December 13, 2006

Communicating Thoughts on the Web

Posted by Urs Schreiber

In school, I remember, I got very upset when somebody once tried to teach me that no thinking is possible without language. While I think (with or without language?) that this is clearly wrong, it is clearly right that language greatly affects – and good language greatly facilitates – thinking.

Thinking without language is possible, but it is like computing without RAM: it is hard to think a complex thought without the ability of saving big sub-thoughts using a convenient address: a word. Or an equation. Or a diagram. Or a word for an equation or a diagram.

Even with lots of language, thinking just by yourself may be inefficient. Many a thought wants to be communicated and recycled once or twice until reaches a desireable form. At least for me, a blog like the one we are running here is a means to greatly increase the potential for thought exchange.

That requires language. And good language. In our business this means: it requires good means to express math on the web. s One of the marvelous things of this blog, for me, is the sophistication its administrator, Jacques Distler, has put and is putting into web-based math technology. I imagine that in a few years using equations and diagrams in electronic communication will be no less unusual than discussion with your colleagues in front of your office’s blackboard. But somebody has to make it real.

And it’s not as trivial as one might wish it were. It’s rather an entire research all in itself. Check out Jacques’s report on a conference Evolution of Mathematical Communication, where he gave a talk on on Blogging with MathML.

MathML is the communication protocol for electronic mathematical expressions that is at work behind the scenes when we transmit thoughts like

(1)$0 = e^{i \pi} + 1$

in $n$-Café-communication.

Interestingly, as Jacques mentioned in his talk, the discussion that is archived on the three blogs hosted by him, his own Musings, as well as the (now somewhat dormant) String Coffee Table and the $n$-Category Café here, now constitutes one of the largest collections of MathML on the web.

While I find nothing more convenient than being able to include proper LaTeX in everything I write here, with the output seamlessly embedded into everything else, there are still some technological hurdles that want eventually to be removed.

One is on the server side. The reason that there are so few weblogs with full WebTeX/MathML support like here becomes quite apparent once you follow Jacques’ frequent accounts on what kinds of problems he had to solve to make it work.

As a result, other scientific blogs, whose owners feel the desire of transmitting a formula over the web once in a while, try to resort to solutions like mimeTeX, as for instance Clifford Johnson over at Asymptotia did now.

It’s not at me to discuss the pros and cons of these different solutions in detail. All I’ll notice here is that most solutions I know so far have the one big drawback that they are restricted to a fixed subset of LaTeX. They won’t allow you to load your own packages. In particular, this means: little support for diagrams.

But, in this respect, mimeTeX has at least a slight advantage: it does allow picture environments. While not the same as things like xypic, this does allow to communicate thoughts of this form

$\Large\hspace{5}\unitlength{1} \picture(175,100){~(50,50){\circle(100)} (1,50){\overbrace{\line(46)}^{a}} (52,50){\line(125)}~(50,52;115;2){\mid}~(52,55){\longleftar[60]} (130,56){\longrightar[35]}~(116,58){r}~(c85,50;80;2){\bullet} (c85,36){q}~(c165,36){q} (42,29){\underbrace{\line(32)}_{a^2/r\;\;\;}}~}$

by typing the relevant LaTex directly (more or less) inline with the surrounding text. See the mimeTeX site for how to do this, if you want to use it here.

Of course there is always the, in a way, most primitive option: simply compile your LaTeX on your own machine as usual, convert it to a pdf and link to that. As John remarked recently (I cannot find the comment right now) this is, while by itself perfectly fine, for some funny psychological reason not as vivid a communication technique as having the LaTeX output directly on the web page.

To get that, of course, you can always turn the LaTeX output into gif and include that directly using the img tag.

To see the difference, notice that the following example will inevitably attract your attention, while you will probably have ignored this diagram - and its explanation - when I first linked to the pdf it appeared in #

You can do all this gif-conversion by hand, if you know how to. But there is also a little script freely available online, which facilitates and automates the task a little: TeX to GIF.

