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.
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.