I got three slides in and the "Swooshing!" was driving me nuts. I'm sure the content is fine, and the presentation is simply gorgeous.
For me ... unusable.
Edit: In the end, at the end, I found the PDF. It seems a little light on content, but I guess I'm not the audience. Not sure who the audience would be, though.
For the people suggesting reading the pdf or disabling JS, you're missing the point of this submission.
90% of the value is in playing with their interactive demos. (though all of them seem to be from https://www.complexity-explorables.org/ so it might be better to go there directly instead)
A far more appropriate title would be "Complexity: A very brief introduction to major themes with bibliography".
The booklet is 20 pages covering aspects with a one-paragraph description, several examples as a bullet list, list of concepts, and two references for further readig.
It is so slow, that after the title slide I scrolled through three slides and stopped, because I thought something was wrong. Then the slide appeared and I realized I missed three slides, because of those animations being so slow and not at all correlated to how fast I scroll or how far I'm in.
> Edit: In the end, at the end, I found the PDF. It seems a little light on content, but I guess I'm not the audience. Not sure who the audience would be, though.
Thanks for that. I suspected as much. I'll wait to read something more serious, less market-y.
What really bothered me was that the animation only started when the new slide hit the top of the page. When I was not scrolling perfectly, the top most rows of text where already hidden.
When I first load the page I have to wait what is probably only 1/2 a second or so, but feels like an age, for the initial load to fade up. (I've timed it ... from hitting Ctrl-F5 to full text on the first page takes 3 seconds. It looks like the first 2 seconds are load, the last second or so is the "Fade Up".)
The last thing on that page "above the fold" is the quotation:
"There's no love in a carbon atom, No hurricane in a water molecule, No financial collapse in a dollar bill." – Peter Dodds
I don't see the connection with a page about complexity.
So I "PgDn" and the screen is initially empty, then text "swooshes" in from the right. I timed it, from the time I hit "PgDn" to the time the text stops moving is over a second. It feels an absolute age and breaks any flow of reading the content.
It's easy to miss that there's an animation to trigger ... initially I missed it completely. When I find it I see it says:
Jujujajaki networks: A dynamic network model that was designed to capture the emergence of community structures, heterogeneities and clusters that are frequently observed in social networks.
I watch for over a minute and think: "Does it show that?" I can't see it. It's pretty, but it imparts no information to me at all.
Again I hit "PgDn". Again the text "swooshes" in, this time from the left. And again, over a second to stop moving. It's taking an age, and already I'm fed up with the whole experience. Add that to the poor contrast and I'm not inclined to bother reading further. I'm starting to feel that the authors are more interested in showing their leet presentation skilz than they are in presenting the information itself.
And so on.
Does that help you understand my experience and why I found it frustrating?
I recently had the (possibly flawed) epiphany that all behavior is emergent. If you think about it, all things that we consider objects are just semi-permanent aggregations of fundamental particles that we recognize and label as objects for convenience of thought. When the patterns in such aggregations are outside the space and time scales that allow human minds to recognize them, the only label available is "complex".
I'm curious how this epiphany came to you. This strikes me as very similar to the Buddhist concept of the Five Aggregates, which describe five elements that combine to make up our existence: Physical form -> Sensation -> Perception -> Mental formations -> Consciousness
I was just trying to understand what people mean when they say that "consciousness is an emergent property", which always felt like a hand-wavy explanation. I was weighing that explanation against panpsychism and then this thought emerged.
I'm wondering which sort of consciousness is under scrutiny. We know when we're conscious and unconscious. E.g. Awake vs Asleep. Even animals exhibit that dichotomy.
The other consciousness is self-awareness. Which is hard to detect from the outside. Some animals may have it. Do they understand when they look silly? Do they recognize themselves in a mirror? These may be diagnostic.
It's important to know which one is intended since they are so very different, at least in their distribution among living creatures.
I claim that this is not true as stated. The main bulk of the habit-forming nearly everyone needs to do when learning to lucid dream is to recognise when you're dreaming, because almost nobody natively knows when they're dreaming. You have to learn to spot it by paying attention to the things which the dream machinery is very bad at (like text, clocks, and your own breathing).
