Galileo Galilei proved the constraints of scale

Galileo Galilei proved the constraints of scale more than 400 years ago. How large animals, trees, buildings or other things can get is fundamentally limited:

When an object is scaled up in size, its volumes increase at a much faster rate than its areas. Let me give you an example: if you double the dimensions of every length in your house keeping its shape the same, then its volume increases by a a factor of 23=8

while its floor area increases by only a factor of 22=4

Therefore our fantasies of mega buildings, giant beetles, ants, spiders, or for that matter, Godzillas, so graphically displayed by the comic and film industries, are physical impossibilities. Thanks to physics we can have a very good idea where to draw the line between fiction and reality.

This has huge implications for the design and functionality of much of the world around us, whether it’s the building we live and work in or the structure of the animals and plants of the natural world.

In plain English, for each dimension increase of one order of magnitude (that is jumping from 1

sq foot to 10 sq foot) the volume increases 3 orders of magnitude (1000 or 103) while the area increases by 2 orders of magnitude (100 or 102).

What that means is that the weight disproportionately increases relative to the increase in strength. Simply put scaling dimensions by orders of magnitude will run into physical impossibilities because the strength (denoted by increases in surface areas) cannot support the increase in weights (denoted by increases in volume).

Scaling works on the opposite direction as well. That is why it is far easier for a small dog to carry 3 dogs on its back but a horse cannot even carry 1 horse. As we get smaller strength gets disproportionately bigger. A small ant can carry 100 ants because the smaller the body the greater its relative strength.

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