Gulliver's geometry

Gulliver's geometry was very well observed by the author of Gulliver's Travels. He very discreetly avoided the danger of being entangled in geometric relations. The reader will no doubt remember that in the land of the Lilliputians a foot was an inch, and in the land of giants, on the contrary, an inch was a foot. In other words, among the Lilliputians, all people, all things, all works of nature were 12 times less than normal, among giants - as many times more. These seemingly simple relationships, however, became much more complicated when they had to solve issues like the following:

Gulliver's geometry was very well observed by the author of Gulliver's Travels

  1. how many times did Gulliver eat more at dinner than a midget?
  2. how many times did Gulliver need more cloth for a suit than midgets?
  3. how much did the apple of the land of giants weigh?

The author of "Travel" coped with these problems in most cases quite successfully. He correctly calculated that since a midget is 12 times smaller than Gulliver, then the volume of his body is 12x12x12, that is, 1728 times, therefore, for saturation of the body Gulliver needs 1728 times more food than a Lilliputian, and we read in The Journey this description of Gulliver's dinner:

"Three hundred cooks prepared a meal for me. Huts were set up around my house, where cooking took place and cooks lived with their families. When lunchtime came, I took 20 servants in my hands and put them on the table, and 100 people served from the floor: some served food, the rest brought barrels of wine and other drinks on poles thrown from shoulder to shoulder. Those who stood at the top, as needed, lifted it all onto the table with the help of ropes and blocks".

Swift correctly calculated the amount of material for Gulliver's suit. The surface of his body is 12x12 = 144 times larger than that of the Lilliputians; by the same number of times he needs more material, tailors, etc. All this was taken into account by Swift, who tells on behalf of Gulliver that "300 Lilliputian tailors were assigned to him with instructions to sew a complete pair of dresses according to local samples". (The haste of work required twice the number of tailors).

The need to make such calculations arose for Swift on almost every page. And, generally speaking, he did them correctly. Only occasionally did he fail to maintain the proper scale, especially when describing the country of giants. Major mistakes are sometimes encountered here.

"Once, - says Gulliver, - a court dwarf went with us to the garden. Seizing a convenient moment, when I, walking, found myself under one of the trees, he grabbed a branch and shook it over my head. A hail of apples, each as big as a good barrel, fell noisily on the ground; one hit me in the back and knocked me off my feet".

Gulliver rose safely to his feet after this blow. However, it is easy to calculate that the blow from the fall of such an apple should have been truly crushing: after all, the apple is 1728 times heavier than ours, that is, weighing 80 kilos, collapsed from a 12-fold height! The impact energy should have exceeded the energy of an ordinary apple falling by 20000 times and could only be compared with the onslaught of an artillery shell...

Swift made the biggest mistake in calculating the muscular strength of the giants. The power of large animals is not proportional to their size. If we apply this to the Swift giants, it turns out that although their muscular strength was 144 times that of Gulliver, their body weight was 1728 times greater. And if Gulliver was able to lift not only the weight of his own body, but also approximately the same weight, then the giants would not be able to overcome even the weight of their huge body. They would have to lie motionless in one place, powerless to make any significant movement. Their power, so picturesquely described by Swift, could only appear as a result of an incorrect calculation.