Talk:Mathematics/Archive 7

message: An anon contributor added a new section headed Example of Physically "False" Mathematics, with various examples related to triangles and non-Euclidean geometry. I removed it because it intertwines the non-Euclidean 4D geometry of relativistic spacetime with the 2D spherical geometry of the Earth's surface. The implication that there is some sort of link between these two concepts because "our universe is not described by Euclidean space" is both confusing and misleading. Gandalf61 15:35, 22 May 2006 (UTC)
thread_title: Reasons for removing new "triangle" section

message: Instead of simply reverting them and saying they make the page look "awful".  What I think looks awful is the big white space next to the table of contents and the math portal link in the wrong section. VegaDark 00:38, 24 May 2006 (UTC)
replies: text: Yes you are right, it is good to discuss things. But your changes filled in the white space to the right of the table of contents with a very narrow column of text, making that article section hard to read and not so pleasing. You also moved the nice picture from the top somewhere down under the narrow column of text I mentioned above, and putting the TOC to the right is not standard in the article namespace. Since it was only a minor edit, I took the liberty of reverting it. My edit summary was surely poorly thought out, sorry. Oleg Alexandrov (talk) 01:13, 24 May 2006 (UTC)
replies: text: I've seen articles that have the TOC off to the side.  I think it is a good way to get rid of the white space if there is an especially long TOC.  It can go off to the right side if you want, that will look fine as well.  I just don't think it looks good with all the white space as is.  Also, as far as I know links to the portal an article is in should go in the see also section.  At least that is how I have seen it linked in other articles. VegaDark 02:09, 24 May 2006 (UTC)
replies: text:  But again, it mangles the text. On my screen the TOC takes at least half of the width of the screen, and then the text has to fit on the other half. I think that space is too small to be filled usefully. Maybe if we have a picture or two we cut stick them into that space. But I agree with putting the portal down, I just did. Oleg Alexandrov (talk) 04:03, 24 May 2006 (UTC)
replies: text: Hmmm...on my screen the TOC only takes up a third of the space, so it doesn't look bad at all with text next to it.  I wouldn't object to a pic or 2 there instead. VegaDark 05:38, 24 May 2006 (UTC)
thread_title: Please discuss reverting changes

message: I propose adding a new Major Theme: Handling uncertainty. This would cover Probability Theory, Measure Theory, Statistics, Brownian Motion, Quantum Theory and Information Theory. Stephen B Streater 08:15, 24 May 2006 (UTC)
replies: text: I tend to agree, there is a tendancy to focus on pure mathematics reducing applied mathematics and statistics to a foot note. I've also though about moving the whole Major Themes section up in the article, maybe just after the introduction. --Salix alba (talk) 09:01, 24 May 2006 (UTC)
replies: text:  I agree with this idea of moving the themes up. It lets people know how varied and powerful Mathematics is. Most laymen identify Mathematics with Arithmetic, and it is important to remove this misconception as soon as possible. Stephen B Streater 09:20, 24 May 2006 (UTC)

text: I support the new theme. Uncertainty has occupied the minds of many great mathematicians and would be a worthy theme. -- Avenue 09:40, 24 May 2006 (UTC)
replies: text: What we need is a reference naming the themes of mathematics. --MarSch 10:22, 24 May 2006 (UTC)
replies: text: Take your pick - Dewey Decimal, AMS Mathematics Subject Classification, Library of Congress Subject Classification, another Mathematics Classification System, yet another MCS; no lack of choices, but they are all different. Gandalf61 12:23, 24 May 2006 (UTC)
replies: text: I feel that the AMS classification system is the professional standard. I would name the theme simply Chance, myself. Measure Theory and Chaos wouldn't quite fit there, to my mind. Prediction is another possibility. JJL 14:44, 24 May 2006 (UTC)
replies: text:  Of course, Chaos is deterministic, unlike (for example) Brownian motion. I agree that this section should not include deterministic branches of Mathematics. Stephen B Streater 17:35, 24 May 2006 (UTC)

