The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was no consensus. Based on this discussion it looks clear that the article as it exists now is not a preferred solution, but as far as what the best solution is I cannot say. I would suggest that those interested in the future of this article work something out, be it through improvement, merging or redirection, so as to avoid a rehashing of this discussion in a future nomination. Shereth 18:08, 17 September 2008 (UTC)[reply]

Non-Newtonian calculus[edit]

Not notable; furthermore, the primary sources are self-published. NB: The originator of the article identifies himself as one of the creators of the theory, so he has a WP:COI.

Clarification: I do not believe that a COI is a reason to delete the article. I believe that lack of notability is the reason to delete the article. I further believe that lack of notability is well-established by the lack of references to the concept in mathematical journals which I demonstrate below. Ozob (talk) 22:20, 14 September 2008 (UTC)[reply]

Note: This debate has been included in the list of Science-related deletion discussions. Ozob (talk) 00:32, 13 September 2008 (UTC)[reply]
Delete well-attested in books [1], [2], [3] and seen in a journal [4] , but it seems largely associated with Jane Grossman, Michael Grossman, and Robert Katz, and the books seem to be from little-known or vanity publishers. JJL (talk) 01:05, 13 September 2008 (UTC)[reply]
Comment The article creator has posted in opposition to the nomination at my talk page. See User talk:Ozob#Citation, reviews, and comments re "Non-Newtonian Calculus". Ozob (talk) 01:07, 13 September 2008 (UTC)[reply]

Delete - WP:OR. / Blaxthos ( t / c ) 02:05, 13 September 2008 (UTC)[reply]
Redirect to Mathematical analysis — having studied in the field of mathematics, this seems like an alternate term for the subject mathematical analysis, which is a rigorous formalization and study of the basic concepts of calculus developed by Newton, Leibniz, etc. MuZemike (talk) 02:40, 13 September 2008 (UTC)[reply]
Keep. A legitimate and respectable journal, the Journal of Mathematical Analysis and Applications, has published a paper on this subject, not written by Grossman or Katz. The abstract for the paper reads as follows:

Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. In the period from 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. In the present paper our aim is to bring up this calculus to the attention of researchers and demonstrate its usefulness.

The JMAA article also cites the Lee Press book and an article in the (legitimate) journal Primus. I conclude that the subject is not OR, in the Wikipedia sense: WP:OR says "'Original research' is material for which no reliable source can be found." I also fail to see any conflict of interest in the article as written. -- Dominus (talk) 02:51, 13 September 2008 (UTC)[reply]

Comment it still seems non-notable to me. No one uses or teaches this--it's an intellectual diversion of the "What If?" variety. It's not akin to Infinitesimal calculus. Certainly, the term non-Newtonian calculus is not in general use among mathematicians, the way one discusses non-Newtonian fluids. JJL (talk) 03:21, 13 September 2008 (UTC)[reply]

If the name is wrong, the article can be moved. -- Dominus (talk) 03:28, 13 September 2008 (UTC)[reply]

Comment I thought this was about Leibniz, from the title, or Japanese calculus, Archimedean calculus or somesuch, perhaps a dab page is required as well. 05:55, 13 September 2008 (UTC) —Preceding unsigned comment added by 70.51.9.124 (talk)
Keep Per Dominus and other independent references in article. I note the JMAA paper says submitted by Steven G. Krantz, not at all someone who I think would endorse in any way strange, speculative or fringy stuff. The problem is there is not enough mathematics in the article to really understand what it is, whether it something really novel, which I have my doubts about. But even if it isn't, further research and reading of the refs (which make it satisfy the notability criterion in any case) would be necessary for figuring out what to eventually redirect it to. The quotes about it on Ozob's talk page from Arrow, Boas, Grattan-Guinness and Struik lend some real support from some big names.John Z (talk) 10:29, 13 September 2008 (UTC)[reply]
- Comment the Talk page comments also appear here [5]. The Talk page comments make clear the WP:COI issue, as smithpith who created and has primarily edited the article is identified as Michael Grossman. I have "The Rainbow of Math." to hand. On pg. 332 is a footnote mentioning Grossman and Katz 1972 as having developed on a 1754 comment by Besicovitch. But pg. 774 is in the Bibliography and is just the actual citation for Grossman and Katz 1972. This is only one reference to Grossman and Katz in a footnote plus its Bib. entry. The terms "non-Newtonian" and "bigeometric" do not appear in the footnote; the former is in the book title in the Bib. I still feel this is one person pushing his somewhat WP:FRINGE-y theory (correct, I'm sure, but far off the mainstream). Which of the Grossman books is from a reputable, non-vanity press? I don't think policy is that every technical term used in a journal or book merits a page. JJL (talk) 15:00, 13 September 2008 (UTC)[reply]
Hmm. Stinks of OR, but has book references. I'm gonna have to go with delete. —Sunday ^Note 12:18, 13 September 2008 (UTC)[reply]

