I was in Boston last week attending the ASME International Mechanical Engineering conference demonstrating MapleSim, our new tool for physical modeling.  I had the opportunity to speak to a large number of delegates, but I remember one conversation in particular; a professor who taught freshman students was bemoaning the fact that he found it harder and harder to impress students with his relatively simple animations of physics phenomena.  A simple animated pendulum no longer captivated students who were already immersed in the interactive physics-enabled environments of video games.  He had to escalate the intricacy of his demonstrations, but generating them was starting to consume too much of his time.

Twenty years after I first plotted the Mandelbrot set on a ZX Spectrum with 48K of RAM and a 3.5MHz processor, I’m still amazed by the sheer complexity and beauty contained therein.  I now have access to far more computing horsepower and can create ever more vivid visualizations.  It’s surprising what you can do with some creativity and a modicum of patience.

I was fortunate enough to spend the last two weeks on vacation in the south of Spain. Spain is a country composed of intricately layered history and traditions; influenced over thousands of years by its various inhabitants and conquerors: the Phoenicians, Greeks, Romans, Visigoths, Moors, and of course the Christians (the Reconquista ended with the surrender of Granada in 1492 to Ferdinand and Isabella, the same year Christopher Columbus made his famous journey). Its food, music, art, architecture, and customs display these intertwined influences in unique and sometimes surprising ways.

Modern software tools should allow engineers to design, develop and test their designs before a single part is sent to the prototyping shop. So why is it not happening? Why are hundreds of prototypes manufactured, tested and then rejected? Why is so much time wasted at the testing and then redesigning stage?

Individually, the components for the ideal virtual prototyping tool are available, but they have not yet been wrapped up into a single integrated environment that’s based on design principles that engineers find intuitive.

Why is that?      

For the last couple of weeks, I’ve been flying around the world on a press tour … sounds glamorous doesn’t it? Images of Brad Pitt or Prince William come to mind? Well, any similarities between a Brad Pitt press tour and one that I’m involved in is purely coincidental (if not miraculous). So what does one do on a Maplesoft press tour?

 Well, as it turns out, there actually is a fairly active community of journalists from far and wide who have a particular interest in recent developments in engineering and mathematical computing. And every year or so, we like to meet the press face to face to keep the lines of communication open between the company and these influential people of letters. This year, my tour took me through key regions in the US, UK, and Germany.

This weekend was reunion weekend for me. On Saturday I made the return journey to my alma mater, the University of Waterloo (i.e. I walked 10 minutes to the campus from my house), for the 20^th reunion of my Engineering Class of 1988. Among the various events and activities, I had the pleasure of having a sitdown chat with Professor Peter H. O’N. Roe, retired professor of Systems Design Engineering (my undergrad department) at the University.

I can always tell when it’s back-to-school time... My morning drive becomes just *slightly* more congested: those extra school buses, new college students, and vacationers back from their time away certainly add up on the roads. For us here at Maplesoft it’s always a busy time as well, working with students and educators to get them ready for the new school year.

The modern engineering achievements of Japanese industry are the stuff of legends. And for an engineering nerd like myself, Japanese industry quite often equates with the many qualities that drew us into engineering –precision, vision, and technological ambition.  So it’s no surprise that each time I visit Japan, I feel like a kid again, eagerly waiting to discover yet another technological marvel -- whether it’s something very important like automotive powertrains that consume ridiculously small amounts of fuel or something that’s just plain fun (like this), I’m generally in a constant state of amazement if not giddiness during my visits.

Like most students studying engineering in the 90s, spreadsheets were the de facto calculation tool.  I used them for everything from food budgeting to pump and piping sizing calculations. 

Computing power has since exploded, and engineers have far better choices.  But engineers still continue using spreadsheets. 

Why?

There’s really only one reason – ubiquity and familiarity.  A spreadsheet is installed on nearly all desktop computers, but even though most engineers are aware of at least some of their design deficiencies they keep on using them.

Math is boring. Math isn’t useful. You’ll never need to use math again after school. It isn’t necessary to learn math, now that we have cash registers, calculators and computers. Math is just plain boring.

It’s not the fault of my world-famous professors at M.I.T. who gave me a M.Sc. degree in Electrical Engineering, but it’s a fact – I know less about engineering than most (if not all) of you.

Way back then, “Computer Science” was a fledgling field of study, and in many schools it was an offshoot of either math or engineering.  In my case it was an offshoot of engineering, and ergo my inappropriate degree.

So much for my sordid past.

Yesterday I watched a demonstration of Maple being applied to the modeling and simulation of the internal deformations of human bones. The researcher was a mathematician working primarily in the biomedical modeling fields. The actual technique was to utilize the symbolic mathematical power of Maple to formulate the necessary equation pieces for a finite element model (FEM) of the internals of the bone. The equations are then fed into the legendary FEM solver ABAQUS.

Due to the notoriously non-linear qualities of human flesh and bone, traditional formulation methods developed for modeling beams and metals simply do not work. So as in the case of so many impressive engineering applications, the power of Maple is being deployed in the formulation or the pre-solution phase of modeling and in doing so, previously infeasible models now become feasible.

That’s a mantra I need to have drummed into me, and perhaps tattooed on the inside of my car so I’m reminded every morning.  But I keep on making the same mistakes. 

 I seem to think that if I’ve “optimized” my portfolio with a few flashy calculations that I’ve done my due diligence, and the next stop is financial independence.  It’s the black box syndrome – trusting the output of a computer program without truly understanding the real issues.  Most portfolio analyses, for example, hinge on historical data, which of course doesn’t predict the sub-prime blow-up in the US or whether Brazilian coffee growers are on strike.  They’re all backward looking.

 However, in the absence of a neighbourhood scryer, historical analyses are a good indication of how to position a portfolio for the long term.

 Being a geek (however much I strenuously deny it), I tend leverage my tech skills wherever I can.  I wrote the attached worksheet to import stock quotes, including historical data, from Yahoo using the Sockets package.  Simply type in the appropriate NYSE stock tickers into the appropriate text boxes, check the quantities you want to download, and click the big gray button.

 All the stock quotes and historical data can be manipulated on the command-line and can be accessed via command-completion. 

 It then finds the best distribution of stocks in a portfolio by maximizing its Sharpe Ratio (through the Optimization package). 

The Sharpe ratio quantifies how effectively a portfolio of risky assets utilises risk to maximise return.  It’s defined as follows.

It essentially measures how effectively a portfolio uses risk to maximize return – the higher the ratio the better.  The expected portfolio return is predicted from historic data, the portfolio standard deviation is traditionally used as a proxy for risk, and the risk free return is the return that can be expected from a zero-risk investment (i.e. the interest on US Treasury Bills or the redemption yield on UK gilts).

What I find particularly fascinating is how Maple is now the centre of my technical desktop.  Through the combination of the interface and its math tools, I now use it for everything from the simplest calculations through to making wild guesses about my financial future.  If any of the developers are reading this, I want you to know there’s a lot riding on you...

Ruined your life?  Well, almost.  But now that you’re intrigued with my wild claim, let me explain.

The science of mathematics has a very long heritage.  The language of mathematics, as we recognize it today, is a bit younger – widely credited to François Viète, who introduced the first systematic algebraic notation in the last half of the 16^th Century.

Along the way, over the course of many centuries, the power of mathematics increased steadily, through the contributions of many great men. 

One of the greatest pleasures of my job is meeting users and learning first hand of their achievements (hopefully with our products). Last week was a particularly eventful week and a distinct highlight was a visit our friends at the Canadian Space Agency (CSA) in Montréal.