Diffusion is a random-walk: items move from a place of high concentration to sites where they are less common. A good rule of thumb to remember in all diffusion situations is "square-root-of-N": on the average, after N steps a thing is the square root of N away from where it started. Another good rule of thumb is "equal energy": objects in equilibrium come to a single temperature and have the same average energy as each other.

Molecules provide a classic example. Place a drop of ink into still water, or open a bottle of perfume at one end of a room, and in a short time the material spreads throughout the entire available space. The rate of spreading is ruled by the square-root-of-N law, with each particle taking steps of length equal to the mean free path between collisions. The speed of motion is ruled by the equal energy law, so (since kinetic energy goes like velocity squared) heavier molecules diffuse more slowly (proportional to the square root of molecular weight). Eventually the concentration approaches a constant everywhere --- unless there are penalties (energy costs) in some zones which cause density gradients to persist.

People "diffuse" too, through an organization, within a region, and among nations. Individuals move away from unfavorable surroundings --- crazy bosses, towns where the culture is too boring, countries that lack career opportunities, etc. --- and move toward better circumstances. Some go faster than others; some travel more direct routes, while others take a series of slow (perhaps even multigenerational) steps.

Ideas also "diffuse". Tiny ideas (e.g., catchy tunes, or brand name logos) can leap great distances almost instantly. Big ideas (concepts that require thought or experience to grasp, such as liberty and justice) take longer, but spread just as inexorably.

Wednesday, January 19, 2000 at 08:23:08 (EST) = 2000-01-19

TopicScience - TopicSociety

(correlates: PrimeDirective, SmallIdeas, GibbonChapter48, ...)