Awareness, definitely. I'm using consciousness in the same sense Julian Jaynes used it (he used to call the other form "reactivity", a term that never quite caught on).
This is the reality of bottom up organisation, and is basically a completely different metaphysics to the current Western modernist one. Going further down this path of thought will lead you to ideas like constructivism, teleology, and non-dualism - all ideas that have long philosophical histories but are currently out of vogue.
> Sir David R. Hawkins, M.D., Ph.D. was a nationally renowned psychiatrist, physician, researcher, spiritual teacher and lecturer. The uniqueness of his contribution to humanity comes from the advanced state of spiritual awareness known as ” Enlightenment,” “Self–Realization,” and “Unio Mystica.” Rarely, if ever, has this spiritual state occurred in the life of an accomplished scientist and physician. Therefore, Dr. Hawkins was uniquely qualified to present a spiritual path that is scientifically compelling to modern society.
It has already been done. One of the oldest Schools of Indian Philosophy called Samkhya (which is atheistic) has a very beautiful model of the Universe/Elements/Evolution of the World which has influenced all other Schools (including Buddhism) and is worth studying.
You might find the book Modern Samkhya: Ancient Spirituality for the Contemporary Atheist a good starting point.
Is this not similar to the philosophy of capitalism (at least as posited by Adam Smith) upon which much of modern Western thought rests? Arguably it's also very much reflected in John Locke's work as well as many philosophical foundations for democratic institutions.
yes there are some Western philosophical foundations which treat organisation as bottom-up at certain levels of abstraction - Adam Smith on the economic level, Locke and Hobbes on the sociopolitical level, and so on. I think we have a good cultural understanding of human beings as existing in a network. But we don't consistently apply this perspective. For example:
- individualism treats individuals as good or bad, successful or unsuccessful based on their outcomes without regard for the structural incentives around that person.
- we still categorically divide between "life" and "not-life", treating life (and especially consciousness) as a conundrum and "not-life" as dead matter. We try our best not to look at the fuzzy edges between life and not-life. I would argue that this is a hang-over from Abrahamic dualism (the spiritual inhabiting the material), and that there is no distinction but instead a continuum from less-organised to more-organised. We do the same as the above with many other issues of category.
- Identity isn't concrete in bottom-up organisation. The Ship of Theseus, for example, is not a paradox when you take a bottom-up metaphysical approach. The illusion of identity is only propagation of a pattern.
TL;DR - yes, we do have some ideas around bottom-up organisation, but they're not applied consistently or across the board.
If you think all this sounds like woo, then you are at least in agreement that these ideas are not Western modernist canon.
I'm not sure we treat individuals as good/bad or successful/unsuccessful based on purely on outcomes. Criminal law, for example, depends upon intent in many cases.
The general biological view of viruses certainly demonstrate the absence of a categorical divide between "life" and "not life" as does the philosophy of the Turing Test. I'd argue that level of organization is less useful than the level of feedback loops in something, particularly if those loops are internal rather than external.
We daily operate with the idea of the Ship of Theseus as non-paradox in any number of ways. The City of Philadelphia retains its identity not because it is composed of the same people, geography, and structures established in its founding but rather because of the role it plays as an organizational concept, the Mississippi River retains its identity despite course changes over the centuries (let alone the constant replenishment of the individual water atoms within it).
I'd agree that we do not consistently apply bottom-up organization across the board, but that also necessarily means that we apply no consistent philosophy across the board. That leads to the question of how you're defining "Western modernist canon" given such an absence of a unified system.
> I'm not sure we treat individuals as good/bad or successful/unsuccessful based on purely on outcomes. Criminal law, for example, depends upon intent in many cases.
I mean the tendency to see someone who is for example a burglar and contrast them with a business owner and say that one is bad and the other is good. Which could be true if you removed all context, but usually when you add in context these kinds of absolutes dissolve. But my broader point is that we make value judgements based on the agent, minus the environment, which is IMO erroneous.
