For example, why can you slap a fly mid-air and it’ll probably survive just fine, but if you scaled the same amount of force to the size of a human’s size/weight, they’d probably die?

In: 14

Here is a great video giving a fun animated explanation. This whole channel is pretty great if you like this sort of thing!

It’s a thing called the square cube law.

Imagine a cube of water 1cm by 1cm by 1cm. If it’s resting on the ground, it has an area of 1cm^2 to rest on, and it has a volume of 1cm^(3).

If you take that same cube and scale it up in all directions so that it is 10x10x10cm, then it will have an area of 100cm^2 but a volume of 1000cm^(3). There is 10x as much volume for the given surface area.

Another way of thinking of this is that in a 1cm^2 area, there is now a 10cm column of water instead of a 1cm column.

How does this apply to insects? All sorts of ways. So many things dealing with motion and force transfer and so many other things care about both the surface area and the mass, and the ratio of mass to surface area is wildly different at that scale, meaning our preconceptions based on what happens at our scale are completely wrong.

Look at a column. The strength of a column is related to how thick it is, not how tall it is. If it’s radius was doubled, it’d be able to hold a lot more weight, but if it was twice as tall, that doesn’t make it stronger.

To be more specific, it’s strength is related to the area of its cross-section. Since areas are 2D, when you scale them up, they get bigger by the square of the scaling factor. Simply put: scaling a shape by 2 increases its area by 2^(2) = 4. So scaling the radius of a column by 2 increases the cross-sectional area by 4, and it’s 4 times as strong.

But weight is related to volume, which is 3D, so it scales up by the *cube* of the scaling factor. Scaling a 3D shape up by 2 increases its volume by 2^(3) = 8. So scaling the radius *and* height of a column by 2 increases its volume, and therefore weight, by 8. It weighs 8 times as much.

So scaling something up increases its weight much faster than it increases its strength. So more of its strength must be used to support that weight, until it is so heavy it can’t even support that weight with its given strength so it collapses.

Conversely, scaling it down decreases its weight faster than its strength, so more of its strength is freed up to do other things, like resist a swatting human hand.