John Bell has highlighted the role played by Linfoot's political awareness, in particular his relationship with Heilbronn who had been forced to flee Nazi Germany.
Other contributing factors to this change in focus were his lifelong fondness for astronomy and, by Linfoot's own testimony, a feeling that he had reached the limits of his pure mathematical creativity.
During World War II Linfoot put his skills to use for the Ministry of Aircraft Production, producing optical systems for air reconnaissance.
During this time Linfoot took a great interest in Claude Shannon's new field of information theory and also in computers, writing several programs for the Electronic Delay Storage Automatic Calculator at Cambridge.
These papers cover a wide range of areas in Fourier analysis, number theory, and probability, the first of these being applied later to his optical studies.