> The general biological view of viruses certainly demonstrate the absence of a categorical divide between "life" and "not life" as does the philosophy of the Turing Test. I'd argue that level of organization is less useful than the level of feedback loops in something, particularly if those loops are internal rather than external.
Feedback loops are the exact kind of organisational structure I was referring to, but I didn't know if you were cybernetically-oriented so left it vague. Loops are the mechanism of self-organisation.
> We daily operate with the idea of the Ship of Theseus as non-paradox in any number of ways. The City of Philadelphia retains its identity not because it is composed of the same people, geography, and structures established in its founding but rather because of the role it plays as an organizational concept, the Mississippi River retains its identity despite course changes over the centuries (let alone the constant replenishment of the individual water atoms within it).
I agree - we certainly act this way, but we culturally value reductionistic thinking; system-2-thinking is typically not oriented in this same way, and is more culturally valued. It's not necessarily how we act that I think is bad - it's how we think.
> I'd agree that we do not consistently apply bottom-up organization across the board, but that also necessarily means that we apply no consistent philosophy across the board. That leads to the question of how you're defining "Western modernist canon" given such an absence of a unified system.
It's our cultural institutions of thinking and understanding that are flawed, IMO. We generally act relatively well when we act on instinct, refusing to draw rigid boundaries and treating our environments teleologically. But in terms of the "right way" to solve problems, we go away from this and towards reductionism and mechanistic thinking (essentially ignoring the small or inconvenient relationships in the systems we examine, in classic "spherical chicken in a vacuum" style). We try to fix malignant systems by looking for the bad people who made it that way (the simplest, and usually most incorrect, approach possible), or by fixing proximal symptoms rather than following longer causality chains for root causes (think medicine - problems are addressed locally rather than systemically).
I'd agree that we tend to frame things in a reductionist way, but I don't think that's peculiar to Western thought so much as it is endemic to humans and their limitations. Given limited resources of time and knowledge the vast majority of people either attempt to limit the scope of the problem domain or opt for satisficing behaviors to achieve "good enough" results. It is rare that when confronted with a problem that a person has the luxury of time, creativity, and/or attention to derive first principles. It is doubly difficult when examining systems because the failings of most systems are not immediately obvious but instead the result of unintended consequences or the complexity of multiple conflicting behaviors resulting in perverse incentives... and if at the creation of the original system such problems were not foreseen what guarantees that the replacement system does not create worse results? Most people are cautious in proceeding when they are facing unknown (or unknowable) obstacles.
I believe that the toolset that we have created for ourselves for solving hard problems ossifies this limited approach, and that we need to make tools for improving complex systems more widely available/understood. We could even benefit if those in governance roles just knew about second order thinking and how to avoid unintended consequences from linear thinking, let alone any of the more advanced problem solving tools that systems theory provides.
Also I say that it's a Western thing, not because it's exclusive to the West, but because reductionism is part of our philosophical foundations since the Enlightenment. Compare to, say, SE Asian philosophical foundations - SEA religions are typically non-dual and metaphysically idealist.
if all of reality is just emergent phenomena (excluding some presumed "bottom thing" that we haven't found yet), there is no such thing as an "object" as a coherent whole - just collections of collections of collections. The ship of theseus does not exist as a distinct entity with clear boundaries - it is just the thing that Theseus uses to sail. If you replace every piece, as long as Theseus considers the ship his own then it's still the ship of Theseus, or in other words, identity is perceptual and based on a continuous structure or pattern rather than the present constituent pieces being all together.
If you are discussing the macroscopic day-to-day reality we human live in, sure, all things and all characteristics-of-things are emergent in broad sense. Every distinct, discreet thing here comes out of the interactions of quantum fields and gravitational fields, so yeah.
The problem is saying "everything is X" makes X useless as an adjective.
Usually, when you talk about this stuff, you look just a couple layers of reality. For example, if your lower level is water molecules and the upper level is observation, then "waves" "whirlpool" and so-forth are emergent objects/characteristics and water is a primitive object/characteristics - never mind that water molecules emerge from still lower level processes.
"...a thing is defined by... systematizations of coincidental aggregates of the properties of lower things [and] the emergence of the systematic from the non-systematic"
So-called emergent properties are just categorical abstractions that we've created in our mind to cognitively handle the complexity of the macroscopic world around us. These are evolved mental heuristics.
