December 24, 2003
Death by black hole
From Gravitation, a gigantic textbook on General Relativity by Misner, Thorne, and Wheeler, in Section 32.6, "Gore at the Singularity" (pg 860):
Consider the plight of an experimental astrophysicist who stands on the surface of a freely falling star as it collapses to R=0.As the collapse proceeds toward R=0, the various parts of the astrophysicist's body experience different gravitational forces. His feet, which are on the surface of the star, are attracted toward the star's center by an infinitely mounting gravitational force; while his head, which is farther away, is accelerated downward by a somewhat smaller, though ever rising force. The difference between the two accelerations (tidal force) mounts higher and higher as the collapse proceeds, finally becoming infinite as R reaches zero. The astrophysicist's body, which cannot withstand such extreme forces, suffers unlimited stretching between head and foot as R drops to zero.
But this is not all. Simultaneous with this head-to-foot stretching, the astrophysicist is pulled by the gravitational field into regions of spacetime with ever-decreasing circumferential area, 4 pi r squared. In order to accomplish this, tidal gravitational forces must compress the astrophysicist on all sides as they stretch him from head to foot. The circumferential compression is actually more extreme than the longitudinal stretching; so the astrophysicist, in the limit R->0, is crushed to zero volume and indefinitely extended length.
The above discussion can be put on a mathematical footing as follows.
There are three stages in the killing of the astrophysicist: (1) in the early stage, when his body successfully resists the tidal forces; (2) the intermediate stage, when it is gradually succumbing; and (3) the final stage, when it has been completely overwhelmed.
Unamuno
Still thinking of solitaire, or history. Solitaire represents the play of chance. A good mathematician could calculate the probability of a game's working out. And if two individuals were to set themselves to solving the problem competitively, the natural result would be that they would both find the same percentage of solutions to the same game. But the point of the competition should be to determine who can find more solutions in a given time. The best player is not the one who plays the fastest, but the one who breaks off the most games at the earliest moment, as soon as he foresees their lack of solution. In the supreme art of taking advantage of chance, the superiority of a player consists in his being able to make up his mind to abandon one game in time to start another. The same goes for politics and life.
Miguel de Unamuno, "How to Make a Novel," 1926
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