Conceptual Science

​ Richard Feynman’s discussion of conservation of momentum in Chapter 10-2 of  The Feynman Lectures on Physics  is a careful construction of a universal physical law from simple but deeply constrained ideas. Rather than presenting momentum conservation as an axiom, Feynman shows how it follows naturally from the mutual character of forces and from the symmetry properties of space and motion. The result is not merely a rule for solving problems, but a statement about what kinds of change are possible in nature. The starting point is the recognition that forces between particles arise through interaction and are inherently reciprocal. When two particles interact, each influences the other, and the changes produced by these influences are linked. The significance of this reciprocity becomes clear when one considers the system as a whole rather than focusing on individual particles. Changes in motion can occur internally, but when all interacting particles are considered together,...

​ In Chapter 10-1 of  The Feynman Lectures on Physics , Feynman situates Newton’s Third Law within a broader methodological discussion concerning the limits of analytical and numerical approaches in classical mechanics. While Newton’s Second Law provides, in principle, a complete prescription for determining motion from known forces, Feynman emphasises that practical and conceptual considerations motivate a deeper examination of the laws themselves. Analytical solutions, where they exist, reveal general structures of motion - parabolic trajectories under uniform acceleration, harmonic oscillations described by trigonometric functions, and elliptical planetary orbits - that numerical methods, though powerful, do not naturally expose. These solutions contribute not merely computational efficiency but conceptual understanding. Feynman then contrasts such analytically tractable systems with those that resist closed-form solutions. Even modest increases in complexity, such as deviations...