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There is a funny scene from the cartoon Adventure Time where there is “Powers of Ten” zoom to such an extreme degree that the zoom ends up returning to where it began, leading the protagonist to yell “Everything small is just a small version of something big!”. Thinking about the physics of the situation, are similar structures and objects really repeated and copied at different orders of magnitude? Let’s start by considering the fundamental interactions that make up all the objects we can see.

There are four forces that we know of in the universe:

1. The electromagnetic force, which is what you think about when you see a compass needle move, or see lightning, or feel a statically-charged ballon raise the hair off your head.
2. The strong force, which is what keeps the protons and neutrons in the atomic nuclei together.
3. The weak force, which is responsible for radioactive decay, and finally
4. gravity, which keeps us firmly on the Earth’s surface.

Both the weak and strong force only really act on atomic scales and do not extend past the diameter of a nucleus. We don’t see their interactions in our day to day life. The strong force doesn’t have a lot to do with keeping the bricks together in a building or making steel and stone as hard as they are, and isn’t noticeable unless you’re looking at things as small as nuclei. Gravity, on the other hand, has an infinite range of distance, and we definitely notice how apples fall to the Earth and how the Earth orbits the Sun, but gravity is so weak that we need things as big as the Earth and Sun before we begin to see its effect. The gravitational force between my desk lamp and my pencils is completely unnoticeable.

So really, the interactions that we most readily grapple with as human-sized beings are those caused by electromagnetism. The pencil does not fall through the desk because of electromagnetic forces from the atoms in the pencil repelling the atoms in the desk. The pressure I feel on my back and bottom when I sit down in a chair is a similar kind of repulsion. The light I use to see the world is electromagnetic radiation interacting and reflecting off the charged particles of the objects around me. Taste and smell, which are chemical reactions, are exchanges of ions and electrons which are all primarily governed by electromagnetism. My brain and muscles are predominantly electrical impulses and signals.

Planets and stars all really look the same, and that’s predominately the fault of gravity. Atoms are practically/theoretically indistinguishable from each other. But animals, plants, and minerals- their wide difference in form, color, shape, texture and motion is all a product of electromagnetism. What variety! It’s amazing how one force can create such diversity. And yet, even in all this diversity, how do things change as you zoom in or zoom out?

Look at this picture of a mountain. How big are the rocks in the foreground, if you had to guess? How high? 4 feet high? 400 feet high? A mile high?

Do you see those colors close to the base of the picture? Those yellow, blue, and red spots? It looks like trash on the ground, right? Let’s look closer.

It’s actually base camp of Everest. (Here is the website where you can really play/zoom with the image).

What looked like scattered trash is actually the living structures of quite a few hundred people. And those rocks that looked like boulders that might rise up 4 feet or so, are actually cliffs that rise up a few 100. Our eye ( without context) can’t seem to recognize how big something with a ‘natural’ shape (like the shape of a rock) is. So nature really does copy and repeat its patterns at multiple scales of size. It’s a lot like a fractal, in which you can zoom in quite a bit and then return to a copy of the thing you started out with.

So in a sense, sometimes big things are just copies of small things, but it depends on how small or how big you go! If you go too small, like the size of an atom, you won’t see these shapes repeated again. Once you get to the size of a nucleus, the electromagnetic force stops being the only player in the way things are structured, and you need to start taking into account the strong force. Same thing for when you go too big. Gravity plays a much larger role on the scale of planets and stars and will have a similar effect on changing how things are structured.

But for sizes that aren’t as big as planets or small as atoms, why do shapes repeat at different scales? Why can’t I tell if the rock is 5 feet tall or 500 feet tall? It’s a fascinating question! I like to think it has to do with the fact that it’s a product of how the force of electromagnetism likes to align molecules in regularly repeating patters, whether in a crystal or other such structure, and that structure can simply keep on repeating and growing and repeating to any size. Whether that size is a mile or a meter, the underlying, organizing structure is the same, and so it looks the same.

But even with the tendency to repeat the same pattern at different scales, how is it that electromagnetism can allow such diversity of phenomenon? The fact that electromagnetism can create forests and trees and animals, as well as being the source of how we look and feel (consciousness is electricity, if you reduce it enough) while on the other hand gravity only seems adept at making very big spheres— is there something special about the mathematical nature of electromagnetism that gives it the ability to be so myriad?