Talk:WikiJournal of Science/Spaces in mathematics

Plagiarism check
✅ WMF copyvio tool using TurnItIn. Text found in external page but is attributed as quote, so not regarded as plagiarism. T.Shafee(Evo&#65120;Evo)talk 11:15, 9 January 2018 (UTC)

First review
{{Editor's comments
 * name=Marshall Sumter
 * version=https://en.wikiversity.org/w/index.php?title=Spaces_in_mathematics&oldid=1692999
 * 1) Space (mathematics) was submitted by IP 77.126.70.80 but authored by the Parent article editors. Who answers the reviews? w:User:Tsirel appears to be a major contributor with necessary and sufficient background to respond to the reviews. --Marshallsumter (discuss • contribs) 18:33, 5 June 2017 (UTC)
 * 2) The sentence ending in "compared to classical mathematics." has [citation needed]. The classical history period dates from around 2,000 to 1,000 b2k.
 * 3) Is a space defined as a universe, a class, or a set of points with some added structure?
 * 4) Since some structures do not change a set to a space, the phrase "some added structure" is vague. --Marshallsumter (discuss • contribs) 20:34, 1 May 2017 (UTC)
 * 5) "and the inner product is indicated enclosing in by angle brackets." to "and the inner product is indicated by enclosing in angle brackets."
 * 6) "In the ancient mathematics," should be "In ancient mathematics," --Marshallsumter (discuss • contribs) 23:03, 6 May 2017 (UTC)
 * 7) ""space" was a geometric abstraction of the three-dimensional space observed in the everyday life." to ""space" was a geometric abstraction of the three-dimensional space observed in everyday life."
 * 8) "The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude" to "The above-mentioned fixed point S is called the homothetic center, or center of similarity, or center of similitude." in Homothetic transformation.
 * 1) "The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude" to "The above-mentioned fixed point S is called the homothetic center, or center of similarity, or center of similitude." in Homothetic transformation.

Text comments:

The structure that every space has to be a space is called the norm. It is the real-valued function
 * $$\|x\| = \sqrt{\langle x,x \rangle}.$$ --Marshallsumter (discuss • contribs) 23:20, 5 May 2017 (UTC)

This article should be demonstrating the relevance to science of mathematical spaces. --Marshallsumter (discuss • contribs) 23:01, 6 May 2017 (UTC)

Homothetic transformation should be condensed and included where "homotheties — into similar figures." are mentioned in Space (mathematics). --Marshallsumter (discuss • contribs) 21:09, 27 May 2017 (UTC)

There are 21 footnotes to Bourbaki and 3 to other authors. This article appears to be an abridged paraphrase of Bourbaki. --Marshallsumter (discuss • contribs) 00:10, 28 May 2017 (UTC)

You mention 65 spaces in the table at the bottom, but only describe 16 from the table in the article, some large numbers of times. An article on mathematical space should mention many more than 16 in some developmental form. --Marshallsumter (discuss • contribs) 01:25, 28 May 2017 (UTC)

Perhaps there is a bit more precise definition of a mathematical space:

Def. a "set along with a collection of finitary functions and relations" is called a structure.

Def. "a set [of points] with [some] added structure", is called a space. --Marshallsumter (discuss • contribs) 04:10, 8 June 2017 (UTC)

"In mathematics, a space is a set (sometimes called a universe) with some added structure." is from Space (mathematics), perhaps referring to Universe (mathematics). --Marshallsumter (discuss • contribs) 04:16, 8 June 2017 (UTC)

Perhaps WikiProject Mathematics can be contacted for responses to the reviews. --Marshallsumter (discuss • contribs) 19:14, 27 May 2017 (UTC)

Just FYI: here (Wikiversity) you can perform OR by synthesis or anyway you like! --Marshallsumter (discuss • contribs) 04:19, 8 June 2017 (UTC)

Imported; what now?
The article is imported hereto: Space (mathematics). It contains a lot of red links. What to do with them? Sometimes we have something appropriate here; for instance, I just changed set to set. What to do when we have nothing appropriate? Of course, I can change Euclid to Euclid (using the slanted font as a hint on escape from Wikiversity), or just to Euclid (no link). What is better? Boris Tsirelson (discuss • contribs) 06:25, 8 June 2017 (UTC)

