What I am thinking: differential geometer and structural engineer Allan McRobie

On Wednesday, the academic bookshop Heffers at Cambridge (UK) was packed for the book launch of “The seduction of Curves: the lines of beauty that connect mathematics, art and the nude”. The author Allan McRobie is a Reader in the Engineering Department at the University of Cambridge, where he teaches stability theory and structural engineering. He previously worked as an engineer in Australia, designing bridges and towers. We are intrigued by the work and writing of Allan and asked him some questions.

McRobie DSC_0369_copyBW

Sigrid Adriaenssens: Why did you, a structural engineer, write a book about the seduction of curves?

Allan McRobie: My structural engineering specialism is stability. Even if my buildings are boringly rectilinear, more like a standard office block than your lovely gridshells, their stability is governed by a smoothly curved energy surface.  My stability lectures are thus full of curves. A few years ago, I introduced life drawing classes to the Engineering Department here in Cambridge, and in one such class it occurred to me that the curves I was so contentedly drawing on my sketchpad were speaking the same language as the curves in my stability lectures – a beautiful language of folds and cusps and swallowtails. The worlds of careful engineering calculation and of freer graphical expression were thus suddenly and unexpectedly linked. And the more I thought about the link, the more it exploded into wider realms of optics, physics, architecture and art. My book even has a section on the history of landscape gardening, and another – related to the seduction part of the title – on evolutionary biology. To my mind at least, these areas are all connected by a rather beautiful thread of ideas, all related to curves.


What is the relationship between art, the nude, and engineering?

The curves are the link. In stability theory, there is a precise notion of how you look at a curved surface, and of how the act of perception creates outlines. In engineering these are the stability boundaries we must not cross. Exactly the same happens in art – how the act of perception of a painter or a photographer takes a smooth surface curving through 3D – the body of the model –  and “flattens” it down to 2D in the painting or the photograph. Or when you look at a sculpture, your eyes create a 2D image of the 3D object on your retinae. The language of folds and cusps is created by this “flattening”. The reason “the nude” enters is because the nude constitutes a large part of art history, and because a large part of our fascination for curves originates, I believe, from evolutionary biology. The bodies of our mates are curved and our genes predispose us to like the body shapes of our mates. I think a number of architects have drawn on this. Obviously there is Oscar Niemeyer, but also more recently, Future Systems have knowingly tapped into this with their Selfridges in Birmingham, UK.  I think a lot of beautiful modern buildings draw on this, but without saying so.


What is your favorite curve and why?

Like Salvador Dali, my favourite curve is the swallowtail. It has two back-to-back cusps connected by folds.  You can find swallowtails in many beautiful locations on the body.  I chose a lovely example for the cover of my book. For me, it is rather emblematic of how the mathematics of catastrophe theory has something to contribute, not just to the understanding of downfall and disaster, but to beauty. For me, the swallowtail is The Line of Beauty.

The swallowtail curve

Can you give an example of where this curve (or another curve) appears in engineering theory and can you explain the meaning of that engineering curve?

The easiest example is the cusp. In my book, I describe how a cusp can most readily be found on a sort of “ski slope” surface. On one side of the ski slope you can ski down smoothly, as per usual. On the other side, there is a smoothly overhanging precipice, and if you ski down that side, you have to jump from the overhanging lip to the slopes below.  There is a smooth transition between the two sides, so the whole ski-slope is smooth everywhere.  If you draw that ski-slope, you end up drawing a cusp.  Now, not only can you find this morphology at many beautiful places on the body, but that surface is exactly the object that underlies my first three lectures on stability theory. I can explain exactly how a column does or does not collapse by looking at that surface from different directions.


What is your greatest achievement and why?

Well, after my children and any positive contribution I may have made to my students, it is probably one of my recent papers on graphic statics. It is entitled, rather pompously, The Geometry of Structural Equilibrium, and it extends the field of graphic statics into whole new realms of possibility. It only appeared this year, in the Royal Society Open Science journal. One thing I really like is that the description of structural equilibrium that emerges looks remarkably like Maxwell’s description of electromagnetism.  The geometry that Maxwell used to fuse electricity and magnetism into a coherent whole – electromagnetism – was so radical that it did not even fit into the Universe. It took another forty years before Einstein came along and said “Well, we’d better change the Universe then”. Maxwell was also one of the founding fathers of graphic statics, and whilst my contribution is utterly minor in comparison, I like to flatter myself that if anyone would like my new description, it would be Maxwell.

Oh, and I think the ending of my book is pretty good, too. I am secretly quite pleased with that.

What question are you never asked and would like to be asked? What would be the answer?

That’s a good question but a tough one. I guess it is all those questions whose answers are important, but where no-one ever asks my opinion, let alone follows it. One example would be my views on student fees in the UK. I think they are a disgraceful injustice, a tax by which my generation trick young people into paying off our debts. This deeply affects me as a University lecturer. Previously I taught because I enjoyed it, and students listened because they wanted to.

Now, I am told that I am just paid to deliver a service that will allow those who pay me to go out and earn a higher salary. That is not why I get out of bed every day. Fortunately, my students remain as wonderful as ever, but I am deeply embarrassed by the knowledge that each of them will be repaying my wages for decades to come. It is such an injustice, and no-one ever asked me – they simply made me complicit in it all.

All images courtesy of Allan McRobie and Helena Weightman, unless otherwise specified.

Check out the book, The Seduction of Curves, here.






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