text:  Chance is a catchy title. Perhaps Stochastic Processes would be a more general name. Probability Theory is a special case of Measure Theory, which is why I included it in my original concept. Stephen B Streater 17:35, 24 May 2006 (UTC)

text:  The AMS list is pretty comprehensive! I think we need a shorter list of themes. Being Mathematics, perhaps some things should be in several themes. For example, Quantum Theory could come under Chance and Theories of the Universe, though I can't see a lot of obvious candidates yet. Stephen B Streater 17:35, 24 May 2006 (UTC)
thread_title:  Handling uncertainty 

message: I suggest to put in bold characters the words "Understanding and describing change ", undoubtely it's a key concept 
Brian Wilson 13:28, 26 May 2006 (UTC)
replies: text: Yes, it is a key concept, but why does it need to be in bold? JPD (talk) 13:40, 26 May 2006 (UTC)

text: It doesn't fit with the format of the rest of the article. No other key concepts are bolded. JPD (talk) 14:02, 26 May 2006 (UTC)

text: The question would be whether bolding under these conditions is "judicious," as used at WP:MOS#Legibility.  I think bolding all "key concepts" in mathematics might not be a good idea for legibility.  John (Jwy) 14:04, 26 May 2006 (UTC)

text: My view is that lots of things in Maths are important. I wouldn't bold the change idea in the text (at least at the moment), as bolding everything makes text illegible. Change has its own theme, with some nice pictures, so people will realise it is important from this. Stephen B Streater 15:22, 26 May 2006 (UTC)
thread_title:  Understanding and describing change 

