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Building A Shrink Ray? Consult This Grisly Physics Paper About Exploding Horses

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In the 1920s, J.B.S. Haldane published a paper entitled, "On Being the Right Size." It is deliciously gruesome, and to this day, it remains one of the most accessible papers on the intersection of biology and physics.

The paper shows its age a little when Haldane opens with a reference to Pilgrim's Progress. My exposure to that terrifyingly pious tome was when Meg, Amy, Jo and Beth, America's most sickeningly moral girls, read it every morning in Little Women. Little Women is set during the Civil War. Pilgrim's Progress was considered old-fashioned even then.


Suffice it to say, there are sixty-foot-high giants in Pilgrim's Progress. Haldane explains why it isn't good to be big. It basically comes down to some very old geometry; area versus volume.

Imagine a cube resting on one of its sides. The side it is resting on is the length of one side, L, squared. The volume is L cubed. As the cube gets bigger, L x L x L amount of volume is resting on L x L amount of surface area.


This isn't just a problem for the part of a giant that touches the ground (although their feet have got to be hurting). It's a problem for every cross-section of the body that takes weight. Making something giant-sized looks cool in science fiction. Seeing it basically disintegrate under the strain of its own weight wouldn't look nearly as cool. Okay, maybe it would. But it wouldn't make for an interesting fight for the protagonist.

But Haldane doesn't stop there.

By shrinking or expanding, all sorts of new physics phenomena have to be dealt with. Most of us have been dunked in water. When we come out, we brush the drops away. Most of us have also seen insects in water. They aren't able to brush the droplets off them when they come out. Water has a certain surface tension that allows droplets to form a certain size. That size is tiny to us. To an ant, it is huge, and heavy. A good-sized water droplet can be, to an ant, a swimming pool big enough to drown in.


Of course the most vivid imagery happens when Haldane explains what happens to various animals when they're dropped from a great height:

"You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes."


It's no wonder why the paper has stuck around. It's entertaining, informative, and gives the reader a perspective that is usually entirely new. It's a paper to consider before you test out that shrink-ray.

[Via: UCLA. Top cartoon by Nicholas Gurewitch via Perry Bible Fellowship.]