A reminder of my mathematical past … and my connection with a princess

Browsing 3 Quarks Daily, my eye caught a particular title: ‘AI has cracked a key mathematical puzzle for understanding our world‘. Reported in the MIT Technology Review, the article’s sub-title explains that “Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve.”

As I followed the link, my mind went back nearly five decades to my mathematics honours year at university. One of the units I studies was ‘Optimisation’, the focus of which was partial differential equations (PDEs). ‘So what?’, you may ask. Well, the thing is that PDEs are:

kind of magical. They’re a category of math equations that are really good at describing change over space and time, and thus very handy for describing the physical phenomena in our universe. They can be used to model everything from planetary orbits to plate tectonics to the air turbulence that disturbs a flight, which in turn allows us to do practical things like predict seismic activity and design safe planes.

The catch is PDEs are notoriously hard to solve.

First page of my Honours Thesis – ‘Euclid Now’ – nothing to do with PDEs

They are so hard to solve that, even when studying them at honours level (i.e. at the end of four years of university maths), we made no effort to solve them. Our task was to set them up, that is, develop a set of PDEs to describe a particular physical phenomenon. Examples that I recall are the forces on the sails of a yacht and finding equations to analyse the forces acting on a rocket sent into orbit. Typically there would be four or five unknowns and we’d be required to set up the corresponding four or five equations (in partial differential form) to enable the phenomena to be analysed.

Our lecturer for the small group of maths honours students (only about half a dozen of us) was John Donaldson, who’d spent time in the US working with NASA on the latter type of problems, so he knew his stuff pretty well.

John and daughter Mary Donaldson

Alert readers may recognise the name – John is the father of Mary Donaldson, now the esteemed Princess of Denmark. A tough, doughty Scot, he was also a talented rugby player in his time, captaining Tasmania on more than one occasion.

Getting back to the cracking of the PDE puzzle, it seems that a team at CalTech (home of the legendary Richard Feynman) have made giant strides:

Now researchers at Caltech have introduced a new deep-learning techniquefor solving PDEs that is dramatically more accurate than deep-learning methods developed previously. It’s also much more generalizable, capable of solving entire families of PDEs … 1,000 times faster than traditional mathematical formulas, which would ease our reliance on supercomputers and increase our computational capacity to model even bigger problems.

I’ll spare you further details (read it yourself if you have the technical nous, but the essence is using Fourier space instead of Euclidean space), suffice to say that it’s struck so many nerves that even the rapper MC Hammer has tweeted it!

And out of respect, for this really is an insightful and creative piece of work, I should name the people who cracked it: Anima Anandkumar, Andrew Stuart and Kaushik Bhattacharya.

Finally, if you’d like to read their groundbreaking publication (I admit to understanding the Introduction, but not much else), click on the link in the quote above or click the pic below.

Interactive video teaching and learning – decades ago

Students and teachers around the world have been engaged in various forms of online and video-based education this year. Overall it seems to have been reasonably successful, another step in the advances in teaching with technology.

But is it new and innovatory? No, of course not. And, coincidentally, I’ve been cleaning out cupboards, drawers and shelves lately, in preparation for a move, and came across a project report from over three and a half decades ago concerning this mode of education. Continue reading

My greatest contribution to Monash University – changing one letter

A fine moment – but not my finest!

I worked for Monash University for eight years, in two stretches – from 1998 to 2001 and from 2005 to 2008. My first appointment (the more pleasurable) was as Associate Professor of Flexible Learning in the Centre for Higher Education Development (CHED), and the second stint involved a progression in a number of steps, culminating in my role as Professor and Director of the Centre for the Advancement of Learning and Teaching. I resigned/retired hurt in 2008. Continue reading

Why I love sailing

Though I’ve never owned a yacht, I’ve always liked sailing, especially in small dinghies. This comes from my early teenage years, when I was lucky enough to spend summer weekends as a forward hand with a couple of school friends. Hobart is the perfect place for sailing, with its large river estuary and regular southerly sea breezes blowing up the River Derwent. There are plenty of clubs scattered around the bays and points, and the one I joined was the Sandy Bay Sailing Club. Continue reading

Reminiscence – Kevin Sinclair

In 1985, as a young family, we moved to Hong Kong, where I had obtained a job at Hong Kong Polytechnic, now (in)famous for the student occupation and protest of 2019. As an expatriate staff member, I was entitled to subsidised housing, and we were duly allocated to Pak Tak Yuen, out at Shatin in the New Territories. The accommodation was spacious by Hong Kong standards, and we shared the quarters with a motley collection of families from around the globe (UK passport holders were unsurprisingly predominant, and there were also Hong Kong Chinese families, albeit with foreign passports). Continue reading

“Ho perduto due corone!”

Ho perduto due corone! – My two Rosary beads are missing! – these were the first words (not that I understood them) uttered by Linda’s mother as we arrived to help her with the recarpeting of her bedroom. We got there nice and early, as the carpet layer was due at 8:30 am. It was no great surprise that the Rosary beads were missing, as she is nearly 90 years old (not Linda, her mother) and legally blind. She can apparently still see vague shapes, and manages to live alone in her house and beloved garden, with the regular assistance of Linda and her two sisters, one of whom lives next door. Continue reading

Martin Weller does it again!

I’m older than Martin Weller. So his new book, 25 Years of Ed Tech, doesn’t seem to cover a long enough period to me (reminder: print is a technology). Nevertheless, it’s a full and enriching outline of the impact of the internet and associated technologies on education, so you’d better read it. Thanks to Martin and Athabasca University Press, the online version is free. Continue reading