The giants of legend have a humanoid form, and they undertake generally human activities — walking, stomping, carrying heavy loads, running — only at a larger scale. But if human giants did exist, could they actually survive in this form?
In his foundational 1638 text "Dialogues Concerning Two New Sciences," Galileo Galilei argues that this folklore understanding of the nature of giants is fundamentally flawed. He contends that this idea of a massive humanlike creature is, quite simply, physically impossible.
To begin his argument, Galileo asks us to imagine a structural beam of sturdy oak supporting a heavy load — a load of bricks, or a great stone. Now imagine a much larger oak beam, scaled up but with the same proportions and material. It will naturally support more than the smaller one. But how much more? Will it support the same load, scaled up?
Galileo first observes that the load-bearing strength of a beam depends on its cross-sectional area, since the beam fails by breaking across a cross section. Area scales as the square of the linear factor, so a 10-times larger beam will have a cross-sectional area 100 times larger than before. In other words, a 10-times larger beam is 100 times stronger!
That may seem good. But the weight of the load, for a given material density, is determined by its volume, and volume scales with the cube of the linear factor. Scaling that load up by a linear factor of 10 causes a 1,000-fold increase in volume — a 10-times larger stone weighs 1,000 times more.
Now put the two together. A 10-times-larger beam is 100 times stronger, yes, but the similarly scaled-up load became 1,000 times heavier. If the smaller beam had been carrying the optimal load, the scaled-up beam would support only one-tenth of it. At a sufficient scale, a beam will no longer support even its own weight: its strength scales with the square, but its mass scales with the cube.
Now back to giants. Picture the bones of a giant serving, in effect, as structural "beams" supporting its body mass, its flesh, and muscles. If the giant's bones are made of the same stuff as ordinary men, his strength has not scaled the same as his mass.
The same logic applies to everything around such a giant. Scaled-up wooden ladders would not support a scaled-up giant climbing them; scaled-up wooden houses would not support their own roofs; a scaled-up wooden chair would not support even itself, let alone a giant sitting in it. The entire world of giants as pictured in folklore does not fully make physical sense.
Galileo's argument explains more than the nonexistence of human giants. It also explains why animals such as rhinoceroses, elephants, and dinosaurs tend (or tended) to be stocky, with proportionally thicker, sturdier bones than smaller animals. Elephants have much thicker legs relative to their size than do dogs and cats: bone strength depends on cross-sectional area and scales with the square, while the weight of the animal scales with the cube, so the bones must become proportionally thicker to carry the extra weight.
Galileo glimpsed a subtle, secret aspect of our physical existence: he perceived the core dimensional nature of strength and mass, realizing as a purely mathematical consequence that they scale differently in different dimensions. Our lives would not be the same at a different scale. Giants are impossible. And as for humans, there is a very good reason we are the size we are.