User talk:KSmrq

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Wallpaper group & Crystallographic restriction theorem

Greetings KSmrq and welcome. I noticed you added an external link for the crystallographic restriction theorem on the wallpaper groups page. Just letting you know I intend to write a more complete article on that topic in the next month or two. That external link is a little misleading, the content there suggests the result is identical in the higher dimensional cases, which is not true (e.g. there are 5-fold rotations in 4-space etc). Feel free to beat me to it if you like. Dmharvey File:User dmharvey sig.png Talk 14:58, 5 Jun 2005 (UTC)

Hello again. Before I respond to your comment, I wanted to mention that the convention on WP appears to be to reply to comments in the location that they were posted (with indent), even if that's your own talk page. It makes it easier to follow the thread of conversation; you can use your watchlist to keep up with things. Please correct me if you think that's not true. (I'm fairly new around here too.) Actually, I'll paste your comments here and pretend that nothing happened :-) Dmharvey File:User dmharvey sig.png Talk 21:58, 5 Jun 2005 (UTC)

Re: Wallpaper group

Agreed, the geometric proof for 2D cannot be used unchanged for all dimensions. However, the linked page seems adequate for wallpaper groups, and it is explicit about its limits:

We will give the proof for ℝ². The proof for ℝ³ is similar. It is harder for higher dimensions!

One generic proof depends on the transformation matrix having only integer entries in terms of a lattice basis. But one of the nice properties of your edits is the introduction of a great deal of visual material, and the 2D geometric proof, though more limited, seems more in line with that style.

Two dimensions of tension are apparent in content of this nature: abstract mathematics versus concrete examples, and specific (2D only) versus general (such as 3D crystallographic groups). Given the topic of the entry, it seems wise to stick with specific and not worry about higher dimensions. As for mathematics, readers may be young or inexperienced, and we'd hate to give them a bad taste, to make them feel like this material is unpleasant or too difficult. A matrix proof might do that.

KSmrq 21:25, 5 Jun 2005 (UTC)

I fully agree. I intend the following to happen. The wallpaper group page needs lots of pretty pictures and an informal explanation (which just got another rewrite today), because it is one of the very few mathematical topics that is accessible to just about anybody. On the other hand, it needs some formal definitions, along the lines of what I have included, to satisfy mathematicians. (And it still needs a lot of work on that count, e.g. there is only the barest mention of lattices.) The only mention of higher dimensional cases should be: (1) very briefly in the introduction, (2) slightly more detail (but still no more than a sentence or so) in the formal section. The article on the crystallographic restriction theorem should include (1) the easier geometric proof that works in 2-d and 3-d, and also (2) the high-tech proof for higher dimensions. I am a very big fan of the idea that WP should make mathematics completely accessible to anybody who has the barest minimum of background necessary to understand a given topic, yet should also give as much rigour, detail and comprehensiveness as would satisfy the most demanding mathematician. Dmharvey File:User dmharvey sig.png Talk 21:58, 5 Jun 2005 (UTC)

"mirror" vs "reflection axis", and other things

Hi KSmrq,

First, just want to say thanks for your work on Wallpaper groups and Euclidean plane isometry. It's nice not to be the only person working on something. When I look around on the web for other articles on this topic, I think it is possible for the wikipedia article to become the definitive resource. But it will take a lot of work and time. (Just found out yesterday that we'll need to wait about 40 years or so for Escher's work to become copyright-free... oh well....)

Ain't it grand? So many times with technical writing we work in solitary confinement; not here. And speaking of copyrights, there was a comment that many of the wallpaper images came from the Grammar of Ornament; is there a potential problem?

The author of Grammar of Ornament died in 1874, so the copyright has well and truly expired in all jurisdictions. Dmharvey File:User dmharvey sig.png Talk 28 June 2005 10:48 (UTC)

To business: want to discuss some terminology on these pages. I've noticed you've used the term "mirror" quite often. There's a little ambiguity here. Sometimes you use "mirror" to mean the isometry itself, and sometimes you use it to refer to the axis of reflection. I think it might be better to stick to one meaning, or at least make it clear somewhere that it can be both. Perhaps the term "mirror" should be introduced right near the beginning, where "reflection" is defined. Also, sometimes it seems that "mirror" includes glide reflections, and sometimes it doesn't. I've tried to distinguish my use of "reflection" and "reflection axis" rather carefully.

The reason I am a bit hesitant is that it has been many years since I've seen a book on this topic, and I'm not sure whether "mirror" is used at all in the literature (including stuff aimed at non-specialists), or whether you are simply using it to make the material more palatable.

What's your take on this?

I hadn't noticed a conflict between meanings of mirror. I'll check and try to clarify where necessary. In the orbifold notes at the Geometry Center the term mirror is used often, with emphasis on the idea of a "mirror string", for example. A mirror as transformation unambiguously selects a line of fixed points, which in the physical world would be the (one-sided) mirror itself. If we want to refer to the line only, we may call it a mirror line. Likewise, the mirror line uniquely determines the mirror transformation.

---

OK, I've reviewed my contributions on wallpaper groups and Euclidean plane isometry. My use of the term mirror seems to be consistent, as I read it. The meaning is always a geometric line implying a reflection isometry. By itself, a mirror (line) cannot imply a glide reflection, only a reflection. In a symmetry group, a mirror line parallel to a translation inevitably generates a glide as well; however, we call it a mirror line if we have mirror symmetry without translation. We only label a line a glide axis if it does not allow reflection without translation. Still, if you find a particular sentence or paragraph that particularly troubles you, point it out. However, we should probably put such discussions on the talk page for the article in question, since later editors are unlikely to find their way to my talk page.

BTW do you have a reference for where Conway introduced orbifold notation? Thanks for writing that section, it's great.

