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 delete. There is consensus that this is not a notable topic on its own as it is not adequately covered in reliable sources. – bradv🍁 20:20, 28 March 2020 (UTC)[reply]

Multiplicative calculus

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I have collapsed the rationale for AfD nomination by Createangelos, and the discussion with Smithpith, who is !voting keep, because these posts are very long, and very technical. It follows that, without collapsing, non-specialists must scroll several screens before finding the core discussion based on Wikipedia rules. D.Lazard (talk) 17:24, 18 March 2020 (UTC)[reply]

Rationale for AfD nomination by Createangelos, and discussion with Smithpith, who is !voting keep
The justification for the existence of this Wikipedia article is articles which refer to it, such as Florack, Luc; Van Assen, Hans (2011). "Multiplicative Calculus in Biomedical Image Analysis". Journal of Mathematical Imaging and Vision. 42: 64–75. doi:10.1007/s10851-011-0275-1. That article, on the second page, says It is not difficult to show that ... ln f(x) = (ln f)'(x) This can be taken as the definition of . This is indeed a correct formula for the action of the operator d/dx when y=f(x) if we use u=ln(y) as a coordinate. But even here it is written in idiosyncratic notation. The normal, and very very old, way to write the action of d/dx on f(x) coming from its action on ln(f(x)) is to write write ln(d/dx)(f). That is to say, differentiation by x is pulled back via the function ln before you apply it to f. There are many references to many standard calculus texts which explain this, and physicists' notion of how vector fields (which they call 'covariant tensors of rank one') 'tranform' when you change variable. Such as page 28 of the book 'The very basic theory of tensors.' The theory of manifolds is even more general, and describes tangent fields without needing to choose any* coordinate. An existing Wikipedia article vector field already describes this, "This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other." If someone wants to improve Wikipedia's treatment of the subject, someone can insert the formula there where it is needed. The article of Florak and Van Assen does exist, but despite the title, the article does not, and could not, make any substantial use of a notion that 'multiplicative calculus' is any different than ordinary calculus. Because ordinary calculus already subsumes 'multiplicative calculus.' Except in a few textbooks, the real line which occurs as the domain of single variable functions does not have any operation of multiplication or addition. It has a smooth structure only. The distinction between 'multipicative' versus 'additive' calculus is nonexistent except with reference to expository texts which make the simplifying assumption that the actual real number line happens to be the domain of single-variable functions; and the publication in reference [4] could not possibly be notable. Just because a research article is published and refers to something does not make that thing notable. Wikipedia does not have an encyclopaedic command of all strains of astrology, for example. The notion that there is such a separate subject as 'multiplicative calculus' which is any different than ordinary calculus would rest on the idea that whatever variable y one is tempted to use, it is always better (or different) to use ln(y) instead. If I can give an analogy, suppose I say, addition is good, but some numbers have no predecessor, so I am going to define "augmented addition" which is defined by saying xy + 1 = (x+1) + (y+1) Then we see xy = x+y+1 and we can think of this as adding the successors. Well, I've only conjugated ordinary addition by the successor function. In the case of 'multiplicative calculus' which recommends using log(y) in place of y, the process could of course be repeated, one could say, it is always better to use log(log(y)) and so-on. It is like calling functions 'logarithmic functions' which are of the form ln o f and insisting that you need a whole separate theory about 'logarithmic functions.' Seriously, it is like the theory of elements of groups which are preceded by the inverse of some other element. It is not a subject. And if articles were published by referring in a complimentary way to the subject, it is just either sad or a corrupt use of the refereeing process. Not that the originators of 'multiplicative calculus' would be to blame, but just vulnerable. Sadly, also, in situations like this, there is the possibility that the only reason such references were ever published is because an article only needs one referee to be accepted, and editors are not always conversant with the subjects of articles in their journals. As a postscript, the notion that 'multiplicative calculus' is 'scale invariant' is prejudiced by a particular notion of what should be the group of scale transformations. This whole subject was clarified beginning with work of Cartan, described here for instance http://www-math.mit.edu/~helgason/Paper45.pdf, and the algebra of vector-fields invariant under a group of transformations is an existing and very old subject, including symmetries that are not required to commute, and which have various physical interpetations. Createangelos (talk) 19:54, 17 March 2020 (UTC)[reply] 17 March 2020 Dear Createangelos, The article “Multiplicative calculus” should not be deleted. Multiplicative calculus Is different from classical calculus. It provides alternatives to classical calculus in the same way, for example, that the geometric average provides alternatives to the arithmetic average. As clearly indicated by the many items in the Reception section, multiplicative calculus and non-Newtonian calculus have been well-received by researchers, and have been applied in a wide variety of subjects by applied mathematicians, scientists, and engineers worldwide. Please read these items carefully. As indicated in the History section, multiplicative calculus is a “widely recognized theory with applications.” From: Smithpith — Preceding unsigned comment added by Smithpith (talk • contribs) 23:41, 17 March 2020 (UTC)[reply] It's great that we have an expert on board. Can you please give some clarification for what this sentence ought to mean, "Infinitely many non-Newtonian calculi are multiplicative." Then infinitely many of them are additive? Shouldn't the additive ones be the basis for readers to understand the theory (in the same way that there shouldn't only be an article about geometric means)? The multiplicative ones come from these by the substitution which you well know, even if not all engineers/economists do. In clarifying what are the infinity of additive non-Newtonian calculus theories: should non-Newtonian really be defined here to mean nothing besides that there are inverse notions of differentiation and integration? So by this article any pair of bijections like adding 1 and subtracting 1 comprise a non-Newtonian theory of calculus? Why does the history section leave out Heaviside calculus, Laplace transforms, etc? Is this an alternative history? Does it include Stochastic calculus? Also, it is strangely npov to have a 'Reception' section in a Math article talking about all the people who like and approve of the subject. Also, it just isn't right to have a whole article about how d/dx commutes with addition while {1\over x}d/dx commutes with scalar multiplication, and how much people love learning about that, and ignore the general issue of symmetry and differentiation whose history predates anything in the article. There might be material that can be rescued, but serious errors would have to be fixed. In the section 'Relation to classical calculus' you say that A and B are canonically isomorphic with R as an ordered field. This would require a restriction on the cardinality of A and B. The sentence "one can define the following (and other) concepts of the -calculus: the -limit of f at an argument a, f is *-continuous at a, f" has no content since the definitions are not given. Why have a huge long article about how important some definition is, and how well-received it is, and how the whole history of it is due to you and your collaborators, without including that important definition in the article? You say that you use the 'natural operations, natural orderings and natural topologies' on A and B. If they are uniquely naturally isomorphic with R you can identify them with R, and then when represented as 'subsets' of R but not subfields, this chooses two embeddings of the underlying set of R into R. Then you take the embeddings to be log and exp as a roundabout way of describing the substitution y=e^u? Anyway, you really have to address why the content is notable enough to direct Wikipedia readers to pages upon pages of very recent testimonials about the `reception' of why {1\over x}d/dx is invariant under scalar multiplication -- a special case of Cartan's type of analysis which would be un-known only to the weakest applied researchers -- and has a history section which credits authors from the 1960's til 2019 for all of `non-Newtonian' calculus, ignoring all earlier authors including Sohus Lie, Elie Cartan, Killing, Klein, Dieudonne, and even Cartan who is the person who actually did originate the substitution y=e^u which this article features, but decades earlier. This Stack Exchange comment by user conifold describes some related history although it is more general than what we're talking about here https://hsm.stackexchange.com/questions/3558/how-did-the-exponential-map-of-riemannian-geometry-get-its-name . Createangelos (talk) 07:36, 18 March 2020 (UTC)[reply]

