My title here is a phrase strongly associated with a controversy stirred up by CP Snow back in the Space Age, when many in the West feared we were falling behind the Soviets in science and technology. For the English and the American upper class, part of this worry was related to the bias of their higher education systems toward non-technical subjects. What Snow observed was that as our culture matured, the most highly educated people in the humanities tended to know scandalously little about science; and likewise, those with the greatest technical knowledge tended to be rather uncultured.
Snow was well aware that there were always and would always be exceptions to this general tendency. In fact, Snow himself was one of those exceptions, being both a respected novelist and a student of physics (he earned a doctorate in the subject). So the many takedowns of the Two Cultures idea you may find online that say, point to JBS Haldane--look, a mathematically minded scientist who could write! who knew Greek! who wrote history!--as proof there aren't two cultures, are completely missing the point. Haldane and Snow were exceptional. Snow didn't argue that it was impossible to inhabit both cultures--being who he was, how could he?--only that it was not the norm.
In speaking of Snow, we should also acknowledge how much his piece is of its time and place: Part of Snow's thesis, an important part, was his particular attack on the English school system as a source for the split between technical and cultural knowledge. (He actually holds up the American university system as a positive counterexample.)
However, the basic conflict he is observing goes much farther back, to the very beginnings of the modern world and the conflict between the ancients and the moderns in the 17th century. That conflict was essentially a conflict between ancient wisdom and modern, mostly scientific knowledge. Swift's Battle of the Books was a satiric look at this conflict which came down, as we might expect from a literary man who hated math, pretty heavily on the side of ancient wisdom. Over the long haul, though, science has mostly won this battle--shaping and changing our world to an extent that even Swift could hardly have imagined.
And, worse still from Swift's point of view, science is increasingly the arbiter of truth in our society.
But not the only one. Anyone taking a look at say, the controversies over global warming can see that science often has an uphill battle against "common sense" when its truths are inconvenient. Science is, no doubt, still the servant of our desires; though a servant upon whom we are as dependent as Wooster is upon Jeeves.
And yet our universities are--still!--filled with people who smilingly admit to incompetence in basic mathematics; who don't know anything about science aside from the fact that its advances sometimes harm the environment; people who criticize science but who cannot distinguish the real thing from ridiculous parody. If Bertie Wooster were a doctrinaire ingrate as well as an ignorant fool, he'd be the model for many of our present day humanities professors. But such a character could never win even the provisional sympathies of any reader.
Such a response to science does little honor to the tradition that Swift defended. As was the case in Snow's day--the worst offenders in the two culture business are on the side of the humanities. One is far more likely to find an articulate and cultured scientist than a scientifically knowledgeable humanities type. There are more Goulds and Lewontins and Orrs out there than there are George Levines.
Which is a shame. Because there are also scientists out there who have very little knowledge of or respect for the Western tradition who now want to explain it all for us. Who don't seem to appreciate that you cannot explain "it all" without a conception of what "it all" is. Who don't seem to realize that there simplistic explanations have been around for a long, long time, and have been roundly and soundly rejected by those to whom the phenomenon in question is most familiar.
One of the things I hope to see in future is a generation of humanities and social science people who embrace science but are not in thrall of it.
Sadly, I haven't seen much that looks much like that, though.