The problem with the term “computer science” is that it’s not purely a science, although it often requires a scientific approach, and it isn’t really about computers except in the abstract. Most of us, when we think of “computers”, are actually thinking about machines designed around integrated circuits, not the larger category of beasts that could defensibly be called computers (such as our brains).
If one wanted to be pedantic and also make up a word that would require too much explanation to be useful in practice, one could call the field teleotechnology. This is a fusion of telos (meaning “end” or “purpose”, as in teleology) and technology. The reason for the prefix is that not all of human technology involved computing, and most primitive technology (e.g. levers, inclined planes) didn’t. What we are observing, however, is that modern demands often necessitate that lifeless but complex problem-solving agents live inside the technology. Phones and thermostats and toasters are converging on computers. (They happen to be integrated circuits, but that’s an incidental detail.) This field is really about problem solving, automated when possible. We used to compute square roots by hand, and now we have machines that perform the same task in nanoseconds to a much greater degree of accuracy.
All of that said, while teleotechnology may be a more correct term for what this new body of knowledge “is really about”, computer science is close enough that most people take no issue with it and most people understand what is meant by it.
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Interesting. I’ve only heard of computational mathematics as a sub-area of mathematics that uses computers as part of its work, e.g. to investigate the 4-color theorem, or to do simulation-based modeling of various systems that are too complex to solve analytically. I don’t think the term has significant currency in CS as a description of what happens in CS, though some of the things linked there do. But I think even those don’t really fall under “computational mathematics” in most people’s understanding. For example, “computational science” or “computational science and engineering” is a known term, and in some places its own department, but it’s considered a subfield of applied science, or of engineering, not a subfield of mathematics. As a personal preference, I tend to think subsuming everything under mathematics would be Very Bad, leading to a pretty methodologically and culturally narrow view of the field (which is fine if it’s a narrow subset of the field, but not if it tries to subsume everything). But I don’t think such subsumption is likely anyway.
As for a 3-way split, Georgia Tech made one a few years ago, but a bit different. The College of Computing there is split into three Schools: the School of Computational Science & Engineering (houses bioinformatics, big-data processing, work on computational physics/meteorology/etc., etc.), the School of Computer Science (houses “traditional” or “core” CS: systems, theory, databases, logic, algorithms, networking, etc.), and the School of Interactive Computing (houses artificial intelligence, robotics, vision, graphics, ubicomp, HCI, etc.). I prefer this split to the one you propose because it doesn’t try to throw everything that has an application into the catch-all bucket “applied”, but instead splits more by subject areas. As an AI person, I especially want my own field to stay unified as an interdisciplinary field, not get diced into pieces. In my opinion most of the interesting work in CS needs to deal to some extent with all three of information, theoretical models, and applications.
Yes, like computational biology, computational neuroscience, computational physics.