Rationale for AfD nomination by Createangelos, and discussion with Smithpith, who is !voting keep

The justification for the existence of this Wikipedia article is articles which refer to it, such as Florack, Luc; Van Assen, Hans (2011). "Multiplicative Calculus in Biomedical Image Analysis". Journal of Mathematical Imaging and Vision. 42: 64–75. doi:10.1007/s10851-011-0275-1. That article, on the second page, says

It is not difficult to show that ...  ln f*(x) = (ln f)'(x)

This can be taken as the definition of *. This is indeed a correct formula for the action of the operator d/dx when y=f(x) if we use u=ln(y) as a coordinate. But even here it is written in idiosyncratic notation. The normal, and very very old, way to write the action of d/dx on f(x) coming from its action on ln(f(x)) is to write write ln*(d/dx)(f). That is to say, differentiation by x is pulled back via the function ln before you apply it to f. There are many references to many standard calculus texts which explain this, and physicists' notion of how vector fields (which they call 'covariant tensors of rank one') 'tranform' when you change variable. Such as page 28 of the book 'The very basic theory of tensors.' The theory of manifolds is even more general, and describes tangent fields without needing to choose *any* coordinate.

An existing Wikipedia article vector field already describes this, "This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other." If someone wants to improve Wikipedia's treatment of the subject, someone can insert the formula there where it is needed.

The article of Florak and Van Assen does exist, but despite the title, the article does not, and could not, make any substantial use of a notion that 'multiplicative calculus' is any different than ordinary calculus. Because ordinary calculus already subsumes 'multiplicative calculus.' Except in a few textbooks, the real line which occurs as the domain of single variable functions does not have any operation of multiplication *or* addition. It has a smooth structure only. The distinction between 'multipicative' versus 'additive' calculus is nonexistent except with reference to expository texts which make the simplifying assumption that the actual real *number line* happens to be the domain of single-variable functions; and the publication in reference [4] could not possibly be notable. Just because a research article is published and refers to something does not make that thing notable. Wikipedia does not have an encyclopaedic command of all strains of astrology, for example.

The notion that there is such a separate subject as 'multiplicative calculus' which is any different than ordinary calculus would rest on the idea that *whatever* variable y one is tempted to use, it is always better (or different) to use ln(y) instead.

If I can give an analogy, suppose I say, addition is good, but some numbers have no predecessor, so I am going to define "augmented addition" which is defined by saying x*y + 1 = (x+1) + (y+1) Then we see x*y = x+y+1 and we can think of this as adding the successors. Well, I've only conjugated ordinary addition by the successor function.

In the case of 'multiplicative calculus' which recommends using log(y) in place of y, the process could of course be repeated, one could say, it is always better to use log(log(y)) and so-on. It is like calling functions 'logarithmic functions' which are of the form ln o f and insisting that you need a whole separate theory about 'logarithmic functions.' Seriously, it is like the theory of elements of groups which are preceded by the inverse of some other element. It is not a subject. And if articles were published by referring in a complimentary way to the subject, it is just either sad or a corrupt use of the refereeing process. Not that the originators of 'multiplicative calculus' would be to blame, but just vulnerable.

Sadly, also, in situations like this, there is the possibility that the only reason such references were ever published is because an article only needs one referee to be accepted, and editors are not always conversant with the subjects of articles in their journals.

As a postscript, the notion that 'multiplicative calculus' is 'scale invariant' is prejudiced by a particular notion of what should be the group of scale transformations. This whole subject was clarified beginning with work of Cartan, described here for instance http://www-math.mit.edu/~helgason/Paper45.pdf, and the algebra of vector-fields invariant under a group of transformations is an existing and very old subject, including symmetries that are not required to commute, and which have various physical interpetations. Createangelos (talk) 19:54, 17 March 2020 (UTC)[reply]

17 March 2020

Dear Createangelos,

The article “Multiplicative calculus” should not be deleted.

Multiplicative calculus Is different from classical calculus. It provides alternatives to classical calculus in the same way, for example, that the geometric average provides alternatives to the arithmetic average.

As clearly indicated by the many items in the Reception section, multiplicative calculus and non-Newtonian calculus have been well-received by researchers, and have been applied in a wide variety of subjects by applied mathematicians, scientists, and engineers worldwide. Please read these items carefully.

As indicated in the History section, multiplicative calculus is a “widely recognized theory with applications.”

From: Smithpith — Preceding unsigned comment added by Smithpith (talk • contribs) 23:41, 17 March 2020 (UTC)[reply]

It's great that we have an expert on board. Can you please give some clarification for what this sentence ought to mean, "Infinitely many non-Newtonian calculi are multiplicative." Then infinitely many of them are additive? Shouldn't the additive ones be the basis for readers to understand the theory (in the same way that there shouldn't *only* be an article about geometric means)? The multiplicative ones come from these by the substitution which you well know, even if not all engineers/economists do. In clarifying what are the infinity of additive non-Newtonian calculus theories: should non-Newtonian really be defined here to mean nothing besides that there are inverse notions of differentiation and integration? So by this article any pair of bijections like adding 1 and subtracting 1 comprise a non-Newtonian theory of calculus? Why does the history section leave out Heaviside calculus, Laplace transforms, etc? Is this an alternative history? Does it include Stochastic calculus? Also, it is strangely npov to have a 'Reception' section in a Math article talking about all the people who like and approve of the subject. Also, it just isn't right to have a whole article about how d/dx commutes with addition while {1\over x}d/dx commutes with scalar multiplication, and how much people love learning about that, and ignore the general issue of symmetry and differentiation whose history predates anything in the article.

