Abstraction in Mechanics

  1. Only physical phenomena and basic tools should be used as the starting point of one's study. Advanced and abstract theories should be only considered peripheral. If one only studies the side notes without seeing the main context, then there will be no incentive for further study, no way to understand its physical meanings, and no way to appreciate the theory's applications.
        [Ashc, p.270, l.-8] refers readers to [Lan3, p.459, (112.8)]. The order of study in this case should be [Ashc, p.270, chap. 14][Lan3, pp.458-460, 112] rather than [Lan3, pp.458-460, 112][Ashc, p.270, chap. 14].

  2. Abstraction serves to clarify the image by focusing on the main point and eliminating the peripheral.
         wc appears in both [Ashc, p.13, (1.18)] and [Ashc, p.234, l.23]. However, in each context, the main point is not to explain  wc. Thus, the meaning of wc is restricted to its mathematical definition [Asc, p.13, (1.18)]. In contrast, the physical meaning of w in [Lan2, p.54, (21.8)] is clear because [Lan2, pp.53-55, 21] is designed to explain w.

  3. If we proceed from concrete to abstract (e.g. the process of abstraction), all we need is a single example. For example, if we want to demonstrate the tunnel effect, all we need is [Fur, p.86, Fig. 2.9]. However, if we proceed from abstract to concrete (e.g., theorizing an example related to the tunnel effect), we must justify each step of our theoretical reasoning with a concrete example. Sometimes this task can be difficult. For example, we have to find [Fur, p.117, (2.165)] in order to verify the existence of a medium with a pure imaginary index of refraction [Coh, p.37, l.9].