Daily Archives: December 13, 2006

A note on mathematical and programming notation

In the immediate prior post I wrote of musical notation. I have only casual knowledge of that notation, but I do know a bit about some other notations: mathematics and programming.

Wikipedia has a good overview of mathematical notation. Wikipedia supports the display of mathematical notation, Help:Displaying a formula.

Mathematics just visually can be an art in its own right. For example, one of the most memorable stories in mathematics is that of the collaboration of G.H. Hardy and Srinivasa Aiyangar Ramanujan. Ramanujan made excptional contributions to the theory of continued fractions. For a brief example, see Ramanujan Continued Fractions and
Rogers-Ramanujan Continued Fraction
. By the way, these last two examples come from wolfram.com, the authors of Mathematica, a commercial software product for mathematics. Mathematca provides another way to display and manipulate mathematical formulas.

An extended example of mathematical notation, in the form of a proof consisting of about 15000 pages, can be found in the multiple papers on the solvability of finite groups. [1] See Classification Theorem of Finite Groups.

There is also a close linkage between Unix and the display of information. The original Unix from Bell Labs included many software packages concerned with text formatting and laser printing. The fundamental work in creating software for displaying mathematics is the work of Donald E. Knuth, as mentioned in my previous post On mathematics and programming: Donald E. Knuth. Software packages such as Tex and LaTex are widely used throughout the world to display mathematics.

My IBM colleage Bob Sutor, IBM’s VP of Open Standards and Open Source, did some work in displaying mathematics in a browser back in the 90’s. Indeed, that’s how I first came to know his name, as his Techexplorer plugin was one of the first alphaWorks offerings, in September 1996. I recall coming across the download stats for it when I perused the download stats for Jikes after it went out. Bob has written about this in his blog recently, I’m a document guy.

I’m familiar with other notations. Each programming language defines a notation for writing code. Here for example is the code that prints the “Blog stats” as part of the WordPress Dashboard, from the file index.php:

<?php _e(‘Blog Stats’); ?></h3>
$numposts = $wpdb->get_var(“SELECT COUNT(*) FROM $wpdb->posts WHERE post_status = ‘publish'”);
if (0 < $numposts) $numposts = number_format($numposts);

$numcomms = $wpdb->get_var(“SELECT COUNT(*) FROM $wpdb->comments WHERE comment_approved = ‘1’”);
if (0 < $numcomms) $numcomms = number_format($numcomms);

$numcats = $wpdb->get_var(“SELECT COUNT(*) FROM $wpdb->categories”);
if (0 < $numcats) $numcats = number_format($numcats);
<p><?php printf(__(‘There are currently %1$s <a href=”%2$s” \
title=”Posts”>posts</a> and %3$s <a href=”%4$s” title=”Comments”>comments</a>, \
contained within %5$s <a href=”%6$s” title=”categories”>categories</a>.’),
$numposts, ‘edit.php’, $numcomms, ‘edit-comments.php’, $numcats,
‘categories.php’); ?></p>

To fully appreciate this code you have to know something about both HTML and the programming language PHP. I’ll attempt to provide a brief introduction to each in forthcoming posts.


1. One of my classmates from Caltech, Michael Aschbacher, made fundamental contributions to this work. He is currently a professor of mathematics at Caltech. He was also a fellow waiter at the Caltech faculty club, the Athaneum, during our undergraduate days.

The most important WordPress command

In my previous post on musical notation I spoke of the importance of open data formats, “While most folks in the open-source arena think mainly about the code, it’s also important that the data be open.” This is especially so when the data is your writing. It’s your work. You own it. Yet sometimes you don’t.

I’ve been a big fan of plain old HTML for a number of years. I write my WordPress posts using it, and try to use it whenever I can. It’s the most portable format in the web world — any browser can display it and as best as I can tell every computer has a browser these days. I’ll be writing more about HTML in future posts.

That’s why I avoid Microsoft Office whenever I can. If I create a document using Office, then you have to have a copy of Office to read it. From my fingers to your eyes, all my work — yet Microsoft manages to insert itself in the middle and collect a tax. It’s a hefty tax, and accounts for most of Microsoft’s profits.

This is also why you’ll find Bob Sutor and others writing so much about open document formats. See for example, I’m a document guy, and all his other writings on Open-Document-Format (ODF), Sutor Blogs on “ODF”. and Bob’s del.icio.us ODF tags.

That’s one of the reasons I so admire WordPress.com. Not only is the code open-source but the folks at WordPress support open data also.

I say all this as a reminder that perhaps the most important WordPress command is “export.” More precisely, if you go to your WordPress Dashboard and select “Manage” you will see a tab “Export.” There you will instructions on how to download all your blog posts, including comments, in a single file in XML format.