There might be material that can be rescued, but serious errors would have to be fixed. In the section 'Relation to classical calculus' you say that A and B are canonically isomorphic with R as an ordered field. This would require a restriction on the cardinality of A and B. The sentence "one can define the following (and other) concepts of the *-calculus: the *-limit of f at an argument a, f is *-continuous at a, f" has no content since the definitions are not given. Why have a huge long article about how important some definition is, and how well-received it is, and how the whole history of it is due to you and your collaborators, without including that important definition in the article? You say that you use the 'natural operations, natural orderings and natural topologies' on A and B. If they are uniquely naturally isomorphic with R you can identify them with R, and then when represented as 'subsets' of R but not subfields, this chooses two embeddings of the underlying set of R into R. Then you take the embeddings to be log and exp as a roundabout way of describing the substitution y=e^u?

Anyway, you really have to address why the content is notable enough to direct Wikipedia readers to pages upon pages of very recent testimonials about the `reception' of why {1\over x}d/dx is invariant under scalar multiplication -- a special case of Cartan's type of analysis which would be un-known only to the weakest applied researchers -- and has a history section which credits authors from the 1960's til 2019 for all of `non-Newtonian' calculus, ignoring all earlier authors including Sohus Lie, Elie Cartan, Killing, Klein, Dieudonne, and even Cartan who is the person who actually did originate the substitution y=e^u which this article features, but decades earlier. This Stack Exchange comment by user conifold describes some related history although it is more general than what we're talking about here https://hsm.stackexchange.com/questions/3558/how-did-the-exponential-map-of-riemannian-geometry-get-its-name .

Createangelos (talk) 07:36, 18 March 2020 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. D.Lazard (talk) 11:09, 18 March 2020 (UTC)[reply]

