Talk:Fractional calculus/Archive 1

Archive 1

Fractals?

IMHO, there should be a section on the relationship of fractional calculus to fractals. There are books that this is discussed in. Many of them bring up the Wierstraus function. I wrote a little paper (doc) on it myself elucidating the intuitive spatial relations, which I think makes the connection clear (if one can comprehend the rather idiosyncratic terminology - a lot of allusion to information theory) and answers the "Hmmm...". Kevin Baas^talk 19:32, 2004 Dec 30 (UTC)

Clarification. I wrote a little supplementary (doc) to clarify my little paper. Kevin Baas^talk 00:03, 2005 Jan 3 (UTC)

Point of the paper regarding the "Hmmm..." and D₁, D₂, is that for a unique x (statistically-uncorrelated/linearly-independant/non-redundant/orthogonal) parameter function, integrated over a unique y (bla bla bla) parameter region, there is a unique x-y (bla bla bla) parameter result.

Given two unique operands and a unique differential metric, the solution is completely specified, and thus the operator is unique.

The apparent confusion could result from not realizing that the integration operator requires a complete specification of not one, but two operands: the integrated function and the region of integration, and that the number of integrations (single, double, etc.) ("degree" of integration) is rigidly fixed to the dimensionality of the region of integration.

Or the confusion could result from equivocating multiple valid metrics with multiple valid operators. The chain-rule/differential-geometry shows that there is not a problem; in d(f(x)) = df(x)dx, a change in dx results in a change in df(x)dx, by no "fault" of the operator d. Kevin Baas^talk 21:56, 2005 Jan 3 (UTC)

Fractional derivative - nonlocalizable

The above little paper(doc) is a geometrically intuitive explanation for the fractional derivative "peripheral vision" (non-localizable) property. It shows how to make sense of it geometrically, and that it really amounts to nothing special - we've just been making a mistake in our conception of a derivative as a unary operator. it doesn't have any of the citations filled in in the esoteric page, but that page isn't important. one just needs to know basic calculus and maybe a little about fractals to be able to understand the main idea. I think it's important, and forgive me for endorsing it here, but i jsut want to get it out there, and frac calc is a pretty esoteric field, and i'm not in college, so it's hard to find an outlet. Kevin Baas^talk 01:04, 2005 Feb 18 (UTC)

Kevin - please see Wikipedia:What Wikipedia is not 1.3.5, i.e. under Wikipedia is not a soapbox and Primary research. Charles Matthews 06:25, 18 Feb 2005 (UTC)

I have read the policy. I am not suggesting putting this in the article. I'm just posting a link on the talk page for anyone who is interested and/or wants to try to get a clearer picture of the spatial meaning of fractional calculus. People having a clearer understanding may benefit the article, and in any case benefits the general knowledge. Kevin Baas^talk 20:13, 2005 Feb 20 (UTC)

If you say I just want to get it out there, you are using WP for a purpose which is not the intended purpose. Charles Matthews 20:33, 20 Feb 2005 (UTC)

I suggest you read the Wikipedia:What Wikipedia is not that you refered me to more carefully. Kevin Baas^talk 20:35, 2005 Feb 20 (UTC)

How about this: If you have done primary research on a topic, publish your results in normal peer-reviewed journals, or elsewhere on the web.

Clear enough? Charles Matthews 20:40, 20 Feb 2005 (UTC)

that refers to the article, not the talk page. how about this:

"Self-promotion. While you are free to write about yourself or projects you have a strong personal involvement in, remember that the standards for encyclopedic articles apply to such pages just like any other. A very few somewhat famous Wikipedians have significantly contributed to encyclopedia articles about themselves and their accomplishments, and this has mostly been accepted after some debate. Creating overly abundant links and references to autobiographical articles is not acceptable."

Clear enough? Kevin Baas^talk 20:42, 2005 Feb 20 (UTC)

Or how about this:

"Discussion forums, or Everything2 nodes. Please try to stay on the task of creating an encyclopedia. You can chat with folks on their user talk pages, and should resolve problems with articles on the relevant talk pages, but please do not take discussion into articles. " Kevin Baas^talk 20:44, 2005 Feb 20 (UTC)

I don't think you should quibble about this. I think you should just take down the link to your (unfinished) paper. Charles Matthews 22:09, 20 Feb 2005 (UTC)

I do not think it is hurting anyone. Kevin Baas^talk 06:33, 2005 Feb 21 (UTC)

And I think self-promotion is something about which Wikipedians should be scrupulous. Charles Matthews 09:05, 21 Feb 2005 (UTC)

Then we are in agreement. Kevin Baas^talk 17:52, 2005 Feb 21 (UTC)