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It's Alive!

Michael LaBarbera

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performing-arts

Introduction

  • Similarly, volumes are proportional to length cubed, so the new volume is not twice the old, but two cubed, or eight times the old volume (2L × 2L × 2L). As "size" changes, volumes change faster than areas, and areas change faster than linear dimensions. Size is thus a slippery concept; we tend to notice linear dimensions, but volume (how much is there all told or how much does it weigh) is often more important.
  • The biological significance of these geometric facts lies in the observations that related aspects of an organism's biology often depend on different geometric aspects. Take physical forces: • The magnitude of surface tension forces is proportional to the wetted perimeter (a length); a water strider needs long feet with lots of edge, not big feet, to skate on the surface of a pond. • Adhesive forces are proportional to contact areas; geckos need broad, flat feet covered with millions of tiny setae to walk on the ceiling. • Gravitational or inertial forces are proportional to volume (assuming that density is constant); a bird that flies into a window may break its neck, but a fly that flies into a window will bounce off without injury.
  • As is apparent, bone stress does not grow as the cube root of body mass. Indeed, the working stress in the bones seems to be independent of body size, running from about a fourth to a third the breaking stress of the bone for all mammals, regardless of body size. In a sense, what we have here is nature's "design principle" for mainstream skeletons: all have evolved to have a safety factor of three to five.
  • As mentioned above, this result is achieved by changes in posture. Small mammals run with their limbs bent; large mammals always run with their limbs straight. If you've ever seen a slow-motion movie of a horse running, you may have noticed that the horse's leg is perfectly straight when it contacts the ground and it stays straight as long as it's bearing the horse's weight. This behavior is even more obvious in elephants.