Posted at December 13, 2006 8:43 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1073

Diagrams

Given the ability to create pictures using any number of different programs (and then include them in your pages), I’m not sure that XYpic is the most attractive solution.

As you know, I’ve been using SVG figures on my blog for a long time. I happen to use Adobe Illustrator, but you might want to try InkScape. One of the many good things about SVG (unlike GIFs) is that, if worst comes to worst, you can edit them in a text editor. All of the figures on Sam Ruby’s blog are created in a text editor.

In Minneapolis, Roger Sidje claimed that Firefox either does, or would soon, support svg:foreignObject, which means that we could directly embed MathML in SVG (in XHTML). That would make for some really cool possibilities.

In the meantime, you might want to check out InkScape.

Posted by: Jacques Distler on December 13, 2006 2:41 PM | Permalink | PGP Sig | Reply to this

Re: Diagrams

I’m not sure that XYpic is the most attractive solution.

[…]

but you might want to try InkScape.

Thanks for the link! I’ll have a look at that.

What makes XYpic (and related) output to the blog desireable (for me) is that it allows me to simply copy and paste excerpts from my LaTeX documents to the blog.

But maybe you are saying I should better be using something like InkScape instead of XYpic even in my non-blog documents?

Posted by: urs on December 13, 2006 3:03 PM | Permalink | Reply to this

Re: Diagrams

They say Inkscape exports to Postscript and PDF, so I imagine you could use those for figures in your TeX papers as well.

That’s one of the things I like about Illustrator. I can prepare one figure, and export it to EPS, PDF, SVG and GIF.

Posted by: Jacques Distler on December 13, 2006 3:53 PM | Permalink | PGP Sig | Reply to this

Re: Communicating Thoughts on the Web

How do you feel about working out your ideas in public here? Are you ever inclined to hold some ideas back? With the kind of support you can expect from readers, does it change what you dare to set out to do?

Posted by: David Corfield on December 13, 2006 4:18 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

How do you feel about working out your ideas in public here?

I will try to write a reply to that later today.

But since you asked: I would eventually also be interested in the converse question: how do you feel about this strange behaviour of mine?

Posted by: urs on December 13, 2006 4:51 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

I don’t see it as strange at all. Right from the first my interest has been in a philosophy which justifies and requires that the formation of mathematical ideas be exposed. Historians would give their eye teeth (now what’s the German equivalent of that?) for a record, such as yours, of the research path of some major figure from the past. Some, like Faraday, have left notebooks, but there’s nothing like the interactive, conversational jottings to be found here. I only hope you feel you benefit from the exercise.

I wonder if you’ll eventually take on something of John’s more didactic style.

Posted by: David Corfield on December 13, 2006 6:59 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

I don’t see it as strange at all.

Thanks for saying so.

but there’s nothing like the interactive, conversational jottings to be found here.

I am far from doing anything with an eye on posterity, but what you mention here is one of the big advantages of all this blogging - for myself.

Often do I get back to my own entries and reread them, just to remind me of something.

For instance, in conversation with David Ben-Zvi over at Peter Woit’s blog, I realized that I was beginning to mix up things I had once known about geometric Langlands #.

The reason was, that when I was more actively thinking about this stuff a certain dictionary was beginning to emerge - but I never blogged it down. The result: it began to fade away.

So that’s why I now typed that recent entry. It’s a way of establishing language. Next time I will be able to think just of “that geometric Langlands dictionary” and either recall it or look it up - on a blog.

Posted by: urs on December 13, 2006 9:42 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

Hey Urs, wouldn’t it be cool if you could quickly write your physics thoughts, in LaTeX, into a little interconnected web-viewable wiki that you could even carry around on a USB memory stick? Would make for a neat augmented memory, notebook, and place to send people for reference, eh?

physicswiki

:)

Posted by: garrett on December 14, 2006 4:51 AM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

physicswiki

Interesting. Looks good!

