“Celeriac, the distinction is that Tom McCabe seemed to me to be suggesting that the search space was small to begin with—rather than realizing the work it took to cut the search space itself down.”
The search space, within differential geometry, was fairly small by Einstein’s day. It was a great deal of work to narrow the search space, but most of it was done by others (Conservation of Energy, various mathematical theorems, etc., were all known in 1910). The primary difficulties were in realizing that space could be described by differential geometry, and then in deriving GR from known postulates. Neither of these involve large search spaces; the former follows quickly once you realize that your assumptions are inconsistent with Minkowski space, and there’s only one possible derivation of GR if you do the math correctly. I don’t know why the first one is hard, but Einstein showed twice that physicists are very reluctant to question background assumptions (linear time for SR, Euclidean space for GR), so we know it must be. The second one is hard because the human brain does not come equipped with a differential geometry lobe- it took me several hours to fully understand the derivation of the Schwarzschild solution from its postulates, even though the math is simple by GR standards and there is only one possible answer (see http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution).
“Celeriac, the distinction is that Tom McCabe seemed to me to be suggesting that the search space was small to begin with—rather than realizing the work it took to cut the search space itself down.”
The search space, within differential geometry, was fairly small by Einstein’s day. It was a great deal of work to narrow the search space, but most of it was done by others (Conservation of Energy, various mathematical theorems, etc., were all known in 1910). The primary difficulties were in realizing that space could be described by differential geometry, and then in deriving GR from known postulates. Neither of these involve large search spaces; the former follows quickly once you realize that your assumptions are inconsistent with Minkowski space, and there’s only one possible derivation of GR if you do the math correctly. I don’t know why the first one is hard, but Einstein showed twice that physicists are very reluctant to question background assumptions (linear time for SR, Euclidean space for GR), so we know it must be. The second one is hard because the human brain does not come equipped with a differential geometry lobe- it took me several hours to fully understand the derivation of the Schwarzschild solution from its postulates, even though the math is simple by GR standards and there is only one possible answer (see http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution).