A short story in three scales

12 Jun, 2026

Let's imagine a Danish field under the afternoon summer sun. On the smooth rolling hills you see a herd of cattle going about their daily business. You stop by the fence and greet them in your most polite mooo. Applying the pancake rule, the first one is always bad, you try again and this time you manage to attract some attention from you bovine soon-to-be-friends.

One of them, their spokescattle you suppose, approaches the fence and you can't avoid but noticing a swarm of flies hovering the animal's eyes and nostrils. 'Don't they feel the itch?' you think right before the mesmerizing movement of the flies steals your train of thought. "How would I model the movement of these annoying little insects?" you inquire.

You start from the most obvious point and think about the trajectories of all the flies. "If I were to draw them as lines they will look like a hairy sausage extending over the prairie" you pointedly observe. Not only that, but the thickness of that stochastic braid is relatively constant as it hovers the field. You decide to consider the movement of a single fly as your new acquaintance meanders through the pasture.

As every sane person would do, you take out your little notebook and scribble a simple sketch. Few moments later you tilt the page to the ruminating audience. "Not bad eh?" you say with a triumphant grin. You wait for a reaction as their distant stare penetrates your soul and a new batch of to-be-ruminated grass travels up their esophagus.

Looking back at your drawing you grasp the edge of an idea. "The fly is never too far from the cow... It moves and sways with it adjusting to the speed of the animal". And suddenly one of those intuitive thought jumps happen and you eloquently scream "The Moon is a fly! Or maybe the fly is a shaky moon to the cow". And the thought stampede arrives. "When we talk about the Moon" you gesticulate to the cattle "we say that it moves around the Earth. We assume the movement of the earth around the Sun does not influence a first approximation description of the Moon's orbit". They loosely follow your hands with their unfocused stare and that subtle nod propels you forward in thought. "I have to be able to separate the fuzziness of the fly and the slow drift of the cow. Not only that, I should be able to neglect the movement of the cow altogether!".

The fact that the fly more than 1000 times lighter than the cow accounts for how easy it can alter it's speed (accelerate). The smoother cow trajectory (dashed white line) implies a smaller change in velocity (acceleration). This makes it easy for the fly to adjust to the new position of the cow in order to center it's unpleasant flight path.

It may seem obvious that now you have semi-graphical way of proving that if you were to estimate the probability of finding a fly on the grassland you only have two independent tasks:

• Study how the fly moves around a static cow
• Study how a cow moves across the land

The solution to your question is the addition of these two decoupled stochastic movements.

As more grass-dung converters approach the fence you look at the camera¹ and, slowly walking towards it, say: "Now, kids, if you change cow for atomic nucleus and fly for electron you will have a loose intuition of the Born-Oppenheimer approximation.

#physics #post #writing