A prolonged winter is one of the challenges of living where I do. But each year, we also get the pleasure of experiencing the very first spring day and that’s a special feeling that I would not trade for all the tropical weather in the world. For me, spring in my town is not defined by the temperature or amount of sunshine. It’s defined, oddly enough, by robots … the third week in March is typically the week of the FIRST Robotics Waterloo Regional Tournament. FIRST stands for “For Inspiration and Reward of Science and Technology”. It is an international team sport where high-schools from around the world compete in complex robotic games with full sized remote controlled and autonomous robots on the playing field about the size of half a basketball court.

As I was preparing for an upcoming presentation, I stumbled on a graphic that I always thought was one of the best ones in my endless collection of Powerpoint slides. This particular graphic portrays the evolution of engineering modeling software and I always thought it was an incredibly impactful and clear view on a very complex topic. Unfortunately, I really can’t take any credit for it. The basic concept was created by Mr. Alex Ohata of Toyota. I remember the first time I saw it at a conference.  It really was one of those light-bulb moments where the Universe unfolded as it should … and now I pay due homage to this work of scientific art.

In the media today, there continues to be much discussion about how students in North America are moving away from the math, science, and engineering disciplines. It is an established fact that countries such as China, South Korea, and Taiwan graduate a much higher number of engineering students than those in North America. This is a cause for great concern in today’s highly complex world, and schools are attempting to solve the problem with math in a variety of ways, with varying success rates.

I suspect many of our readers are already on to this, but for the few uninformed among us, tomorrow is the 21^st annual Pi Day. On March 14, this “holiday” is celebrated by those of us geeky enough to realize that this date, 3/14, is also the common approximation of the number π. The first Pi Day celebration was held in 1988 at the San Francisco Exploratorium, led by its creator, Larry Shaw. Those attending this year’s festivities have a chance to work on pi puzzles, sing pi songs, and of course, eat lots of tasty pie. Their Pi Day website includes lots of fun information and activities you can even do at home. If you’re not in the area, be sure to check out their webcast, or join the revels on Second Life at the ‘Splo, the online version of the Exploratorium.

Hi. I am the Marketing Communications Manager at Maplesoft. This is the first piece of writing where you get to know who I am, but many of you have probably already read a lot of what I’ve written. I am responsible for the promotion of Maplesoft products. It’s my job to take what the really smart Maplesoft employees create and turn it into something engaging (and typically say all I need to say in 3 paragraphs or less, or in the case of subject lines, 49 characters or less). Within every piece of highly technical math-filled piece of writing is a gem of a story waiting to be brought out. I try (sometimes successfully, I hope) to bring out these stories. Every time you’ve read our newsletter “The Maple Reporter,” an email, or a letter from Maplesoft, you’ve read my work. My goal is for people to read what I write and say “I want that!” or “how do I do that?”

It’s no secret that I have a soft spot for matters of space and space exploration … so even if we have all sorts of great news about modeling advancements in automotive, or electronics, it will never be as thrilling (yes this is the right word) as the things I encounter through my work at Maplesoft that deal with space. In countless blog posts, I’ve commented on aerospace engineering and space exploration, and once again this week, several events have confirmed that inside me, there is still this wide eyed boy staring into the night sky in amazement …

Great playwrights and poets are drummers – they craft the written word so that the rhythm and the cadence of their dialogue when spoken are a drumbeat, and combine with the meaning of the language to create emotion.  Shakespeare, for example, used syllables as his drumbeats (as did many other playwrights and poets).  Analyzing linguistic structure isn’t a common application for a math tool (and for a very good reason), but can Maple tell us more about Shakespeare’s favourite drumbeat?

We need to find some way of programmatically counting the number of syllables in a word. In an irregular language like English, this is a hit-and-miss affair.  Maple’s SyllableLength command, for example, tallies the number of vowel-consonant changes in a word to calculate the number of syllables (but increases the count by one if the word ends in a “y”.)  While this is a good start, for many words it’s merely an approximation. Conscious and serious, for example, have the same number of vowel-constant changes, but a different number of syllables when spoken.

I chose to modify the basic premise of SyllableLength with several empirical adjustments that give a more accurate tally of the number of syllables in a word.  This simply involves increasing or decreasing the calculated number of vowel-consonant changes if a word contains a particular letter structure.  For example, terrible has two vowel-consonant changes, but we increase this count by one (to calculate the number of syllables) because it ends in ble.

