Zach Dexter

College, tell me why things are important. And three new courses to do just that.

Or: Why technical coursework should instill an understanding of Robert Pirsig’s Quality, and what to do about it.

During my first year at Chapel Hill, I found myself memorizing equations for calculus, function calls for computer science, and models for economics. Throughout my time at UNC, I asked smart friends why they were learning about the rational abstractions in their fields. The questions can be reverse-engineered to get a syllabus of three questions college should force students to ask.

I follow each question with a subheading (in [] brackets), but not the name, of a course I will suggest near the end of this essay that will empower students to answer each question with competence - and maybe even a newfound arete.

- What analytical rational tools that do not currently exist might be useful, and how would you go about developing them? (Got some good answers to this one. Most involved some specific form of stronger artificial intelligence. Most answers were things students learned about outside of school.)

[Romantically-inspired rational-tool production]

- How is the power of the rational tools you are using bounded? (For example, practical computational tools are usually bounded by the power of Turing machines. Mathematics generally cannot prove everything about itself without resorting to ideas outside of math - see Gödel’s incompleteness theorem. Economic policy involves tradeoffs that the models cannot moralize about.)

[The power of reason in your field]

- Can you place the rational abstractions you’re learning in a larger context? (For example, for what human purposes are we learning to code on practical implementations of Turing machines? Has nobody ever thought to start by making students figure out what might be best to study!?)

[The big picture]

Four years ago, a first grasping at my frustrations

My first year, I sat down with then-Chancellor Holden Thorp, who was awesome because he liked to stay in touch with campus life by speaking with students. I told Thorp that majors in science, math and other technical fields should begin their studies with an introduction to what people can do with these intellectual tools. He countered (very sensibly, given my unrefined argument and phrasing) that it’s best to actually teach the fundamentals of chemistry, biology, math, physics or computer science than to teach what their applications are.

But as time went on, I realized that’s not exactly what I meant.

I wanted to know why I was studying computation, how what I was currently learning related to the big picture, the big picture of the big picture, and so on, until I could place my learning in context of the ultimate big picture: human thought itself.

This sounds grandiose, but is actually not much to ask at all. If I believed higher education in science, math and technical fields as it is today were anything more than vocational training, then upon developing the views I am writing about here, my immediate reaction might have been be that we have philosophy departments for training in the theory of knowledge, and that I should go study philosophy. This reaction would have sent me spiraling down into modern philosophy, which can at times and without physicalism be, somewhat ironically, simultaneously internally consistent and vapid. It is also somewhat lacking in new ideas outside of mathematical logic.

(Note: Some old ideas do have much to teach us. But the point is that philosophy as a field evolves only so much, and its evolution does not really drive the evolution of our understanding of the world. The sciences and humanities - fields which actually apply rational inquiry - do that.)

I came to believe that teaching methods before theory is the essence of vocational education. Higher education is about context, theory, the study of abstractions for the ability to manipulate symbols in the appropriate way as to take advantage of those abstractions (methods), and, crucially, the study of abstractions for the sake of understanding the purpose of the abstractions.

The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old questions from a new angle, requires creative imagination and marks real advance in science.

- Albert Einstein

Smart students find it much more interesting and engaging when instructors explain the rational context for knowledge (i.e., symbolic manipulation for math, or abstract computational models for programming) before or at least while asking them to learn about methods (i.e. integrals or programming).

But, critically, it’s not just about motivating study of methods. It’s actually the case that this context makes for a more rigorous technical foundation for study. As I’ll show later, it turns out MIT and Stanford already do this.

Methods and theory should be one because, at the highest levels of intellectual activity, they already are

College is supposed to be a place for higher learning, but really, we undergraduates are just learning about the implementations of established techniques for problem solving. For example, if my math education had begun with an explanation that math is a symbolic manipulation system of limited power, I would have been much more interested in learning calculus and other specific methods because I would have understood that only by getting into the details of other peoples’ established techniques could I hope to arrive at an understanding of what it means to create good techniques in the first place.

This means, for example, that calculus students would come into college with a base level of knowledge in math, most of which was acquired through rote. But their introductory coursework would help them develop some rudimentary understanding of the fact that math is a system of symbolic manipulation of limited power whose methods we study not only because we hope to become proficient in those methods, but also because we hope to construct better, more mathematically beautiful methods.

Looking at methods’ details with an eye to esthetic is the zen bit of Zen and the Art of Motorcycle Maintenance and its approach to true intellectual mastery of a subject. Become a mechanic in order to see why abstractions are useful and generate better ones.

This isn’t essential to my argument, and is almost an aside, but one way we might tell which abstractions are good is something akin to Pirsig’s Quality.

Quality is the esthetic rational toolmakers compare their work against. Rational tools exist, and exist in their specific forms, for reasons motivated by an undefined but detectable rational or mathematical beauty.

The author doesn’t mean to suggest that students learn most from vocational curricula. He actually prescribes a path for self-study, I suppose because no vocational and few higher ed curricula care to enlighten students about rational toolmaking in their fields. For college, Pirsig ends up recommending Quality Studies. I think that class would be a moderately stimulating addition to a philosophy curriculum, but that it would be insufficient for higher technical education.

I’m not committed to Pirsig’s ideas. But I do believe that undergraduates can experience their own journey into the details (becoming motorcycle mechanics, so to speak), and emerge with a sense of what makes abstractions good instead of merely the ability to use abstractions, by making a study of rational toolmaking in their various technical fields.