Comment. Most of the above discussion is misplaced and should appear in article talk page. This page must be devoted to discuss whether the nominated article satisfies Wikipedia rules that all Wikipedia articles must satisfy. So, please, restrict this discussion to this aspect. D.Lazard (talk) 11:21, 18 March 2020 (UTC)[reply]
Delete. Despite of a large number of references, this article is not reliably sourced (see WP:Reliable sources). All references are WP:Primary sources and most of them are not really published. Although, this is an article of mathematical analysis, I have not found in the reference list any article that has been published in a non-predatory journal that uses to publish articles in this area. The lack of WP: Secondary sources strongly suggests that the article does not satisfy the WP:Notability criteria. In fact, multiplicative calculus is a WP:Fringe theory that is not recognized in the main stream of mathematics. Moreover, this is a trivial theory in the following sense. The exponential and the logarithm define an isomorphism between the additive group of the reals and the multiplicative group of positive reals. The multiplicative calculus is simply the transfer through this isomorphism of some concepts of calculus that use the additive structure of the reals. It follows that every theorem of multiplicative calculus is a corollary of the corresponding theorem of usual calculus (this is what I mean by a trivial theory). D.Lazard (talk) 11:55, 18 March 2020 (UTC)[reply]
Delete: For a subject like this, we really need to see a textbook on the subject; articles on math journals cannot be adequate. I myself can propose new kind of calculus and might even succeed to excite some other people with it (anyone can dream!). But we need a widetly-used "textbook" to appear before we can cover that in Wikipedia. Some research-level topics may not have textbooks, but, as far as I can tell, the subject of this article does not seem to be a research topic. -- Taku (talk) 17:49, 19 March 2020 (UTC)[reply]
Comment The sourcing is plentiful but poor. Many citations are to marginal references: a conference speech, a passing mention in a tech-press story about something else, Chaos, Solitons & Fractals, etc. It is hard to shake the impression that a very simple and not too dramatic idea is being drastically overhyped. XOR'easter (talk) 21:27, 19 March 2020 (UTC)[reply]
Delete. This appears to be a frequent reinvention. Review MR 2356052 makes clear that this is just a disguised version of the standard calculus. Review MR2724186 points out that it is the same as the "Non-Newtonian calculus" of a 1972 book by that title, which MR didn't even bother to review. MR also didn't bother to review doi:10.1080/10511979908965937 in a mathematics education journal, reinventing the same wheel (nor did zbMATH review it). MR2864779 is a negative review of an attempt to show that this formalism is useful for differential equations; the reviewer disagrees. I might find it acceptable to have an article that points out that exp/log can be used to translate everything in the usual calculus into this form, and that reviews the history of reinvention of this not-very-deep concept, but that's not what we have here. Instead we have a lot of dancing around the point that this is all trivial, more or less as the first review I linked states. I think WP:TNT applies: it might be possible to have something here, but not this. —David Eppstein (talk) 01:18, 21 March 2020 (UTC)[reply]
Delete Having read and reflected further, I don't think this article stands up. As David Eppstein points out, there's a lot of wheel reinvention going on here, and it's not even a very interesting wheel. The heaps of forgettable publications applying this trick don't add up to significance; we need something like review articles or textbooks that do the work of summarizing and synthesizing to demonstrate that it really is a trick worth writing about. I concur that WP:TNT applies. XOR'easter (talk) 18:11, 21 March 2020 (UTC)[reply]
Keep I believe the article is of note, but requires very significant cleanup, which I am willing to do. I believe the article overestimates the use and notability of Non-Newtonian Calculus due to bias. The user Smithpith is likely personally connected to the author of several books on NNC, as a quick google search shows smithpith is the publicly available email of M. Grossman. However, I believe that due to the interest in the research community in the most recent decade, the subject is of note. The subject is not notable enough note to merit a page of nearly this length or grandeur, but it has been used in educational and research contexts enough to merit an article. For instance, I propose deleting the sections on the General Theory of Non-Newtonian Calculus and pruning the Reception section. This is because I agree with the majority of previous commenters who believe that NNC is not significant enough to be notable to Wikipedia as its own mathematical branch, and I believe that the Reception page is repetitive and oversized to the point of illegibility. I wrote the majority of the History section, which I hope to improve, and plan to clean up the rest of the article. This should be in accordance with guidance on WP:TNT as XOR'easter suggests.MathTrain (talk) 00:48, 27 March 2020 (UTC)[reply]