Also, I restored a table (Section "Differences") that was deleted as my OR by synthesis... Boris Tsirelson (discuss • contribs) 06:50, 8 June 2017 (UTC)

Linking to Wikipedia is a good choice. It can be replaced later if a learning resource exist. For the readers of the article it is sometimes important to look up the definition of mathematical expression. Therefore no learning resource in Wikiveristy is required in general for a specific term linked in the article. --Bert Niehaus (discuss • contribs) 12:44, 11 May 2018 (UTC)

Definition of mathematical space
According to Kevin Carlson:
 * Neither of these words have a single mathematical definition. The English words can be used in essentially all the same situations, but you often think of a "space" as more geometric and a "structure" as more algebraic. The best approximation to a general "space" for many purposes is a topological space, but Grothendieck generalized further than that, to what are called topoi.


 * In model theory a "structure" is a set in which we can interpret some logical language, which is to say a set with some distinguished elements and some functions and relations on it. Some of the most common languages structures interpret are those of groups, rings, and fields, which have no relations, functions are addition and/or multiplication, and distinguished identity elements for those operation. We also have the language of partially ordered sets, which has the relation ≤≤ and neither functions nor constants.


 * So you could think of "structures" as places we do algebra, and "spaces" as places we do geometry. Then a lot of great mathematics has come from passing from structures to spaces and vice versa, as when we look at the fundamental group of a topological space or the spectrum of a ring. But in the end, the distinction is neither hard nor fast and only goes so far: many things are obviously both structures and spaces, some things are not obviously either, and some people might well disagree with everything I've said here.

Quoted from math.stackexchange, 2012 Boris Tsirelson (discuss • contribs) 08:04, 8 June 2017 (UTC)

Another source: Robert C. Reed, Review of Leo Corry, Modern Algebra and the Rise of Mathematical Structures. Some quotes:
 * The book is therefore an attempt not merely to show how the concept of structure evolved, but to demonstrate that the concept itself is not strictly mathematical at all in the narrow sense [...] (p.183)
 * Corry does not go so far as to call the rise of structure a scientific 'revolution' [...] but [...] it would not be too inaccurate to describe the theme of this book as the claim that the rise of structure can best be understood as a paradigm shift. (p. 184)
 * In his book Corry uses italics to make a distinction between the structures Bourbaki defines formaly and the usual informal notion of structure. (p. 187)
 * Corry does not seem to feel that any formal definition of structure could do justice to the use of the concept in actual mathematical practice [...] Corry's view could be summarized as the belief that 'structure' refers essentially to a way of doing mathematics, and is therefore a concept probably just as far from being precisely definable as the cultural artifact of mathematics itself. (p. 189, the end)

Boris Tsirelson (discuss • contribs) 08:30, 8 June 2017 (UTC)

The relevance to science and engineering
A quote from annotation to the book "Some Modern Mathematics for Physicists and Other Outsiders" (vol.1, 2014) by Paul Roman:
 * The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions.
 * The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

Boris Tsirelson (discuss • contribs) 19:53, 8 June 2017 (UTC)

A quote from Sect. 2.2 of "Mathematics and other disciplines" by V.G Masanja (2002):
 * Examples of mathematical results that got inspired by physical ideas include Donaldson's proof of the existence of different differential structures on simply connected 4-dimensional manifolds. This has very deep consequences for quantum gravity [...] The new conservation laws developed in the last part of the 20th Century are believed to be the most fundamental in physics. The application of modern abstract mathematics in physics has resulted in astounding discoveries of the 20th Century in the physical sciences, the life sciences and technology.

