How does complexity theory benefit real people? Unlike theories of physics or economics, it doesn't appear to describe how anything actually works, rather that things are just more complex than they seem. For instance, complexity theory just points out that the double pendulum is hard to predict without adding value, while controls theory was more useful by stabilizing the double pendulum.
So what are some real-world benefits of complexity theory?
Macro-economic theories are based on high-level relationships that economists have observed in reality, and that have some theoretical basis. For example, supply and demand can be represented as curves (aggregates of individual positions), and that in a perfect market the value of a good will converge at the intercept of supply and demand. There are a considerable number of assumptions required to make a statement like this, most of which are made to 'manage away' complexity.
Complexity theory helps us find ways to address and model complexity, such that we can reduce the number of assumptions required. For example, if we can build an agent-based simulation of supply and demand, and we model these agents as realistically as possible (few assumptions), we can then see if the same realisation of a good's value occurs.
The value in this is that we can then test the assumptions directly (what happens if 20% of people make irrational decisions?) and see how it affects the emergent behaviour.
Complexity theory can help in properly building these kinds of fine-grained simulations in a smart way, and can also help in understanding and debugging such simulations when the wrong behaviour emerges.
In my field (power systems) complexity theory can help us investigate and understand why large-scale blackouts have a fat tail distribution. That is, to understand why our macro-level statistical models aren't accurate in the edge cases. Primarily it is because these outliers occur 'emergently' due to the complexity of power systems, in ways that we overlook by applying old-school approaches to grid development and system operation.
In short: complexity theory helps us look beyond our 'mostly right' high-level statistical models and theories.
I mentioned this in another thread, but I was wondering if you had any examples of complexity theory informing what investments to make into the power grid? e.g. emergent behaviour is predictably reduced by adding X MWh of batteries in a certain region?
There's a distinction to be made between chaotic and complex systems. You cannot model chaotic systems at their chaotic level of abstraction (higher levels may form more predictable behaviour, eg. The weather patterns). Complex systems cannot be predicted with certainty but you can interact with and model them. Consider the human body - it's impossible to know the total state of the body and predict exactly what will happen next, but we can model different states of the body and understand what interventions can counteract undesired states. Of course the specific fields for working with the body have made many discoveries long before systems science existed, but in the same way that the scientific method provides tools for understanding linear causalities across fields, systems science provides tools for understanding nonlinear causality across fields.
Critics say complexity has no predictive power. That’s the point. The field studies systems that are unpredictable by instead modeling them and studying how their conditions or parameters affect their behavioral characteristics.
I second that. I see it as something to build intuition for "complex" problems. To make this more concrete: If you want to study the brain you can go the "biology" approach and describe neurons really well and build mathematical models for all the neuron types. Or you could do it the other way around with the "psychology" approach and put people/monkey/rats in an MRT. Both ways you learn important stuff but it will be hard to connect both worlds because simulation of enough neurons to predictive power over the outcome of an MRT is probably far fetched (although there are the human brain project or its US counterpart, the brain activity map project which attempt to do something like this). Complexity theory might help to learn how to close this gap. Things like synchronization (http://www.scholarpedia.org/article/Synchronization#Chaotic_...) or Self organized criticality (form the critical brain theory) could help distinguishing which parts of neuronal dynamics are due to biological restrictions and which form the function of the brain. With this knowledge one might be able to "dumb down" neuronal models enough to make large scale simulations without loosing to much of the processing dynamics.
You might still not have predictive power then, but then again, complexity theory might help you to understand what the limitations of your approach are.
The same intuitions could be applied to other things. Large scale power grids are also often hard to predict when not moving into a sure fail state. Being able to analyze how you stabilize these systems without basically dumping a lot of money on them is the way to go (Looking in the past, the money will probably not be spend).