There's nothing beyond fundamental physics that's required, in principle, to explain these emergent properties, so in this sense I'm a philosophical reductionist. Emergence is just an illusion created by our brain's inability to deal with the true nature of fundamental reality.
There is no point in talking about the temperature of a single atom/molecule, but it is an important statistical property of a group of molecules with unique “features”.
The sum is more capable than each of it’s constituents. You could argue that a hyper-intelligent entity can explain everything due to temperature by the simple movements of atoms but that is not true, since with temperature, we can reason about a system we know only one property about, while the said entity would have to know every detail about every atom. In other words, we created a new thing that could not have existed alone.
(Perhaps it is not the best example, but there are countless others :) )
These emergent properties that you mention (temperature, intelligence) can in principle be described by the individual components (particles) along with the fundamental laws of physics that govern their interactions. The emergent property that we observe is just a cognitive abstraction designed to strip away the complexity and describe the aggregate behaviour of the group of individual components.
Our mind was designed to work this way. The most advantageous way to perceive a rock is as a single object with properties pertaining to utility (hardness, potential weapon, etc). This takes the least cognitive load and is the most beneficial way to perceive the world from a fitness perspective.
There's nothing epiphenomenal above and beyond the individual components (and the laws governing their interactions) except in our minds. In that specific sense, emergent properties are an invention.
I wrote an explicit example for a case where your analysis doesn’t seem to be correct, but you didn’t resolve the issue — temperature makes new observations possible that were not possible before and it is not tied to the human reasoning (also, it is only but one example, perhaps not even the best).
I don't know if the assertion you made is true, ie that an omniscient entity can't explain everything there is to know about temperature by looking at the simple movement of atoms. What's the basis for this? I know you followed that up with a rationale, but I didn't really follow. Just because this abstraction (temperature) allows us to come to conclusions and inferences about state and state changes doesn't mean that there's anything real about the abstraction aside from the cognitive structure in our brains that helps us to process the world around us effectively.
Complexity is not just about these larger features, although they are certainly manifestations of complexity. So like a mechanical watch is complex, but it is complex in a very different way than weight gain or weight loss is.
Nevertheless yes, this is the basic idea. Systems theory speaks about how you have substances flowing between different buffers or containers, as well as feedback loops that look at the buffers and adjust new flows based on those buffers. Or at least that is one of the most universal models. A nice general set of theorems about this are the fixed point theorems, which say that in a very large set of circumstances such systems find themselves in a “fixed point,” a set of buffer quantities and flows that is self-sustaining and usually healing from small perturbation. This is why when you stop dieting you gain back the weight; the same causes lead to the same effects.
The complexity of systems theory in particular comes from a few different properties worth thinking about:
(a) not being able to predict the whole from the parts and thus not knowing how to change the system to facilitate the overall behavior change [in other words “if dieting doesn't work, what does?]
(b) metastability transitions where there is enough random variation to allow for spontaneous reorganization between multiple fixed points [in other words if I get skinny in the Netherlands and fat in the US, then maybe American pandemic-me is skinny but Dutch pandemic-me is fat—as a corollary there is no such thing as “best practices” really, the same “causes” do not produce the same effects: what is the difference with the above?]
(c) when you do manage to create change, it is typically by thinking wishfully about what the system should do and then driving it to produce that “at whatever cost” and initially some “bottlenecks” emerge which appear to be resistant to the desired change, which you want to think is bad, but what actually starts to happen is that everything else about the system re-architects to reinforce that “bad” thing and that makes it okay. [In other words the journey from fat to skinny may seem to be limited at first by my love of food and joyous hedonistic eating... if that's the main bottleneck then unlike a diet’s plan to make me deny myself, my healthy relationship with food will actually feature more of that, indeed the reason that I was fat was that I did not love food enough and with delectatio morosa consumed whole boxes of cookies not for my truest enjoyment of them but because the pleasure of even a few cookies was always denied to me. If you read Marie Kondo's book you may be struck that her diagnosis of mess is that you have too much stuff and her prescription for having too much stuff is perversely not to love your stuff less and be more stoic but to actually love your stuff more. Ecclesiastes seems to come to a similar conclusion.]