To be more precise, Conway's notation applies to 2-orbifolds. As you probably know, a great deal of interesting and useful mathematics circulates informally long before it achieves publication. Mathworld cites Zwillinger, CRC Standard Mathematical Tables and Formulae, 1995. Goodman-Strauss refers to a talk documented in 1993, but given often before that. And these Oak Ridge Crystallographic Topology pages give the earliest specific citation I've found in a brief web search:

• J. H. Conway, "The Orbifold Notation for Surface Groups", in Groups, Combinatorics & Geometry, M. Liebeck and J. Saxl, Eds., Cambridge University Press, pp. 438-447 (1992).

Yes, I found that reference and pulled it out of the library. Conway states in it that this is the first place the notation is used; I find no reason not to believe him. The book is a record of the proceedings of the L.M.S. Durham Symposium on Groups and Combinatorics, July 5-15, 1990. Dmharvey File:User dmharvey sig.png Talk 28 June 2005 10:58 (UTC)

Finally, is the term "rosette group" the correct name for what I called the "two-dimensional crystallographic point group" (under Wallpaper group#The independent translations condition)?

Close, but I think not. A crystallographic point group includes the restriction of lattice compatibility; a rosette group is only required to be discrete (and hence finite). Thus D₈ would be rosette, but not crystallographic. Consider what the chemists might say if we were talking about a single molecule in 3D; the molecule has point symmetries with no lattice restrictions. Because you specifically said "crystallographic point group", we have a distinction.

In speaking of ornaments, the 2D pattern groups seem to be called wallpaper, frieze, and rosette, names that make sense in that context. Frieze may also be replaced by strip or border. Rosette groups get far less mention, at least by that name; but I hesitate to say point group precisely because of the crystallographic confusion. Hubcaps (aka wheel covers) are a popular teaching tool. KSmrq 2005 June 28 09:42 (UTC)

Thanks, that's very interesting. You seem to know a lot about this stuff. I just pulled out a few books, maybe I'll look over them the next while so I can write with a little more authority! :-) Dmharvey File:User dmharvey sig.png Talk 28 June 2005 10:58 (UTC)

I've enjoyed playing with the mirror ideas previously, though more in a 3D setting. A friend runs a rock shop and an amateur rockhound group, and I wanted to make the mathematics more accessible. The mirror approach is the simplest I've found in the literature I've examined. So much of what we learn today is based on coordinates and formulae that the pure geometry is lost.

I'm tinkering (in SVG) with an illustration of translation addition, along with other isometry images; it's pretty to see what can be shown without equations.

And I think it's good to stimulate that part of the brain. Apparently Hilbert and Cohn-Vossen thought so! Conway, Doyle, Gilman, and Thurston liked the idea enough to use the same title for a summer workshop and a Princeton course, "Geometry and the Imagination". That's pretty good company. KSmrq 2005 June 28 12:26 (UTC)

Dmharvey File:User dmharvey sig.png Talk 11:57, 26 Jun 2005 (UTC)

superscript template

That superscript template you're using doesn't look very good on my browser (either Safari or Mozilla (mac)). The superscripted character is quite a long way from the base character. But honestly I've had enough of this discussion. :-) Dmharvey File:User dmharvey sig.png Talk 6 July 2005 19:47 (UTC)

mathbot links

Please note that it was not my bot which made the link to finite in crystallographic restriction theorem. But I agree that the links to positive number and negative number being a bit silly. I will not link to those anymore.

Did you find useful any of the other links my bot made? You can reply here to keep the conversation in one place. Oleg Alexandrov 15:47, 18 July 2005 (UTC)

Marginally. I was too annoyed to rip them all out, as I had already made a number of substantial edits before I noticed the bot additions. I spend hours writing and illustrating, and thinking carefully about what to say and what to omit. This is Wikipedia, where anyone can edit, but I'd strongly prefer a comparable amount of care go into modifying an article. The bot additions are clumsy and heavyhanded. With wise human oversight, suggestions of links could be helpful; but, for example, I had included links for rotation and for symmetry in the opening sentence, yet the bot added a link in the second paragraph for the phrase rotational symmetry. The link for determinant is reasonable. But we must consider the reader. The higher dimension generalization is aimed at a more sophisticated reader, who surely does not need a link for integer! Wikipedia guidelines caution about overlinking, which the bot blatantly ignores. I don't appreciate cleaning up after it. But I do appreciate you asking and trying to be helpful. Thanks. KSmrq 06:45, 2005 July 19 (UTC)

Good points. You made me realize that the linking operation can't be done with a bot, and that is very much appreciated. For future reference however, if you don't agree with something, a message on the talk page (say my talk page) would be much more helpful than an (annoyed) edit summary. This because it was rather an accident that I saw your comment; one can't possibly have on the watchlist all the pages a bot can operate on, and besides, information in the edit summary gets obscured as soon as there is a more recent edit summary.

I saw you removed some of the links while kept the other. I assume you used your judgment of what is helpful and what is not, so I will not attempt to remove the ones you left. Cheers, Oleg Alexandrov 11:47, 19 July 2005 (UTC)

Manifold

As I wrote on Talk:Manifold/rewrite, I think it is best if we let it rest for a week and calm down a bit. It would take me quite some time to react on the points you and Markus raise with the required care and I am afraid the situation would get out of hand before, so please take a rest and work on something else. See you in a week, Jitse Niesen (talk) 22:34, 26 July 2005 (UTC)

I appreciate your concern. I was trying to post a detailed response to Markus and noted at the end that I had used a great deal of emphasis. :-)

You'll likely have noticed I did take a break earlier. You cannot know I composed a message for your talk page before I added my comments to Markus on Talk:Manifold/rewrite. However, I did not feel right involving you, and decided I should address Markus directly. Since you have no prior history with me, I should inform you that I've been on the internet for decades, and seen flame wars. I do my best to turn the talk more productive, to improve the "signal to noise ratio", as it were. It is my intention to do that with Markus as well, though we do seem to have a communication barrier.

That said, I'm not convinced you have chosen the best route forward. I don't like to let misunderstandings fester, which is what I fear will happen. I suspect, from various hints, that Markus has been upset ever since my first edit. Thus he pauses briefly then reverts, not literally, but in the sense that the forward progress is discarded. I have tried hard not to do that, but rather to incorporate stated (and unstated) concerns in each new draft. For naught.

