Who’ll Freeze First? A Puzzle About Size and Staying Warm

Forty two years ago, I read an essay from 1928 by J. B. S. Haldane titled "On Being the Right Size" [1], it appeared in the wonderful four volume set The World of Mathematics.

I've always remembered the main point: volume and properties related to volume increase as the cube of the scale factor for similar objects while area (surface or cross-section) increase as the square. See for example the Google interview question that appears in the movie "The Internship".

[1] http://irl.cs.ucla.edu/papers/right-size.html

I thought it was always a "common knowledge" that small animals tend to eat constantly and suffer sooner from food shortage because of higher relative heat dissipation. Some mice eat up to 50-80% of their weight per day, opposed to just few percents for biggies like elephants. Mice also have much faster metabolism in the same conditions.

The same concept applies to animal (and plant, building, structure, etc.) size: weight varies with the cube of the "size", while the cross-section of the supporting structures (trunk, legs, etc.) varies with the square.

So the relationship "weight/supported weight" increases with size, to the point where it won't support itself.

    In Professor Haskell’s book, The Forest Unseen, he says he wanted to “experience the cold as the forest’s animals do, without the protection of clothes,”