Can I remind you that this is supposed to be a discussion, not a vote? -- Dominus (talk) 19:28, 13 September 2008 (UTC)[reply]

Comment. Since the discussion seems to hinge on whether or not the article's content is notable, perhaps it would be worthwhile to quote from Mathematical Reviews. The review of the first reference, "Multiplicative calculus and its applications", says after a one-sentence description of the article:

"...you are left with some avatar of the classical calculus to unfold. The authors of this original paper do play this game. Their stated purpose is to promote this new kind of multiplicative calculus. The work is entertaining, but not fully convincing."

User:JJL has described the relevant portions of the second reference, the Grattan-Guinness book. The third reference, Grossman and Katz's Non-Newtonian Calculus, did not receive a proper review; it was indexed, but the review is an extract from the preface and a listing of the table of contents. Finally, the fourth reference was not indexed by Math Reviews.

Plugging "Non-Newtonian calculus" into the "Anywhere" field of MathSciNet turns up three references: The above-mentioned book of Grossman and Katz, the book The first systems of weighted differential and integral calculus by Grossman, Jane; Grossman, Michael; Katz, Robert, pub. Archimedes Foundation, Rockport, Mass., 1980. vi+55 pp., and the book The first nonlinear system of differential and integral calculus by Grossman, Michael, pub. MATHCO, Rockport, Mass., 1979. xi+85 pp. I think it's instructive to quote from the review of the last book:

"The system in question is based on a "derivative" of $f$ equal to $\exp{(\ln f)'}$, where the prime indicates the conventional derivative. ... It is not yet clear whether the new calculus provides enough additional insight to justify its use on a large scale."

The only one of these works which has received any citations is Non-Newtonian Calculus: There's the first reference given in the article and self-citations.

Similarly plugging "Non-Newtonian calculus" into Zentralblatt gives three references: The first reference of the article, the book of Grossman-Katz, and the book of Grossman. Ozob (talk) 20:54, 13 September 2008 (UTC)[reply]

Strong Keep. I'm glad this has come up for deletion because ironically the topic has thereby caught my attention. This topic has been referred to in a mathematical journal, so it's notable enough as far as I'm concerned. So what if this is a "what if?" kind of thing? The usefulness remains to be seen, but wikipedia is not just for practical information. The word 'fringe-y' theory is mentioned above but the word fringe describes theories held by a small minority which contradict widely accepted theories and are thus rejected, however that is not the case here. This does not contradict anything, it is simply not widely known about. The word fringe does not apply. There may be a so-called COI, but really that just means the article should be subjected to close scrutiny. It is not a reason for deletion. Wikipedia would be a very much poorer place if articles like this are deleted. The fact that it has been referred to in a journal means that WP:OR does not apply. Delaszk (talk) 12:40, 14 September 2008 (UTC)[reply]

Keep. Since when was WP:COI a reason for deleting an article? Okay, it is a reason for impartial editors to remove promotional and/or non-encyclopedic information from the article with extreme prejudice, but as long as the subject meets WP:NOTABILITY, we don't delete the article itself.

This article is about a rather trivial idea (conjugating calculus with an invertible function such as the exponential function) but it is an idea that has been published and cited, and an idea that some qualified people have stated may be useful in some situations. Since the main examples seem to be the "geometric" calculus (exponential function) and "bigeometric" calculus (power functions), we could consider moving the article to multiplicative calculus which appears to be a term with some currency beyond the work of Grossman et al. Geometry guy 13:17, 14 September 2008 (UTC)[reply]

If kept, I will support the move; but I would delete it, as a triviiality. Septentrionalis PMAnderson 17:20, 14 September 2008 (UTC)[reply]

Plugging the term "multiplicative calculus" into MathSciNet produces two reviews: The J. Math. Anal. Appl. article with Turkish authors that is citation number 1 in the article, and Glickfeld, Barnett W., The theory of analytic functions in commutative Banach algebras with involution. Ann. Mat. Pura Appl. (4) 86 1970 61--77. The latter article is about interpreting the Cauchy-Riemann equations for maps C → B, where B is a Banach algebra (with certain restrictions); the author calls this "multiplicative" calculus (quotes in original) and says it is "so-called because the differentiability of a function depends on the multiplication in $B$". On Zentralblatt, "multiplicative calculus" produces only the J. Math. Anal. Appl. article. Ozob (talk) 22:19, 14 September 2008 (UTC)[reply]

Comment I support moving to a less pretentious name, but keeping and sorting out COI issues. But is there a better article to be written under this title (which could link to wherever this one goes)? Richard Pinch (talk) 22:24, 14 September 2008 (UTC)[reply]

Comments by Michael Grossman:

The mathematical community's reception of non-Newtonian calculus has been lukewarm. Naturally the subject has little appeal to mathematicians engrossed in the abstract realms of modern mathematics. Nevertheless enthusiastic interest has been expressed by some mathematicians, and by many scientists and engineers.