Thus I decided to confront the issue head-on, fully aware that some flames might fly. I don't want the flames, I don't like them, and I don't think they are helpful. But neither is it helpful to pretend strong emotions don't exist when they are clearly affecting behavior. I see a page that is nearly stalled, and I see Markus' behavior as the main factor. It is hard to confront someone, and almost impossible to do it without unintended side effects. I suppose I'm willing to do it because of the "never again" idea associated with the Holocaust; if we don't speak up early we'll have much worse to deal with later. Much as I hate confronting Markus myself (and I really do hate it), I cannot in good conscience ask someone else to do it for me. So I killed the message I was composing for your talk page, knowing what I had to do.

Frankly, if it were only a matter of the manifold article, so what; one weak piece of writing on all of Wikipedia is a drop in the ocean. For that matter, Wikipedia itself is only one drop in the larger web. But I've seen it too many times; I know where the road leads. If the behavior is allowed to repeat without correction, it grows stronger and more destructive. I saw repeated expressions of discomfort from others, yet no one willing to step forward; that's quite common. I do it because I'd rather confront Markus now so I don't have to deal with worse later. But if you want to take it on yourself, please do so. I'm more than happy to let someone else do the confronting, so long as it does get done. The main difficulty is that I don't know that someone else can represent my concerns. To that end, here are excerpts from the response I was trying to post for Markus when you froze the page:

• You ask "… what good is it to feature an incorrect article?" Sigh. Do you really expect that every article on Wikipedia is 100% correct? Even the ones you have worked on? From time to time I have read featured articles and made corrections. Are those articles worthless? Again I insist, you are missing the bigger picture. It is quite possible to write an article that satisfies your sense of correctness, yet which is unreadable. What is the good of that? I use a simile, which means I say "is like", using colloquial English in an introduction, and you can't live with it. That's an absurd demand for "correctness"!

• I am more familiar than you with what manifold means in English. It does not mean repetition, and I never claim so. Nor do I claim that Riemann uses Mannigfaltigkeit to mean repetition. The words are not false friends, as you claim; but that's beside the point. I'm not giving a definition; I'm not giving a translation. I'm giving a mnemonic, a way to help people associate the idea with the word. Somehow that eludes you. We can go over Riemann paragraph by paragraph, line by line, and for no gain. I can see what he's getting at; you cannot seem to see what I'm getting at.

• My frustration is evident in the number of times I've used various forms of emphasis. Let me just close with this thought: Really great mathematics is drawn from insight, not pedantry. Consider Bishop Berkeley's critique of Newton's fluxions, and ask yourself if that means Newton was a poor mathematician. We may publish to different standards today, but we can only hope to think with Newton's insight. Berkeley is a footnote, Newton the main text. If I had to choose, I'd rather inspire a Newton than a Berkeley. Fortunately, this is a false dichotomy; we can have both, if you will only let both live.

Well, that's more than enough for now. I promised to fill in another section of Wallpaper group. Thanks for stopping by, and good luck. KSmrq 00:31, 2005 July 27 (UTC)

"German pride" apology

Greetings. On the manifold/rewrite talk page I made a remark referring to German pride. It has been brought to my attention that such a remark could be offensive in the context of German culture. Please let me assure you I intended no offense, and sincerely apologize if my attempt to be friendly may have backfired. I will apologize on the page itself when it is unfrozen, but I am mortified at my blunder and did not want to wait until then to speak to you personally about this one specific issue. KSmrq 22:10, 2005 July 30 (UTC)

Thank you for your apology. In fact I felt a little bit offended and didn't realised it was an attempt to be friendly. I really hope we can work something out satisfying both of us. Markus Schmaus 15:57, 31 July 2005 (UTC)

Graphics

How do you make your SVGs? With what program? Thanks, Markus Schmaus 12:06, 7 August 2005 (UTC)

The source SVG files I make with a text editor. I have tried Inkscape, but so far it falls short of my desires. My development loop is to edit the source, then render with Adobe's browser plugin. Once I am satisfied with the appearance, I use Batik to produce a PNG. Finally, I add text information to the PNG, possibly reduce the colors or alpha for compression, and place it on Commons.

For some illustrations I have used external calculations, as from a symbolic algebra program, to assist with numerical details. My content is primarily mathematical, not artistic, so this is feasible. Also, I have a great deal of experience with computer graphics, which makes it easier for me to work in this primitive way. In the past, I preferred to make illustrations with a commercial program called Canvas. However, I lack a modern version that can produce SVG output.

For the Web, I confine myself to W3C standards: SVG, PNG, JPG, XHTML, MathML, CSS. Beyond that, I look for cross-platform, cross-browser, and free or open-source solutions.

A circle manifold chart based on slope, covering all but one point of the circle.

Example. To make the illustration of circle-slopes-as-manifold-chart, I relied on two familiar Pythagorean triples, (3,4,5) and (7,24,25), which yield simple and exact decimal coordinates (0.6,0.8) and (0.28,0.96). I distributed the values relatively evenly around the circle, leaving room for the interior triangles and their labels. I deliberately included antipodes 1/3 and −3, both to stimulate curiousity and to provide insight into the t = 1/s transition. The pair 3/4 and 4/3 subtly suggest reciprocals occupy mirror positions. I placed the labels at the point positions, then adjusted them for clearance. I chose a sans-serif font face that had the Unicode fractions I needed. I chose a font size that would be readable in the thumbnail. For the segment labels I used decimal fractions at a smaller size, both to distinguish them and to fit. The colors (red, green, yellow, blue) are sRGB values I calculated based on published research results on human vision. I chose line thickness, dot size, and color placement to harmonize with the previous illustration. The colors of the blue and green dots are hard to distinguish, as predicted by vision theory; but I felt that was less important in this illustration. I adjusted the dasharrays to get clean corners. I displaced the horizontal lines vertically up and down by half a line-width so they would not overlap. And so on.