Although we can implement a number of these workarounds, this (admittedly very clumsy) approach is never going to account for the full irregularity of the English language, and we have to accept the results in that light.  The attached worksheet contains the chosen approach, and I’d appreciate feedback on more accurate ways of programmatically counting the number of syllables in a word.

So, let’s start by examining the monologue in Act 3 Scene 1 of Henry V.  Here’s the number of syllables per line as computed by the attached worksheet.

“Once more unto the breach, dear friends, once more;”
10 syllables

“Or close the wall up with our English dead”
10 syllables

“In peace there’s nothing so becomes a man”
10 syllables

“As modest stillness and humility”
10 syllables

“But when the blast of war blows in our ears,”
10 syllables

“Then imitate the action of the tiger”
11 syllables

So it looks like Shakespeare used ten beats, or syllables, per line, but placed an extra syllable in the final quoted line.  In fact, he often wrote monologues in a style called iambic pentameter, in which each line consists of five syllable-pairs (the first syllable in each pair being unstressed and the second stressed)

In much the same way that the darkening of a cinema is a visual cue that implies that a movie is about to begin, Shakespeare used iambic pentameter as an audio cue to signify emotionally resonant or particularly important dialogue, occasionally varying the number of syllables (or the number of polysyllabic words) per line to create a sense of discord, or a quickening or slowing of pace.

You might want to check out the following video – it’s Kenneth Brannagh’s version of the full speech in his 1989 film adaptation of Henry V.

Here’s another example from Romeo and Juliet (Act 3 Scene 5), together with the syllable counts given by Maple.

“Wilt thou be gone? It is not yet near day”
10 syllables

“It was the nightingale, and not the lark”
10 syllables

“That pierced the fearful hollow of thine ear”
11 syllables

“Nightly she sings on yond pomegranate tree”
11 syllables

“Believe me, love, it was the nightingale”
10 syllables

Again, Shakespeare shifts between 10 and 11 syllables per line to indicate emotionally resonant and poetic dialogue.

Shakespeare did not write entirely in verse with a defined metric structure.  He also wrote in free prose with no defined syllable structure, sometimes to indicate that the speaker was vulgar or mentally unbalanced, or in short question-answer dialogue.

Given the limitations of a purely programmatic approach, we’re never going to fully deconstruct the beauty of Shakespeare’s language.  Maple can, however, offer a small insight into how he controlled the rhythm and pace of his dialogue.

Download the attachment: Shakespeare.mw

Last week I had the distinct pleasure of attending the retirement celebration for Dr. Keith Geddes, founder of Maplesoft and inventor of the Maple system. I’ve known Keith for over 20 years now and I consider him one of the few people I know well who has had, without exaggeration, a profound impact on the world.

Keith earned his chops as a numerical analyst in the 1970’s. Then as a young faculty member at the University of Waterloo, he developed an interest in symbolic computation. The lore has it that he had no intention of designing a complete new system but wanted to use the “grand-daddy” of symbolic systems MACSYMA from MIT. During those wild frontier days of computing, the only way to get access to such specialized systems was remote dialing to the MIT machine in the wee hours of the night (to reduce phone costs),  using  a 90 Baud modem … those were the days!

I'm one of several technical writers at Maplesoft.  It's our job to craft the text in our brochures and user stories, and on our web site.  We all have differing styles, but we share a common goal; we want to write in a manner that’s technically compelling but simple to understand.

After recently exploring Maple’s string manipulation tools, I was surprised to find a command that measures the readability of a sample of English text.  It seems that as well as making you a better mathematician, Maple will poke and prod you into being a better writer.

StringTools[Readability] returns a measure of readability called the SMOG index (but, when asked, will also give the Flesch Reading Ease, Flesch-Kincaid Grade Level Formula, Automated Readability and the Coleman-Law indices).

These measures do not gauge the quality of the writing, its grammatical correctness, or account for specialized discipline-specific vocabulary. They simply use guidelines determined from in-the-field studies (largely conducted in the US) to quantify the degree of education or effort it takes to understand a sample of text.  Additionally, the calibration of the results against the required reading effort is only meaningful for readers whose native language is English, and whose schooling resembles that of the US system.