Yeah, I think those are the most outrageous parts of dealing with systems which makes me astonished by their “complexity.” I often find that if I ask “why can't we do that,” I get some response “because of such-and-so” and then I surprise my interlocutor by saying “but what if I accept the such-and-so?” and, we eventually arrive at a whole different self-consistent system.
One example of this in a tech context since I feel I have overmilked the health context: “What if we don't have merge conflicts?” “psh, yeah right, you're never gonna get rid of merge conflicts.” “ok but pretend I am dumb, tell me why?” “because people modify the same code in different ways and you have a conflict!” “so if I could make them take turns then there would be no conflict?” “well you can't make us all take turns on the codebase! That would mean only one person is allowed to work at any given time!” “Ah I see your point, but what if it's more like a Google Doc where everyone sees other peoples' changes in realtime, that sequences the edits so that they never have merge conflicts.” “but then we couldn't do code reviews properly!” “why does that matter?” “because when I am setting out to rewrite the auth logic, I put the thing into a half-finished state! The code review protects those failing states from getting to prod.” “Ok, so is there a way to develop without failing states?” “Well, kind of. Like I can write `if (false)` and then write breaking code. But if our codebase were littered with those I would never be sure what I needed to re-enable.” “So there's no way to define your own version of true and false for this thing you're working on?” “I mean, I guess a boolean variable. But that won't work either.” “why not?” “if you have 10 of those then you have 1,024 different states that the system can be in, it becomes a nightmare.” “and you can't remove them when a developer is done?” “not without proper code review! That's what I am saying!!” “okay but what if you then have both mini review and proper review, mini reviews just check to make sure that everything is behind a feature toggle, very quick approval-at-a-glance of work in progress: then bigger reviews happen when you instate the new code path and delete the old one. We could detect those mass deletions, yeah?” “I mean, yeah, but, I mean, this is just not how it's done. Nobody develops code like this.” “Well, can we try it as an experiment for a month and see if we like never having merge failures more than we hate doing things a new way?”
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.
If you are interested in complexity, Complexity Explorer from the Santa Fe Institute has courses and other resources available:
https://complexityexplorer.org
This website was a neat resource. The whole point of complexity science is that there are domains with computational irreducibility where in order to estimate system behaviors we can not rely on formulaic models, in complexity science we instead make use of computer models via simulation to try and approach dynamics.
"It may not be entirely vain, however, to search for common properties among diverse kinds of complex systems... The ideas of feedback and information provide a frame of reference for viewing a wide range of situations."
Thank you! This is why I read the comments on HN. I was thinking while reading that I'd like to find some good resources to explore complexity theory in more depth, this looks great.
Side note: 14 people created something of value and distribute it for free, and still many of the comments here are just complaints about auto-scroll, websites, and JS. Pretty sad to see.
Couldn’t agree more. I often read some top comments even before checking an article just to get a quick read on whether something is likely e.g. clickbaity. Reading the comments it seemed like there was some consensus that this was a page with mostly information that would be better presented in a flat form like a pdf rather than an interactive website... but it’s actually a super fun collection of interactive visualizations for some of the classic complexity examples, and it worked perfectly for me except for a kind of ostentatious fade-from-white effect on page load.
Ah I see. I was on mobile and didn't get the left/right swooshing, but do on desktop. I also find the left/right swooshing from the outside pretty clunky and unnecessary. But the content is really nice, and I personally appreciate a bit of fun in experimenting with content presentation. Esp. given the topic.
> 14 people created something of value and distribute it for free, and still many of the comments here are just complaints about auto-scroll, websites, and JS.
Or, to put it another way, 14 people created fantastic material with all sorts of genuinely wonderful animations, then put links to them on a page that was so annoying that potential readers clicked away before finding the useful and intriguing stuff that had been shared so freely. Pretty sad to see.
I wrote the book "Understanding SEO"[1] with Systems Theory in mind.