In other words, the appearance of the figure has very little to do with a program, but a great deal to do with my attention to (obsession with?) detail, and with my choices based on experience in mathematics, graphics, and typography. I cannot in good conscience recommend this strategy to others; it is time-consuming, and requires an uncommon background. KSmrq 20:53, 2005 August 7 (UTC)

Thanks for your answer. I allmost suspected, that you do your SVGs with a text editor only. I did some research on the web and found a geometrical construction program which might be more appropriate for me.

By the way, it took me pretty long to grasp the above example. Maybe something like

<?xml version="1.0" encoding="utf-8"?>
<svg width="1014" height="592">
<ellipse cx="505.12020519966717" cy="296.47827308529054" rx="95.72940535020797" ry="95.72940535020797" style="stroke:rgb(0,0,0);fill:none;stroke-width:3"/>
<line x1="409.3907998494592" y1="296.4782730852906" x2="600.8496105498751" y2="105.0194623848746" style="stroke:rgb(180,0,0);stroke-width:1"/>
<line x1="600.8496105498751" y1="105.0194623848746" x2="594.0" y2="118.0" style="stroke:rgb(180,0,0);stroke-width:1"/>
<line x1="600.8496105498751" y1="105.0194623848746" x2="587.0" y2="112.0" style="stroke:rgb(180,0,0);stroke-width:1"/>
<line x1="409.3907998494592" y1="296.4782730852906" x2="600.8496105498751" y2="392.2076784354985" style="stroke:rgb(0,0,178);stroke-width:1"/>
<line x1="600.8496105498751" y1="392.2076784354985" x2="586.0" y2="390.0" style="stroke:rgb(0,0,178);stroke-width:1"/>
<line x1="600.8496105498751" y1="392.2076784354985" x2="590.0" y2="382.0" style="stroke:rgb(0,0,178);stroke-width:1"/>
<path d="M 406.0 293.0 H 411.0 V 298.0 H 406.0 Z" style="fill:rgb(0,124,0);stroke:rgb(0,124,0);stroke-width:1"/>
<line x1="601.0" y1="1309.0" x2="601.0" y2="-718.0" style="stroke:rgb(0,0,0);stroke-width:1"/>
<path d="M 598.0 102.0 H 603.0 V 107.0 H 598.0 Z" style="fill:rgb(180,0,0);stroke:rgb(180,0,0);stroke-width:1"/>
<text x="606.8496105498751" y="123.0194623848746" style="font-size:0;fill:rgb(180,0,0);font-weight:normal">1</text><path d="M 598.0 389.0 H 603.0 V 394.0 H 598.0 Z" style="fill:rgb(0,0,178);stroke:rgb(0,0,178);stroke-width:1"/>
<text x="606.8496105498751" y="410.2076784354985" style="font-size:0;fill:rgb(0,0,178);font-weight:normal">1/2</text><path d="M 502.0 198.0 H 507.0 V 203.0 H 502.0 Z" style="fill:rgb(180,0,0);stroke:rgb(180,0,0);stroke-width:1"/>
<path d="M 560.0 370.0 H 565.0 V 375.0 H 560.0 Z" style="fill:rgb(0,0,178);stroke:rgb(0,0,178);stroke-width:1"/>
</svg>

or

<?xml version="1.0" encoding="utf-8"?>
<svg width="1014" height="592">
<ellipse cx="570.0" cy="296.0" rx="3.0" ry="3.0" style="stroke:rgb(0,124,124);stroke-width:1;fill:none"/>
<ellipse cx="507.0" cy="296.0" rx="63.375" ry="63.375" style="stroke:rgb(0,0,0);fill:none;stroke-width:1"/>
<path d="M 478.0 235.0 H 483.0 V 240.0 H 478.0 Z" style="fill:rgb(0,0,0);stroke:rgb(0,0,0);stroke-width:1"/>
<line x1="507.0" y1="1309.0" x2="507.0" y2="-718.0" style="stroke:rgb(0,0,0);stroke-width:1"/>
<ellipse cx="507.0" cy="255.0" rx="3.0" ry="3.0" style="fill:rgb(180,0,0)"/>
<ellipse cx="507.0" cy="255.0" rx="3.0" ry="3.0" style="stroke:rgb(180,0,0);stroke-width:1;fill:none"/>
<ellipse cx="444.0" cy="296.0" rx="3.0" ry="3.0" style="stroke:rgb(0,124,124);stroke-width:1;fill:none"/>
<ellipse cx="507.0" cy="199.0" rx="3.0" ry="3.0" style="fill:rgb(0,0,178)"/>
<ellipse cx="507.0" cy="199.0" rx="3.0" ry="3.0" style="stroke:rgb(0,0,178);stroke-width:1;fill:none"/>
<line x1="443.625" y1="296.0" x2="481.41930190822734" y2="238.0170843253154" style="stroke:rgb(153,153,224);stroke-width:1"/>
<line x1="443.625" y1="296.0" x2="507.0" y2="198.7719234024745" style="stroke:rgb(0,0,178);stroke-width:1"/>
<line x1="507.0" y1="198.7719234024745" x2="503.0" y2="213.0" style="stroke:rgb(0,0,178);stroke-width:1"/>
<line x1="507.0" y1="198.7719234024745" x2="495.0" y2="208.0" style="stroke:rgb(0,0,178);stroke-width:1"/>
<line x1="570.375" y1="296.0" x2="481.41930190822734" y2="238.0170843253154" style="stroke:rgb(225,153,153);stroke-width:1"/>
<line x1="570.375" y1="296.0" x2="507.0" y2="254.69104104953345" style="stroke:rgb(180,0,0);stroke-width:1"/>
<line x1="507.0" y1="254.69104104953345" x2="521.0" y2="259.0" style="stroke:rgb(180,0,0);stroke-width:1"/>
<line x1="507.0" y1="254.69104104953345" x2="516.0" y2="266.0" style="stroke:rgb(180,0,0);stroke-width:1"/>
</svg>

might be easier to understand.