message: While  can mean "fond of learning", which is cute, a more basic meaning is: "related to ", which for one of the meanings of  amounts to "mathematical". Hence (with the female form)  "the mathematical art", which can be shortened to , and with the neuter plural form  "things mathematical". I think that the plural form we have in English comes from the last. But I must admit my classical Greek is rusty, and I have no sources for any of this. Anyone with a good Greek dictionary? --LambiamTalk 20:35, 27 May 2006 (UTC)
replies: text: Well the definitive Greek lexicon, Liddell and Scott, is online at Perseus project, but seems to be not responding at the moment, and I don't have my paper copy handy.  But for the purposes of etymology it is useless to translate mathema as mathematics.  The word originally and literally means learning, so the word mathematics means "things related to learning".  I think that would be a better etymology.  There is nothing about fondness in the word.  But I don't think you should change the translation to "mathematics".  That would be like saying that the etymology of "geometry" is that it is the Greek word for "geometry".  While true, it is not a very useful etymology, etymology is supposed to give you some source meanings. -lethe talk [ +] 20:40, 27 May 2006 (UTC)
replies: text: But the general meaning of "learning" already acquired during classical Greek times among its several meanings the more specialized meaning of "the mathematical sciences". What is wrong with saying that "landscape" comes from Dutch "landschap", meaning "landscape"? --LambiamTalk 20:59, 27 May 2006 (UTC)
replies: text: It's incomplete.  I wonder what the purpose is of including an etymology anyway?  Etymologies are interesting when they come from simpler roots that allow you to recognize the word or tell you some history of the word.  Both of these are accomplished by saying that "geometry" comes from the Greek "geos" = Earth, "metron" = measure.  Nothing useful at all is conveyed by saying "geometry" is from the Greek word "geometria" meaning "geometry".  I think the latter applies to the word "mathematics" as well.  Don't know about the etymology of "landscape", though I'll bet there is a Dutch root "land" which has a relevant meaning, which should be mentioned in any useful etymology of the word. -lethe talk [ +] 21:22, 27 May 2006 (UTC)
replies: text: What exactly is incomplete? My remarks addressed correctness. We should not substitute an interesting but incorrect etymology for a correct but boring one. By the way, this fondness thing is one of the meanings. You can say there is nothing about excellency in the word "cool" since it originally means "cold", but in current English "cool" can and does also mean "excellent". --LambiamTalk 23:44, 27 May 2006 (UTC)
replies: text:  If you give the shortest possible etymology which contains no information other than the source language then you are doing your reader a disservice.  If you don't mention that "cool" derives from an english word meaning "cold", then you haven't given a good etymology. -lethe talk [ +] 01:55, 28 May 2006 (UTC)
replies: text: And if you say that "cool" comes from "ghoul", you're wrong. And if you give the longest possible etymology, occupying many pages, the reader won't be happy either. I agree with all of this. But what does that have to do with the question whether the etymology currently given on the page is correct? --LambiamTalk 02:13, 28 May 2006 (UTC)
replies: text:  Liddell and Scott is back online responding now, and you can see that "fond of learning" is exactly the translation it gives for mathematikos.  So the etymology in the article is a good one.  It also lists "scientific, esp. mathematical", "mathematics" as definitions, so those might also provide good etymologies.  For mathema (of which mathematikos is just an adjectival form), it gives "that which is learnt", "lesson", "learning", "knowledge", "esp. the mathematical sciences".  and manthano, "learn", "perceive", etc.  Now the question is only: which of these lexemes do we want to list in the article?  Which will be most useful to the reader?  Should we simply list the L&S first translation of the word mathematikos?  This is what's currently done.  I guess I'm OK with it. -lethe talk [ +] 02:34, 28 May 2006 (UTC)
replies: text: I think etymology is more subtle than that. Just because mathematics is derived from mathematikos and one of the meanings of mathematikos is "fond of learning", does not mean that that is the meaning from which mathematics is derived. I'd be more comfortable if we used some kind of dictionary. For instance, the Oxford English Dictionary says that mathematics is derived (via French and Lati) from the Greek mathematikos meaning mathematical or mathematics; it does not mention the "fondness of learning" meaning of mathematikos, but it does say that derives from mathema = knowledge and the suffix -ikos. So, just from the OED, I'd say that the best is to say that it derives from mathema = knowledge, without the "fond" part. -- Jitse Niesen (talk) 02:53, 28 May 2006 (UTC)
replies: text: I was actually thinking that as far as listing the root from which the obviously derived word comes, manthano is the better choice.  As for the "fond of learning" in Liddell and Scott, I think they were just searching for an adjective to which to attach "learning", since there isn't a neutral adjectival combining form in English.  Anyway, I would be in favor of a longer etymology than just mathematikos.  That's what I was trying to persuade Lambian of, afterall.  My only point was, nothing in the article is wrong at this point, so if we change it, it's only because we like something else better. -lethe talk [ +] 03:04, 28 May 2006 (UTC)
replies: text:  I was about to change it according to what you said, but I see that it already mentions mathema.  I suppose there is nothing to be done, the article is fine. -lethe talk [ +] 03:05, 28 May 2006 (UTC)
replies: text:  Phew ;-) Stephen B Streater 09:18, 28 May 2006 (UTC)

text: I looked up mathematics in The Oxford Dictionary of English Etymology (1983 reprint). According to the ODEE mathematics has a dual pedigree. Middle English has matematik (attested 14th c), via Old French/Spanish/Italian from Latin (feminin singular) mathematica, namely mathematica ars or mathematica disciplina, from Greek mathematike, namely mathematike tekhne or mathematike theoria. The current plural form (attested 16th c.) is said to be probably modelled after French les mathematiques (also 16th c.), from Latin (neuter plural) mathematica (Cicero), from Greek ta mathematika (Aristotle). There is no explanation of mathematikos except that it is from mathema something learnt, science, from manthanein learn. Jasper Klein.
The verbal noun from , "learn",  "that which is learnt, learning" and its adjective  "related to learning" are used of science in general and the mathematical disciplines in particular by Archytas, by Plato and by Aristotle. One may assume that this use of the word originated in the school of the Pythagoreans. Archytas, a close friend of Plato's, was a Pythagorean philosopher and mathematician, and he wrote the book about mathematics with the title  or , which is known only in fragments. The prominence of numbers and mathematics in the Pytheagorean tradition is wellknown, and it may have been the reason why mathematical studies would be labelled simply "learning". Enkyklios 11:48, 28 May 2006 (UTC)