After the 1000 meeting w people talking about tips and tricks and competing theoretical constructs including bullshit and thoughtcancer constructs like "linkjuice, pagerank, pinguins, pandas, ..." I set out to build a bullshit free theory of SEO. For my own sake - otherwise I would have had to quit my job.
And yeah "All models are wrong, but some of them are useful." Rephrased: It's a model, therefore it's wrong. But we'll, I deem it damn useful.
Wow.. love your clear and straightforward writing. And it's the first time I've felt I understand what SEO is and isn't (super secret magical sorcery).
How come you would have had to quit the job wo this book?
I got clients via word of mouth and then worked with them to have a more structured & systematic way to think about SEO and online growth.
Now I get most of my clients via the book. And
I already start with them from a systematic baseline.
------
Or think of it the other way, imagine getting contracted to create a webapp and the first thing that you need to do is to explain how the internet works.
Vs. Getting contracted and starting to talk about the advantages/disadvantages of different frameworks and app paradigms.
Instead read John Holland’s “Complexity: A Very Short Introduction”
To dig deeper (and something that will apply directly to many here) I loved “Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies” by Geoffrey West
Certain topics like "complexity theory" or even "artificial intelligence" attract this sort of thing. It's easy to appear that you're saying insightful things without actually saying anything at all.
I have an entire undergrad degree in complex systems theory, found it great and useful, yet in the instance of discussing this website I agree with you.
Likewise, I had a great deal of my studies occupied by quantum mechanics, yet it's also another topic that attracts cranks and people saying nothing of substance, at an alarming rate ;)
However, because it's approximately descriptive, rather than accurately predictive, the field is haunted by quantum woo merchants, grand metaphysical unifiers, quasi-ecological musings and Buddha-lite pantheism. Which is neither interesting nor useful, except perhaps as a sociological phenomenon. Discuss.
I don't think there's anything wrong with thinking about the philosophical side of complexity theory, I do quite a lot and arguably fall into the second and fourth categories you've described. You are, of course, free to not be interested in metaphysical philosophy.
Woo merchants latch onto anything science-sounding that they can, as they're trying to steal authority by use of jargon, so I don't think that's unique to systems science - but their influence is of course extremely toxic as they both kill people and erode the authority of the subjects they steal from.
The site already has simulations so one must assume it has code that could codify those LaTex eqs.
Perhaps a ‘things ever ___ should know about ___’ is needed for mathematicians and notation.
Ala, “some disciplines use the same symbols for different functions” and “many symbols are intended to obfuscate details for ease of hand writing”.
Perhaps this is meant as a collection of reference material and I am wrongfully assuming complexityexplained is trying to be educational material, but if the intended audience is people hoping to have complexity explained to them then I think code and its underlying abstractions are going to better explain to a higher percentage of people who click through than LaTex.
> I hope to see the end of LaTex only explanations.
I don't know what you mean by this. LaTeX is a type-setting system ... in what way is this site/page a "LaTex only explanation"?
I'm also confused by this:
> The site already has simulations so one must assume it has code that could codify those LaTex eqs.
I don't know what LaTeX equations you might be referring to.
Also:
> ... code and its underlying abstractions are going to better explain to a higher percentage of people who click through than LaTex.
What LaTeX are you referring to?
Seriously, LaTeX is a type-setting system, and LaTeX equations are just markup. I see neither of those on this page, so I don't understand your comment at all. Could you explain?
So, you actually mean that you hope not to see equations. But it's the equations that are the real meat of these things. Pictures are pretty, but they are generated from the equations, and the equations capture the understanding and the modelling. The equations are the content, it's the equations that let us do calculations, predictions, and quantitative analysis.
What would you hope to see instead?
I don't understand what you're asking for. Are you asking to understand these things without doing the actual mathematics? That would seem rather ambitious, so I'm guessing I don't know what you're asking for.
That amounts to an entire course on the subject. So if you're asking to have that sort of thing instead of a page that shows the equations and the maths, then you're asking that someone produce an entire course on the subject, instead of just a primer. That feels like someone complaining that an overview page isn't a degree level textbook.
So I guess I still don't understand what you're asking for.
