Welcome to the Lectures on Infinity, a series of lectures exploring all my favorite paradoxes and conundrums.
In this third lecture, we shall explore the paradox of giants, showcasing Galileo’s argument that the traditional giants of folklore—taking human form but at much larger scale—are physically impossible. He argued on the basis of an understanding of how size scales differently in different dimensions. Similar ideas lead to the paradox of Gabriel’s horn, the painter’s paradox, paradoxical fractals, and to many further paradoxes of dimension. By the end of the lecture, we shall glimpse some genuinely troubling conundrums in high dimension.
A transcript of this lecture is available.
Find the lectures here on Infinitely More in the lectures-on-infinity tag.
The lectures will appear on YouTube.
The whole lecture course is hosted at Ergo: Lectures on Infinity.
Find other philosophy lecture courses at Ergo.org.
This lecture is based on my essay The Paradox of Giants.
The essay also appears in my new book, The Book of Infinity.
Another interesting aspect of the paradox of giants feels like it cuts the other direction. Wind resistance is proportional to cross section, so grows as a square. But the energy available is proportional to the number of mitochondria, which is the same as the number of cells, which grows as a cube. All other things being equal, larger beings can fly faster. This is why birds can catch insects, and why falcons can catch pigeons, and eagles are kings of the sky. Hand-held drones are slower than the big ones, and the big ones are slower than the very big Shaheds, which still rain down on Ukraine at a rate of hundreds per day. But even the newest jet Shaheds can be hunted by the larger fighter jets. And a swarm of flying nano-bots will chase you with the speed of a glacier.
Of course, all other things are not equal, and it becomes challenging to bring all the energy produced by a body into one purpose (flight) as the body gets large. We don't have jumbo-jet-size fighters, and we don't have pteradactyl-sized eagles.
The paradox of giants is also why large people sweat more with the same workout: generated heat is a cubic, but the surface area to release that heat is only quadratic.