Orion Nebula, Photo Credit: NASA
It’s no secret that it is sometimes necessary to convince STEM majors that the Columbia Core’s Frontiers of Science class is worth their time. A good number of my friends who study the natural sciences skip the lectures of the units pertaining to their fields of forthcoming expertise. On the face of it, one can hardly blame them. What’s the point of requiring those Columbia students who study the natural sciences to take Frontiers of Science? Why might one think that those who skip lectures or who fail to take the class seriously are making an unfortunate mistake? I hope that my answer here will not only shed light on the relationship between STEM majors and Frontiers of Science, but also on the relationship between philosophy majors and CC, between art history majors and Art Hum, etc.
Frontiers of Science does not purport to be a mathematically or experimentally rigorous class, even for applied mathematical standards. We don’t regiment our discussion of general relativity in (pseudo-)Riemannian geometry, we don’t enter the lab in discussing the physiological-behavioral bridge laws in our unit on mind and brain, and we don’t model possible time-evolutions of animal populations using mathematical game theory. The focus is far more conceptual, and the general methodology is one of giving an intuitive gloss on some of the most exciting areas of current research in various natural scientific disciplines. But this is exactly one of the virtues of the class, for both the “seasoned” budding scientist and the novice humanities student.
The further we progress within the confines of the assumptions of a particular discipline, the more we forget that its foundation is laid on just that – a class of assumptions that must, as a necessity of methodology, be taken as primitively axiomatic. It is only when we step back into a more intuitive and conceptual framework that these assumptions once again become apparent, and we may more fruitfully question whether they could be modestly revised in fine-grained ways that would prove conducive for advances in the discipline in question. Better still, when we adopt this framework together with peers who, in virtue of lacking extensive formal training in the area, have not been academically conditioned to accept those assumptions as self-evident, we are often forced into a reckoning with the foundations of our disciplines that lead to a better understanding and appreciation of their limits.
For instance, our discussion of the historical development of Special Relativity in Frontiers of Science, correctly exposited on the basis of accepting Einstein’s synchronization convention for light clocks, often gives rise to a number of theoretical objections from students who are being introduced to the subject for the first time. Why think, for instance, that modeling the phenomena of instrument measurement contraction by carving spacetime into hyperplanes of simultaneity is closer to the truth than modeling by stipulating a contraction equation for measurement instruments (and all other objects) moving relative to a stationary ether? The latter, sometimes called neo-lorentzianism, is empirically equivalent to Special Relativity – that is, no physical experiment will ever separate the two (including, of course, Michelson-Morley). It is then an open question as to why we ought to accept Special Relativity.
The choice between empirically equivalent theories is thus not a scientific question, but rather a meta-scientific question – a question about model-theoretic virtues – that has great consequence in our scientific theorizing. In general, logicians have shown that for any body of scientific data, there are infinitely many theoretically distinct but empirically equivalent theories that can perfectly predict the data. Even if, as a result of the discussion, one still believes in Special Relativity (as I do), the discussion itself will prove to be deeply helpful in understanding and appreciating the discipline and limits of mathematical physics to a greater extent. The same can be said for debates over uniformitarianism in climatology, probability theoretic debates at the foundations of evolutionary biology, debates over neuroscientific methodology, etc.
My claim is not, of course, that these types of debates will actually occur in the Frontiers of Science seminar room. That would be naïve. My claim is that a conceptual overview with students who have not become accustomed to simply accepting the dogmas of a particular field in Frontiers of Science provides unique grounds for well-read students in that field to personally reflect on some of the aforementioned problems. This is unique to the course. One will not encounter students asserting “it is not obvious to me that difference in the measurements between light clocks entails that simultaneity itself is relative” in an upper-level physics class. One will not encounter students worrying about probability considerations that undergird certain evolutionary mechanisms in an upper-level course in evolutionary biology. These things are simply expected to be assumed, and the technicality of such upper-level courses precludes these discussions from ever arising. It is in this sense that Frontiers of Science is radically unique for the STEM major at Columbia.
But uniqueness doesn’t entail importance. Why think that Frontier of Science, being unique in this way, is uniquely important? While many answers can be given, I’ll give just a couple. Firstly, a short reflection on the structure of scientific advancement teaches us that scientific advances seldom occur within the strict confines of the extant dogmas of a particular discipline. Rather, just like the revision of Newton’s geometry of physical space or the revision of Descartes’ kinematics of the mind/brain, advances in scientific disciplines often occur through modest revisions to their foundations to better explain experimental data. Suddenly, with such revisions, all of the data “makes sense.” But these calculated revisions can only occur if these foundations are well-understood, and there is a warranted worry that these foundations are being forgotten for the sake of technical specialization. Secondly, in the midst of technical mathematical formalism, we often forget the intuitive, conceptual, and elegant ideas that made us fall in love with the natural scientific disciplines in the first place. Returning to the beginning for a time and watching others be captivated by those same ideas can provide us with the needed inspiration to earnestly continue our work.
Like any class, Frontiers of Science will return what one puts in. But, unlike any other class, Frontiers of Science has the potential to return benefits to the STEM student that no other class at Columbia could offer.