User talk:Grokmoo

From Wikipedia, the free encyclopedia

Welcome!

Hello Grokmoo, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you have any questions, check out Wikipedia:Where to ask a question or ask me on my talk page. Again, welcome!  Fawcett5 13:26, 21 October 2005 (UTC)

Contents

[edit] Edit summary

Thank you for your edits to calculus and other places, and for commenting on the talk page of those articles. That is all very useful. I would also like to ask you to use an edit summary, which, while while it cannot contain as much information as on the talk page, it is still a useful pointer for what you change in an article. Thanks a lot, Oleg Alexandrov (talk) 23:25, 16 December 2005 (UTC)

Hi Grokmoo, I appreciate your discussing the topic with me. I hope we can both see the matter objectively. After reading your comments, I did a little searching on the Newton & Leiniz's contributions. My understanding is that things are not as clear (as far as where credit is given) as you present them - that Archimedes discovered integrals, Fermat (or Madhava) differentiation, and Newton and Leibniz calculus for their enunciation of the fundamental theorums. It is acknowledged that N & L both built upon the knowledge of their predecessors, but the volume of work they did, application to physics, their tieing it all together, as well as their key discovery of the fundamental theorum and notational system is what made them the biggest contenders for the prize. I don't believe it was just the fundamental theorum. Can you point me to a source for that statement? Among the others involved in the development of calculus, their contributions were significantly larger than the others and so, in the quest to credit one person, they are credited with it's development. The way I see it, Madhava, despite the tremendous work he did, is not acknowledged AT ALL in mainstream calculus history. While his path of developing calculus is not the same as it evolved in Europe, it does touch most of the work of individual European contributors, 3 centuries before them. If one can point to a single most significant contributor to calculus (without euroentric lenses) it is Madhava. Newton with fundamental theorums might have taken it much further just as Cauchy took Newton's work further. (BTW, Madhava did Cauchy's convergence tests as well) --Pranathi 16:01, 17 December 2005 (UTC)

Wanted to discuss your edits on Indian Mathematics page. Madhava's contribution are foundational to eventual development of calculus. Please help me understand this. Are you understanding calculus as tieing together differential and intergral calculus with the fundamental theorum ONLY? Do the invidual components not count as part of calculus? Can you point me to sources that see calculus in this light? I wanted to discuss here instead of the page because it ties in with our previous discussion.--Pranathi 16:34, 17 December 2005 (UTC)
Hi Pranathi. While I agree that Madhava made important contributions to the development of calculus, the reason Newton and Leibniz are credited with the "invention" of calculus is not only unification, as you say, but the insight of the fundamental theorem. If mathematicians referred to defining the derivative (as Madhava did) or the integral (which wasn't really well defined until Riemann) as developing calculus, why credit Newton? It is well known that the derivative and integral were known about and used well before him. This view is very prevalent among mathematicians, but here is a source: http://www.southwestern.edu/~sawyerc/cal1/history_of_calculus.htm The reason the fundamental theorem is so important is that it is immediately applicable to a wide range of problems in science, and is a prototype solution to a differential equation. If I had to point to one development that most advanced science, it would be this.
I don't want to step on anyone's toes here; I certainly agree with the assesment that Madhava should be credited with the development of the derivative. However, the insight that derivatives and integrals are almost inverses of one another, and the organization of the field goes to Newton and Leibniz. I'm not sure why you give Cauchy such huge credit in the development of calculus. He was probably the largest contributer to the rigourization of calculus, but it was the contributions of many individuals, such as Riemann, Weierstrauss, Bolzano, that completed that task. I would be interested to see some sources about Madhava's development of convergence tests. Which ones did he develop, and how did he do so without a rigorous framework to work with? I eagerly await your reply.Grokmoo 16:00, 20 December 2005 (UTC)

Grokmoo, Per your link, the foll reasons are given for N & L's recognition (not just Fundamental theory):