Robert Katz and I met personally with Dirk Struik and with Ivor Grattan-Guinness, both of whom were quite optimistic about the possibilities opened-up in science by non-Newtonian calculus. Professor Grattan-Guinness wrote: "There is enough here [in Non-Newtonian Calculus] to indicate that non-Newtonian calculi ... have considerable potential as alternative approaches to traditional problems. This very original piece of mathematics will surely expose a number of missed opportunities in the history of the subject."

In Mathematical Reviews Ralph P. Boas, Jr. made the following two assertions: 1) It is not yet clear whether the geometric calculus provides enough additional insight to justify its use on a large scale. 2) It seems plausible that people who need to study functions from this point of view might well be able to formulate problems more cleary by using bigeometric calculus instead of classical calculus. Clearly Professor Boas understood that: a) non-Newtonian calculus does provide alternatives to the classical calculus, b) non-Newtonian calculus does provide additional insight, and c) non-Newtonian calculus can be used to simplify formulations.

David Pearce MacAdam reviewed "Non-Newtonian Calculus" in the Journal Of The Optical Society Of America. Here is an excerpt: "This [Non-Newtonian Calculus] is an exciting little book. ... The greatest value of these non-Newtonian calculi may prove to be their ability to yield simpler physical laws than the Newtonian calculus. Throughout, this book exhibits a clarity of vision characteristic of important mathematical creations. ... The authors have written this book for engineers and scientists, as well as for mathematicians. ... The writing is clear, concise, and very readable. No more than a working knowledge of [classical] calculus is assumed." Clearly, Professor MacAdam (probably a physicist) is also optimistic about the possibilities of using non-Newtonian calculus in scientific work.

The omission by Wikipedia of information about non-Newtonian calculus would be a disservice to the scientific community. Non-Newtonian calculus IS a mathematical theory that provides scientists, engineers, and mathematicians with alternatives to the classical calculus of Newton and Leibniz.

I thank you all for your interest and consideration. —Preceding unsigned comment added by 74.166.238.187 (talk) 00:21, 15 September 2008 (UTC)[reply]

Comment: A search of google scholar shows that "multiplicative calculus" is used in several different contexts to mean different things so I would oppose any renaming. Moreover there are an infinite number of these non-newtonian calculi and the term "multiplicative calculus" is not appropriate for all of them, rather a new article should be created to cover "multiplicative calculus" (what G and K call "geometric calculus"). Delaszk (talk) 08:47, 15 September 2008 (UTC)[reply]

I left out Google Scholar before, since Mathematical Reviews/MathSciNet and Zentralblatt are the authoritative indices of published mathematical work. But since Google Scholar has been mentioned, I figured that I may as well look and see what "Non-Newtonian calculus" turns up there. I get:

Grossman and Katz, "Non-Newtonian Calculus"
Grossman, "Averages: A New Approach"
Grossman, "An introduction to non-Newtonian calculus"
Grossman and Katz, "Isomorphic calculi", International Journal of Mathematical Education in Science …, 1984 - Taylor & Francis
A review of Grossman and Katz, "Non-Newtonian Calculus" by Karel Berka in Theory and Decision, vol. 6, no. 2, May 1975. Those with Springerlink access can read it here.
The Bashirov, Kurpınar, and Özyapıcı article.
"BOOK NOTES", T de Chardin, F le Lionnais… - Philosophia Mathematica - Oxford Univ Press. I can't figure out what this is--there's no link, and besides Teilhard de Chardin was a philosopher and theologian.
Grossman, J., and Grossman, M., Dimple or no dimple, The Two-Year College Mathematics Journal, Vol. 13, No. 1 (Jan., 1982), pp. 52-55, an expository article on limaçons. Non-Newtonian calculus is only mentioned in the brief author bios at the beginning.
Advertisements:
- Science News, Vol. 118, No. 25/26 (Dec. 20-27, 1980), p. 393. [6].
- Science News, Vol. 118, No. 5 (Aug. 2, 1980), p. 78 [7].
- Science News, Vol. 119, No. 2 (Jan. 10, 1981), p. 30 [8].
- Science News, Vol. 118, No. 24 (Dec. 13, 1980), p. 382 [9].
A listing in "Books received"/"Publications received"/"Libri ricevuti" from
- Theory and Decision, December 1972. See [10].
- Australian & New Zealand Journal of Statistics, vol. 15, no. 3. See [11].
- Il Nuovo Cimento A, August 1972. See [12].
Grossman, J., Grossman, M., and Katz, R., Which growth rate?, International Journal of Mathematical Education in Science, vol. 18, no. 1, pp. 151-154. See [13].

