In 'De Motu', as in the first edition of the "Principia", Newton did not specifically state a basis for extending the proofs to the converse. The proof of the converse here depends on its being apparent that there is a uniqueness relation, i.e. that in any given setup, only one orbit corresponds to one given and specified set of force/velocity/starting position. Newton added a mention of this kind into the second edition of the "Principia", as a Corollary to Propositions 11–13, in response to criticism of this sort made during his lifetime. A significant scholarly controversy has existed over the question whether and how far these extensions to the converse, and the associated uniqueness statements, are self-evident and obvious or not. (There is no suggestion that the converses are not true, or that they were not stated by Newton, the argument has been over whether Newton's proofs were satisfactory or not.) The details of Edmund Halley's visit to Newton in 1684 are known to us only from reminiscences of thirty to forty years later. According to one of these reminiscences, Halley asked Newton, "...what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it." Another version of the question was given by Newton himself, but also about thirty years after the event: he wrote that Halley, asking him "if I knew what figure the Planets described in their Orbs about the Sun was very desirous to have my Demonstration" In light of these differing reports, both produced from old memories, it is hard to know exactly what words Halley used. Newton acknowledged in 1686 that an initial stimulus on him in 1679/80 to extend his investigations of the movements of heavenly bodies had arisen from correspondence with Robert Hooke in 1679/80. Hooke had started an exchange of correspondence in November 1679 by writing to Newton, to tell Newton that Hooke had been appointed to manage the Royal Society's correspondence. Hooke therefore wanted to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, and then gave a whole list, mentioning "compounding the celestial motions of the planetts of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items.