XML format is an open-standard. You’ll be able to read that format years or decades from now. Most importantly, if you periodically export your blog, you will have on hand your own copy of your work. If WordPress goes bust tomorrow, you won’t have to worry. You won’t lose your work. You aren’t locked into a proprietary format.

So you can be in the export/import business. Or at least the export business.

Go ahead, export your blog. You’ll feel better for doing so.

It will confirm your trust in the good folks at WordPress.com.

Perhaps you’ll even write a post reminding others of their good work — as I have just done.

A note on musical notation

While writing my prior post on the posting of all of Mozart’s manuscripts online, I got to thinking about other forms of writing than plain text, of which music is one example.

Mozart’s manucripts are in a musical notation. According to the cited Wikipedia article, musical notations have existed for thousands of years, and the current “Western” notation dates back almost a thousand years.

It’s a good thing that music notation has been around so long. Imagine if it were a recent invention, and was available only in a proprietary format such as that used by Microsoft Office? Or imagine our grief if Mozart’s Marriage of Figaro had been published using Salzburg Office, version 1786? And let’s not think about the DRM measures that would be put in place to lock down that wonderful music these days …

While most folks in the open-source arena think mainly about the code, it’s also important that the data be open. For example, suppose Mozart had been subject to the whims of a colonial upstart, Micro Doodle software, and had written his music using the proprietary music font, TrueMusic Macaroni. See Yankee Doodle, and Yankee Doodle. He might even have written some songs about it:

Micro Doodle went to town,
A-Riding mono-poly;
It stuck a new fork in its code,
And called it macaroni. [1]

Micro Doodle, keep it up,
Micro Doodle dandy;
Mind the music and the step,
And with the cash be handy!


1. This is common practice, particularly in large software projects. It’s called “spaghetti code.”

Open Mozart – Ecco la marcia, andiamo

I spent most of last week at the Sixth Sakai Conference in Atlanta. I took along 3 CD’s containing a recording of Mozart’s Marriage of Figaro. [1] While in Atlanta I listened to most of CD 3, and came across one of my favorite sections, not too far into the CD.

On my return, I noted with pleasure the post Mozart’s entire musical works now free on Net, announcing that

Wolfgang Amadeus Mozart’s year-long 250th birthday party is ending on a high note with the musical scores of his complete works available from Monday for the first time free on the Internet.

The International Mozart Foundation in Salzburg, Austria, has put a scholarly edition of the bound volumes of Mozart’s more than 600 works on a Web site.

The financial backing came from the Packard Humanities Institute of Los Altos, Calif. [2]

I decided to see if I could find the score for that section. I put on the CD, listened until I found that section, and learned it was “Ecco la marcia, the fourth th scene in Act 3. I went to the web site, and was then able to find the piece. It can be found at NMA II/5/16/1-2: The Marriage of Figaro Vols. 1-2, Edition (Finscher, 1973), page 432.

I also located another online version of the score at W. A. Mozart
Die Hochzeit des Figaro
, Page 292, Courtesy of William and Gayle Cook Music Library, Indiana University School of Music. (I was pleasantly surprised to learn this came from the good folks at Indiana University. Indiana has a famous music school in addition to the Cook Music Library.)

I was able to locate the text of the section: Ecco la marcia:

N. 23. Finale

Ecco la marcia, andiamo;
ai vostri posti, oh belle,
ai vostri posti.
Susanna, dammi il braccio.

Here’s the march; let’s go
to your places, girls,
to your places.
Susanna, give me your arm.

I was also able to locate a performance via You Tube, Ecco la marcia, in a recent performance by the University of Texas Campus Opera Society. Listen for the march in the background right at the beginning. I think it’s supposed to be the band of a regiment.

I have previously written about Mozart. See Wolfgang Amadeus Mozart: Why censor him?, “Hello World” through the ages, A musical magic moment and Open-Source: Music to my ears.

My wife and I were in Salzburg in the summer of 2005. It’s a great place to vist — you hear Mozart’s music constantly. We visited two places where he lived. While in Vienna a few days earlier we stayed in a hotel in the building in which Mozart lived from 1780-1781, and also attended a concert in a room at the Hapsburg Palace in which he performed over two hundred years ago.

By the way, if you’re ever in NYC then I suggest a visit to the Morgan Library. They have an excellent collection of musical manuscripts, including works by Mozart and Beethoven written in their own hand.

Ecco la marcia, andiamo.


1. The CD’s were Nos. 32-34, Volume 9, of the marvelous Wolfgang Amadeus Mozart: Complete Works (170 CD Box Set) [BOX SET], consisting of 170 CD’s for less than one dollar per CD.

2. Thank you, Packard Humanities Institute!

no-account accounting 2006-12-08

This is the first of an occasional series of posts prompted by looking at the blog stats, prompted in part by the observation that a post about an aircraft carrier and open-source somehow caught the attention of some folks on Wall Street. (High-fliers no doubt, or would that be rats on a sinking ship?)

