Talk:Fractal/Archive 1

message: The list of points is terrible writing. There must be a better way to do this. Intros that read like Powerpoint slides are the opposite of good writing. I realise it was turned into this by the death of a thousand tweaks, but there's gotta be a better way that's both accurate and readable - David Gerard 21:19, 4 Aug 2004 (UTC)
replies: text: Personally, I don't see anything wrong with it.  Actually, my attitude is the opposite of yours --- I generally think writing in point form is more readable than paragraphs.  In this case the 5 points offer a clear, convenient checklist for deciding whether a given object is or is not a fractal. --Shibboleth 00:54, 5 Aug 2004 (UTC)

text: My opinion is that the current intro has reached a reasonable compromise between being both accurate and concise. But if you can re-write it without (a) losing content or (b) turning it into a mini-essay (which takes us back into the "can't we summarise this ?" loop) then go for it. Gandalf61 09:37, Aug 5, 2004 (UTC)
I've rewritten it. There is a fair chance I've missed something or interpreted something incorrectly, so please edit the lead further. The list was generally inappropriate, all the items were really the same thing. The the nature of fractals really only depend on one property (just like they only depend on one equation); their recursiveness. ❝Sverdrup❞ 14:15, 16 Aug 2004 (UTC)

text: I was the one who basically came up with the "Power-point" presentation. I don't think it's bad writing style, where is it written (in Elements of Style??) that bullet points are bad style, if used judiciously? I was trying to reach a compromise, as Shibboleth mentioned, between two extremes — on the one hand, an intro that would please a finicky mathematician but be totally incomprehensible to most people, and on the other, an intro that would be completely understandable and pleasant to everyone, but be superficial and contain subtle fundamental inaccuracies. You are quite wrong to say that everything on the list is the same. My point is that "fractal" really is a fuzzy term, even in math it's just a catch-all for a family of definitions. The key part for me was, "satisfy most, if not all". I understand and confess that I approach this from a technical bias just because of my training, but I also thought it was important to make the point early on that it's a fuzzy term. Is something a fractal? Well, check the list. If it seems to have most of those, then probably yes. If it's missing one, so what. If it only satisfies ONE or TWO, it's probably not. But, to just say, "A fractal is a recursively defined object of infinite detail and self-similarity, etc., etc." may give people the impression that if something isn't recursively defined, or isn't self-similar, then it's not ever considered to be a "fractal", and that just isn't true. Revolver 05:06, 13 Oct 2004 (UTC)

text: Actually, the entire introduction as is currently stands seems pretty good, at least with regard to accuracy. I might want to change or reword a couple things (how is something broken up in a "radical" way?), but it seems to be going in a good direction. Revolver 05:28, 13 Oct 2004 (UTC)
thread_title: Intro reads like a Powerpoint slide

message: Well, I'm not happy with the page, even though it is a featured article today. The 'definitions' business has gone off track, and the tone is too propagandist.
Charles Matthews 08:44, 19 Aug 2004 (UTC)
thread_title: Not happy

message: In Jr. High School, I remember calculating the dimension of a curve. Something about calculating the difference between distances when using different sized "rulers". Does this sound familiar to any of you deep math guys (I was going to just say "math guys", but I consider myself one of them, so I thought "deep math guys" was more appropriate)McKay 00:49, 20 Aug 2004 (UTC)
replies: text: See Hausdorff dimension. David.Monniaux 21:09, 20 Aug 2004 (UTC)
thread_title: Dimension

message: From the article: That is, the traditional mathematical methods zoom in, in order to simplify the local picture; fractals flag the way this may fail when ever-finer detail is seen, with no definite limit.
This sentence seems wholly ungrammatical, and I don't know what it's supposed to be. --Golbez 17:02, 20 Aug 2004 (UTC)
thread_title:  Grammar check 

message: I have got a load of images at my gallery page (in swedish but most of the titles are in english and also the titles of the pages has an english translation). Some of them are uniqe fractals invented or modified by me. All images at the pages are rendered from my own code and are free to use for anyone. If you find something useful then do not hesitate to make a copy and upload it to here. // Solkoll 07:04, 9 Sep 2004 (UTC)
thread_title:  Copyright free images of fractals 

message: [EDIT: Removed by poster]
...Second, as far as the link:  I believe the Fractal Metaphysics Web Page represents a unique and valuable resource.  Every science and every geometry has a sister philosophy, and I believe one of the most important legacies of chaos theory will be in expanded dimensions of human thought.
It's unfortunate that Revolver chose to focus on one of the less mathematical external links leading out from FMWP and to use it as a reason to deride the enterprise as a whole.  I do believe that less mathematically rigorous applications of chaos theory can have validity.  But for those who disagree, there are also articles on the site dealing, in a mathematically valid manner, with the construction of the Koch snowflake, the geometric structure of the Sierpinsky Gasket, and several different constructions of the Harter-Heighway dragon --as well as the relationship of each of those to (respectively) the nature of motivation, social structures, and the nature of reality itself.
In summary, I think that both contributions to the article were valid, and the use of one decontextualized secondary link to discredit the entire enterprise was a cheap shot.
kitoba Oct 19 5:27 EST 
:about the section. there is a farily lengthy article on recursion, which i think might be appropriate for an "ancient" example; the comparisons with plato and the biblical quotes to fractals are pretty facile. many fractal-ish structures exist throughout the world regardless of whether people mentioned them. Frencheigh 22:59, 19 Oct 2004 (UTC)
replies: text: Every science and every geometry has a sister philosophy, and I believe one of the most important legacies of chaos theory will be in expanded dimensions of human thought.
I'm not sure what exactly this is supposed to mean, or what "sister philosophy" is. Of course, I think the legacies of chaos theory will be in expanding human thought, but then again, I think the same way about modular forms, manifolds, and non-standard analysis, but of course, none of these are popular fads. "Chaos theory" and "fractals" seem to be attractors (no pun intended) in the public imagination for everything thought to be revolutionary about math, and this is why it's been given this strange aura and significance by postmodernists, poststructuralists, and literary theorists.
As for the other articles on the page, yes, I did look at them, and yes, I did choose the worst one. The most harmless was the one written by the math professor...while I'm not sure what the point was, the references to math were at least accurate. (Although the analogy between projections onto a subspace in Hilbert space and shadows on a cave seemed stretching.) Also, the constructions of the fractals you mention seem to be done fine — I just don't follow the grand metaphysical leaps in those papers. This is probably a fundamental disagreement between mathematicians and philosophers who choose to "apply" math to their work. The whole point in applying math is to apply it in a rigorous way. Mathematical ideas are preicse — if you lose the precision in mathematical ideas, you've lost the whole idea itself.
Upshot: I just don't see how this relates either to the mathematical basis of fractals or its application, and (as a mathematician) I find the co-option of the terminology of fractals and chaos by recent philosophers (in an explicitly mathematical sense) as an abuse that often demonstrates little understanding of the math. Revolver 00:16, 20 Oct 2004 (UTC)
thread_title: In Response