Maplesoft Blog

The Maplesoft blog contains posts coming from the heart of Maplesoft. Find out what is coming next in the world of Maple, and get the best tips and tricks from the Maple experts.

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 (but first stripping out code snippets or URLs that would distort the score).  The top 10 and the bottom 10 scores are given below.


The Ten Most Readable Blog Posts





SMOG Index


Who Needs Math?

Fred Kern



China on my Mind

Fred Kern



Maple Goes Social (Networking)

Tom Lee



Top 10 things to evangelize about …

Tom Lee



“Every time I walk into math class a little part of me dies”

Tom Lee





India on my Mind

Fred Kern



The Physics of Santa Claus

Stephanie Rozek



Stringing Me Along

Samir Khan



A Better Tomorrow in Engineering Software

Samir Khan



Good Vibrations

Samir Khan



The Ten Least Readable Blog Posts





SMOG Index


An Animated Discussion about Pendulums

Samir Khan



Algebraic Surface Blending

Tom Lee



An Optimal Day

Tom Lee



Repaying Old Debts

Tom Lee



Taking the Lead

Tom Lee



Postcards from the road: Part 1 -- On rocket science

Tom Lee




Postcard from the road: Found in translation Part II

Tom Lee



Postcard from the road: Found in translation Part I

Tom Lee



Physical Modeling - Killer Application No. 2 for Symbolics

Laurent Bernardin





Let's Get Physical

Samir Khan

18.1 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.

A dramatic change in how we interact with the environment demands an equally dramatic change in how we develop technology. The evolution of predictive technology – in other words, software - has been a precursor to the development of environmentally progressive technologies like clean coal power stations and hybrid energy vehicles.

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...

One of the great parts of my job is getting to meet all sorts of incredible people from all over the world. One of these, a math professor, is very close by to us, both geographically and professionally. Professor Jack Weiner is one of the most popular educators at the nearby University of Guelph. He is passionate about his work and it shows: he has won numerous awards, including the award for most "Popular Prof" in a national annual survey of Canadian Universities, for eight out of the last nine years.

I was recently forwarded a link to this Snopes article.

According to the urban legend described therein, text is still readable if all the letters in a word apart from the first and last are randomized. I quickly threw together a Maple worksheet, primarily using its flexible string manipulation tools.

Go to Maplesoft on Facebook? Math talk mingling with my meaningless personal status reports? Are we now laying a clear path for the Maple world to walk right into our private lives? Now I’m worried.

We’re now at an inflection point in which symbolic technology will automate physical modeling and equation generation through tools like MapleSim. As a recent webinar hosted by Maplesoft and the Society of Automotive Engineers proved, engineers are fascinated by the application of the technology, and the technology itself.

  • Voting patterns in Mexico and Florida.
  • The size of files in your Maple 12 installation
  • Stock trading volumes on the NYSE

What do all of these have in common? They, and other data sets drawn from the real world, often follow a non-intuitive pattern called Benford’s Law.

A colleague of mine recently mentioned something to me about an article that circulates every year during the holiday season, entitled “The Physics of Santa Claus”. This was news to me, so I ran a few Google searches to find out what she was talking about.


It seemed that some enterprising person had taken the time to go through and explain just what is involved in Santa’s Christmas Eve trip around the world delivering presents. How many households does he have to visit? How much do all those presents really weigh? How fast do the reindeer need to fly in order to get it all done in a finite amount of time? There is much speculation as to the origins of this piece; the general consensus seems to be that it began life published in SPY magazine in the early 1990s. Whatever the true story, it’s still an entertaining read in 2008.

I’ve taken some time to update the original with more current data – for instance, it seems the world’s population has grown a bit in the last 20 years. According to the Population Reference Bureau, the world population in 2008 was approximately 6,705 billion; 28% of these are children (defined as being under 15):

In fact, making some assumptions about the percentage of these children that celebrate Christmas and the number of children per household, it turns out that Santa needs to visit close to 200 million homes in one night.

We assume he distributes gifts from 5 pm to midnight, or for 7 hours. Due to the Earth's rotation, there is an overall time difference of 24 hours between different time zones, so we can therefore say that Santa has 31 hours to finish his work (assuming he logically travels east to west). Visiting 200 million homes in 31 hours means that Santa has to visit approximately 1586 homes per second:

This gives him about 1/1600th of a second to do everything at each home, such as parking his sleigh, looking for the right gifts, climbing down the sleigh and chimney, binge on snacks, fill the stockings, come up again and rush to his next stop!

For the complete details of his annual trip, visit the Applications Center where I’ve posted the Maple document in which I’ve recreated the Santa calculations. Happy Holidays!!

My wife will tell you that I am horrible at remembering important things like birthdays and sending Christmas cards on time … or at all. As we approach the end of another remarkable year, it’s always rewarding to reflect on the events of the year and take the time to thank all those who made the year so remarkable. So, in no particular order

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