Life (and chemistry) is a box of models

One of the most important challenges in teaching students chemistry is in conveying the fact that chemistry is essentially a milieu of models. Too often students can misinterpret the conceptual devices taught to them as "real" entities. While models seem to perpetually and cruelly banish the concept of "reality" itself to fanciful speculation at best, the real beauty of chemistry is in how the simplest of models can explain a vast range of diverse chemical phenomena. Students' understanding can only be enriched by communicating to them the value of models as a window into our world. How can we achieve this?

We can start by emphasizing the very fact. Very few of my chemistry teachers even mentioned the word "model" in their discourse, let alone emphasized the preponderance of models used in chemistry. One can claim that all of chemistry is in fact a model. The reason for this is not hard to grasp: models come to our aid when the world gets too complex. The complex nature of chemical systems wherein one cannot describe them using first principles lends especially this 'central science' to modeling.

You can start with the simplest fact taught in freshman chemistry class- the structure of methane as it is drawn on paper. The methane molecule of course exists in real life, but that does not mean that you can actually see four bonds growing out tetrahedrally from a central carbon. Recent advancements in techniques like scanning tunneling microscopy have brought an astoundingly real feel to molecules, but what you see is still diffuse electron density and not actual bonds. The tetrahedral representation of methane that we draw on paper is very much a model.

Once students realize that even their simple representations of molecules are models, the road ahead becomes easier. Since we are talking about methane, we will inevitably talk about hybridization and describe how the carbon is sp3 hybridized. But of course hybridization is merely a mathematical and conceptual device- and a very powerful one at that- and this needs to become clear. Hybridization in methane leads to discussion about hybridization in other molecules. This is usually followed by one of the most conceptually simple and useful models in chemistry where you can make back-of-the-envelope calculations to get real and useful results- VSEPR. VSEPR is a great example of a simple model that works in a great number of cases; asking whether it is "real" is futile. Thus, one can drive home the importance of modeling even in the first few sessions of chemistry 101.

Once these facts become clear, the floodgates can open. Students can cease to think of the world as real and still be happy. Think the famous Van der Waals "12-6" curve is real? Think again. It does a marvelous job of representing in simple terms an incredibly complex and delicate tension between attraction and repulsion engendered by point charges, dipoles and higher order terms, and it's no more than that. But it works! It's a disarmingly simple model that's even incorporated in popular molecular modeling programs. How about crystal field theory? Another fantastic model that does a great job of explaining the properties of transition metal complexes without being real. Of course, let's not even get started on that ubiquitous act that initiates a newbie into the world of organic chemistry- arrow pushing. That's the very epitome of modeling for you. And after this onslaught, students should have little trouble understanding that those ephemeral, seductive twin forms of benzene that seem to interconvert into each other on paper are pure fiction.

Want a book that teaches chemistry through models? You are in luck. One of the best books that conveys the reality of chemistry as model building also turns out to be one of the most influential scientific books of the 20th century- Linus Pauling's "The Nature of the Chemical Bond". In this book Pauling introduces dozens of ideas like polarization, hybridization, ionic and covalent character of bonds, resonance and hydrogen bonding. All of these are enshrined in his Valence Bond Theory. And all are models. If conveying the importance of models to students gives us an opportunity to introduce them to this classic text, the effort would already have been worthwhile.

So would students turn fatalistic and despondent once they have been convinced that the world is not real but is a model? Not at all. The singular fact that snatches hope from the jaws of defeat is the very fact that we can in fact build such models and understand the world. Think about it; we build models that are almost laughingly simplistic representations of a hideously complex reality that's probably going to remain out of our reach forever. And yet these apparent embarrassments help us understand protein folding, design new drugs against cancer, build solar cells, bake a cake and capture the smell of a rose in a bottle.

What more could we want.

Can natural sciences be taught without recourse to evolution?

That's the question for a discussion over the American Philosophical Society museum website. I think the answer to the question would have to be no. Now of course that does not mean it's technically impossibly; after all before Darwin natural sciences were taught without recourse to evolution. But evolution ties together all the threads like nothing else, and to teach the natural sciences without it would be to present disparate facts without really connecting them together. It would be like presenting someone with a map of a city without a single road in it.

In fact natural sciences were largely taught to us without recourse to evolution during our high school and college days. Remember those reams of facts about the anatomy of obscure animals that we had to memorize. If it wasn't the hydra it was the mouse. If not the mouse then the paramecium. I can never resent my biology teachers enough for not connecting all these animals and their features through the lens of evolution. What a world of difference it would have made if the beauty of the unity of life would have been made evident by citing the evolutionary relationships between all these exotic creatures.

In fact "Evolution" was nothing more than a set of two clumsy textbook chapters that got many of the details wrong and left countless other facts wanting. Granted, some of the teachers at least had good intentions, but they just didn't get it. Teaching biology without constantly referring to evolution is like asking someone to learn about a world without using language. Would you teach physics without recourse to mathematics? Then you should not teach biology without recourse to evolution, at least not in the twenty first century.

This is how science should be taught

The Viki Weisskopf way

From Jeremy Bernstein's review of noted physicist Victor Weisskopf's 1991 memoir. Bernstein first took a class from the utterly brilliant and impenetrable Nobel laureate Julian Schwinger at Harvard. After a couple of days of withstanding the barrage, Bernstein decided to attend Victor Weisskopf's class at MIT. The result is endearingly described:

My visits to Viki's class in quantum mechanics at MIT were, in every way, a culture shock. The class and the classroom were both huge—at least a hundred students. Weisskopf was also huge, at least he was tall compared to the diminutive Schwinger. I do not think he wore a jacket, or if he did, it must have been rumpled. Schwinger was what we used to call a spiffy dresser.

Weisskopf's first remark on entering the classroom, was "Boys [there were no women in the class], I just had a wonderful night!" There were raucous catcalls of "Yeah Viki!" along with assorted outbursts of applause. When things had quieted down Weisskopf said, "No, no it's not what you think. Last night, for the first time, I really understood the Born approximation." This was a reference to an important approximation method in quantum mechanics that had been invented in the late 1920s by the German physicist Max Born, with whom Weisskopf studied in Göttingen. Weisskopf then proceeded to derive the principal formulas of the Born approximation, using notes that looked as if they had been written on the back of an envelope. Along the way, he got nearly every factor of two and pi wrong. At each of these mistakes there would be a general outcry from the class; at the end of the process, a correct formula emerged, along with the sense, perhaps illusory, that we were participating in a scientific discovery rather than an intellectual entertainment. Weisskopf also had wonderful insights into what each term in the formula meant for understanding physics. We were, in short, in the hands of a master teacher

The trick in any class is not to let the students know how much you know (the Schwinger technique) but to let them know how much you, and indeed everyone else, do not know.