  • Codification and Unification of Methods. The earlier work was mostly a collection of clever devices which applied only to polynomials. Newton and Leibniz saw that these methods were general and that they could, by the effective means of expressing non-polynomial functions as infinite series, be applied to a great variety of problems.
  • Development of Algorithms and Notations. Both men developed general algorithms by which their methods could be applied. Leibniz was especially good at devising effective notation. The dy/dx notation for the derivative and the "lazy S" integral sign are both from Leibniz.
  • Insight of the Fundamental Theorem. The recognition of differentiation and integration as inverse processes and the exploitation of this fact is truly "fundamental" to the calculus.
  • Awareness of Creating a New Subject. Both men were aware that they were developing a new and general method of great importance.

Madhava also expressed non-polynomial functions as infinite series (1). Infact, many of his results were acheived only by Newtons successors in the study of Calculus (Bernoullis, Gregory etc). I can't speak to the fourth point - but I know that the Kerala school are basically astronomers that used these methods for solving astronomical problems - so it seems that they did apply it to physics and were aware of it's importance and applications. seeing as the field took a different path from how it did in europe, it cannot be compared perfectly.

I will try to dig up specifics on their work on Cauchy's test - I just saw a statement that he worked on them but have seen no specifics. --Pranathi 01:43, 23 December 2005 (UTC)

Hello Pranathi,

I am not sure what you are trying to argue. Listed are the codification, development of notation, fundamental theorem, and awareness of creating a new subject. None of these can be attributed to Madhava. The only one you might attribute to him was development of algorithms. However, most of this still must go to Newton and Leibniz, for development of integration rules, methods of integration like parts and substitution, and of course, the evaluation of integrals by finding a primitive. I don't think that the explanation on "codification" is very good, since clearly there is much more to this than expressing trig functions and exponentials as power series, which is only one small part of beginning to analyze general functions.

I am sorry if I implied that the fundamental theorems were the only thing of importance. However, they are the single most important thing, and if you had to pick a single event and call it "the development of calculus", it would be the development of the fundamental theorems. Sorry about the long delay in this response, I was at my parents house and did not have easy access to the internet. Grokmoo 14:53, 5 January 2006 (UTC)

[edit] Allais effect

Grokmoo, please see my comments about your disputed NPOV label on Allais effect. The article was heavily edited by Steven G. Johnson a year ago. He is an Assistant Professor of Applied Mathematics at MIT and is sceptical of the existence of the Allais effect, so I believe the article as it stands is written from a NPOV...see in particular the concluding line. -- Etimbo ( Talk) 23:05, 14 January 2006 (UTC)

Etimbo's remarks are misleading. The article as it presently stands does not reflect my editing, and is not neutral or even factually accurate. Please see my comments on Talk:Allais effect, and feel free to try to improve it. For myself, I don't have the energy any more to fight battles with pseudoscience fans in relativity articles. —Steven G. Johnson 01:07, 8 February 2007 (UTC)

[edit] This is me

Yeah, you know what to do. --Cyde Weys 06:07, 26 February 2006 (UTC)

[edit] Galaxies as Emergent phenomena

Hi Grokmo. I asked a clarifying question to your comment on Talk:Emergence. If you get a chance, I would appreciate your perspective. Just leave it on that talk page and I will find it. N2e 15:49, 27 September 2006 (UTC)

[edit] Request for Comment: Indian Mathematics

Talk:Indian_mathematics#Request_for_comment:_Reliable_Sources_for_Indian_Mathematics Feedback is requested for a problem on the Indian mathematics page, where two users have a disagreement about what constitutes reliable sources for claims in the article. 19:33, 23 February 2007 (UTC)

[edit] Indian Mathematics

Hi Grokmoo, I finally have some time to start doing a major revision of the page, which I had originally planned to do much earlier (after the RfC in March). I hope you'll have some time to look in every now and then and offer criticism. Thanks. Regards, Fowler&fowler«Talk» 01:15, 17 May 2007 (UTC)