International Society of Biomechanics
Gold sponsor

ISB NOW

 

Here, you will uncover historical information about the society. Enjoy these nuggets curated by John Challis, our Archives Officer.  

btt_march.jpeg

 

Ever since its publication in 1726 Jonathan Swift's Travels into Several Remote Nations of the World by Lemuel Gulliver, commonly known as Gulliver's Travels, has been popular. The book offers a satirical perspective of the politics of the time, and an examination of whether human nature is inherently corrupt or just susceptible to corruption. Modern readers may miss some of these elements but be intrigued by Gulliver’s travels to different (fictitious) lands. In Part I he finds himself in Lilliput where the inhabitants are less than 6 inches (~15 cm) tall. While in Part II he finds himself in Brobdingnag where the inhabitants are about 72 ft (~22 m) tall. For the biomechanist these different heights raise questions about how human movement scales with such extremes in standing height.

Questions about body size are not new and were considered before Swift, for example by Galileo Galilei (1637). The ISB has been producing newsletters for its members for over 40 years. In 1993 in issue 49, Jan Oderfeld, professor at the Warsaw University of Technology, presented an analysis of aspects of Gulliver’s time in Lilliput and Brobdingnag. For Lilliput his analysis focused on: the machine used to transport Gulliver; Gulliver’s ability to tow most of the fleet of an enemy; and the jumping ability of the Lilliputians. For Brobdingnag his analysis focused on the production of vocal sounds by the people of Brobdingnag. Oderfeld was able to conclude that the majority of Swift’s mechanical analyses were correct. To provide context, writing on the systematic application of dimensional analyses to mechanical phenomena did not occur until after 1726 (De A. Martins, 1981), and its formalization occurred much later (e.g., Buckingham, 1914). Swift’s ability to correctly scale many aspects of human movement is all the more impressive considering Swift, a graduate from Trinity College Dublin, had focused his studies on subjects required for the priesthood.

In Part I, Chapter 3 there is the following text,


“…the emperor stipulates to allow me a quantity of meat and drink sufficient for the support of 1724 Lilliputians. Some time after, asking a friend at court how they came to fix on that determinate number, he told me that his majesty’s mathematicians, having taken the height of my body by the help of a quadrant, and finding it to exceed theirs in the proportion of twelve to one, they concluded from the similarity of their bodies, that mine must contain at least 1724 of theirs…”


Swift’s assumption here is that energy consumption is proportional to body mass. For geometrically similar objects their mass (M) is proportional to their height cubed (H3), therefore if Gulliver was 12 times taller than the average Lilliputian then his energy consumption would be greater by a factor of 123 = 1728 ≈ 1724. Measurements of basal metabolic rate (P) indicates P does not scale so that P ∝ M, for example Sarrus and Rameaux (1839) argued that P ∝ M2/3. Kleiber (1932) presented evidence that the relationship might be P ∝ M3/4. While the value of the exponent and the mechanisms governing it are hotly debated (e.g., Glazier, 2022) it is typically less than 1, suggesting that Gulliver was provided with too much food. Swift’s assumption about the amount of food his protagonist would need was in error in light of more recent studies, but it is clear that the amount of food specified was based on a reasonable, albeit incorrect, assumption.

For more analysis of the scaling featured in Gulliver’s Travels see the old ISB newsletter article by Jan Oderfeld.

 

References:

  • Buckingham, E. (1914). On physically similar systems; illustrations of the use of dimensional equations. Physical Review,  4(4), 345-376.
  • Galilei, G. (1637). Dialogues Concerning Two new Sciences (H. Crew & A. DeSalvio, Trans.). New York: Macmillan.
  • Glazier, D. S. (2022). Variable metabolic scaling breaks the law: from ‘Newtonian’to ‘Darwinian’approaches. Proceedings of The Royal Society B, 289(1985), 20221605
  • Kleiber, M. (1932). Body size and metabolism. Hilgardia, 6(11), 315-353.
  • De A. Martins, R. (1981). The origin of dimensional analysis. Journal of the Franklin Institute, 311(5), 331-337.
  • Sarrus, F., & Rameaux. (1839). Rapport sur un memoire adresse a l" Academie Royale de Medicine. Bull Acad. Roy. Med. Belg, 3, 1094-1100.

Back to Table of Contents