Can you somehow integrate this into Wikipedia? (Maybe while still having it collected to carry it around on your USB stick? :-)

Would be a pity to write all these entries without them being linked to the larger Wikipedia context, which benefits from the power-of-a-thousand-eyeballs.

Posted by: urs on December 14, 2006 2:34 PM | Permalink | Reply to this

Re: physicswiki

Well, I thought a lot about using Wikimedia as the back end instead of Tiddlywiki, even to the point of setting up mySQL and PHP. But in the end I decided to go with the smaller and cleaner solution. If my intent was to build a database of notes larger than a gigabyte I would have gone with Wikimedia – but I don’t think I’ll be able to type a gigabyte over the course of my life!

And I wanted to be able to work offline, and just sync the local copy of my notes up to a server from wherever I was. The bizarre and cool thing about a tiddywiki site is that it exists as one web page. The downside of this is that it’s not the right tool for collaboration. But it makes for a great personal notebook.

Also, as technology develops, my notes are stored in human readable LaTeX text code along with some wiki formatting that will easily port. Porting anything to or from Wikimedia looked like a nightmare. Tiddlywiki also had the advantage of an easily customizable interface.

You are correct though in observing the problem that it’s unlikely anyone but me will look at my notes and offer corrections, because there’s as of yet no way for others to edit or add comments. Adding a comment button with a haloscan link off each note is an easy hack to fix that. But, at this point, I’ve kind of gotten use to not getting help from others unless I actively seek it. I have to be my own grad student.

And, when it comes down to it, my wiki is my augmented brain – not a collaborative brain – so I don’t really want others messing with it directly. It’s strange enough that I’ve put it out there for people to look at. When I encounter a question and need help I go looking for it elsewhere, then add the new understanding to the wiki.

Posted by: garrett on December 14, 2006 5:45 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

With the kind of support you can expect from readers, does it change what you dare to set out to do?

I did get invaluabe input as a reaction to things I posted to the $n$-Café.

Exchange with David Roberts shortly after the inception of the $n$-Café here crucially catalyzed the insight that we need to pass to inner automorphisms of structure 2-groups to realize the Breen-Messing data of gerbe connection in terms of surface transport.

Jim Stasheff’s continued interest in a couple of consequences of that which I was beginning to see were very motivating, and just replying to all the good questions he asked helped me clarify issues for myself. Now we are writing a paper on related things.

Bruce Bartlett was an invaluable source of inspiration and information. Thinking about his (apparently totally unrelated) question on the right way to think about algebras of functions made me see the right categorification of the “monoid of observables”. Combined with a remarkable triangular communication on the work of his advisor Simon Willerton (who of the people mentioned here, was the only one I ever met in person), this made me see what should be a true gem, once properly cut by somebody: the Freed-Hopkins-Teleman result in terms of the 2-monoid of observables on the 2-group $\mathrm{String}_G$. I wish I would receive more comments on that by somebody.

Then, just very recently, also catalyzed by a question by Bruce Bartlett, I had a highly useful conversation with Toby Bartels, which I should have had long ago, but for some reason had not. The picture of a chemical reaction requiring a catalyst really seems rather apposite here.

And I haven’t even mentioned communication with John Baez yet.

And by the way, this is one thing I told myself to improve on: I should ask more and more dumb questions on the $n$-Café. There is that old USENET law which says that the best way to get lots of knowledgeable people commenting is to ask a dumb question or to make a stupid mistake in public. That’s a great catalyst.

For instance my “basic question on Homs in 2-Cat”, a result of me running against an obstacle in my research thinking, lead to plenty of very generally interesting comments, to my mind.

Maybe a general comment: while I am aware that it may not be the optimal configuration for having a perfect academic career, I am interested in math/physics not as a big Bingo game. There is a very complex and at the same time very elegant structure which is being explored and every single person can only see that far by him- or herself. So, let’s talk about it.

Posted by: urs on December 13, 2006 7:13 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

while I am aware that it may not be the optimal configuration for having a perfect academic career, I am interested in math/physics not as a big Bingo game.