Sorry for cluttering your talk page. The SVGs don't use all the things you mentioned above, but just illustrate what I'm thinking about. Markus Schmaus 21:55, 7 August 2005 (UTC)

If we're going to talk about the specifics of this illustration much, we should move the conversation to the project. Briefly, yes, this mapping is equivalent to (scaled) stereographic projection, and that's simpler to illustrate. (The factor of 1/2 might be awkward.) But to do so would fight the point I make in the text, that charts need not be based on geometric projection. We don't want readers thinking of homeomorphisms or diffeomorphisms or manifold charts in general as embedded geometry; this example is (among other things) a small step in that direction. It's not such a bad thing if a little mental effort is required to understand the slope chart, because we soon introduce much more abstract examples where imagination is essential. I'm hoping high school students have already learned about the slope-intercept description of a line. (True in my time, but maybe no longer. Sigh.) Also, this particular circle parameterization is heavily used in applications; it is important in older algebraic geometry, and is one of the motivating examples for NURBS.

An alternative would be to drop the four-chart description and go straight to stereographic projection. KSmrq 23:51, 2005 August 7 (UTC)

XML-safe WP for MathML

Congrats on admin-ship. Dmharvey says you're the point man for the mathematics-writing community's efforts to have WP generate valid XML so that MathML can be enabled. It seems like a good idea for other reasons as well; I'd really like to see this happen. How's it going? Anything you could use help with? --KSmrq^T 23:36, 2005 August 27 (UTC)

Thank you for your interest, and for pointing out some documents on meta some time ago. The main problems at the moment are:

• As you know, Internet Explorer does not accept any of the XML media types, so we need to find a way to work around this. We might either have different media types depending on the browser (I don't know how much needs to be changed to achieve this) or embed MathML in a non-XML document (we need to evaluate the UniWakka trick, using different media types in the HTTP header and the HTML meta tag, and Jipsen's trick, using JavaScript to rewrite the HTML depending on the browser).
• I'm trying to get a test installation of MediaWiki running (currently at Berlios and Sourceforge), so that we can showcase the current state of affairs and test different approaches, but I haven't succeeded yet (it doesn't help that I'm now at my parents' place working via a modem).
• A lack of feedback from the developers of WP.

Any help on these points would be very welcome indeed. Do you have any experience with putting MathML on the web? By the way, what is your interest, MathML specifically, XML in general, or perhaps even more generally compliance with standards? -- Jitse Niesen (talk) 21:33, 28 August 2005 (UTC)

This page is interesting reading about MIME-type issues. Ian Hixie, a noted W3C expert, wrote about many of the issues some years ago. Note that Javascript/ECMAscript can break if the MIME-type changes. Perhaps IE7 will support "application/xhtml+xml"; that would be a Good Thing.

My interest is multifaceted. I have written a number of things using XHTML+MathML and CSS, all of which validate and look fine in Mozilla. I have had little interest in spending my personal energy compensating for Microsoft's misbehavior; for my own pages, use a standards-compliant browser or lose. WP and commercial web sites must cope.

What I really want is to be able to put mathematics on the web in a decent way, especially in a wiki. Currently MathML holds the most promise. MathML syntax is absurdly bloated, layout could use improvement in places, and fonts are awkward for a little longer; but otherwise it's great. I've both used and written mathematics typesetting systems, so have an appreciation of their strengths and weaknesses — and of the challenges they face — beyond that of most folks.

I'd be curious to talk to developers myself. Typically, folks work on things that specially interest them, that offer big rewards for little effort, or that someone insists be treated as a priority. Many programmers have grown up worshipping Microsoft; others feel it's a waste of timing fighting. Either way, if IE flouts W3C standards then developers may want to direct their efforts in more productive directions, especially if they themselves can be satisfied with subscripts and superscripts. One web-site author had this to say.

I prefer standards-compliance even when the standards aren't the greatest. That does not appear to be a strong force in MediaWiki development. Unfortunately, it's considerably harder to add it later.

We need to know who we're dealing with and what motivates them. And we need a champion; a developer who is strongly committed to making the Right Thing happen. It is so discouraging to "work around" Microsoft and to clean up old code that without a champion it probably won't happen. For my own life and career, I have found Everett M. Roger's ideas on diffusion of innovations a valuable guide. --KSmrq^T 00:59, 2005 August 29 (UTC)

Mathematics and God

KSmrq, can you please justify these edits you made to Mathematics and God? I'm particularly wondering why you removed the Hardy tidbit about rain.

FYI: the "minor edit" tag should generally only be used for purely prose edits, see Wikipedia:Minor edit. You also shouldn't delete content without explanation (unless its patent nonsense, etc).

SpuriousQ 02:46, 30 August 2005 (UTC)

hyperlinks in equations

Hi KSmrq, I read your comment about "scary" hyperlinks in equations on the village pump proposals page, I'd like to discuss this a bit further, but I thought it was getting a bit off topic for that post so I thought I should try here instead.

My question is, why do you think it's so scary? I happen to think it could be quite useful in certain situations.

Take something like $x^{2}\equiv -1{\pmod {p}}$. If this equation appeared in the article on modular arithmetic, then surely I agree with you, the surrounding article should be explaining very clearly what each symbol means. However, if it appeared in an article on quadratic reciprocity, we might prefer to simply make the $\equiv$ symbol into a link to the modular arithmetic article, and not clutter things by again explaining the meaning of each symbol. Someone wanting to learn about quadratic reciprocity may well need some reminding about the meaning of the symbols. But if the equation appeared in an article on class field theory, we might well not make any link at all, since the intended audience should already know the meaning of the symbol. Symbols in equations can be "defined" or "undefined" depending on the intended audience, just like any word in any other article. Dmharvey File:User dmharvey sig.png Talk 23:58, 30 August 2005 (UTC)

Not that you asked me, but I find hyperlinks in equations ugly. I think the only place hiperlinks look good is in plain text, and even there when they are not in bold. Oleg Alexandrov 00:24, 31 August 2005 (UTC)

