The Two Cultures and strange circles

This is another selection from my book Playwiths, available from Amazon or through Polymoth Books. The apparent supplier is really just me, trading as Polymoth Books, but I set the firm up so I can supply booksellers and libraries more cheaply (note that some conditions apply).

This bit is free, and it probably is not for the faint-hearted

1. The Two Cultures

In very early 1959, I argued with a pompous headmaster who had a Master of Arts degree, because I wanted to continue my studies in Latin, and also study physics. He rejected my request with a crushing dismissal: “Boys who do physics do not do Latin.” That was how I became the victim of something neither of us would have heard of back then, the notion that learned society was made up of “two cultures”, the Arts culture and the Science culture.

The divided cultures had been around for a century or more, but the name “two cultures” was only proposed in 1958 by C. P. Snow, a physicist who wrote fine novels, making him a member of both cultures. Snow said that, as the Arts people saw it, the “Arts Culture” contained all the witty, urbane and articulate people.

The “Science Culture” was, according to the Arts people, made up of scruffy men (and just a few equally scruffy women back then) who were incredibly clever about extremely difficult things, but who were absolutely useless when it came to dealing with people. Scientists were stolid and uncreative manipulators of objects, lacking in personal skills.

The scientists were often absent-minded, we were told, where the Arts culture people were clear-thinking. Leave us to do the ruling, puffed the Arts people. The scientists and engineers let this go, but in their turn, they puffed that the Real Work should be left to them.

According to this divisive pair of stereotypes, creativity is only found in the Arts people, and practicality lies only with the Science people. Fuelled by these notions, the two camps are encouraged to regard each other with a less than friendly contempt. My regard for people who accept that view is far less polite. To survive and do well, it helps to have a foot in each camp. To work in STEM, you badly need the art of debate, the ability to write clearly, sketch neatly, take photos and more. You need STEAM, and the M is important.

2. Strange circles

Some non-standard round shapes. 

Once upon a time, astronomers were certain that all the moving bodies in space travelled in circles, “because circles are perfect”. In many ways, modern science began when Johannes Kepler saw that the orbits of planets were ellipses.

Or maybe science emerged when Isaac Newton proved that the orbits had to be that shape, because of the way gravity worked. Whichever way it happened, those odd squashed circles called ellipses were involved. 

 

A 19th century engraving of a Gatling gun: notice the shape of the wheels. 

To me, ellipses are important, because in perspective, circles look like ellipses, but I am no artist, and I need help to get my ellipses right. When I am drawing on paper, I use plastic templates to draw my ellipses, but with a simple graphics program like Paint.Net, I can draw ellipses of any shape and size.

If you want to work on shading and stippling geometric shapes, use a colour printer to print out pale sky-blue ellipse outlines. Make just enough fine black points on the paper to show the outline, then photocopy it: pale blue (often called “dropout blue”) usually fails to show in a photocopy, and away you go.

We will meet Piet Hein again in chapters 15 and 20 of my book (and I may get to them here, one day), but now we need to look briefly at his superellipses, which were adopted as a suitable shape for rounding-off a space in the centre of Stockholm, rather more nicely than the rounded rectangle above. If you look online for <Sergelstorg>, you can see the result in maps and aerial photos of Stockholm.

By an odd chance, Hein came up with his solution in 1959, the year in which I encountered the two cultures, and C. P. Snow published a book about his them. Surely, if anybody ever showed how the Two Cultures notion breaks down, it must be Hein. And now, we need to venture into mathematics of a Heavy Kind. 

There is a whole family of curves with this formula:

As a group, they are called Lamé curves, after Gabriel Lamé, who discovered them. If n is between 0 and 1, the figure is a four-pointed star. If n= 1, it is a parallelogram, and for n between 1 and 2, it is a rounded-off rhombus. If n=2, we get an ellipse or a circle (depending on the values of and b), and above that, we get squircles, or superellipses.

Sergelstorg has n=2.5, and a/b=1.2. Over to you, but look around on the internet for 3D supereggs and ellipsoids…