Which is why we can agree with Vershik’s article mentioned here, and with William Thurston:

I think that our strong communal emphasis on theorem-credits has a negative effect on mathematical progress. If what we are accomplishing is advancing human understanding of mathematics, then we would be much better off recognizing and valuing a far broader range of activity…the entire mathematical community would become much more productive if we open our eyes to the real values in what we are doing…What we are producing is human understanding. We have many different ways to understand and many different processes that contribute to our understanding. We will be more satisfied, more productive and happier if we recognize and focus on this. (pp. 171-2).

Thurston W. 1994, ‘On Proof and Progress in Mathematics’, Bulletin of the American Mathematical Society 30(2): 161-177.

What needs to be done to make public thinking a part of an ‘optimal configuration for having a perfect academic career’?

Posted by: David Corfield on December 13, 2006 8:44 PM | Permalink | Reply to this

Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

I strongly agree with the Thurston quotation:

“I think that our strong communal emphasis on theorem-credits has a negative effect on mathematical progress. If what we are accomplishing is advancing human understanding of mathematics, then we would be much better off recognizing and valuing a far broader range of activity…the entire mathematical community would become much more productive if we open our eyes to the real values in what we are doing…What we are producing is human understanding. We have many different ways to understand and many different processes that contribute to our understanding. We will be more satisfied, more productive and happier if we recognize and focus on this.” (pp. 171-2).

Thurston W. 1994, ‘On Proof and Progress in Mathematics’, Bulletin of the American Mathematical Society 30(2): 161-177.

The notion that the purpose of mathematics is UNDERSTANDING, not the roughly 1,000,000 theorems published annually, was perhaps first enunciated by Plato:

“[The] science [of Geometry] is in direct
contradiction with the language employed by its adepts. .. Their language is most ludicrous, for they speak as if they were doing someting, and as if all
their words were directed towards action… [they talk] of squaring and applying and adding and the
like… whereas in fact the real object of the subject… is knowledge … of what eternally exists, not of anything that comes to be this or that at some
time and ceases to be…”
[Plato, as translated and quoted by Shapiro, 67, p.7]

This is a debate topic on seqfans, the email networking associated with the Online Encyclopedia of Integer Sequences. This has roughly 125,000 web pages, searchable in various ways, with an explicit linkage to related sequences, as well as to trhe hardcopy world of journals and books.

The debate comes down to the claim that the database is being diluted in value by “contrived” sequences, rather than important ones from actual publications. The counterclaims include that these are collaborationware, and enhance investigations by publicizing partial results.

OEIS is limited to formatted text. But one is enouraged to link to pages of equations, illustrations, PDF, or to run Mathematica and Maple programs embedded in the text.

I don’t want to go tangental here with Ted Nelson’s original theory of hypertext, but much can be found by Googling “intertwingle.”

Posted by: Jonathan Vos Post on December 17, 2006 7:08 PM | Permalink | Reply to this

Re: Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

I agree that we can read Plato’s quote in this context, but I’m pretty sure that it’s not what he meant. He was saying that the language of geometry was philosophically wrong.

Elements I.1, for instance, states that we “can draw” a straight line between any two points. Plato would say that it should state that such a line exists, and that the straightedge construction exhibits it. The line exists before we draw it, and would exist even if we did not draw it.

Posted by: John Armstrong on December 17, 2006 9:57 PM | Permalink | Reply to this

Re: Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

Yes, the passage concerns Plato’s views on the nature of being. In the everyday world we do not encounter anything which fully is. Mathematics concerns something intermediate between this world and the permanent Forms, and so its study is an excellent preparation to wake the eye of the soul which alone can apprehend the Forms. To use the language of worldly construction - adding, applying, etc. - is to step in the opposite direction, from mathematics to something lesser.

Posted by: David Corfield on December 18, 2006 8:47 AM | Permalink | Reply to this

Re: Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

To use the language of worldly construction - adding, applying, etc. - is to step in the opposite direction, from mathematics to something lesser.