(comment reply) Further to MathTrain's concerns, note that there is a subject, or at least a Wikipedia category, known as 'Non-Newtonian calculus' I'm not sure how to link to it, https://en.wikipedia.org/wiki/Category:Non-Newtonian_calculus and it includes Black Scholes, compound interest, alternative calculi, fractal derivative, geometric brownian motion, geometric mean, etc. The list does include 'multiplicative calculus' as one of the pages, so deleting this article outright might make a broken link there. My reason for nominating deletion has to do with having two names for the same thing (calculus) necessitating constant disambiguation (like saying, let's explain that in non-Peano arithmetic when we say '3' we really ought to always mean '4'). It should be OK to delete that page from 'Non Newtonian Calculus' because it is the one which is isomorphic to ordinary calculus while none of the others are, with the exception of compound interest, which is part of ordinary/multiplicative calculus. I had a look at some of Newton's books, he does often refer to 'translations', perhaps because he's writing about celestial objects. If there were going to be a history of the relation between non-Newton calculus and 'multiplicative calculus' it can't just skip over the years 1700 to 1966. The stack exchange article which gives the history of 2 interpretations of exponential maps really just shows that in the prior history, the notion of transforming through an exponential map to preserve invariance under symmetries goes back in two different threads. The history ends before 1965 though, with the work of Ehresmann from 1935 until 1960. User smithpith is a well-known and well-admired mathematician who is a neutral and objective Wikipedia editor, however the History section is not due to that editor, it is incorrect history, it is not mathematics and my reason for nominating the article for deletion is that it is powerful marketing. Just the fact that it can be subsumed into a small part of the earlier history wouldn't be an argument for deletion. Often, to introduce students into a subject, a thinker like smithpith will make an easy example. I can think for instance of how questions about group algebras were a way of easing students into von Neumann algebras, or how quivers, developed by Gabriel after his work on categories, is a way of easing students into his earlier work. Or how toric geometry is a way of easing students into projective geometry. And no-one can or should insist that 'you can't understand group algebras until you understand von Neumann algebras' etc. But when it comes to describing the conceptual history, it just would be, to be frank, dishonest, in any such situation, to pretend that easy examples made to attract students to an earlier interesting theory represent a dawning of a whole new mathematical epoch. Because it is one thing to be careful not to intimidate students, but it is another thing entirely to mislead them, and this especially when, in the case of some publishers, the motive having to do with marketing gets very close to tendentious journalism and business.Createangelos (talk) 02:16, 27 March 2020 (UTC)[reply]
(comment reply) In reply to Createalgelos: I am not entirely sure, but I think we may be in disagreement on the overall subject of the page. The linked page Non-Newtonian Calculus is not the subject to which I believe the article refers. I believe the intent of the article is to describe the particular type of multiplicative calculus which Grossman and Katz introduced in 1967, not the general topic. This holds both before and after the edits I propose on my sandbox page (I am editing this as a project for a university class). I completely agree that the history of ideas like this does not begin in the 1960s, but the particular formalism which is being replicated in current research articles does appear to begin at this time. It should not be presented as the start of a new math epoch, but literature generally attributes the creation of this specific topic to Grossman and Katz in the 1960s. https://www.sciencedirect.com/science/article/pii/S0022247X07003824?via%3Dihub is an example of this historical attribution. Is there an older example of this formalism not mentioned in the history section? If not, I don't believe that documenting the history starting in the 1960s constitutes marketing. MathTrain (talk) 04:27, 27 March 2020 (UTC)[reply]

