do you guys think of the following argument? (Apologies in advance if it’s too technical)

TLDR: effective complexity matters, not just ideal complexity, and the current level of technological advancement likely enables horizontal structures to have a higher effective complexity than hierarchical structures

It all starts from the fact that complex problems need complex solutions (Ashby’s law of requisite variety), and societal problems are complex. Decentralized systems are more complex than centralized ones, and decentralized planning is more complex a market that is just based on price signals. This would then in theory justify decentralized governance over centralized governance and a decentralized planning economy over a market economy.

This justification is not really new. However, this justification only really considers ideal cases. In reality, just like hierarchical systems have an information bottleneck via lossy data compression as information travels upwards, horizontal systems can have an informational bottleneck through noisy raw data when people don’t communicate or coordinate effectively. These information bottlenecks essentially translate to an effectiveness of a system.

I doubt that the following is very original, but the effectiveness of an information bottleneck is essentially directly influenced by the current level of technological advancement in society. However, the effectiveness from a horizontal information bottleneck scales differently with technological advancements than the effectiveness from a hierarchical bottleneck. At low levels of technology, hierarchical systems may have a higher effective complexity, but at high levels of technology (which we are at or approaching) systems approach their ideal complexity, such that horizontal systems would have a higher effective complexity.

This is all to say that while previous anarchist or horizontal societies over the long have been defeated or replaced by more hierarchical systems due to a variety of reasons, one important reason to consider is that maybe technological advancement weren’t at the level yet to enable large scale horizontal societies. I don’t know when technology advanced sufficiently to enable large scale horizontal societies, but I’d definitely we are at that point now.

Looking forward, this also frames the development of information technologies and coordination methods as one of the most important aspects that an anarchist movement should actively try to develop. I would think that a society should to try to optimize for its current effective complexity while being forward to looking to try to continue increasing its effective complexity. So, while certain hierarchies may be temporally justified based on the level current technologies (even in some future), we should always be trying to develop technologies or methods that enable the effective complexity of horizontal structure to surpass that of their hierarchical alternatives

What do you guys think of the following argument? (Apologies in advance if it’s too technical)

So I'm a bit of a math stickler, so honestly it's not technical enough for me 😁

TLDR: effective complexity matters, not just ideal complexity, and the current level of technological advancement likely enables horizontal structures to have a higher effective complexity than hierarchical structures

Issue: define complexity. Your complexity framing basically requires you to either choose or formulate a definition. There are several definitions in the literature which are useful for their domains of applicability...but I honestly think you might have to formulate your own definition

It all starts from the fact that complex problems need complex solutions (Ashby’s law of requisite variety), and societal problems are complex.

Not necessarily though. E.g., many highly complex industrial processes can be controlled sufficiently with PID controllers. For a more mathematically rigorous example, we often control high-dimensional linear systems with reduced-order models, because certain modes dominate the behavior, even though you might have a bunch of other modes that you're neglecting. And also, lots of machine learning algorithms and dynamical systems analyses are based on a manifold hypothesis: basically, even though the state of the system might be high-dimensional, most of the important behavior can be explained by projecting onto a lower-dimensional manifold.

Decentralized systems are more complex than centralized ones

That really needs evidence and quantification. There are some incredibly complex centralized systems running around, e.g. opamps can have dozens of state variables related by a nonlinear differential-algebraic circuit equation. (If you have studied electronics, you probably saw the ideal opamp model, or maybe an opamp with a first-order section, both of which have reasonably simple models. These are both crude approximations. And really, the underlying Maxwell's equations are PDEs, which are infinite dimensional, and these are simplified versions of the equations of quantum electrodynamics.)

and decentralized planning is more complex a market that is just based on price signals. This would then in theory justify decentralized governance over centralized governance and a decentralized planning economy over a market economy.

I don't think that the complexity, on its own, ever justifies a system. It certainly can be part of the justification, but complexity is just an operational concern. IMO, more important justifications are fairness, dignity, preservation of life and liberty, stability of horizontalness over time, robustness to adversarial actors—social factors come before operational factors.

And just from a pragmatic perspective: "it's more complex" is not a selling point for decentralized systems...or anything..Most people prefer simple solutions to complex ones. And frankly, this is a reasonable instinct. Just because a model is more complex does not mean it will give you more accurate results.

This justification is not really new. However, this justification only really considers ideal cases. In reality, just like hierarchical systems have an information bottleneck via lossy data compression as information travels upwards, horizontal systems can have an informational bottleneck through noisy raw data when people don’t communicate or coordinate effectively. These information bottlenecks essentially translate to an effectiveness of a system. I doubt that the following is very original, but the effectiveness of an information bottleneck is essentially directly influenced by the current level of technological advancement in society. However, the effectiveness from a horizontal information bottleneck scales differently with technological advancements than the effectiveness from a hierarchical bottleneck. At low levels of technology, hierarchical systems may have a higher effective complexity, but at high levels of technology (which we are at or approaching) systems approach their ideal complexity, such that horizontal systems would have a higher effective complexity.

I mean intuitively I agree with this, but this could definitely use some formal justification and quantification.

This is all to say that while previous anarchist or horizontal societies over the long have been defeated or replaced by more hierarchical systems due to a variety of reasons, one important reason to consider is that maybe technological advancement weren’t at the level yet to enable large scale horizontal societies.