text: That is half the point I was trying to make; it is an improvement. I don't understand why it is so problematic that mathema already took on its meaning of maths in ancient times, but if that is considered a humiliating revelation, then let's leave that out. --LambiamTalk 19:10, 28 May 2006 (UTC)
replies: text: Hmm well I guess that is where you and I disagree.  I really think that the purpose of providing the etymology of a technical word is to see where the technical word took its meaning from nontechnical language.  The incomplete etymologies do not do this, and providing the technical usage in Greek conveys exactly zero information about the origin of this word.  I think the translations provided by our Ancient Greek literati friends above testify the interesting fact that the word has a nontechnical origin in Ancient Greek.  -lethe talk [ +] 19:25, 28 May 2006 (UTC)
replies: text: In German, they use the word der Blackout.  It means "blackout", the same as in English.  If you were writing a German dictionary, and simply sited that "the blackout" is the English word for der Blackout, it would be an entirely useless etymology.  Much better to mention the words "black" and "out", to give some small inkling of the feel and history of the word.  This is the purpose of etymology, I think.  Your position on the word mathematikos ignores this purpose, it makes it rather just a useless translation. -lethe talk [ +] 19:50, 28 May 2006 (UTC)

text: Perhaps there is no problem.  I have no problem mentioning that the technical meaning was the same for the Greeks as it was for us (and in fact I made an edit to mention that fact).  I just had a problem with what I thought you were proposing: replacing the nontechnical definition with the technical.  Now it seems you favor including both, something I can definitely get on board with.  How do you like the edit I already made? -lethe talk [ +] 03:12, 29 May 2006 (UTC)
thread_title:  Etymology of "mathematics" 

message: The version with the most support at the moment seems to be Jitse's version:
: Mathematics is a discipline that studies topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.
(That includes Lambiam's trivial suggestion of changing including to such as).
Two more comments from me..
*Should the word result be used to describe something that hasn't been justified yet? Maybe a word like ideas should be used in place of results, which might even help get the idea accross that mathematics isn't a process of following rules, it has a creative aspect to it too.
*I think the growth and size of mathematics today, should be left to another paragraph, but still included in the introduction.
--darkliight[πalk] 05:26, 4 June 2006 (UTC)
replies: text: Mathematics is a discipline that encompasses topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians prefer to prove results by rigorous deduction from axioms and definitions.
Stephen B Streater 08:43, 4 June 2006 (UTC)

text: I'm sure the word prefer is inappropriate in the last sentence -- surely aim is better here? Also, since the sentence begins with mathematicians, not A mathematician .., then doesn't that imply they work on each others work? So I think aim to prove their results/ideas/work by.. fits better here. --darkliight[πalk] 09:20, 4 June 2006 (UTC)
replies: text:  I think "aim" works here, and agree that "their" is not the same as "their own" so your wording for the last sentence works fine for me (with results or ideas rather than work - they might do it for play). Stephen B Streater 11:07, 4 June 2006 (UTC)

text: Yeah, I like Jitse's version too. Anybody willing to add it to the article? Oleg Alexandrov (talk) 15:51, 4 June 2006 (UTC)

text: Mathematics is the study of topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.
Regarding the problems that a "result" that isn't justified isn't yet a result, by one definition of result, and the fact that not all mathematicians are so concerned with rigor, please keep in mind that this is only an overview.  Its job is only to summarize what is already written later in the article, without going into so much detail and precision.
--Ben Kovitz 16:51, 4 June 2006 (UTC)
replies: text:  OK -- I've tried to add something meeting the above (I removed the Oxford comma and made the suggested adjustment from studies to encompassing).  Feel free to change back if you wish.  --Richard Clegg 16:55, 4 June 2006 (UTC)
thread_title: Close to a consensus?