The paradox of giants
Galileo argued that the giants of folklore, taking human form but at much larger scale, are physically impossible. Similar ideas will lead us to many other paradoxes of dimension.
According to legend, giants once roamed the Earth. Odysseus encounters the Cyclops, the one-eyed son of Poseidon, living in a huge cavern, hungry and angry—he grasps men and sheep in one hand, devouring them whole. In the days of King Arthur, a clever young boy earns the title Jack the Giant Killer, using his sharp wit to outsmart and slay the various giants plaguing the land. Another Jack—or perhaps it is the same Jack—famously plants some magic beans and climbs the beanstalk to a castle in the clouds, cleverly outwitting the giant residing there. Jonathan Swift's character Gulliver travels to lands afar, encountering the Lilliputians, a society of tiny people to whom he appears as a giant, as well as the Brobdingnagians, a society of giants to whom he appears Lilliputian, thereby experiencing giantism from both perspectives without himself ever changing size.
All these giants of legend have generally human form, but at larger scale, and they undertake generally human activities—the giants walk about, stomp, dance, carry heavy loads, run, climb ladders, throw stones, and so forth. They act and move about in a human manner, but at scale.
Gallileo's paradox of the giant
Galileo argued that this naive folklore understanding of the nature of giants was fundamentally flawed—the very idea of a humanlike creature, acting and moving in a humanlike manner, but at much larger scale, he argued, was simply impossible physically. In short, giants are impossible creatures.
To begin his argument, Galileo calls for us to imagine a structural beam of sturdy oak. The beam might be used to support a heavy load—perhaps a load of bricks or a great stone.
Let us now imagine also a much larger oak beam, scaled up in size, but with the same proportions and material. A thicker solid oak beam, of course, will naturally support more than a slender beam of the same wood. But how much more can it support? Will the larger beam be able to support the same load, but also scaled up in size? Should we expect the larger beam to support a scaled-up load of bricks or a great scaled-up stone?
Galileo ingeniously argues no, the larger beam will not support a similarly scaled-up load. Indeed, he argues that at a certain sufficient scale, the beam will no longer support even its own weight!
His argument relies on a certain subtle observation concerning the nature of scaling in different dimensions. His observations will lead us to many further paradoxes of dimension.
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