(comment reply) Where you say "I am editing this as a project for a university class," this a very important thing to say, and if you'd like to collaborate on something we can figure out a way we can get in contact. Your course grade should not be connected with success at rescuing a Wikipedia article which violates WP:OR . It would be a conflict of interest for you. I do see that you deleted loads of nonsense references already and show good understanding. Whoever assigned that method of assessing your project made a mistake, though because how are you going to get any credit if you now decide to support [WP:TNT] including sacrificing your own work? What teacher assigned you a project to edit Wikipedia? My own greatest successes in Wikipedia were times I decided to admit total defeat. How are you going to get credit for doing the right thing in the event you decided on your own that your deletions didn't go far enough, and to support [WP:TNT]? When you ask, "Is there an older example of this formalism not mentioned in the History section," did you have a look at that Stack Exchange page yet? Maybe I'm still under the influence of the way the article currently includes so much pretense about non-Newtonian things, still, I'd be interested in your thoughts about it, and we can work our some way to get into direct contact for that. The article wasn't wrong to imply that Newton was a bit obsessed with translations in Euclidean space, and that Stack Exchange article mentions Albert Einstein as one of the main influences in relation to starting to get away from that limitation. I do see that you are now proposing starting a totally different article which is essentially a disambiguation, to sort out the confusion people might have fallen into because of how you have to compose all your functions with log or not, depending on whether you define variables to be multiplicative or additive. This confusion would have started in the 1960's maybe, I do understand that. If you have been a victim of getting confused by the preponderance of conflicting notations and motivations in Wikipedia I'm really sorry, and that is what we are both trying to deal with here. I notice in your work on it, that the existing article about 800 meters mentions that it is a bit shorter than a half-mile, but there is no separate article about the 'half mile' because it isn't notable enough difference to have two separate articles. The situation here is where there is no difference at all. Anyway, do you or your teachers know what to do after a WP:TNT has occurred? How to pick up the pieces in an ethical and considerate way? Maybe that would be a better school project, more advanced, if it weren't for the continuing conflict of interest in editing Wikipedia for assessment. As one final comment, if someone says, "The sound in this microphone increased by 3 decibels in one second, what is the rate of increase," there already is the ambiguity between energy (impedance times the square of RMS voltage), the log base 10, the log base e, or the number of decibels (ten times the log base 10). Or you might mean the RMS voltage. Note that the change in db is not affected by impedance which adds a constant to 10 times the log of the square of the RMS voltage. But if you also say you might have meant either the additive or multiplicative rate of increase of any of these four coordinates, that is replacing a 4-fold ambiguity with an 8-fold amgibuity. Crucially, derivatives are the ratio between two differentials, and differentials have exactly ONE unambiguous definition in Mathematics. Here is that definition https://en.wikipedia.org/wiki/Differential_of_a_function#Definition. They do not depend on units of measurement, for example, because they replace the concept of units of measurement coming from coordinatizations in physics or engineering. This is my true reason for having nominated the article for deletion, and for supporting WP:TNT most sincerely. The reason I can't have one Wikipedia article about de^x and another about e^xdx isn't some political point about hurting people's feelings, or some power play. It is because de^x and e^xdx are equal and that means, they aren't two different things, they are one and the same, they have the relation of equality, and an article which writes about one is already written about the other. And practically speaking, it implies that people shouldn't be required to publish their microphone article twice because they trust Wikipedia, and Wikipedia made them start to worry if decibels are non-Newtonian, and you aren't allowed to say "three decibles per second" without getting some sort of permission from a referee and adding a reference to multiplicative variable theory. Createangelos (talk) 11:35, 27 March 2020 (UTC)[reply]

