This never really happened. John Brockman, a literary agent to many bright scientists, resurrected and amended Snow's term. Brockman's third culture meant a streetwise science culture, one where working scientists communicated directly with lay people, and the lay challenged them back. This was a peerage culture, a peerage that network technology encouraged. But the most striking aspect of this new culture was its immediacy.
Technology is simply more relevant than footnotes.
There are other reasons why technology has seized control of the culture. These questions, of course, are the same ones that natural philosophers and scientists of the first two cultures have been asking for centuries. Despite the cartoon rendition I've just sketched, the nerd way is a third way of doing science. Classical science is a conversation between theory and experiment. Technological novelties such as computer models are neither here nor there.