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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Surface area is a large limiting factor for life. And note that surface area is measured in square units, volume in cubed. So when you convert from one unit to another, you need to take that into account. Changing the “starting scale” also changes the ratios.
Say a meter is equal to 3 ft(approximate so that we get whole numbers). A square meter is 9x a square foot, for a total of 54 square foot. A cubic meter is roughly 27x a cubic foot. That’s a area-to-volume ratio of about 2:1, down from the 6:1 ratio of the foot measurements.
Additionally, some processes in bodies don’t scale up or down infinitely. Capillary action stops working in tubes above a certain size. Vacuums cannot lift water above about 14m.
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