One of the saddest things I see is people who say they want to understand maths without actually putting in any work to do so. They want it "explained" so it's all obvious without expending any effort beyond reading about it.
Math isn't the notation, the notation isn't the math, and I don't know any mathematician who thinks it is. Notation is a tool for communication, and its survival and persistence is evidence that the fastest and most effective way to communicate deep understanding is for the one doing the understanding to learn the language being used.
But equations are more than a tool for communication, they are also for the processing and manipulation of concepts. Learn to read and understand those equations and you gain much more than just an understanding of these concepts here.
The pages "behind" the one submitted here do have explanations which are then quantified in the equations. You don't need to read the equations to get a general sense of what's going on, and once you do have a sense of what's going on, the equations are not too hard to read.
I'm guessing I'll never convince you, but I really do think your demands are misguided, and your characterisation of mathematicians is wrong.
> ... one of the saddest things that comes from academically trained mathematicians ... pretend to to retain a sense of superiority to those yet to learn it.
That's a pretty nasty thing to say, and to be honest, I rather resent it. I'm also saddened that it's your experience of mathematicians, as most of the ones I know spend much of their time genuinely trying to help people understand stuff, and get joy out of seeing the lights go on. I'm sorry you haven't met them.
This repo explains computational fluid dynamics (an example of a complex system!) from “what is a python function” to “2d Navier stokes”.
It shows the work of how to discretize ‘latex beautified’ notation, shows the relationship between the computations and the notation, and even explains when their LaTex strays from “conventional use of notation” and why.
The authors even throw in traditional handwritten board lecture videos if that helps you learn better.
complexityexplained reads like it’s written by the Spider-Man points at Spider-Man meme.
I'm still not sure of what you mean by "notation only explanations". Do you have a problem with standard mathematical notation? Or with explanations that involve mathematics at all?
Can you give me an example of what you consider to be a "bad LaTeX explanation"?
For what's worth, I find your link infinitely more confusing than the few pages of Landau which cover the same topic... ;) The explanation in your link is lost among details of implementation and python syntax, whereas a clear and lucid explanation in a good textbook like Landau lets you understand the actual physics of what's going on. Of course your mileage may vary, and at any rate a few animated graphs are very valuable as a complement to aid in that understanding. This is a relatively recent tool that should be embraced more.
If I was incorrect with thinking you were trying to be condescending by inexplicably equating LaTeX to "...maths", then I apologise for my assumption but, as noted in another comment, now I'm concerned that you actually believe the notation to be the math.
Even knowing that the '/' symbol represents division, which of course in the entire lexicon of mathematics is unlikely to be its only shorthand, fails to explain to the individual what division is or how one uses or performs it, and conversely one could teach the algorithm and use a different symbol.
> Can you give me an example of what you consider to be a "bad LaTeX explanation"?
Unsure how I could when it seems from our comment history that you originated this quoted text?
> I'm still not sure of what you mean by "notation only explanations". Do you have a problem with standard mathematical notation? Or with explanations that involve mathematics at all?
I have a problem with claiming to be a resource that explains a thing but explains it to people in such a way that you have to first have the thing actually explained to you through a secondary resource allowing you to then return to this resource and think "Yeah, this explains it now that I already had it explained to me elsewhere."
Maybe call it 'complexitysimulated' or 'complexityexpressedthroughapproximatedspecialcaseinteractiveanimatedcalculations' or even 'complexityexplainedtocomplexityresearchers'.
Seriously, ask yourself why my saying "I hope to see the end of LaTex only explanations." and "Show both if you can." triggers an initial snarky response from you and now this doubling down?
Mathematical notation changes.
Your equating symbols to '...maths' fails to uphold any rigor in its statement considering math needed to introduce such notation at some point.
> Where we would write 12 + 6n/n2 − 3, Diophantus has to resort to constructions like: "... a sixfold number increased by twelve, which is divided by the difference by which the square of the number exceeds three"
You seem to be taking for granted your previous knowledge and using it to defend a resource claiming to explain elements of that knowledge.
Do you want 'complexity explained' to anyone interested in having it explained to them? I do.