Why do you (and Plato?) believe this? This is related to the traditional ‘philosophy of mathematics’ debates from the early 20th century that you find so overblown; but in those debates, I’ve never had any sympathy for the ‘Platonist’ position. I very much like the constructivist language of Euclid (even when he uses proof by contradiction—that is not the main issue), and I have no feeling for why people see such talk as base and ‘worldly’.

Posted by: Toby Bartels on December 18, 2006 8:26 PM | Permalink | Reply to this

Re: Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

This was my rendition of Plato’s views, rather than my own. I have no problem with mathematics represented as human activity in the world. Something in me, though, sympathises with the other worldliness many have found in mathematics.

Posted by: David Corfield on December 18, 2006 9:20 PM | Permalink | Reply to this

Re: Plato, hypertext, and OEIS; Re: Communicating Thoughts on the Web

This was my rendition of Plato’s views, rather than my own.

OK, that makes sense then.

Posted by: Toby Bartels on December 18, 2006 9:35 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

I like jsMath for displaying math on the web. The displayed equations scale properly, it uses pretty native fonts or tiny image pieces at the viewers discretion, and it’s true to LaTeX.

Posted by: garrett on December 14, 2006 12:54 AM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

I like jsMath for displaying math on the web.

Does this allow to display anything we cannot display using the TeX-support here?

I see a diagram in displayed in this jsMath example, but looking at the page source code reveals that it is just an array. In other words, that it would not be possible to have, for instance, curved arrows in arbitrary direction. Or would it?

But of course an advantage is that it does not require additional fonts. I know a couple of people who never managed (maybe to convince their sys admin) to get the fonts required here installed.

Posted by: urs on December 14, 2006 11:51 AM | Permalink | Reply to this

Re: jsMath

Does this allow to display anything we cannot display using the TeX-support here?

Maybe, but I don’t know. Both systems seem pretty robust. Most anything I’ve done using standard LaTeX I’ve been able to cut and paste into jsMath. But custom packages aren’t supported – it just does standard LaTeX. Though you can add your own preamble and LaTeX commands.

I see a diagram in displayed in this jsMath example, but looking at the page source code reveals that it is just an array. In other words, that it would not be possible to have, for instance, curved arrows in arbitrary direction. Or would it?

No, I don’t think that’s possible. You’d probably want to use SVG for that, instead of LaTeX. The neat thing is, the way jsMath works is by going over your web page source and replacing LaTeX with the corresponding typeset math – either with tiny images or local fonts. So, at least in theory, you could have SVG and LaTeX on a page side by side.

But of course an advantage is that it does not require additional fonts. I know a couple of people who never managed (maybe to convince their sys admin) to get the fonts required here installed.

Yep. Anyone can go to a page rendered with jsMath and they will get pretty good looking typesetting delivered in the form of many tiny assembled images. If they do elect to download the fonts, jsMath will use those instead and produce beautiful typesetting.

Another thing that led me to use jsMath is that my source is standard LaTeX. I can cut and paste from papers, in either direction, with no changes needed. And, when something better than jsMath comes along, years down the line, I would hope that LaTeX would remain a standard portable format.

Posted by: garrett on December 14, 2006 5:17 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

Just a quick’n dirty remark: If you’re using the LaTeXRender plugin (as Clifford is), it is possible to include whichever LaTeX packages you may want.

I have this done for my blog and for a Moodle installation that I have overhere as well, and i use packages that range from the amsmath to the dsfont, wasysym, pstricks, and xy (among a few others).

On top of this, i also use the IllustRender plugin (on both, my blog and the Moodle installation that i set up for my advisor’s courses).

I could be wrong, but i think that this covers a pretty wide basis of “desires” that myself and my readers may have. (For an example, take a look at: Testando MathML. Even though it’s in pt_BR, i’m sure you’ll be able to get the main point. ;-)

Another good source of information is LaTeXRender, together with DruTeX. (N.B.: Note that using DruTeX with something like CivicSpace, say; and you can have a pretty “math-savvy” community, from Wikis to Forums and Blogs! :-)

That’s it… for now. :-)

[]’s.

