When reading this chapter, I suddenly started thinking about why it was that in the 1880s there was this rush of thought on the fourth dimension. We discussed the social climate when Flatland was written, and the popular response to the book, but I am still not satisfied as to what it was about the political/social climate that inspired people to think about other dimensions? Was it tied in with the sudden link of science and mathematics to business at the turn of the century? Or was it tied in with imperialism and a need to understand and explore many worlds? What made the time so ripe for multidimensional exploration? Especially as it seemed to be consistent over the whole world. On p.95, you state that ≥there was a veritable polytope rush among mathematicians in the United States, Scandinavia, and Germany.≤ Why not Great Britain or France? If the climate of the time so directly affects mathematical thought, why do you think that fractals became an obsession at the time that they did? And what is the ≥mathematical rage≤ right now? How eager are people to discuss the fourth dimension in the 1990s? The majority of people I talk to just brush it off as ≥time.≤ This is very interesting to me. Also, when were the concepts of duality thought up? Was it Greek- based?

Prof. Banchoff's response