As the author of this blog I have a dual role of being both an editor and a reader. Yes, I admit it, I often go back just to read my earlier posts, I admire them so.

As an editor, I get to see the readership statistics reported by WordPress. (Why only I can look at them and you can’t is the subject of a forthcoming post.)

That is one of the most addictive aspects of blogging. WordPress, as well as other related tools such as Technorati, give you some sense of who is reading your blog, but the coverage is sketchy, and in some cases inconsistent. But though they may be be accurate, the stats can be fun, and sometimes can give you surprising insight into things of probably no value at all.

For example, I wrote a post Intrepid open-source last week. It was prompted by seeing a picture in the New York Times of the U.S.S. Intrepid, on its way to drydock from its home on NYC’s West Side. [1] As it happens I had written about the same ship in the first post on this blog, and I managed to make some comments about open-source. Near the end, to remark on the maturity, of open-source, I wrote of some work I knew IBM was involved in about Linux and Java, but since I didn’t have the details at hand, I used google to find a couple of press articles and put links to the articles into the post to back up my statements.

That post sat there for several days, with only a handful of reads. But on Tuesday it shot right up to the top. WordPress happens to provide a list called “referrers” that tells you how people got to your blog. Tuesday’s list include the entry:


If you track this down you’ll find that this site is a stock-related site and someone noticed my post, probably because of a blog search, and mentioned my post with the comment, “Write-up about Open Source and the Defense Establishment. But mentions ANTs.”

That post got 96 views yesterday, and there were 89 views via Ragingbull. There had only been one view in the several days that elapsed since I first wrote the post, so essentially all traffic is due to this one referral.

The post even drew a comment, from Roberta Murphy. Turns out ANTS is a software company. I investigated and learned that Don Haderle, a former IBMer, recently joined ANTS. I was involved, albeit indirectly, with Haderle during the Cloudscape/Derby project, as he was one of the folks we had to convince as part of our pitch that the code should go to Apache.

By the way, you never know which posts will get some traction. Two successive posts, On Ferrara Cafe, and Leigh Anne Tuohy – “God gives people money to see how you’re going to handle it”. have proven quite durable.

One post — for which I had great hopes — has as best I can tell not even been read once. I wrote a whole series on open-source and forking, taking Yogi Berra as my mentor, almost solely for the purpose of being able to write my own variation on a Yoga-ism, “If you come to a fork in the road, pick it up.” Sigh…

The posts on binary search have had a small but steady audience. I had great fun writing these posts and I am pleased some folks have found some pleasure in them.

If you take a look at “http://technorati.com/search/daveshields.wordpress.com&#8221; you will see this blog has been linked to by a couple of sex sites. As best as I can tell this was due to my using the words “open” and “adult” in the same post, not because of the post Open-source is sexy. Writing a post about James Bond also added to this. Go figure.

Tuesday was also a milestone in that the WordPress running-graph of views-per-day for a month finally took my best-day-ever, 451, off the chart. 451 was I think related to the Sun/FSF post.

Readership has been picking up. Here as the daily-view totals for the last month or so, seven per row, with the first being for Monday. I’ve included row and column totals?

Mon Tue Wed Thu Fri Sat Sun Tot
451 183 122 105 127 067 128  1183
145 107 192 133 059 083 089  0808
138 179 168 109 144 127 104  0969
177 129 199 264 299 204 140  1403

911 589 681 611 629 481 461 (column totals)

The spurt last week is due to the postings about Eben Moglen’s presentations at the Sixth Sakai Conference.

Readership has indeed grown lately. The counts for the last two days were 227 and 276, each among the best days ever.

Total views just passed 9000, with almost half of them coming in the last month. The total should pass 10,000 by the end of the year. My guess it takes close to 100,000 views for a blog to really escape from obscurity into notoriety, so there is still quite a bit of blogging on our trail up the long tail to be done.


1. I have a very special place in my heart for NYC’s West Side. Every new Manhattan resident of a certain ilk makes a fundamental statement about themselves by their choice of first residence in Manhattan. East Side or West Side? Uptown or Downtown? East Village or West Village. Those who may or may not have ilk but do have almost no money wind up on the West Side, as did I. Two years on West 95th between Broadway and Ammsterdam, followed by 19 years on West 93rd between Columbus and Amsterdam.

I also have a strong attachment to the area in which the U.S.S. Intrepid is normally docked, West 47th Street and the Hudson River. It is the part of Manhattan known as “Hell’s Kitchen.” My wife was director of an after-school day-care center at West 42nd and 12th for much of the 1970’s, and during that time if I walked with her anythwere between 36th and 56th, West of Eighth Avenue to the river, we could not go more than a block before someone said hello to her, usually in Spanish.

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