Hi there oleg, you seem to be implying that you've seen some hyperlinks in equations before. I don't think I've seen any before. Can you show me some so I can judge for myself? What if they were in the same colour, no bold, no underline -- almost invisible? Dmharvey File:User dmharvey sig.png Talk 00:59, 31 August 2005 (UTC)

Wherevere I saw them, I removed them, so I have no examples. :) Seriously, don't remmeber, been a while. That they can be almost invisible is what I also dislike. Ideally, I prefer

One has 5 ≡ 1 (mod 4), see modular arithmetic

to

One has 5 ≡ 1 (mod 4)

But that's just me. Oleg Alexandrov 01:09, 31 August 2005 (UTC)

yeah, I guess I see your point. I'll have to think about it a bit more. Dmharvey File:User dmharvey sig.png Talk 01:47, 31 August 2005 (UTC)

I see you guys have started the conversation without me. ;-)

Let's start with a simple example, "2+2=4". Most browsers will display the link in blue and underlined, so "+" looks like "±", which makes no sense. Or consider the dictum "For all primes p>2, p is odd." Now the underline changes ">" into "≥", and makes a true statement look false. Even without these disasters, links are a distraction we do not need in the middle of a formula. I hesitate to use footnotes on printed pages for the same reason (nevermind how horrible they are on the web or — gasp! — in the midst of a formula). If some of my readers might have to stop in the middle of a formula to look up a symbol, I probably haven't done my job well as a writer; I shouldn't put them in that position. For example, quadratic reciprocity depends critically on ideas of modular arithmetic, and I've got no business throwing equations at a reader before I've laid the foundation. In summary, a hyperlink in a formula is bad because:

1. it alters the notation,
2. it distracts the reader,
3. it indicates poor writing.

I don't use them, and if I see them I'll want to rewrite to eliminate them. --KSmrq^T 01:50, 2005 August 31 (UTC)

OK, I think I am starting to agree with both of you. However, I can't shake the feeling that there is no difference in principle between hyperlinking symbols in equations and hyperlinking words in a sentence. Assuming that we don't get the notational disasters alluded to above, what is the underlying difference? I can't seem to explain it to myself satisfactorily. Dmharvey File:User dmharvey sig.png Talk 02:20, 31 August 2005 (UTC)

I don't think there is an difference in principle. It is a matter of esthetics as far as I am concerened. Links embedded in formulas look ugly to me. Oleg Alexandrov 03:12, 31 August 2005 (UTC)

I can make a case that careful use of hyperlinks ameliorates all three complaints listed above. Rarely will underlining and blue coloring change the meaning of a word or phrase. For that to happen, color and underlining must have other meanings introduced. Distraction is a real possibility if links are used thoughtlessly and too often. However, writing that uses links in a definitional context where the reader is meant to look elsewhere if necessary can take care of both distraction and quality. Compare to the use of allusion, where used properly a reader has an enriched experience drawing on prior knowledge, but used improperly the meaning is lost. For example, if a Trojan horse attacks your computer it is acting through hidden treachery, as in Virgil's story of how the seige of Troy was won by the Greeks through their gift of the original Trojan Horse. And if you know the story, you'll understand the connection without following the links, just as you will understand "Beware of Greeks bearing gifts." (Spyware, anyone?) So in mathematical writing we should set out the context — especially required prior knowledge — before we focus exposition into a formula; links in a formula are always too late. The same is not true of text links. --KSmrq^T 06:09, 2005 August 31 (UTC)

Binomial coefficient

(I decided to move this to Talk:Binomial coefficient to see what others have to say. Oleg Alexandrov 00:46, 7 September 2005 (UTC))

Please vote

Hello. Please vote at Wikipedia:Featured list candidates/List of lists of mathematical topics. Michael Hardy 23:04, 14 October 2005 (UTC)

Boolean algebra

Ok, it's time for some of that gentle criticism you solicited on your main page...

Continuing to make changes to the intro, when Trovatore, Celestianpower, myself, and now Charles Matthews have asked you to stop, is not helpful. We have posted our objections to your version and support for Trovatore's version on the talk page and/or in history comments. Your Hasse diagram looks like it might be useful, but in the body of the article. Such complex material has no place in an intro, which should be written for a general audience. StuRat 13:19, 29 October 2005 (UTC)

Thanks for stopping by. My view of both facts and interpretation in these matters is so radically at odds with yours I see no point in discussing either. Nevertheless, I appreciate what appears to be a sincere effort at affirming our common humanity by speaking with me. Charles sought allies in what is apparently an on-going feud; now, too late, I see why. --KSmrq^T 16:17, 29 October 2005 (UTC)

I agree there is no pt in discussing our views any further. However, I do expect you to respect the consensus, especially when it consists of people on both sides of this issue. It now appears you are willing to do so, and I thank you for that. StuRat 16:22, 29 October 2005 (UTC)

I do not respect a consensus, because I do not think one exists. What I do respect is my time, which I do not wish to waste further on what appears to be a hopeless cause: jointly writing an opening that is both widely accessible and technically sound. --KSmrq^T 16:53, 29 October 2005 (UTC)

peace

Hi KSmrq,

I just want to say that I think you did a nice job on the intro. It's just not going to work in the current climate. It strikes me that this whole mess is partly a result of a linguistic accident; namely, that the standard term for the structure is the same as the name by which others call a discipline. If the structure were standardly called a "Boolean lattice" or "Boolean ring" I don't think we'd be having these difficulties.

