Complexity Explained

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.

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.

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...