I read the 1963 follow-up to "The Two Cultures", titled "The Two Cultures: A Second Look." He covers a number of points in response to the criticisms he'd received from his surprisingly widely-received lecture, and I have responses to two key aspects.
First, a number of critics were unclear on how, exactly, he was defining the two cultures, or whether he approved of the arrangement. He tried to clarify that he drew a science/humanities line because he saw the "literary intellectuals" as the people who interact more with the wider society, since they write about people, but the scientists are communicating neither with the wider society nor with the intellectuals who speak to the wider society. I think a lot has happened with science communication, science journalism, and science publicity in the last several decades, but I agree that the gap is still there. What's interesting to me is the mechanism by which the National Science Foundation has tried to address this over the past two decades, pushing basic researchers to engage in public outreach via the Broader Impact criterion for funding. While public outreach is laudable for those who have the time, interest, and talent, it is not in everyone's skill set and it is not necessarily the best use of everyone's time. Nonetheless, as I have noted before, Broader Impact is consistent with many of America's democratic cultural notions, so here we are. The implicit assumption is that direct engagement of scientists and the public is what matters at least as much as engagement between scientists and other intellectual classes.
Second, Snow conceded that some of his predictions about economic development had been too rosy, but he believed that what would ultimately improve the lives of billions around the world would be the spread of the Scientific Revolution. On that I think he erred badly. There are plenty of poor countries with universities that actually do a fine job in educating students in science; many of those countries produce a great many science graduates who get better test scores than Americans. What holds those countries back, what stands between their populations and the fruits of modern science and medicine, is NOT a lack of scientific knowledge or appreciation. Rather, it is failings of economic and political systems. The problem is not that the classes of intellectuals who study people and make recommendations about human affairs don't understand the importance of science, but rather that they either fail to make good recommendations about human affairs or else fail to get the people in power to listen to good recommendations. As Kentaro Toyama said in Geek Heresy, technology and the fruits of science are mere instruments, not conductors. Technology can amplify advantage, and the lack of technology can amplify disadvantage, but the mere possession of technology does not improve a society. Human efforts, human decisions about the use of technology, those are the things that improve a society.
There are plenty of good reasons to break down walls between the two cultures, plenty of ways in which science can inform the efforts of the general public, the policy-makers, and scholars of the humanities, but spreading the fruits of science may actually be the least of those. The fruits of science are tremendously valuable, and tremendously beneficial. They will be fairly distributed (by whatever your yardstick of fairness might be) in an economic and political system that efficiently and fairly distributes value and benefit (again, by your yardstick of fairness). Scientific knowledge is a necessary condition but not a sufficient one.
Anyway, my book has several more lectures and essays by C. P. Snow. Let's see what else he had to say.