So only one non-self-citation in over 30 years. The citation by Meginniss which is presently the article's first reference makes two non-self-citations in 30 years.

To be honest, I'm rather surprised that this article has received any support at all. To me it seems obvious from the lack of scholarly references that this concept is not notable. I also note that all of the positive comments are of the form, "This may be useful." So far as I know nobody has actually shown that it is useful, hence the lack of interest! Ozob (talk) 22:53, 15 September 2008 (UTC)[reply]

The phrase "Non-Newtonian calculus" was invented by Grossman and Katz, but the concept of alternative differentiation operators is an old idea. I have added some references in the history section of the article to earlier work. Delaszk (talk) 07:59, 16 September 2008 (UTC)[reply]

The topic is notable per the references and reviews already mentioned and here's another: "Bigeometric Calculus" and "Averages" are both reviewed in The Mathematical Gazette, Vol. 68, No. 443 (Mar., 1984), pp. 70-71 Delaszk (talk) 08:53, 16 September 2008 (UTC)[reply]

Keep: The idea of conjugating the differentiation operator by the exponential function (or some other useful function) sounds interesting to me. Of course it is a very simple idea: other things being equal, the simpler an idea, the better! I don't personally think it's necessary that non-Newtonian calculus (agreed that the name is a poor one, BTW) have some specific successes or applications in order to be kept as a wikipedia article. But the fact that at least one scientist has used this theory in their work makes the decision to keep an easy one. As an aside, the fact the claim of original research has been made here indicates to me that the concept of OR in mathematical articles needs clarification. Would anyone like to take this up on the wikiproject mathematics discussion page? Plclark (talk) 19:54, 16 September 2008 (UTC)[reply]

You are arguing that because the idea is interesting, the article should be kept. This is contrary to the instructions at WP:INTERESTING, which note, "personal interest or apathy is not a valid reason to keep or delete an article". The issue is whether the article is notable. That the idea may be interesting or useful is irrelevant; things like journal citations are. While several others here have noted that they, too, find the idea interesting, they have also said that they believe the very small number of citations the work has received are enough to establish notability. (I disagree; that's my entire reason for bringing this AfD.) If you think those citations suffice to establish notability, then go ahead and argue for keep. But please don't argue for keep on the basis of personal interest. Ozob (talk) 17:30, 17 September 2008 (UTC)[reply]

- There is no confusion here about what constitutes OR in math articles. It was published in a perfectly good journal. Thus it is not OR, according to WP:OR. Although perhaps the OR claim was first raised by the nomination's claim of only self-published sources existing, that ceased to be a point of contention when non-self-published sources were found and now the only point under dispute is notability. --C S (talk) 01:02, 17 September 2008 (UTC)[reply]

A Clarification from Michael Grossman:

It is true that the geometric calculus can be obtained by "conjugating with the exponential function". However, infinitely many non-Newtonian calculi can NOT be obtained by "conjugating with an invertible function". For example, the bigeometric calculus can NOT be obtained that way. Smithpith (talk) 23:21, 16 September 2008 (UTC)[reply]

Whatever. Going from experience, the Primus and JMAA cites are enough to instill a marginal notability here, which is probably why people are saying "keep". But it's marginal, so whether I feel it's worth keeping really depends on my mood, and right now, I don't particularly care. Also going from experience, if the COI problems get too troublesome, marginality isn't really a good defense against a future deletion. That happens too, when people get too tired of policing the article. --C S (talk) 01:11, 17 September 2008 (UTC)[reply]

Comment. If kept, remove from any mathematical categories, including Category:Calculus. Whatever it may be, it isn't mathematics. — Arthur Rubin (talk) 15:40, 17 September 2008 (UTC)[reply]

How do you figure that? I don't understand. -- Dominus (talk) 17:39, 17 September 2008 (UTC)[reply]

delete. The lead paragraph clearly states that "geometric calculus was the first non-Newtonian calculus". The author admits in the discussion above that geometric calculus amounts to conjugating by the log. Now we all know why adders need a log. It is nice for the derivative to be multiplicative, but declaring this to be a mathematical theory, with Newton's name attached to it to boot, seems a bit of an obfuscation. Katzmik (talk) 16:22, 17 September 2008 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.