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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Yes, you could. However, because they’re in different units, you would need to convert between them before you can get any meaningful information out of it. If you invent a new unit for each different edge length of a cube, then you have an infinite number of different units, and if you wanted to say anything like “cube X is twice as big as cube Y” you’d first need to re-measure cube Y using the same unit you measured cube X in.
So, a 1x1x1 ft cube does have a total surface area of 6 square feet, and a 1x1x1 meter cube has a total surface area of 6 square meters. But a 1x1x1 ft cube is also a 0.3×0.3×0.3 meter cube with a total surface area of approximately 0.55 square meters, demonstrating that this 6:1 ratio is really just an illusion of the chosen measuring system, not an actual fact of reality. Remember, units are just something we use to be able to talk and think about reality in convenient ways. Measurements aren’t real. The only real thing here is the fact that the surface area of a cube increases exponentially as you increase the edge length linearly, and this is true in every unit you use to describe a cube increasing in size.
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