I N T R O D U C T I O N T O V O L U M E 1 3 x l i x and discussion sessions, describes as very lively (see Appendix B). Painlevé had, the previous year, made the most prescient foray into the debate on the nature of the Schwarzschild singularity when he adopted a set of coordinates devised by Al- var Gullstrand, said to be the man who prevented Einstein from receiving the Nobel Prize for his work on relativity. In these Painlevé-Gullstrand coordinates, an ob- server’s clocks do not stop as they approach the event horizon, so that Einstein’s reply to Hadamard is no longer valid. (It seems, however, that Painlevé was un- aware of the differences between the observers’ clocks, having merely drawn atten- tion to differences in the spatial dimensions of physical bodies in the two frames see Painlevé 1921a.) This is because this coordinate system presents the frame of reference of an observer actually falling into a black hole, whereas Schwarzschild’s system of coordinates describes the frame of reference of a very distant observer. While physical processes at the event horizon of the black hole do stop as seen by a distant observer, nothing remarkable is noticed by observers who themselves are in the process of falling in. But Painlevé had taken the view that the different mea- surements obtained by use of these contrasting coordinate systems should be taken as evidence of something problematical in the theory. How could it be that the same physical system could appear so radically different to two different frames of ref- erence? Einstein had replied to Painlevé’s point in a letter of December 1921 (Vol. 12, Doc. 314), insisting upon his interpretation that all coordinate frames are equally valid in the theory of general relativity. At this point of the discussion at the Collège de France, Einstein was touching upon many of the features of what we now refer to as black holes. He could point to two coordinate systems showing different behavior at what was then called the Schwarzschild singularity as a means to argue that this is not a physical singularity. He was emphasizing the stopping of clocks, which could have led him to an under- standing of the event horizon (the modern term for the physical location of the Schwarzschild singularity). His point, taken from Schwarzschild himself, that the pressure (an observable quantity) could become singular at the center of the star, could have led him to argue for the existence of a real physical singularity at the center of the Schwarzschild solution. Thus, he and his contemporaries were knock- ing at the door of the concept of a black hole. It would take nearly a half-century before that concept really began to crystallize. During his visit to Paris, Einstein had encountered the full gamut of respectable (or at any rate not politically motivated) anti-relativity sentiment. Guillaume repre- sented those who simply did not understand the theory and imagined that they could create paradoxes at will because all the old rules were broken and the new ones incomprehensible, at least to themselves. Hadamard was an excellent example of someone who understood the theory, knew well that it made some counterintui- tive predictions, and wished to know how and whether these predictions would