Newton focused on forces and gravity. Later physicists generalized newtonian mechanics, coming up with formalisms for expressing a host of different problems using a common approach (Lagrangian mechanics with generalized coordinates). They weren’t losing precision or sacrificing any power to anticipate reality by having an insight that many apparently different problems can be looked at as being essentially the same problem. A cylinder accellerating down a ramp as it rolls is the same problem as a satellite orbiting the L5 lagrangian point. Another unification was Maxwell’s equations for electrodynamics, which unified and linked a large number of earlier, more focused understandings (e.g. Ampere’s law, Coulomb’s law, the Biot-Savart law).
One more example: a physics-trained researcher studying the dynamic topology of the internet recognized a mathematical similarity between the dynamics of the network and the physics of bosons, and realized that the phenomenon of Google’s huge connectedness is, in a very real sense, following the same mathematics as a Bose-Einstein condensate.
Eliezer’s post seemed to denigrate people’s interest in finding such connections and generalizations. Or did I miss the point? Are these sorts of generalizations not the kind he was referring to?
I would add as a counter-example that the problem of explaining mankind’s nature and origin becomes solvable when the problem is extended to the problem of explaining the nature and origin of every species in the biosphere. The problem of explaining Mary’s illness may become easier if it is broadened to the problem of explaining the illness of the 20 people who became sick immediately after the company picnic.
To my mind narrowness should not be called a virtue. Instead we have the tactic or heuristic of narrowing, which is frequently successful. But a skilled pedagogue will present this tactic paired with the tactic of broadening, which is also frequently successful. The trick, of course is to choose the right tactic. Or perhaps to know when to switch tactics when the originally chosen one isn’t working.
Agreed. Newton was in fact takign a broad view compared to his predecessors, who beleived that Earthly happenings and celestial behavour must have different explanations. The point of his lawof gravity is that it uniformally applies to both
moon and apple.
Newton focused on forces and gravity. Later physicists generalized newtonian mechanics, coming up with formalisms for expressing a host of different problems using a common approach (Lagrangian mechanics with generalized coordinates). They weren’t losing precision or sacrificing any power to anticipate reality by having an insight that many apparently different problems can be looked at as being essentially the same problem. A cylinder accellerating down a ramp as it rolls is the same problem as a satellite orbiting the L5 lagrangian point. Another unification was Maxwell’s equations for electrodynamics, which unified and linked a large number of earlier, more focused understandings (e.g. Ampere’s law, Coulomb’s law, the Biot-Savart law).
One more example: a physics-trained researcher studying the dynamic topology of the internet recognized a mathematical similarity between the dynamics of the network and the physics of bosons, and realized that the phenomenon of Google’s huge connectedness is, in a very real sense, following the same mathematics as a Bose-Einstein condensate.
Eliezer’s post seemed to denigrate people’s interest in finding such connections and generalizations. Or did I miss the point? Are these sorts of generalizations not the kind he was referring to?
I think I agree with you, majus.
I would add as a counter-example that the problem of explaining mankind’s nature and origin becomes solvable when the problem is extended to the problem of explaining the nature and origin of every species in the biosphere. The problem of explaining Mary’s illness may become easier if it is broadened to the problem of explaining the illness of the 20 people who became sick immediately after the company picnic.
To my mind narrowness should not be called a virtue. Instead we have the tactic or heuristic of narrowing, which is frequently successful. But a skilled pedagogue will present this tactic paired with the tactic of broadening, which is also frequently successful. The trick, of course is to choose the right tactic. Or perhaps to know when to switch tactics when the originally chosen one isn’t working.
Agreed. Newton was in fact takign a broad view compared to his predecessors, who beleived that Earthly happenings and celestial behavour must have different explanations. The point of his lawof gravity is that it uniformally applies to both moon and apple.