(comment reply) To clarify the conflict of interest, I would like to clarify that my assessment is not at all dependent on my getting this article published or saved on Wikipedia. I am only being assessed on content in my sandbox page, so any motivation to edit the actual page content is my own. On another note, I like your point about notability via the notion of equality (such as the example with d(e^x) and e^xdx). I completely agree with you on the lack of notability of the concept of NNC as its own mathematical entity, since conceptually it may be mildly different (if at all) from existing ideas of variable transforms, but not nearly enough to merit a separate article (akin to the half-mile versus 800m concept). The reason I think this page is notable is not that the mathematical concept is important, but that NNC as a field has seen a wide increase in publications referring to it as such. While I may not think that the concept is a "separate field" so much as an equivalent formalism of an existing field, that does not seem to be the point of view of published literature. The preexistence of this article, which seems preoccupied with the formalism associated with NNC, supports this point of view. I then find there to be a conflict between two important philosophies of editing: 1) all published literature on the subject, of which there is plenty, seems to support that this particular formalism (NNC) is a notable mathematical concept; 2) I believe (I used to be unsure, but I am more convinced now by your arguments) the concept is not an inherently notable one mathematically. The difference here is the social impact versus mathematical impact of the idea. While there is little-to-no inherent mathematical impact of NNC, there is a social impact. Perhaps the social impact is due to it making concepts of change-of-coordinates more intuitive for some people. I believe that social impact makes the idea, which has lots of published literature on it, notable. Ideally, I might like to say in the article that the social impact itself is notable, and to add the clarification that the math concept is equivalent to transformation of variables. The problem is that no published literature I can find actually supports that idea. There are reddit threads, this talk page, and other informal sources which support that idea, but I am yet to find a reliable review which supports adding that claim. This is likely precisely BECAUSE NNC is socially notable enough to have a whole lot of fringe literature on it, but not quite socially notable enough to have published literature which refutes its inherent mathematical importance. I can come to that claim on my own, but publishing it on Wikipedia would amount to a violation of WP:OR. How do we then balance being unbiased in terms of what the most reliable dozens of sources about a published topic say, versus what seems to be actually true but has no actual published work? If sources say something is notable and mathematically important, but it is actually not, yet there are no actual sources saying that it is not, what do we write in the wiki article about it? MathTrain (talk) 18:00, 27 March 2020 (UTC)[reply]

(comment reply) When you write, "1) all published literature on the subject, of which there is plenty, seems to support that this particular formalism (NNC) is a notable mathematical concept; 2) I believe (I used to be unsure, but I am more convinced now by your arguments) the concept is not an inherently notable one mathematically." On point 1) it is a certainty that these articles and others are right to say that NNC is hugely notable, it includes General Relativity, Stochastic calculus &c&c, and it represents the development of ideas beyond thinking that the universe is a Euclidean space with particular God-given translations. On point 2) that Stack Exchange thread said that it was because of NNC that mathematicians (finishing with Ehresmann in 1960) developed calculus the way we know it now. There is no shortage of articles saying NNC is notable. No one would advocate excising post-Newton calculus from Wikipedia. When you write, "...the math concept is equivalent to transformation of variables. The problem is that no published literature I can find actually supports that idea. There are reddit threads, this talk page, and other informal sources which support that idea," you're referring to the idea that the people like me and the other editors who've written here --- who say that fringe articles/discussions which say that NNC was an idea invented in 1965 comprising a requirement to separate variables into 'multiplicative' and 'additive' mis-characterize NNC -- do not write and submit research articles backing up what we say. This is because of a notion of infinite regress. I do understand, then, that this makes it hard to modify the existing article to include reliable references for how bad it is. That is why the discussion is a deletion discussion, and at some stage an issue of trust arises somewhere. Someone like you could pick up the pieces, and fill-in the missing gaps in the existing 'differentials' article and the existing 'vector-fields' article. About your comment about the social event, it is as you seem to suggest the situation that any biased or misleading Wikipedia article is socially notable because of the confusion it can cause; maybe an issue is to ask, is it only notable to people who read that type of article or who edit Wikipedia? Is it only socially notable 'in house'? Might it be more notable if the phenomenon affects other subjects like medicine or law, maybe? With deletion we'd get a wider perspective and you're really free to expand your school project. Createangelos (talk) 20:07, 27 March 2020 (UTC)[reply]

