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Once Upon a Prime...and why Gulliver was lying!

I very much enjoyed this book by Sarah Hart in which she explores the connections between maths and literature - and takes a bit of a detour into physics (and biology) when discussing the work of Jonathan Swift in Gulliver's travels.

Gulliver visited many worlds on his travels. Lilliput - where he was a giant among little people is the most famous - but he also visited the world of Brobdingnag where the residents were 12 times the size of humans, and where he was the 'little person.' But there is a problem with this....

Volume is proportional to the cube of length, so a person twelve times as tall as a typical human would be 1728 (12-cubed) times their volume - and presumably mass. But area increases with the square of length, so the cross-sectional area of their bones would be only 144 (12-squared) times the original.

And pressure is of course found by dividing force by area - and the pressure that our bones must withstand is found by dividing our weight by the cross-sectional area of our bones. This means that the giant's bones would need to withstand pressures that are 12 times the pressures experienced by a typical human bone (1728/144). But Gulliver tells us that the giants are human in form - and human bones can only withstand pressures about 10 times the normal. The Giants would have collapsed under their own weight!

But even more interestingly, for the Lilliputians the effect is reversed. They were only 1/12th of our height and a similar calculation to that above means that their bones were - in relative terms - far, far stronger than ours. So much so that that they could withstand impacts onto solid ground at speeds of up to 42 m/s. And - also due to their small size - If they were to jump from a height, their terminal velocity would work out at about 4.2 m/s! So they could jump from any height and survive the fall!

So the little people are strong and the giants weak - but they would lose out in other ways: scaling down, we know their daily energy requirement would be about 9.3 calories. But as all crops on the island were also scaled down the people on the island would have to eat something like 25 meals a day just to survive. There really wouldn't be times for much else!

All this and far, far more at Buy Once Upon A Prime Book at Easons

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