Giant concerns

Considering the second voyage of Gulliver, i.e. to the land of giants, Brobdingnag, the giants are supposedly 12 times taller than humans. In the case of Lilliputians, they were 12 times shorter. So did Swift get his biology right?
If linear dimension is scaled 12 times, the volume would be 12 cubed, so the mass of such a giant could be easily a thousand times more, whereas the bone area would increase only by a factor of hundred. So each unit area of bone would have to bear a load ten times more than that of in humans. But bones would break at such loads. So as Haldane writes in his essay "On being the right size", each time such giants took a step they would break their bones.
Similarly many other quantities scale with linear size. Even the frequency of the vocal chord will be much lower, so Gulliver would not have been able to communicate with them!

What about trees in Brobdingnag? Would they be 12 times taller than our trees? The reader is encouraged to try it as a problem. Hint: The height of a tree is governed by a balance between gravity and surface tension (which is responsible for capillary action for transport of water and minerals).


What about birds? What would be the size of the largest birds in the land of Brobdingnag. Hint: The flight of a bird is a balance between air drag and gravity. The velocity of take off scales as square root of the wingspan.
Similarly the heat production in the brain would also be ten times more. So the Giants are literally hot-headed!

For details click here
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Further read:
1. On being the right size - J B S Haldane.
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Numerology:
The pair of numbers (5,4),(11,5),(71,7) are called Brown numbers. They satisfy the condition that
for a pair (m,n). Erdos had given a conjecture that these are the only three numbers that satisfy this condition. Can you find other pairs?
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Image courtesy:
1. http://www.theispot.com/whatsnew/2009/12/john-walker-gulliver-s-travels.htm.
2. http://en.wikipedia.org/wiki/List_of_U.S._state_trees.
3. http://www.noelkingsley.com/blog/archives/attitude/.