I thought that this article was fascinating.
“April 3, 2005 — Fascinating new scientific papers suggest how elementary geometry involving animals’ physical dimensions is sufficient to shed light on some very basic biological phenomena. In particular, the papers attempt to determine the metabolic pace of all life and, in the process, help resolve a problem in evolutionary time measurement.
Hold on tight.
Let’s start by considering why an animal can’t be, say, five times its normal adult size. To understand that we can’t simply multiply physical dimensions by a factor of five, imagine what would happen if a 6-foot, 160 pound man were scaled up to a height of 30 (6 x 5) feet. His weight, like his volume (in cubic feet), would increase not by a factor of five, but by a factor of 5^3 and thus would rise from 160 pounds to 20,000 pounds (160 x 5^3) â€” 125 times as great as his original weight if he were proportioned similarly.
And what would hold up such a behemoth? The supporting cross-sectional area of his thighs, say 2 square feet originally, would increase not by a factor of five, but by a factor of 5^2 and would thus rise to 50 square feet (2 x 5^2) â€” 25 times as great as the normal area if he were proportioned similarly. (The same would hold for his spine, knees, and so on.)
But the pressure on his thighs â€” his weight divided by the area of a cross-section of his thighs, i.e., 125 times his original weight divided by 25 times the original area â€” would be five times as great. This would be a crushing pressure and the man would collapse. This is why heavy land animals like elephants and rhinos have such thick legs.
Metabolic Rates: Live Fast and Die
Mathematical considerations not too dissimilar to these also lie behind various scaling laws in biology relating animals’ metabolic rates â€” heart, breathing, twitching, etcetera â€” to their surface areas and masses. Small animals’ hearts, for example, beat faster than large animals’ hearts and, more generally, they live faster and die younger than do large animals who measure out their energies at a more lumbering pace.”
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