This a followup on Wadge’s Law

Every Computer Science course has a tendency to degenerate into a programming course.

This just begs to be generalized.

What about programming courses? Do they degenerate? To what?

For example, according to language teachers I’ve talked to, every, say, French course has a tendency to degenerate into a grammar course. What about other subjects?

My daughter, who teaches Chemistry, says that Chemistry courses (not hers, I assume) can degenerate into math courses. Apparently, it’s the same for other ‘hard’ sciences. Every now and then I walk through the Physics building and look at the posted assignment solutions. Calculus.

In general the kind of math depends on the course. For example, a course on general relativity can degenerate into a course on tensor algebra (nobody understands tensors as far as I know). A course on quantum mechanics can degenerate into a course on Hilbert space theory. A special relativity course can decay into a course on non-Euclidean geometry. And so on.

I used the word “decay” on purpose. The degeneration process reminds me of the phenomenon in nuclear physics where an atom of one element (say, uranium) releases a particle and turns into an atom of thorium, a simpler element. The interesting part of this analogy is that the process doesn’t always stop there. The thorium atom soon turns into a radium atom, which turns into an actinium atom, then a francium atom, and on and on till we reach lead, which basically doesn’t decay. This is called a “decay chain”.

Are there pedagogical decay chains? Indeed there are.

Let’s start with a programming course. Think of it as thorium, the result of a computer science course (uranium) degenerating. There’s still a tendency for the programming course to decay, and in my experience it turns into a programming project (radium) – a big program in a particular language.

And that’s not the end. The project requires a good grasp of the language being used, so there is a tendency for the project course to decay into a language course (actinium). And finally, as in the humanities, a language course decays into a grammar course, which in computer science terminology is a course in syntax. As far as I can tell it ends there, so that programming language syntax is the computer science equivalent of lead.

This phenomenon is not restricted to computing. Science courses  decay into math courses, and math courses in turn decay. A course on calculus can degenerate into one on algebra – symbolic differentiation and integration (as can be performed by a modern calculator or phone app). My niece took a course like this and it killed her interest in mathematics. In fact, the course went even further, with many exam questions requiring only numerical calculation. It seems that arithmetic is the lead of mathematics.

Do other activities decay? It seems so. A counsellor friend says that if you are not careful, a counselling session can degenerate into a gripe session.

I play bass guitar regularly with a great old-time jam (think appalachian fiddle music). Usually everything is fine, but sometime when we get to the key of A (after D and G) and people want to play a lot of tunes which switch harmony between A  and G. These are called “modal” tunes and they are really boring for the bass  player. Thus an old time jam can degenerate into a modal marathon.

Does this decay process work in the other direction? Yes, I call it “enhancement”.

For example, many computer science professors are not happy about teaching a “programming” course. Who wants to teach students to churn out code that probably won’t work, can’t be reused, and is hard to maintain? You also need to teach them some basics of software engineering (SE). So there is a tendency for a programming course to enhance into an SE course.

From my own experience a logic course also has a tendency to enhance. What’s the point of teaching them about completeness or Goedel’s theorem without talking about their significance; e.g. implications for AI. So a logic course tends to enhance to a philosophy course. Especially if it’s given in a philosophy department.

I did some research on natural language courses and it seems the instructors feel constrained talking about just one language. As a result, a language course has a tendency to enhance into a comparative linguistics course.

What do students think of all this? My guess is they are not always pleased with enhancement. They sign up to learn to code or express themselves in French then find they have to learn about OO or the use of the definite article in Spanish. On the other hand, if a programming or French course shrinks to a grammar course, they have less to worry about, just understanding a (hopefully finite) set of rules.

What about outside the classroom? In my experience as a (very) amateur musician, it  seems that every skilled musician really (possibly secretly) wants to play jazz. Jazz is musician’s music. So a music session will tend to enhance into a jazz jam. Thankfully the presence of amateurs will tend to inhibit the process. We amateurs act like atoms of lead, slowing down the reaction.

Finally, what about blog posts – do they degenerate/enhance? Yes, I think in general a blog can degenerate into a list of complaints, or enhance  into philosophizing.

Not mine, of course.