(comment reply) To clarify some word-usage here, what I referred to when I said NNC is ALWAYS in reference to the fringe ideas created in 1967. That's just a terminology issue: I have only seen the term non-Newtonian calculus used to refer to that specific fringe theory, never to anything else such as General Relativity which you are referencing. I see how the term could be used as such, but that's not how I have been using it. This is certainly making a good case for a disambiguation page in my opinion, would you agree? Furthermore, I do stand by the claim that NNC (the fringe theory from the 1960s) is notable in and of itself, not as a mathematical topic, but as a place for confusion and also a place where a lot of academics have written a lot of work. Would it be reasonable to propose the creation of a disambiguation page which includes both the important parts of NNC (general relativity etc) and a link to a short page on the fringe theory? I think the short page could link to the fringe work in order to clarify confusion and just show what it is. My only question if we did that is how to deal with the question of infinite regress. The work by its nature is making bold claims, but there are no official sources to refute those claims. However, maybe the page could be worded to minimize advertising. Thoughts? MathTrain (talk) 22:13, 27 March 2020 (UTC)[reply]

(comment reply) Just to say that you're making a lot of sense. As for the current deletion discussion, when you say 'a place where a lot of academics have written a lot of work,' there are specific agreements in Wikipedia for what comprises notable work, I myself am not an expert in these. They have to be secondary sources, the publications have to ones that have already been agreed to be reliable. Some of these restrictions must be related to that infinite regress concept. No-one wants to silence anything, but if editing articles about scholarship is changed into being done according to popularity, then you're advocating changing Wikipedia into Reddit. I am not a high-up editor, and I do not know how the deletion decision will be made, nor do I understand why you voted 'keep' given your clear understanding of the issues. I have a sad feeling that this feels like a negotiation, which isn't what I wanted at all. The 'differentials' article has weaknesses, the 'vector-fields' article has weaknesses, and none of the historical discussion from Stack Exchange is correctly represented. It is a dismal situation and I feel like you want to accept how bad it is so that in return we won't delete your article. Wouldn't it be an acceptable school project to become a leader in sorting out the deeper weaknesses in other articles which attempt, but fail, to explain how Calculus changed after 1700, and articles in other subjects like this one under consideration where there is a pocket of popular agreement about some topic which ignores the scholarship.Createangelos (talk) 23:04, 27 March 2020 (UTC)[reply]

(comment reply) I certainly wouldn't prefer to accept how bad it is just so the article won't be deleted; I would like to clarify again that this is my own work at this point – the school project has actually been handed in already and I'm only graded on what happens on my sandbox page, not here. Within the class of course there are certain word limits/requirements etc, but that has nothing to do with what I want to do here on the mainspace. I don't want anybody to not delete my article because they think that impacts my grade (it doesn't); when I mentioned that I was doing it for a class, I just meant please to not write or change anything in my sandbox page. In regards to why I voted keep, I think you've reasonably changed my mind. I would propose instead creating a disambiguation article from scratch on NNC, and including in it a link to a short page on the fringe topic which this page is currently devoted to. I am familiar with the rules of using secondary sources and what comprises notable work, and I think that there are plenty of sources already in the article (most are not good, but some are useful) which make this topic notable enough to merit such an article. I questioned myself whether some of them qualified as secondary sources, but given the definitions Wikipedia sets out I believe they are. I am not familiar, however, with the actual organization of Wikipedia when it comes to creating a disambiguation page, properly linking, whether the first step is to rename or to delete this page, etc. Furthermore, if I wanted to do that, would I change my vote above to Delete, or would I write a second vote? MathTrain (talk) 00:28, 28 March 2020 (UTC)[reply]

(Comment Reply) Hey, kid, you're getting over my head already in this, I told you that I'm not a Wikipedia expert so I will leave it up to you. [WP:BB] Createangelos (talk) 00:42, 28 March 2020 (UTC)[reply]

Comment Is a redirect to Product integral (and then starting with a clean sheet for a section on Multiplicative Calculus) an option perhaps? Cheers, 1292simon (talk) 06:42, 28 March 2020 (UTC)[reply]

The multiplicative integral is known, in modern mathematics, as the Haar measure on the multiplicative group of positive integers. IMO, Product integral needs to be completely rewritten for taking the moden knowledge into account, and for clarifying the relation of its content with measure theory. D.Lazard (talk) 11:33, 28 March 2020 (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.