Nah. There have been examples of horizontal societies at all levels of technological development. IMO, anarchist societies have been defeated in one of two ways: (1) torn apart from within due to interpersonal conflicts, and (2) overwhelmed from outside by a much larger enemy. Unfortunately, there's not really a silver bullet for either option...and I don't really think that anarchism itself is inherently vulnerable to these problems. I.e., this could be said with less precision about states, ancient empires, and non-anarchist projects.

IMO, I actually think we need to develop a formal mathematical framework for anarchist modes of organization with provable stability of horizontalness and robustness to adversarial actors. (And if we can't have this exactly, then can we converge to it? Can we bound the probability that things go wrong?) This is what anarchism has had the best success in informally developing and passing on through literature and culture, although of course an imperfect success with some serious failures, from which we must learn. Unfortunately...capitalists are not willing to fund research into their own downfall, so any mathematician interested in this stuff would basically have to conduct this portion of their research in secret...and then materially prepare to get blackballed from academia once it gets put on ArXiv.

And also...anarchists typically have more important stuff to do than formulate mathematics, e.g. mutual aid, direct action, agitation, survival, etc. And mathematics pedagogy is...not exactly egalitarian, and as a result, most people have developed math anxiety. So it is completely understandable that pragmatic anarchists are not wasting time studying mathematics.

Looking forward, this also frames the development of information technologies and coordination methods as one of the most important aspects that an anarchist movement should actively try to develop. I would think that a society should to try to optimize for its current effective complexity while being forward to looking to try to continue increasing its effective complexity.

Yes, yes, a billion times yes! I know it's hard, I know there are huge structural hurdles, I'm living that reality, but I really wish that more anarchists would break into formal mathematics. IMO if you want Solarpunk Utopia to happen...of course we need good anarchist politics and praxis, I cannot stress enough how important a good political education is, but we also need people who can analyze and control differential equations, statistical learning machines, electromechanical networks, industrial processes, information technology, climate change and weather prediction...we need math too. We need mathematicians and scientists and engineers and technologists who aren't fucking ghouls and actually want to make the world a better place.

So, while certain hierarchies may be temporally justified based on the level current technologies (even in some future), we should always be trying to develop technologies or methods that enable the effective complexity of horizontal structure to surpass that of their hierarchical alternatives

IMO one of the exact theses of the anarchist position, as opposed to other communists and socialists, is precisely that these hierarchies are not justified, in particular based on the levels of current technologies. If anything, it's categorical: if these "hierarchies" were justified, then by analyzing them as true hierarchies within an anarchist framework, we would be making a category error, because then they wouldn't be hierarchies. For example, there could not be a level of technology where somehow a State would become justifiable. It is unjust. The level of available technology is orthogonal to the issue.

IMO I know I wrote a lot, but I really really really like what you're thinking about and I recommend you keep pushing this train of thought. I recommend that you look into the mathematics of signal processing, dynamical systems, control theory, statistical learning theory, category theory, and theoretical computer science. I know that's a big ask because it's been a multi-year project for me and I'm probably never gonna finish, but at least I'm learning a lot!

Yes, it will require an absolute shitload of math. Literally all of math, ever. That's what Library Genesis is for. But that's the fun part 😁.

"Cybernetics" as a discipline is ancient history at this point. The fields I listed are the ones that those people ultimately went into. Be wary of works labeled "complex adaptive systems", because these are usually empirical investigations without serious mathematical proofs. They are useful for building intuition, but these authors have a habit of making grand proclamations from specific examples without actually proving those proclamations in general. Ditto for "artificial intelligence", "nonlinear science", and "evolutionary computing" papers. Not to say they shouldn't be read, but that like every paper, they should be read critically.

Thanks so much for the feedback and advice. I have a pretty strong math background but not much in systems or information theory, and these ideas (including anarchism) are relatively new to me, so I just wanted to try to communicate some initial thoughts to see if I was on some sensible track. I definitely plan on reading up on the subjects you mentioned, and trying to figure out how to use my quantitative background for good.

For a more mathematically rigorous example, we often control high-dimensional linear systems with reduced-order models, because certain modes dominate the behavior, even though you might have a bunch of other modes that you're neglecting

This relates to your point of needing to actually define complexity, but a good definition (at least for this purpose) would probably consider “complex” models that can be modeled with a high degree of accuracy by a reduced order model, is not actually as complex as it seems.

There are some incredibly complex centralized systems running around

Sure, not all decentralized systems are more complex than all centralized systems. Not sure how to formalize this at this point, but something along the lines of if the two systems/networks have the same amount of nodes, then the decentralized one is likely to be more complex. From my basic understanding of network theory, you could probably then calculate the correlation in a centrality metric with a complexity metric for different networks.

IMO, more important justifications are fairness, dignity, preservation of life and liberty, stability of horizontalness over time, robustness to adversarial actors—social factors come before operational factors

Definitely agree. Was thinking that I should have clarified this.

And just from a pragmatic perspective: "it's more complex" is not a selling point for decentralized systems...or anything

Agreed, just enough complexity but not too much is a fine balance and is something else that needs to be quantified

so any mathematician interested in this stuff would basically have to conduct this portion of their research in secret

Would be cool if like minded people whether in academia or not could collaborate on stuff like this. Obviously not much money in it, but it could be a sort of operations research that cooperative and mutual aid networks could be interested in and wouldn’t seem so adversarial

There have been examples of horizontal societies at all levels of technological development

Sure, I guess I was suggesting that maybe the level of technological advancement can in part determine the ease with which a horizontal society can increase in size and/or endure in time. For example, could help with developing communication tools that reduce in fighting or reduce coordination costs or could help develop defense tools to defend from larger hierarchical groups

Much more learning to do