While at Uraniborg, Tycho maintained correspondence with scientists and astronomers across Europe. He inquired about other astronomers' observations and shared his own technological advances to help them achieve more accurate observations. Thus, his correspondence was crucial to his research. Often, correspondence was not just private communication between scholars, but also a way to disseminate results and arguments and to build progress and scientific consensus. Through correspondence, Tycho was involved in several personal disputes with critics of his theories. Prominent among them were John Craig, a Scottish physician who was a strong believer in the authority of the Aristotelian worldview, and Nicolaus Reimers Baer, known as Ursus, an astronomer at the Imperial court in Prague, whom Tycho accused of having plagiarized his cosmological model. Craig refused to accept Tycho's conclusion that the comet of 1577 had to be located within the aetherial sphere rather than within the atmosphere of Earth. Craig tried to contradict Tycho by using his own observations of the comet, and by questioning his methodology. Tycho published an "apologia" (a defense) of his conclusions, in which he provided additional arguments, as well as condemning Craig's ideas in strong language for being incompetent. Another dispute concerned the mathematician Paul Wittich, who, after staying on Hven in 1580, taught Count Wilhelm of Kassel and his astronomer Christoph Rothmann to build copies of Tycho's instruments without permission from Tycho. In turn, Craig, who had studied with Wittich, accused Tycho of minimizing Wittich's role in developing some of the trigonometric methods used by Tycho. In his dealings with these disputes, Tycho made sure to leverage his support in the scientific community, by publishing and disseminating his own answers and arguments.