Can anyone explain in simple terms the square cube law and how it applies to animals and people. I have seen it referenced to fictional beast, especially those who are absurdly large. But can anyone explain it what it actually means
In: Biology
Have you ever heard of that funny trick of how a pizza twice as wide actually has four times as much pizza? So a 20″ pizza actually has four times as much pizza as a 10″ pizza. The square cube law is kind of like that.
It’s not so much a biological property as a mathematical one. Let’s take it from 2D (pizza) to 3D (sphere, or pizza’s final form). A sphere has exactly one linear property, radius, which is the difference from the center to every point on the surface of the sphere. The surface area is 4πr^2 while the volume is (4/3)πr^3 . The proofs of those formulae are not hard, but not ELI5. Just know that if the radius doubles, the surface area quadruples, and when the surface area quadruples, the volume is multiplied by 8 times.
So if you’ve got a sphere of radius 10 (the unit doesn’t matter). It has a radius of 10, a surface area of 1256.6, and a volume of 4188.8. If you double that radius, like we doubled the radius of our pizza, you have a sphere with radius 20, a surface area of 5026.5, and a volume of 33510. You see that the surface area increases much faster than radius, and volume increases much faster than surface area. That’s the square-cube relation.
The biological implication of this is outside of my area, but think about it in a simple sense: We human beings cool ourselves with evaporative cooling by sweat; if we double in linear size (height) while keeping all other dimensions proportionate, we would quadruple in surface area, but increase our internal volume by 8 times (give or take), meaning that we would, proportionately, have much less skin to sweat and cool us. We would all die of heat exhaustion. Similarly, an insect that doubled its size would have 4 times as much exoskeleton which means, if its bug-equivalent of muscles didn’t get much stronger, it wouldn’t be able to move.
Again, the biology is not my area, just the math, but if a biologist wanted to chime in and explain some of those biological implications better it would be awesome. But TL;DR – the square-cube relation means that things that increase in one dimension don’t increase in other dimensions the same way, so the same physical adaptations might not work the same.
EDIT – Typos and grammar
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