Complexity Explained
complexityexplained.github.io
complexityexplained.github.io
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.
To be honest I always leave a page immediately if it's way too fancy, especially when stuff starts moving and fading, I simply hate it.
On Safari, simple scrolling makes the content unreadable.
PDF: https://complexityexplained.github.io/ComplexityExplained.pd...
(Multiple languages available.)
"An Introduction to Complex Systems Science and Its Applications" https://www.hindawi.com/journals/complexity/2020/6105872/
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.
The title sets up rather greater expectations.
This is hard to use on wide screens right now - it's kind of like watching a tennis match
Thanks for that. I suspected as much. I'll wait to read something more serious, less market-y.
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)
There's a maxim in publishing: Don't bury the lede.
But their existence is beautifully hidden by the bloody annoying, horribly slow "Swoosh! Swoosh" of the animation.
It's a perfect example of having potentially fantastic content, then making it really, really hard to notice.
Urgh.
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?
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 discovered this book in my early teens and it helped me in structuring my thinking about this sort of thing.
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).
Anyway good point.
I see what you did there...
I can recommend the books of David Hawkins for a modern, scientifically-informed view on the subjective experience of Reality.
https://veritaspub.com/dr-hawkins/
> 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.
You might find the book Modern Samkhya: Ancient Spirituality for the Contemporary Atheist a good starting point.
- 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.
What do you mean by, “bottom-up metaphysical approach.”
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 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).
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.
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?”
"...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"
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.
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.
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 :) )
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.
So what are some real-world benefits of complexity theory?
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)
But a quick search brought this paper to the light which might serve as a starting point: https://res.mdpi.com/d_attachment/energies/energies-11-01381...
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.
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.
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.
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.
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.
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.
As potential further reading, one of the cited authors gave a lecture on intersections of AI and complexity science that I captured in this blog post. https://medium.com/from-the-diaries-of-john-henry/making-the...
Also recommend writings of any author affiliated with Santa Fe Institute, a lot of books to choose from.
"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."
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.
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.
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.
[1] free for HN: https://gumroad.com/l/understanding-seo/hacker-news/
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
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.
Agreed to both points.
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.
Show both if you can.
I thought I was explicit in my criticism of “notation only” explanations, but perhaps a positive example would be more explicit.
https://github.com/barbagroup/CFDPython
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.
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?
http://worrydream.com/AlligatorEggs/
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.
https://en.wikipedia.org/wiki/Diophantus#Mathematical_notati...
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?
Clicking dynamics leads here:
https://www.complexity-explorables.org/explorables/ride-my-k...
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.
I see elsewhere you've pointed here:
https://github.com/barbagroup/CFDPython
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.
The site is called complexity explained and I am challenging the question of ‘explained to whom’?
Someone who already knows the notation or someone interested in having complexity explained to them?
> Are you asking to understand these things without doing the actual mathematics?
This is one of the saddest things that comes from academically trained mathematicians: some believe the notation is the math.
Or worse, pretend to to retain a sense of superiority to those yet to learn it.
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.
> I hope to see the end of LaTex only explanations.
> Show both if you can.
Author, please read: https://contrastrebellion.com/
Another is how some people seem to think that you can only put one idea on the screen at a time, and users should scroll scroll scroll.
Both OP and your link both commit that sin.
Just put everything on one page and let my eyes do the moving.
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.
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.
Cool animations, no details, no math. Profound quotes from heavy names but not math.
Revolutionary, paradigm breaking stuff, but not really.
Almost makes me long for a Stephen Wolfram press release.
The work of OpenAI on Dota show how RL can produce a successful emergent behavior in response to complexity.
It's so frustrating that we seem to have lost any understanding of how to to put information on a screen.
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.