[Note: "~=" means "approximately equals"] I have a M.S. in electrical engineering, so I have a strong background in physics. One thing that happens quite frequently in physics is the use of an approximate substitution in order to make the resulting equations and analysis simpler. The litmus test is as follows: is the final answer obtained as a result of the approximation close enough to the actual answer such that the effort saved in the derivations, analysis, and computations outweighs the consequences of the reduction in accuracy? Here is an example where the litmus test is passed. The motion of a pendulum displaced a small angle (10 degrees or less) can be analyzed with the approximation sin(x) ~= x whereby x is in radians, rather than in degrees, and is small. The resulting differential equations are much simpler than they would be without the substitution, and the closed form final equation is simple, whereas without such approximations, often a closed form answer is unobtainable (e.g., an anti-derivative may not exist), and numerical methods must be used. These approximations quite often result in high accuracy results and are well worth making, especially as pedagogical tools with students. The same litmus test applies to human populations (e.g., races). Most blacks are either violent, or applaud violence (see the OJ murders opinion poll data from the 1990s). Most blacks have an IQ that is substantially lower than that of various Eurasian populations. A small percentage of blacks do not suffer from overt maladies, but this number is small enough that making the approximation [blacks ~= a population of lazy, dysfunctional, violent, trashy cretins] results in a rather small loss of accuracy that is easily outweighed by the utilty of the streamlined simplicity that the approximation provides (e.g. when > 90% of a group utterly sucks, it is much easier and much more efficient to treat the group as utterly sucking than worrying about rare outliers). Thread started at Forum 4 Politics on 04-12-2012 12:00 PM
