The allegory of the axe follows an alien who’s view of reality is limited to a radar screen. When the alien looks at your grandfather’s axe, the alien sees only labeled blips.

From the perspective of the alien, the blue dot looks separable from the red dots. The alien believes that the blue dot can be removed from the rest, for it can surely imagine such a world:

Indeed, the radar screen seems perfectly capable of displaying such a thing. Why shouldn’t the blue dot be separable from the reds?

And yet, try as the alien might, the alien cannot separate the axe from its handle and its blade. No matter how clever the alien’s devices, the axe sticks resolutely to the handle and blade.

Of course, the alien is mistaken. Reality is not thwarting our protagonist. There is no axiom in of reality which states “an axe may not be removed from its handle and its blade”. There is no law that prevents the blue dot from leaving the red dots. Rather, the very idea is malformed. The problem lies in the alien’s labels.

The alien’s labels are overquantified. They are separated in a way that reality is not. The alien’s words have more freedom than the things they’re attached to.

The alien protests:

You say the blue dot has more freedom on the radar than it does in reality. But then what rule of reality is restricting the real blue dot’s freedom?

But there is no rule restricting the axe’s freedom. Rather, the axe is the handle and the blade. The alien has too many labels. The real axe, handle, and blade are tightly interwoven in reality, even though they look distinct on the radar screen.

It’s a simple question – can the axe be removed from the handle in the blade, and if not, why not?

No. Such a thing is impossible. Such a thing is less than impossible. Humans have been doing the impossible for centuries. I do three impossible things before breakfast. But we’ll never manage to remove an axe from its handle and its blade. No matter what technological advancements we make, no matter what new physics we discover, we won’t separate the axe from the handle and the blade.

The word “impossible” implies that a thing is conceivably possible in the first place. The alien goal isn’t impossible: it’s incoherent. It’s disjoint. The labels don’t match reality. The question is overquantified. The alien has too many labels and not enough connections between them.

You may shake your head and laugh at the alien, but be warned: you are not so different. Humans are quick to stick contrived labels on things that they do not understand. Our words are often too powerful for what they mean to say. It’s easy to recognize the alien’s mistake in a world where you get to actually see an axe, where you get to feel the wood and the metal in your hands. This mistake is not so easy to avoid when you step outside your narrow comfort zone.

Reality is tightly connected – more tightly connected than it appears on the surface. A label is not the thing it labels. Our labels for the universe were invented long before we understood the connections. Our labels are less tightly coupled than reality itself.

You may find it easy to imagine magnetism in the absence of electricity. You may be able to picture heat in the absence of motion. You probably think it makes sense to imagine speeds faster than the speed of light. But remember, when you imagine these things, that the alien thinks it makes sense to imagine an axe separating from its handle and its blade.

There are deep connections in physics that you do not know yet. This means that you cannot trust your labels. They are connected in ways that you do not understand, and until you learn what you do not know it is very easy for you to draw silly pictures that look perfectly fine to you.

There is no fundamental axiom that prevents the axe from leaving its parts. There is no mysterious force binding the axe in place between its handle and its blade. The alien just has a bad model.

Similarly, most of the restrictions in physics are not actually laws – you just have a bad model.

Whenever reality thwarts you at every turn, do not take it as a sign that reality is conspiring against yo. Instead, take it as a hint: Your labels are disjoint. The things they label are bound together in a way that you do not understand.

Reality is connected more tightly than you know.