Idealization

When Sadi Carnot carried out the pioneering work on heat engines which led to the second law of thermodynamics, he contemplated an ideal heat engine, one that was completely reversible. Carnot's use of idealization was particularly successful - while the ideal engine cannot actually be constructed, the conclusions he derived for the ideal engine hold a fortiori for actual heat engines. For example, the greater the temperature difference between the two heat reservoirs, the higher the engine's efficiency. But this is not always the case. What holds true in the ideal limit may be false in reality. Nevertheless, the ideal case, simple and tractable, can be expected to shed light on actual cases, the precise treatment of which is impossible or impractical. Idealizations abound in science: ideal gases, closed systems, perfectly rational agents, and evolutionarily stable strategies. Indeed, thinkers as diverse in their outlook as Edmund Husserl and Albert Einstein have pointed to idealizations as the hallmark of modern science.