Posted by: Daniel Doro Ferrante on December 14, 2006 11:49 AM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

If you’re using the LaTeXRender plugin (as Clifford is), it is possible to include whichever LaTeX packages you may want.

How?

Posted by: urs on December 14, 2006 12:00 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

There is a file in the LaTeXRender distribution called class.latexrender.php: inside this file you’ll find a function called wrap_formula. There you have it: this is the place where you can insert a list of the packages you would like. :-)

At least, doing this, solved this question for me: both, on my Moodle installation and on my blog.

[]’s.

Posted by: Daniel Doro Ferrante on December 14, 2006 5:00 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

At least, doing this, solved this question for me: both, on my Moodle installation and on my blog.

So can you use xypic on your blog this way? With source code like, say

 $$\xymatrix{ A \ar@{-->}[rr] && B }$$ 

properly rendered?

Can you point me to an entry where this can be seen in action?

Posted by: urs on December 14, 2006 5:10 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

Hi Urs,

I could be wrong, but i think i may have solved this puzzle of yours… Take a look: 1st comment to “Core dump”.

I’ve also rendered this little xypic fragment of yours straight into TeX in order to see the outcome and compare: 2nd comment to “Core dump”.

I’m sure i’m missing stuff… but, let me know what you think.

[]’s.

Posted by: Daniel Doro Ferrante on December 14, 2006 8:51 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

i think i may have solved this puzzle of yours…

Yes! Cool.

I ran into your spam filter before I could try some of the things I want to try, but what I see so far is excellent.

Posted by: urs on December 14, 2006 9:34 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

what I see so far

is gone now, Daniel’s automatic spam filter did what it is supposed to do. But the results I did get were very nice.

Posted by: urs on December 14, 2006 9:44 PM | Permalink | Reply to this

Re: Communicating Thoughts on the Web

Hi Urs,

(1) I’m happy to be of help – and even more so that you actually liked what you saw. :-)

(2) But, i’m sorry my SPAM filter is a bit annoying… i think all of the xypic commands triggered it… so, i put some special regexps for you in order to try and whitelist you. Hope it works… ;-) This way, if there is a next time, you won’t be ‘shut down’.

You know, i was worried myself, because i saw your comments and was pretty glad to see those convoluted diagrams appear flawlessly… and, all of a sudden, your comments weren’t there anymore! It took me awhile to realize that it was my SPAM filter biting me.

[]’s.

Posted by: Daniel Doro Ferrante on December 15, 2006 12:31 AM | Permalink | PGP Sig | Reply to this

Re: Communicating Thoughts on the Web

I installed mimetex time ago in PhysComments (now defunct) and its associate mediawiki. Problems were diverse. A change in the PHP configuration of the server shut mimetex processing down for a time. And in the mediawiki I was forced to patch heavily the math subsection, so it become really a fork. As it was a midly fork of Drupal, in the main section. Then you are trapped in self-maintenance.

If, on the other hand, you are able to store the pages straighly translated to MathML, then you can upgrade without fear of losing the visualisation. But edition becomes a problem.

Of course, the intermediate solution of storing itex and converting into MathML in the fly can be also a problem for upgrades.

In any case, a source of headaches; I am sympathetic to Distler work in this point.

Posted by: A. Rivero on December 14, 2006 4:08 PM | Permalink | Reply to this

blog2ps

A general comment, not aimed at anyone in particular:

printing the pages of this blog here (or of Jacques’ Musings or of the String Coffee Table) to a file produces an output in which the typesetting quality of all formulas is essentially that one is used to from LaTeX.

Looks pretty good, actually.

Posted by: urs on December 19, 2006 7:22 PM | Permalink | Reply to this
Weblog: The n-Category Café
Excerpt: On research blogging.
Tracked: December 20, 2006 5:26 PM