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Beware the Giant Ants! Or not ...

Is That a Big Number?

Beware the Giant Ants! Or not ...

Andrew Elliott

In the 1956 horror movie, Them, the plot revolves around "atomic testing in 1945 [that] developed ... dangerous mutant ants". 

The relationship between length, area and volume is sometimes called the "square-cube law": as the linear dimension of an object increases, so the surface area increases by the square of the multiplier, and the volume increases by the cube of the multiplier. The square-cube law explains why this great cliché of horror movies is so improbable. 

From the movie poster these ants look to be easily four metres in length, which means they must be around 1000 times longer than the 4 mm ants we are familiar with.But, in accordance with the square-cube law, a thousand-fold increase in length would mean a million-fold increase in measures of area and a billion-fold increase in measures of volume. Since the strength of the ants' legs would relate to the area of the cross-section of their limbs, while the mass of their bodies would relate to their volume, it follows that the ants' bodies would now be 1000 times too heavy for their limbs, and they would simply collapse under their own weight. The same would apply to the mass of their internal organs, now 1000 times too heavy to be contained by their chitinous "skins". Visualisation is left as an exercise to the reader.