The picture is very nice and I think it should be used. I do have one suggestion: Could the second row (with the doubletons) be reflected left-right? Then we could point out that every element is mirror-reflected from its complement, and describe meet and join in terms of the graph as well. --Trovatore 19:15, 29 October 2005 (UTC)

I also think the Hasse diagram should be used, just in the body of the article, not in the intro. And I think you are correct that it would not have been an issue had the article been under a more obscure name. While technically the intro to all articles should be accessible to the general public, if no member of the general public ever stumbles upon the article, then the issue never comes up. StuRat 19:21, 29 October 2005 (UTC)

A ray of hope! Accidental, but consider: All the discussion about what to name things might be handled by moving this article to Boolean lattice. The mathematicians will cope, and the engineers can hit a disambiguation page (or header) for Boolean algebra that makes them happy, too. Yes, articles usually live under their most common name; but if the alternative is the status quo …

That works for me, but convincing all the mathematicians to move it to Boolean lattice and make Boolean algebra into a disambiguation page may well be more difficult than the compromise we've worked out on the intro. If you want to make the suggestion on the talk page, I would be glad to lend it my support, however. StuRat 22:41, 29 October 2005 (UTC)

I have suggested many times moving the current Boolean algebra page to Boolean algebra (algebraic structure). I'm not as happy about moving it to Boolean lattice, because AFAIK virtually all the references in the literature refer to the structure as a Boolean algebra, so I think it's confusing to use a so-much-rarer name. --Trovatore 23:00, 29 October 2005 (UTC)

I prefer Boolean lattice, as Boolean algebra (algebraic structure) is still close enough that it may attract people looking for the content currently under Boolean logic, so would still need a general audience intro. StuRat 17:01, 30 October 2005 (UTC)

You're not going to type "Boolean algebra (algebraic structure)" by accident; you'll find it only by links, for example in whatever dab notice/page we put up. And you could find "Boolean lattice" the same way, since we certainly have to have an easy way for people to find the article after typing "Boolean algebra". So I don't think the claimed distinction holds. --Trovatore 17:51, 30 October 2005 (UTC)

Yes, but the folks looking for Boolean logic will get to the new disambiguation page at Boolean algebra, and won't be able to tell which they want from the names, so will end up in the wrong place by following the wrong link. If the name was Boolean lattice, then they would know that's not what they want. Under your suggestion, they might think "I was looking for Boolean algebra, and that article has it in the name, so that must be the one I want." StuRat 18:02, 30 October 2005 (UTC)

My proposal would actually be to move Boolean logic to Boolean algebra, and put a dab notice at the top for the algebraic structure. That's mainly because I also think "Boolean algebra" is the most common name for Boolean logic, and I can't think of anything good to put in parentheses for it. But hopefully it should take care of your concern as well. BTW we shouldn't really be having this conversation on KSmrq's talk page; it pings him every time there's an edit and clutters the thing up. --Trovatore 18:08, 30 October 2005 (UTC)

I think this is fine for the discussion, since he is the one who reintroduced the idea of the rename and has an interest in it. Your suggestion is a good one, but again, I can't see how you would ever convince your fellow mathematicians to make such a change. There seems to be a strong feeling among the group that rigourous theoretical mathematics is the only valuable subject, and all others are beneath mentioning. Giving the main page away would upset them no end. StuRat 18:16, 30 October 2005 (UTC)

I thought I did a nice job on the intro myself; how many votes do I get to cast? ;-)

Ah, well. Feel free to canabalize it for parts. As for the picture, I made it as I suggested, with Graphviz — specifically "dot" — and the layout is automatic. It's pretty smart, because if you were actually to draw what you suggested, the lines would be much more tangled. But you could certainly use colors or dash patterns or some such for your purposes. The present source file is trivial:

digraph HasseDiagram {
  graph [ratio=0.75, bgcolor="#ffffff"];
  node [fontname="Arial"]
  "xyz" [label="{x,y,z}"];
  "yz" [label="{y,z}"];
  "xz" [label="{x,z}"];
  "xy" [label="{x,y}"];
  "x" [label="{x}"];
  "y" [label="{y}"];
  "z" [label="{z}"];
  "phi" [label="Ø"];
  
  edge [dir="back", arrowtail="empty"];
  "xyz" -> {"yz"; "xz"; "xy"};
  "yz" -> {"y"; "z"};
  "xz" -> {"x"; "z"};
  "xy" -> {"x"; "y"};
  "x" -> "phi"
  "y" -> "phi"
  "z" -> "phi"
}

I rendered a PNG with Batik to have ultimate control, but Commons accepts SVG directly now if you prefer. Perhaps one image could support all the text; if not, it would be simple to generate all the variations you like. For example, here's one way to show the law of the excluded middle in lattice form:

digraph HasseDiagram {
  graph [ratio=0.75, bgcolor="#ffffff"];
  node [fontname="Arial"]
  "xyz" [label="{x,y,z}"];
  "yz" [label="{y,z}"];
  "xz" [label="{x,z}"];
  "xy" [label="{x,y}",style="filled",fillcolor="#fad1c2"];
  "x" [label="{x}"];
  "y" [label="{y}"];
  "z" [label="{z}",style="filled",fillcolor="#d7cd99"];
  "phi" [label="Ø"];
  
  edge [dir="back", arrowtail="empty"];
  "xyz" -> {"yz"; "xy"} [color="#00b1be"];
  "xyz" -> "xz";
  "yz" -> {"z"} [color="#00b1be"];
  "yz" -> {"y"};
  "xz" -> {"x"; "z"};
  "xy" -> {"x"; "y"};
  "x" -> "phi"
  "y" -> "phi"
  "z" -> "phi"
}

Since Graphviz is open-source and available cross-platform, just grab a copy and play. --KSmrq^T 22:04, 29 October 2005 (UTC)

Graphviz

So I downloaded graphviz (for Debian stable), but dotty doesn't seem to work extremely well (labels don't show up; right-click brings up a menu but the menu doesn't do anything). I put together a file (for the free Boolean algebra with two generators, p and q) and figured out how to make a PostScript file, but I can't figure out how to get Unicode into the labels, so the symbols don't work. I also didn't see anything that said you could upload .dot files. Anyway here's the source if you want to see what you can do with it:

