Ramblings on Depth and Breadth in Introductory Science Teaching

About a week ago, I was having dinner with a friend, and the topic of teaching in various science disciplines came up; he got his degree in biology, while I got mine in physics. One of the things that we both noticed in our undergraduate careers was that introductory physics classes tend to go fairly deep right away, focusing only on a few broad topics, whereas introductory biology classes go much more for breadth, with the depth coming in specific topics in later classes. It took us a little time to think of why this might be. I think we came up with a reasonable explanation, so follow the jump to see what that explanation might be (along with extensions of it).

A few warnings are in order. One is that although I've gone through a full undergraduate course sequence in physics, I have only taken one introductory biology class in my undergraduate studies, so I'm essentially comparing an insider view of one subject to an outsider view of another; worse, my insider view of physics was built over 4 years so it is fairly fresh in my memory, whereas my outsider view of biology came in a single semester 4 years ago, so my memory of it is rather fading (though it is augmented by the problem sets and exams that I saved on my computer). Therefore, some things I say about biology might as well come from my posterior. Given all this, if you see that I say something horribly wrong about biology (or physics, for that matter), tell me in the comments! The other is that this post may seem rambling and incoherent at times; that's because this is more of a brainstorm than anything else.

So what's the big reason explaining the difference in depth versus breadth in teaching physics versus biology? I think the primary reason comes from the nature of the subjects. Ultimately, introductory biology classes concern themselves with analyzing various biological systems from a very top-down perspective. From what I can remember of my undergraduate biology class (and from what I can remind myself of by looking at old problem sets and exams), we went over a diverse range of topics such as protein biochemistry, cell biology, genetics from the perspective of DNA chemistry, and virology. From this top-down perspective in an introductory class, each of these systems are governed by similar basic biochemistry, but are somewhat separate otherwise. It is in more advanced biology classes that the nuances and subtleties in as well as relations between those systems are brought in.

Meanwhile, in physics, it is much more common for classes to go deep right away. In my introductory mechanics and E&M classes (which all students were required to take some form of), the focus wasn't so much on specific systems as much as general concepts applicable throughout physics. In physics, the notions of momentum conservation, gravitational attraction, precession, electrostatic interaction, magnetic interaction, electromagnetic induction, and many others are far more applicable than just considering billiard balls colliding, planets orbiting, tops spinning, pith balls repelling, bar magnets aligning, magnets producing currents in coils, and so on. These are all so much more general. Moreover, there is no particular need to focus on specific systems if these concepts are truly general. For example, consider the kinematics of two classical particles colliding. Of course, point masses that collide perfectly elastically are impossible to find in real life, in that there are no classical point masses, and there are no perfectly elastic classical collisions. (I'm choosing my words carefully to avoid invocation of quantum mechanics.) Then the question might be whether such collision kinematics change when the point masses are replaced by spheres, representing rotationally invariant distributions of mass for each particle. The beauty is that by invoking the idea that momentum is conserved for the center of mass of a system with no external forces, the spheres reduce to point particles anyway; moreover, any shape of object can then be considered simply as a superposition of point particles. (I'm being a little sloppy here to convey the basic intuition, rather than a precise physical description; a better explanation would explain the definition of a rigid body, as well as the notions of the center of mass and its conserved momentum.) Ultimately, then, what matters less is the shape of each particle, compared to the broader notions of energy & momentum conservation, because some very general form of superposition can be invoked to describe the physics of any composite system. (This of course fails for very large systems with more realistic assumptions, where statistical mechanics provides better predictions.)

So it has been established thus far that introductory physics classes focus more on the broader concepts that underlie physical systems as opposed to particular systems themselves, while introductory biology classes largely (though perhaps not entirely) do the opposite. But must this be the case, and if so, why? Is it possible to teach biology from a more fundamental perspective? This is one of the reasons why I wasn't a huge fan of my introductory biology class, and why I now appreciate encounters with biology much more from the lens of physics/biophysics/complex systems.

The problem with that idea is that physics and biology are not completely divorced disciplines. The biochemical reactions that govern life are essentially extremely complicated electromagnetic interactions between different atoms and molecules. That means that any attempt to fundamentally explain everything in biology will simply end up with electromagnetic interactions at the end of the day. The problem, as I see it, is that there are so many things interacting that it would be practically impossible to derive biology from pure physics — that's why biology exists as a separate scientific discipline! It exists to be able to make sense of what we see in living things without getting hopelessly lost in the process of attempting to achieve some fundamental understanding of those living things. With regard to that, my friend was telling me as an example how he studies the precise processes underlying cell division (mitosis and meiosis); specifically, he told me how a lot of the explanations in introductory classes for why some processes occur in cell division are so simplified to the point of being wrong, yet they continue to be taught because the truth is so much more complicated as to be suitable only for an advanced class unto itself. Recent advances in complexity theory may be able to abstract the teaching of some topics in an introductory biology class in a manner similar to introductory physics, but I feel that could use more development first. Moreover, it seems to me that complexity theory may be most useful right now in relation to evolutionary theory, and that evolutionary theory is the closest I've seen of biology being taught in a similar way to physics, yet from what I remember, evolutionary theory wasn't covered in any great detail in my introductory biology class, so I won't get into that further.

I realize that last paragraph makes me sound like the stereotypical elitist physicist who pompously claims that physics is the superior science to biology because it is more fundamental. To that, I submit the following two counterarguments (among many possible). One is that as mentioned above, out of the topics that were covered in my introductory biology class, evolutionary theory seems to come pedagogically the closest to physics, in that population models can be cast in a manner very related to statistical mechanics. This is because population dynamics can be taught in a very simplified and general/abstract manner, regardless of the constituent species, with the details added in later (as opposed to, say, cell biology, which at the introductory level does seem to be rather separate from other topics covered); this is similar to how I mentioned that no matter what the billiard balls are made of, their collisions can be taken as those of point masses. Moreover, evolutionary models pervade far beyond biology itself, ranging from evolutionary/genetic optimization algorithms to evolutionary graph theory as applied to economics. Thus, it is clearly possible to see biology (or at least some large parts of it) through the same general abstract lens as physics, at the introductory teaching level. The second is simply the following: applied physics is a thing, and I'm doing it. Witness: my current research concerns characterizing the Casimir force in different geometries involving perfect electrical conductors. The most general theory governing the Casimir force is quite well-known. The problem is that being able to characterize it in specific systems is a hard problem, and it is important because the non-additivity of the Casimir force makes it highly dependent on specific geometries. That's why I'm more interested in considering certain classes of systems rather than making grand statements about the Casimir force in general, because the latter has already been done in principle. In that way, then, what I'm doing bears a little more resemblance to the top-down view of biology as taught in introductory classes (while of course still keeping in mind fundamental principles of physics, such as symmetries, conservation laws, et cetera).

Again, I realize that this post was a bit rambling and incoherent, but I'm OK with that for now. Please feel free to leave your thoughts on the matter, or any other concerns you have with this post, in the comments below!

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