Physiological relationships are not exempt. The forces that can be produced by a muscle or the strength of a bone are in each case proportional to their cross-sectional areas the weight of an animal is proportional to its volume. The same dependence on different aspects of geometry holds for functional relationships. 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 without injury.Adhesive forces are proportional to contact areas geckos need broad, flat feet covered with millions of tiny setae to walk on the ceiling.The magnitude of surface tension forces is proportional to the wetted perimeter (a length) a water strider needs long feet, not big feet, to skate on the surface of a pond.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. As "size" changes, volumes change faster than areas, and areas change faster than linear dimensions. 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 x 2L x 2L). Areas are proportional to length squared, but the new length is twice the old, so the new area is proportional to the square of twice the old length: i.e., the new area is not twice the old area, but four times the old area (2L x 2L). Let's say that you increase the length by a factor of two. If you change the size of this object but keep its shape (i.e., relative linear proportions) constant, something curious happens. In each example, linear dimensions double, but area increases by four times. Equivalently, lengths are proportional to the square root of an area or the cube root of a volume. All areas (surface area, cross-sectional area, etc.) will be proportional to some measure of length squared (i.e., length times length) volumes will be proportional to length cubed (length times length times length). Such an object will have a number of geometric properties of which length, area, and volume are of the most immediate relevance. Take any object-a sphere, a cube, a humanoid shape. The conceptual foundations of scaling relationships lie in geometry. And in the cube on the right, L=3 and V=27. The cube in the middle, where L=2, has a volume of 8. In the cube on the left, length = 1 and volume = 1 (L x L x L). Indeed, the effects of size on biology are sufficiently pervasive and the study of these effects sufficiently rich in biological insight that the field has earned a name of its own: "scaling." Absolute size cannot be treated in isolation size per se affects almost every aspect of an organism's biology. However, Hollywood's approach to the concept has been, from a biologist's perspective, hopelessly naïve. The premise is invariably to take something out of its usual context-make people small or something else (gorillas, grasshoppers, amoebae, etc.) large-and then play with the consequences. Size has been one of the most popular themes in monster movies, especially those from my favorite era, the 1950s. LaBarbera SESSION 1 : Biology and Geometry Collide! The Biology of B-Movie Monsters BY | Michael C.
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