Imagination and Mathematics: A Tale about Knowledge – 1/4

There are no limits to imagination.

Consider an apple falling from a tree. What presses or draws the apple downwards? Gravity, you say. Well, imagine gravity then.

To-dimensjonal «rubber sheet»-analogi av romtidskrumning som er forårsaket av et objekt med masse. Kilde: NASA (
Image 1: Two-dimensjonal «rubber sheet»-analogy of spacetime curvature due to an object with mass. Source: NASA (

There are many ways to think about gravity. For example, one may consider space itself to be a kind of fabric, which is fastened to some structure such that a body of mass lying on top of it will distort it (see image 1 or click here). Alternatively, what drives gravity may be a particle racing back and forth between the apple and the Earth to inform both that they should attract each other.

Did you catch the nuances in how they talk about this in the videos? If not, go ahead and click on the links once more. Physics is about facts, isn’t it? Do they talk about facts? Many people think exactly that, because both ways of explaining gravity have been used so often that it is easy to believe them to be truth, instead of describing truth, which, in fact, they do not actually do very well. For example, think only about how we live in a three-dimensional world, while our piece of fabric is two-dimensional.

Thus, we get lost between what we think we know and what we imagine. For it is possible to come up with solutions to all sorts of questions. Imagination is (almost) without limits after all.

Einsteinkryss. Kilde: ESA/Hubble/NASA (
Image 2: Einstein cross. Source: ESA/Hubble/NASA (

Does that mean we should just invent things?

Look at image 2. This is a so-called Einstein-cross. What you see here is something, which Einstein’s equations on general relativity predict. The effect is known as gravitational lensing. There is a galaxy in the center, while the four smudges around it are light from the same source that gravitational forces led around the galaxy.

The image’s content is not simple, even though one can describe the picture itself rather easily, let us say, in the classroom. However, we do not just want to describe, do we? We would like to know why things look like they do. We want to know how they work.

Consider now a bright pupil, who thinks a little bit more about the Einstein-cross and concludes that this has to be the same phenomenon as when you are up to the knees in water, and your legs look like they are folded forward.

Image 3: Gravitational lensing. Source: NASA/ESA (f.eks.

The student is both interested and shows deductive skills, but fails to grasp the truth by quite some margin. What will you answer as a teacher? Perhaps you point towards image 3. For in this way one has to imagine gravitational lensing: Light follows a straight line which starts at its source and follows the curvature of our fabric – no, let us stop. We have already established that this is not an explanation.

Let us rather admit that we should probably not be so surprised about physics being so alien to many people. Curiosity is not lacking, but it is challenging, since physics deals with things that seem to have no deep, satisfactory explanation. And what is worse, the thoughts above do not just apply to gravity. They apply to quantum mechanics, aerodynamics, the “Big Bang” (?!?) and the particle-wave-duality. With respect to these and many, many other topics like them, it is simply necessary for us to invent something that resembles an explanation.

We do so happily, and the more we use the images we think up, the more we tend to accept them as reality. Do not deny it, but try to pay attention to what you say and do in everyday life. We are humans. Humans do things like this all the time.

Back to gravity and, for some reason, my daughter: When she was around one year old, her favorite game was to drop stuff. Her eyes eagerly followed every lego-giraffe, teddy bear or porridge plate, which she pushed over the side of the table. Then she would smile at me. I usually sat on the floor already, prepared as I was.

Did she know what gravity is? That is a weird question in many ways. It has a rather obvious answer. Then consider this: Do you know what gravity is?

Of course, you do. That is weird, isn’t it?

Why do you know what gravity is, while my daughter did not? How can you know it?

(With thanks to Sebastian Holmgård. To be continued.)

Now read this:  Imagination and Mathematics: A Tale about knowledge – 2/4

2015-03-14 18.46.20Alexander is a physicist, teacher and storyteller. You can follow him on Twitter, Facebook, and Instagram.


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