Boris Tsirelson (discuss • contribs) 20:16, 8 June 2017 (UTC) + Simon_Donaldson + Exotic_R4 + Donaldson's theorem + Geometry and physics

And, of course, Hilbert spaces are indispensable in quantum physics, as well as Einstein spaces in general relativity (including black holes, Big Bang etc). Boris Tsirelson (discuss • contribs) 20:21, 8 June 2017 (UTC)

Also, mathematically, quantum gravity is a theory of a random metric space that is two-dimensional topologically, but four-dimensional metrically! See Quantum Gravity: the Mathematics of Random Metrics by Oded Schramm (2008). Boris Tsirelson (discuss • contribs) 20:32, 8 June 2017 (UTC)

Also, affine and projective spaces are used in computer vision and robotics, see the lecture Introduction to Computer Vision for Robotics of this course; and Chapter 7 "Algebraic curves in structure from motion" by Kaminski and Teicher, pp. 245–296 in book: Computer Vision and Robotics (ed. John X. Liu) Nova Publishers, 2006. Boris Tsirelson (discuss • contribs) 07:53, 9 June 2017 (UTC)

Revised
So, the manuscript is revised according to the first review. Boris Tsirelson (discuss • contribs) 20:18, 10 June 2017 (UTC)

Commentary by non-specialist editor
Having a review by a non-specialist was suggested in the third review of this article. The suggested changes are not critical for WikiJSci, but would facilitate the integration into Wikipedia. Sylvain Ribault (discuss • contribs) 21:59, 4 May 2018 (UTC)


 * See also a relevant essay by Ian Alexander. As for me, it shows that Wikipedia is inherently different from any journal (traditional or wiki-based). Boris Tsirelson (discuss • contribs) 06:59, 5 May 2018 (UTC)
 * Thanks, Boris. I agree, and it's the reason why the Journal is at least one step separated from Wikipedia, so we can accommodate differences from Wikipedia practice if necessary. (Ian Alexander) Chiswick Chap (discuss • contribs) 09:16, 5 May 2018 (UTC)
 * Yes. Here is but one reason not to give the refs. Basic spaces (linear, topological, smooth etc) are treated in dozens, maybe hundreds of textbooks. I could go to a library and find some. What now? How to choose? Those available in our library need not be those available in the library of the reader. Those I like need not be those he/she likes. Let him/her go to a library and find something; it should be easy, unless he/she is too much unprepared to read anything like that (in which case a reference is of no help anyway). Boris Tsirelson (discuss • contribs) 10:07, 5 May 2018 (UTC)
 * I just tried google search on "textbook on linear space" (without quotes). The result is convincing. The same for "textbook on topological space". Maybe this is why a number of professional mathematicians behave on Wikipedia like newbies even after many years of participation. Boris Tsirelson (discuss • contribs) 10:13, 5 May 2018 (UTC)
 * Thank you for checking, I expect that will be fine then. As I said, it isn't for me to say what you should do, and journal papers can and will diverge from Wikipedia practice, but I felt I should mention it. Chiswick Chap (discuss • contribs) 10:46, 5 May 2018 (UTC)

Editorial comment

 * "elements of a set, or functions on another space, or subspaces of another space" — it may seem that functions on another space are not elements of a set.
 * I think 'elements of a set' should come first, as 'spaces of spaces' sound like circular reasoning. The potential confusion that you point out would not bother me in the lead section of an encyclopedic review article. Sylvain Ribault (discuss • contribs) 21:57, 12 May 2018 (UTC)
 * "uniquely determined by Euclid's axioms" — not quite so; the ancient axiomatics misses some things.
 * Again, such subtleties are probably not for the lead section. It would be great to find a formulation that was both precise and readable, but this might not be possible. Maybe adding a footnote would be appropriate? Sylvain Ribault (discuss • contribs) 22:01, 12 May 2018 (UTC)
 * OK, now a footnote. Boris Tsirelson (discuss • contribs) 05:17, 13 May 2018 (UTC)
 * "relation from Euclidean to topological spaces" — is it usual to say "relation from ... to ..." (rather than "between")?
 * The following sentence starts with 'Relations of this kind', so we need to use the word 'relation'. I agree that this use may not be common. Sylvain Ribault (discuss • contribs) 22:04, 12 May 2018 (UTC)
 * "if an isomorphism ... is a one-to-one correspondence..." — it sounds like "if 2+2=4", doesn't it?
 * Right, I have now tried to rectify the formulation. Sylvain Ribault (discuss • contribs) 22:06, 12 May 2018 (UTC)
 * Boris Tsirelson (discuss • contribs) 21:43, 12 May 2018 (UTC)

Abstract/Lead Section - Contribution to scientific community
Scientific articles contribute something to scientific community. Due to the fact that Wiki Journal of Science is not meant to a Journal just for mathematical community, an abstract could contain sentence like "The article contributes .... to the scientific community ... by the analysis/revision/extension/development/a new method .... of ....". Such a recommended sentence might be valuable for the readers. This comment might be relevant for the reviewing of submitted papers to this journal in general. --Bert Niehaus (discuss • contribs) 13:07, 11 May 2018 (UTC)


 * Looking at the 8+1 other upcoming articles I did not find such sentence (not even once). Boris Tsirelson (discuss • contribs) 18:24, 11 May 2018 (UTC)

Pictures in PDF
I am glad to see the article accepted.

