As a scientist you are always in danger of getting stuck in your tiny little corner, struggling with the particular research problem that you haven chosen at the moment. So from time to time I like to remind myself of the bigger picture. One good way of doing this is just looking out of the window and trying to think about which of the natural phenomena you see around you everyday we can understand already.

Instead of a view out of my window, here is a picture I took two years ago. It is a fountain in the Tuileries near the Louvre in Paris. You encounter it when you walk from the Louvre to the Obelisk.

Now that seems pretty simple: Some water, the stone of the fountain, and a dove. Also, there’s part of a chair in the foreground.

Try to think for a moment which natural phenomena enter this picture.

There’s the water with the little ripples, there’s the reflection of the sunlight, there’s the material of the stone.

But before we turn to those things, there’s the fact that you can see this image at all. That is, how do your eyes perceive an image? In fact, all of it can be explained by a very simple rule: Light rays travel in straight lines, until they hit a surface, where they are absorbed or reflected, and finally they hit your eyes. Light rays as straight lines is a very powerful concept: For example, it lets you predict how the shadows should look like, if you know where the light comes from. It’s also the reason for the phenomenon of perspective, and light rays are used in computer graphics to calculate the appearance of a three-dimensional scene.

The Tuileries gardens were created in 1564. So how much of the story about light rays was known at the time? It turns out, pretty much everything! Already Euclid had written a treatise called ‘Optics’ where he used light rays, and the Greek and Romans knew how to make some kind of lenses. Wearable eyeglasses based on these concepts had appeared in the 13th century, at around the same time that perspective was discovered in art. So light rays would have seemed a very well-understood concept to every scientist you might have met at the time strolling through the Tuileries. (see Optics page in Wikipedia)

Then, what about the water? Obviously, the most basic ideas about water were known in a qualitative way throughout history. Otherwise you would have a hard time steering ships through water. Archimedes had described the concept of buoyancy already: An object that is lighter than water will be pushed up. And Leonardo da Vinci had been drawing many sketches of swirls of water (vortices), inspecting them closely. But none of them could have given you predictions of how exactly the water currents would look like when you moved a ship or any object through water. Those insights still had to wait more than 200 centuries. People like Newton and Leibniz would first have to develop the idea to describe changes as composed of many very small steps (differential calculus). That was around 1700. About half a century later, mathematics had become advanced enough to describe in the same way small changes in space and time (partial differential equations). So in 1757 Leonard Euler wrote down the first equations of fluid dynamics, describing how the velocity field of a fluid like water (or air) would change with time. If you know the velocity at every point in space at this moment in time, you can predict it for the next moment, and from there on to eternity. (see Euler equations on Wikipedia)

With a few additional steps (like introducing friction into the equations), these equations for fluid flow have become extremely powerful. They can now be used to simulate the flow of air around the wings of an airplane, completely in the computer before the plane ever takes off for the first time. And they predict the changing weather patterns at least for a few days in advance, which is good enough to be useful. All of that came about because people were not content with just knowing in a rough qualitative way how water may behave, but tried to systematically analyze the details, a process that needed centuries because all the mathematical tools first had to be developed.

(to be continued)