PS: I made a version without any unicode, a little awkwardly; you can see it at free Boolean algebra. --Trovatore 08:23, 11 November 2005 (UTC)

digraph HasseDiagramFree2 {
 graph [ratio=0.75, bgcolor="#ffffff"];
 node [fontname="Arial"]
 "false" [label="FALSE"];
 "pq" [label="p∧q"];
 "pnq" [label="p∧¬q"];
 "npq" [label="¬p∧q"];
 "npnq" [label="¬p∧¬q"];
 "p" [label="p"];
 "q" [label="q"];
 "piffq" [label="p↔q"];
 "nq" [label="(¬q)"];
 "piffnq" [label="p↔¬q"];
 "np" [label="(¬p)"];
 "pvq" [label="p∨q"];
 "qthenp" [label="q→p"];
 "pthenq" [label="p→q"];
 "npvnq" [label="¬p∨¬q"];
 "true" [label="TRUE"];
  
 edge [dir="back", arrowtail="empty"];
  "true" -> {"pvq";  "qthenp";  "pthenq"; "npvnq"};
  "pvq" -> {"p"; "q"; "piffnq"};
  "qthenp" -> {"p"; "piffq" ; "nq"};
  "pthenq" -> {"q"; "piffq"; "np"};
  "npvnq" -> {"nq"; "piffnq"; "np"};
  "p" -> {"pq"; "pnq"};
  "q" -> {"pq"; "npq"};
  "piffq" -> {"pq"; "npnq"};
  "nq" -> {"pnq"; "npnq"};
  "piffnq" -> {"pnq"; "npq"};
  "np" -> {"npq"; "npnq"};
  "pq" -> "false";
  "pnq" -> "false";
  "npq" -> "false";
  "npnq" -> "false";
  }

Good job. Unicode should be possible in two easy ways. The first is to use a text editor that handles UTF-8; the layout programs are supposed to be happy with UTF-8. The second is to use a placeholder character of the same approximate width during layout, to ask for SVG output, and then to edit the SVG to substitute the desired Unicode or an XML numeric character code. Commons now accepts SVG files directly, if you want to try that. You can preview or render SVG using Batik, or in most cases the latest Firefox (release candidate 1) can directly view SVG files. If you upload an SVG, you are at the mercy of the server's fonts and rendering. If you use Batik to make a PNG, you can use any font, such as Code2000, with any characters you may need. There is a "glyph" feature in SVG that allows you to draw a character, but that would be a painful last resort.

Anyway, looks like you've discovered the joys of GraphViz. I've found its input is easy and its output is appealing. Two suggestions:

1. You might want to kill the parens around NOT p and NOT q where they occur alone (on the center line).
2. If you give the graph a different aspect ratio, the graph may be able to spread out enough so none of the arrows have to curve. (This problem may also fix itself if you get the Unicode working.)

Also, if you do render the PNG yourself, use a resolution like 300 dpi with antialiasing. (Or render even larger and reduce smoothly to get the effect of antialiasing.) The Wikipedia server will create (and cache) smaller requested sizes as needed. This allows both screen and printed output to look good. --KSmrq^T 03:34, 12 November 2005 (UTC)

dot doesn't seem to work correctly with UTF-8, and without the parens around ¬p and ¬q it gave me a syntax error. I think it's basically just a little buggy. "dot -Tpng" produces PNG output directly; that's how I generated the file. --Trovatore 04:22, 12 November 2005 (UTC)

Gosper

My recollection is that Bill Gosper introduced the idea of telescoping. He is one of the pioneers of computer symbolic mathematics programs, having contributed to both Macsyma and Mathematica, for example. His web page [2] cites A calculus of Series Rearrangements, which might be the place to look. --KSmrq^T 01:52, 3 December 2005 (UTC)

What!!!??? How could he have introduced this idea if his life was so recent that he worked with electronic computers?? Michael Hardy 22:30, 3 December 2005 (UTC)

Series have been around a long time. I'm not intimately familiar with the history of who did what when, and I don't know what Bill would claim was his and what he dug up or adapted. But it's my impression that he was able to do remarkable new things with series, including telescoping — a term I first heard associated with his work. Obviously people had been rearranging series long before him, but perhaps not in the way he did it. These are vague memories including conversations over Chinese dinners from long ago. Examples of his contributions include Gosper's Algorithm [3], which was extended to "creative telescoping" [4]. A more extended discussion of telescoping and Maple is

• Abramov et al. "Telescoping in the context of symbolic summation in Maple". Journal of Symbolic Computation, v38 (2004), 1303–1326. (PDF)

Perhaps that paper, or its references (especially Lafon 1983), can pin down the history of the ideas or the terminology. My bigger point is that the telescoping series article omits important knowledge and references. I still think Gosper is a good place to start looking for more. It's not my specialty, so my comment is just a drive-by shooting on the talk page to stimulate improvements. --KSmrq^T 03:44, 4 December 2005 (UTC)

Gosper indeed did a lot of work on how to handle infinite sums on computer algebra systems. But as far as I know, he "only" made an algorithm that enabled computers to compute sums that mathematicians could already do (given enough time and motivation and a bit of ingenuity). The idea of telescoping sums must be centuries old; in fact, I wouldn't been surprised if it is older than the telescope. I learnt the term in high school, so it is rather basic. -- Jitse Niesen (talk) 04:09, 4 December 2005 (UTC)

Obviously that's a huge "only", like stating the Pythagorean theorem compared to finding a 3-4-5 right triangle. In any case, the Abramov article offers a wealth of content not found in the Wikipedia article. And I'd still like to know when and where the term "telescoping" was introduced. (I'm fairly confident my high school years predate yours, and I never heard the term; by that reasoning, it must be more recent. Or, more likely, the reasoning is unreliable.) --KSmrq^T 05:56, 4 December 2005 (UTC)

KSmrq, all of the sources you cite were published after I graduated from high school (in 1974), and I learned about telescoping series, by that name, in high school, and I think everybody does. And I'm pretty sure telescoping series were used by Euler in the 18th century. To suggest that they were introduced only in the last two or three decades is false and bizarre. Michael Hardy 21:50, 4 December 2005 (UTC)

Yes, I would be very surprised if Euler didn't know about telescoping. (But I don't have any hard evidence.) By the way, I never heard the term "telescoping series" until I came to the U.S., but I was certainly aware of the concept before then. Dmharvey 22:02, 4 December 2005 (UTC)