Disclaimer: I did see a previous question touching on something like this but what I’m confused about was NOT addressed so hopefully this is allowed.
They say that the surface area volume ratio limits how big things can grow because surface area scales as a square while volume scales as a cube, so the ratio of volume to surface area goes up as you get bigger. Fair enough. BUT: how is this not just a matter of what units you’re using?
For example, a 1x1x1 ft cube has a surface area to volume ratio of 6sq. Ft to 1 cubic foot, so 6:1. A 1x1x1 meter cube has a ratio of 6:1 too but the units are meters. Couldn’t you always define your units so that you have a 6:1 ratio with any size of cube?
To bring it back to the actual question, wouldn’t your ratio be essentially the same no matter how big your object is? Imagine you expanded everything in the universe by the same amount but kept your unit of measurement the same, you wouldn’t suddenly hit some limit where it stops working right? Does it have something to do with the size of molecules and proteins etc? Please help I am so confused
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You seem to have a few misconceptions.
Make cubes with dice.
It has a volume of one and width height and length of one with a surface area of six. (6:1)
Make a 2x2x2 dice and it is two wide, two tall and two deep, it has a volume of eight and surface area of 24 (3:1)
3x3x3 is 3 w/d/t and volume of 27 and a surface area of 54. (2:1)
4x4x4 is 4 w/d/t, volume 64, surface 96 (1.5:1)
Kurzgesagt have a great set of videos on the size of life. I think number 2 covers this pretty well.
The surface area to volume ratio is unit-independent, yes. But that doesn’t change the physical meaning of the ratio.
Say that for each cubic foot of living matter, you need 1 pound/min of oxygen. Each square foot can provide 0.3 pounds/min through it. For your 1ft cubic organism, you can provide 6×0.3=1.8 pound/min of oxygen, which is more than the 1 pound/min needed. Good.
Let’s go to the bigger cube. 1 meter = 3.3 ft. 1 cubic meter is 3.3^3 ~ 36 cubic ft, so 36 pound/min of oxygen needed. The surface can provide 6x(3.3×3.3)x0.3 = 19.6 pound/min of oxygen. Not good.
Just playing with units doesn’t change the inherent fact that volume is what determines cellular needs/uptake, while surface area determines nutrient/gas/excretion availability/rate. Since volume scales up faster than surface area, so too does cellular demand scale up faster than nutrient/gas availability.
No, because you’ll be using the same units for both the regular size, the square, and the cube. If you use different units for each in order to get the same numbers out it doesn’t change the fundamental fact that heat production in a mammal scales with the cube while its ability to dissipate heat scales with the square, so if you double the size of the creature without making any other changes, it will tend to overheat due to producing 8x as much heat but only having 4x the surface area to get rid of it.
Creatures that don’t produce their own heat, such as lizards, don’t have the same problem, which is why dinosaurs were able to get so large. Creatures that live in the sea are also less affected because water is a much more efficient conductor of heat than air is, which is why the largest animal that has ever lived is today’s blue whale.
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