You could study the behavior of crowds and maybe make estimations on the safety large conventions build a "panic index" that calculates the risk of having something like at the Loveparade https://en.wikipedia.org/wiki/Love_Parade_disaster . Again - you would not be able to make a precise prediction of whats gonna happen but I'd say it'd even knowing if you have like a 0.5% Chance of a disaster would be worth knowing. (Of course, there are effective methods taught to prevent this disasters anyway. But sometimes you have new configurations that didn't occur in the past and you might catch these things with a simulation. I could be an additional approach)
Could you elaborate on the power grid idea? It seems like a good example of how to apply complexity theory to make hard decisions, in this case optimal investments in grid stabilization.
For example they report on a project where they used photovoltaic panels to stabilize changing power consumption in a power grids with minimal changes in the existing structure - something that is hard with traditional power plants since they basically have to much momentum for quick switching action. https://ieeexplore.ieee.org/document/7007647
Also, agent based simulations (building on the idea of self organized criticality) are a thing. With these setups you can test power grids on their reaction for certain failure types - something you don't want to test in real life. I assume these simulations would also be quite accurate since consumption and production should be well known, as well as the physical properties of transmission.
Complexity theory is fascinating in itself (talking about how efficiently solvable or complex a problem is in an absolute, mathematical way), but also can spur a lot of research. As an example, integer factoring is strongly believed to be hard for classical computers (in a well defined complexity theory sense). When Peter Shor presented an efficient quantum algorithm for integer factoring in 1994 it was a breakthrough for the field and triggered huge interest into the field of quantum computing and quantum alogrithms. Serious widespread research into quantum computing more or less started then. Quantum computing is estimated (by BCG) to create a market value of 450-850 billion $ by 2050 (mainly in chemistry, optimisation and cryptography).
So, the academically interesting aspect aside, it can spur research for useful things, it can act as a guide to what is worth / not worth researching (if something is proven to be in a "hard" complexity class, then you won't find any efficient algorithm to solve the problem, ever (assuming P =/= NP).) and is generally a great framework for algorithms research. And evidently, algorithms create a lot of value (good and bad, unfortunately).
It's just very much "under the hood". 100 years ago people could have also, rightly, said "how does quantum theory benefit people, what's the value in that". Yet, without the fundamental research in quantum theory we would not have modern technology. Understanding the behaviour of electrons in materials on an atomic level requires quantum mechanics.
Is complexity theory related to computational complexity? The webpage never mentioned big-O notation, and Wikipedia's disambiguation header seems to imply they're mostly unrelated: https://en.m.wikipedia.org/wiki/Complexity
I found the material from the Systems Innovation group instructive on the presence and application of some of the aspects of complexity in the real world:
Thanks for the link! I'm looking for a course that really does get into the weeds about applying complexity theory to create value for my work. Would you recommend one of their listed courses in particular?
I think most of the video media inside the courses are also available on youtube - maybe you can stroll through those to see if any reach the level of detail you could use?
In it are the beginnings of a new simple universal way to measure complexity.
The "real-world benefits" are that you can compare 2 systems that accomplish the same problem and objectively choose the less complex one, much like you could use the measurement of "weight" to pick a lighter material for something like a plane.
You could ask the same question of calculus (or any theoretical domain of knowledge). The rules of derivatives and integrals don't, in themselves, give a model of any particular empirical system. But they are a tool/language that can be used to describe/build/evaluate models for systems.
To give examples requires an agreement on exactly which domains of knowledge you consider to be part of "complex systems", so based on your question I'll assume that you consider chaos to be part of it.
For example, the Poincaré-Bendixson theorem saves researchers time because they don't have to consider the possibility of chaos in 2D continuous state space models.
For example, since we know that weather is a chaotic dynamical system, we can give up on the hope of ever being able to precisely predict the weather a year beforehand. This saves researchers from spending their time on impossible objectives.
Complexity theory provides metaphors for nonlinear change, for one thing.
And most things in business are neither truly linear nor simple exponential. Yet most people in business revert to these two mathematical concepts.
For example, it might convince a CEO to keep working on a project because this 'emergence' thing may be happening -- where a non-complexity-empowered CEO might kill the project because there is no linear return, and no apparent potential for exponential return.
So what are some real-world benefits of complexity theory?