About the PDF version. My pictures in svg format are converted from pdf (and adapted a little to low resolution). If needed, I can provide the pdf files (for high resolution). Should I do? Which way? Boris Tsirelson (discuss • contribs) 06:15, 1 June 2018 (UTC)
 * The svg format will likely be fine. The adaptations for low-resolution will likely be relatively useful for the final PDF version. An optional change might be to use a sans-serif font in the images, however that is merely an aesthetic preference. T.Shafee(Evo&#65120;Evo)talk 06:28, 1 June 2018 (UTC)
 * Yes, but it probably means conversion back and forth (pdf->svg->pdf) which is generally undesirable. Boris Tsirelson (discuss • contribs) 08:34, 1 June 2018 (UTC)

Volume 5?
"Suggested citation format: Tsirelson, B; et al. (2018). "Spaces in mathematics". WikiJournal of Science 5 (1). ISSN 2470-6345." – Really, 5(1)? Boris Tsirelson (discuss • contribs) 18:09, 1 June 2018 (UTC)

It seems I understand what happens. In "Template:Article info" I see "|volume        = Volume number (if left blank, will be autocalculated from year)". Boris Tsirelson (discuss • contribs) 21:39, 2 June 2018 (UTC)

Now fixed. Boris Tsirelson (discuss • contribs) 21:43, 2 June 2018 (UTC)

DOI twice?
Now I see DOI twice:
 * PDF: In preparation
 * DOI: 10.15347/wjs/2018.002
 * XML: In preparation


 * Share article
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 * Suggested citation format:
 * Tsirelson, B; et al. (2018). "Spaces in mathematics". WikiJournal of Science 1 (1): 2. doi:10.15347/wjs/2018.002. ISSN 2470-6345.

Is it intended? Boris Tsirelson (discuss • contribs) 05:46, 3 June 2018 (UTC)


 * Yes, the first mention is part of the metadata list, the second mention is simply part of the recommended citation for copy-pasting. It's actually a little old fashioned to do this, but I think it worthwhile for the WikiJournals initially to ensure that readers understand how to cite the articles. T.Shafee(Evo&#65120;Evo)talk 06:23, 3 June 2018 (UTC)

LaTeX problem? Or cache problem?
Something is wrong, maybe temporarily. For example, Sect. "Normed, Banach, inner product, and Hilbert spaces": the formula $$\lVert x\rVert$$ gives "'"`UNIQ--postMath-00000002-QINU`"'". Should give $$\lVert x\rVert$$ Boris Tsirelson (discuss • contribs) 17:39, 16 June 2018 (UTC)

Null edit did not help. Boris Tsirelson (discuss • contribs) 17:42, 16 June 2018 (UTC)

Purge did not help (recommended here, here). Boris Tsirelson (discuss • contribs) 17:51, 16 June 2018 (UTC)

Old versions demonstrate the same problem. Boris Tsirelson (discuss • contribs) 17:53, 16 June 2018 (UTC)

Without "article info" template I still see the same problem, here. Boris Tsirelson (discuss • contribs) 18:01, 16 June 2018 (UTC)

And even just $$x$$ on the first line gives the same. Boris Tsirelson (discuss • contribs) 18:06, 16 June 2018 (UTC)

Caught! I blame the parameter "part=Part 2" of the "cite book" template! Boris Tsirelson (discuss • contribs) 18:29, 16 June 2018 (UTC)

Interestingly, this parameter is just removed on Wikipedia, see this diff. Wow! Аn applause to w:User:Donnowin1. Boris Tsirelson (discuss • contribs) 18:35, 16 June 2018 (UTC)