The SMOG index wins an award for the most amusing acronym of the month: Simple Measure of Gobbledegook. It's calculated with the following empirical formula.

 It returns the years of education (that is, the US grade level) required to completely understand a sample of text.  Typically, Newsweek has a SMOG index of 10 to 11, the New York Times 13 to 15, and the Harvard Law Review 17 to 18.

I was recently asked to describe MapleSim in less than 70 words; this was the result:

MapleSim is a tool for multi-domain physical modeling and control systems development.  Physical components and signal-flow blocks can be connected to create models that map onto the real system. It features an integrated environment in which the system equations can be automatically generated and analyzed, and new physical components created. It contains tools for optimized code generation, controls analysis and design documentation.

This has a SMOG index of 15.5, which implies the reader needs a university education for complete comprehension.  Since that’s the target audience, I guess I’m in the right ballpark.

As I write this post, I know I’m guilty of making many readability errors.  Are my fellow Maplesoft bloggers as guilty?

To answer this question, I used Maple to calculate the SMOG index for all the blog posts on Maplesoft.com (but first stripping out code snippets or URLs that would distort the score).  The top 10 and the bottom 10 scores are given below.

Well...it appears that I’ve written some of the most readable posts and the single least readable post.  The two least readable blog posts are those that explore abstract, high-level ideas (and hence demand more sophisticated writing), while the most readable blog posts are essentially opinion pieces.

Other than that, the only conclusion we can make is that good writers tend to write to the level of comprehension of the intended audience and the material; they don’t unnecessarily dumb down the sophistication of their writing to the lowest common denominator, or write to a level that’s beyond the scope of the material.

I’ve attached a Maple worksheet that helps you explore the readability of text using all of the measures in StringTools[Readability].  You may want to use it to write a more readable blog post than this one.

It seems like everywhere you turn lately, people are talking about how to be kinder to the planet. One example is just how much interest was generated when GM unveiled its plans for the Chevy Volt last year. As I write this, 46,527 people are on the waiting list for the upcoming electric car, which is scheduled to be released in late 2010 as a 2011 model. At my house, we wash our clothes in cold water; use a programmable thermostat; turn off the lights when we’re not in a room; recycle and compost our waste; use a low flush toilet, energy efficient appliances, and an electric lawnmower; and of course, snuggle our two dogs for warmth!   

Yesterday was one of those remarkable days when everything seems just about right. The highlight was an email message I received from a Prof. Fang from Ryerson University notifying us that we had been both nominated and awarded the Omond Solandt Award by the Canadian Operational Research Society for ongoing and outstanding contribution to the field of Operations Research (OR). No, it’s not a Nobel Prize or an Oscar, but whenever a group of smart people publically recognize our work, the honor and pride are genuine.

I thought I’d exercise my left brain a little with this post and write on something a bit more technical. Actually, this was triggered by a chat I had over dinner last night with our 3D graphics development manager and a client. As you may have guessed math is intimately related to computer graphics of all sorts. My PhD thesis so many years ago was on the topic of creating funny surfaces that smoothly join two complex surfaces with a relatively small number of shape control parameters: such surfaces are called blend surfaces. This required the development of a bunch of algorithms that related either implicitly defined surfaces (i.e. f(x,y,z) = 0) or parametrically defined surfaces (i.e. each point is defined by the triplet (x(t), y(t), z(t)) ). That was twenty years ago and I always thought that any problem that I was wrestling with would have been resolved twice over by now. My ego was pleasantly surprised that indeed such problems are still the stuff of heated debates and vigorous research.

For almost 20 years, Math education has been recognized as the first killer application for symbolic computing. By taking out the grunt work of manipulating equations, calculating integrals and performing matrix computations with symbolic entries, systems such as Maple have transformed the math classroom.

On a recent trip to McGill University in Montreal, I had the pleasure of meeting Dr. Paul Oh of Drexel University in Philadelphia and the Director of the US National Science Foundation’s (NSF) robotics programs. During a fascinating presentation on the US robotics research landscape, Dr. Oh made a few comments that really made me think … and reflect.

Robotics has always been a “sweet spot” for Maplesoft technology. Between the necessary complex...