What does it look like to you for a person who is unaware of what complexity is but wants it explained to them going to this website seeking that explanation?
Can anyone leave having it explained? Does the person need to bring prerequisite knowledge, like deciphering latin runes, or perhaps they are expected to have read some textbook explaining complexity before this website can successfully convey an explanation of complexity to them?
Do you think you, or all people familiar with '...maths', have a gene that tells you what 'sin()' means or is it more likely that these esoteric symbols need also be explained when trying to explain any mathematics using them.
Do you think a 'trigonometryexplained' website could just list trig identities for sine like 'sinX=+|-(1/sqrt(1+cot*2X))' without an explanation for what the symbols 'cot' or 'sqrt' means or even a single right triangle anywhere?
Is 'Lf.(Lx.f(x x))(Lx.f(x x))' a better 'explanation' of the y-combinator by virtue of using mathematical notation, aka '...maths', or do alligators do a better job of explaining?
Does anyone come away from the alligator explanation confronting people by saying, 'when you say "maths", do you mean ...alligators?'
There's a plethora of online debates, many had within these orange walls, lamenting the state of mathematical Wikipedia for the same or similar reasons.
These symbols are, contemporary!, placeholders for ideas.
If you want to explain an idea to someone that requires symbolic placeholders then those obfuscated ideas will need to be borne out as well.
This is great. I try to write about little pieces of this, but mostly from a perspective of new tech, policy, and history: https://unintendedconsequenc.es/
I read the PDF, it looks great but it doesn't really contain that much information. It's all very abstract, which is fine since it's a booklet, but it doesn't offer much in how to go deeper into it.
Holy hell that website is awfully designed. Why does it try to snap my scrolling position to what it thinks is the right position? It doesn’t even work, it jumps around like hell, I try to click through the examples and it just kicks me to the bottom. This is exactly the same idiocy of bad and unaccessible design for aesthetic purposes that the site complains about. The irony is palpable.
The Chinese translation of the title is a bit puzzling to me, as a Chinese mainlander lived in US:
Complexity Explained is translated to "沒說你不知道", literally means "you wont know if I don't tell you". Generally "Explained" usually corresponds to "详解"
But anyway, very good content. I am surprised that double-pendulum is a chaotic system. I thought it's possible to precisely predict its motion, because its apparent simplicity.
If you are doing software engineering, Dave Snowden's Cynefin Framework is worth a look. Considers complexity as one quadrant to deal with when making decisions: https://en.wikipedia.org/wiki/Cynefin_Framework
The parametrized visualizations are fun and useful. They really help with the mental model and intuition.
Also I didn’t know that field existed. Very interesting. One could imagine using visualization and generative testing for software systems to be a subject where this model could be applied.
Have you ever faced a problem or system so complex, that you tried to understand and gave up in frustration? Do you think there are systems out there completely beyond humanity grasp? that we won't even have an entry point to reason about them?
I've learned to think of understanding as a form of compression. The more recurring patterns there are in a system, the better we can understand them. The fewer such recurring patterns in a system, the harder it is to understand them. Fortunately for us, a lot of things in nature are recurrent.
And if you want to understand why they are recurrent, then you'll find the commonality in the shape of the system's components' causality - how they influence each other, often in loops. These are the subject of control theory, cybernetics (also a systems science), and systems dynamics (if you like maths).
It doesn't seem to work on mobile either, for what it's worth. Very low contrast text and general weirdness that makes it hard to tell if it's working that way on purpose or not.
I really appreciate the effort on this, after 8+ years of SEO it can get a little hectic to say the least.
But honestly. Truthfully.
Backlinks are all you need to rank. I've been white/black/grey hat SEO and each and every time, buying a bunch of solid backlinks (a.k.a. you get what you pay for) and within 2 weeks I am on page 1 and still rocking. For 246k keyword too. Spend a bit of time running some searches these days and since the two major algo updates in Dec/Jan all rules have basically gone out of the window.
For me ... unusable.
Edit: In the end, at the end, I found the PDF. It seems a little light on content, but I guess I'm not the audience. Not sure who the audience would be, though.