As a friend put it, we need to ‘turn the scientific method upon reason itself.’ In doing so, we might find ways to focus its ends, sharpen its methods and make our tools more powerful and relevant.

And now [Phaedrus] began to see for the first time the unbelievable magnitude of what man, when he gained power to understand and rule the world in terms of dialectic truths, had lost. He had built empires of scientific capability to manipulate the phenomena of nature into enormous manifestations of his own dreams of power and wealth - but for this he had exchanged an empire of understanding of equal magnitude: an understanding of what it is to be a part of the world, and not an enemy of it.

- Zen and the Art of Motorcycle Maintenance

I think the system can be improved. People don’t learn what math *is* (symbolic manipulation of limited power, as Gödel showed with his incompleteness theorem, designed to solve certain problems humans face) or what computing *is* (implementations of abstract models closely tied to linguistics) or what physics *is* (abstractions, but probably actually just approximations, of the real world, wrapped in symbolic logic for easy manipulation by human brains) before learning about specific methods.

“The system” risks being a creativity-killer and deterring some bright students

By teaching them methods only, I think colleges are throwing away their brightest, most creative students. I think that generally speaking, colleges kill creativity in the same ways Sir Ken Robinson says primary education does. But nobody has really expressed the reason why very well. I think it is because college leaves Quality to philosophy and teaches methods to undergraduate students it treats as human equation-solvers who can only appreciate the place of methods after they study all of them.

The reason for this killing of creativity, I think, is that smart people are deterred when majors appear to be all about memorization of existing tools. COMP 455 opened my eyes to computability, abstract notions of computation, and other thought that helped answer my questions about why I’d bother to go sit in a room and learn about basic Java, data structures and algorithms, operating systems, networks et cetera.

I want to place rational tools in a larger context, analyze their power, and understand why they were created. I believe I am a good student because I want to know why I am studying a thing before I devote my life to it. For me, devotion to study before answering that “why” question meant acceptance without good reasons. It was entirely irrational.

I felt like I was mindlessly studying methods, with no direction beyond vocational application. I am capable of seeing the big picture, and was capable of that four years ago. I want more than vocational education; I want higher education.

An aside: Now that I have been enlightened, I am excited about MOOCs. I just have to teach myself where abstractions fit in the web of human understanding. Ironically, given our country’s focus on four-year college, I will be responsible for my own education as a motorcycle mechanic, so to speak.

How things should be: A general description

Higher education should include thinking about how our romantic notions actually lead to our rational abstractions. By starting out seeking something like Pirsig’s notion of Quality, students will see why the great thinkers of the past developed the abstractions they did. They will learn to appreciate what mathematical beauty is, and why it is more than mere esthetic.

How things should be: Two very specific solutions

Solution 1: Three classes that develop students’ abilities to critically analyze abstractions

I think undergraduates should take one theory class in their field (i.e. COMP 455/Models of Languages and Computation, or What is Modern Physics, What is Modern Math) before (potentially and probably, depending on the student’s prior exposure to the field) blindly and purposelessly memorizing techniques as if college is some kind of vocational program where you learn how to use existing tools.

I also think that everyone in technical fields should take an Introduction to Symbolic Logic, in order to appreciate what math is, the upper limits on its power, and to develop mathematical maturity easily. There is no reason students should be afraid of symbols. But every year, smart students drop out of math courses because they don’t understand what it is they are studying. True, some can’t do the work. But others are inquisitive and unwilling to blindly follow unlit paths. Light up the path a bit and you’ll get a flood of bright students from the humanities flowing into technical fields.

I think everyone in all fields should take Introdution to Linguistics and Computation. The ideas behind the two can be analyzed using similar toolkits. The parallels are fascinating to me, and even if they aren’t fascinating to everyone, everyone has to use both language and computation these days. The least higher education can do is enlighten us to their Quality.

There are three practical benefits to this three-course introduction to modern thought. First is the sudden, widespread development of mathematical maturity (or the state of being unafraid of symbols) among undergraduates. I believe that “my students don’t have mathematical maturity” is a cop-out. We should just teach students what symbolic manipulation is all about, since it is so fundamental to modern technical thought.

Second, I just think technical subjects would make a lot more sense, and fewer truly bright and extremely inquisitive students would give up, if they could place the methods they learn in college in context in a) their field of study and b) the whole of human knowledge. For example, students whose minds are open to the theory of computation while they study programming will develop a deeper understanding of why functional programming exhibits rational beauty. This seemingly lofty theoretical suggestion would actually have a low-level vocational impact by making them better job candidates.

Third, I think that treating theory (ex. abstract computation) and methods (ex. programming) as one is the only way to generate creativity on a broad scale in higher ed.

Solution 2: Develop an intuition for Quality in abstractions by viscerally experiencing their relative utility (i.e., by studying the lower-order abstractions first)

This solution is perhaps the most clever didactic approach to higher education I have seen because it relies on students’ introspection on the material to help them develop an understanding of the importance, meaning and romantic notions behind abstractions in the technical fields.

MIT teaches computer science from the ground up. They start with math and physics, building upon Maxwell’s equations and logic gates to get to computation.

I pose a question about the best students in society. Which of them, given this introspection-derived intuition for beauty in abstraction, for Pirsig’s Quality, could not be prepared to accept the crystallization of mathematically beautiful new thoughts, given a set of patterns to recognize from past inventors of mathematically beautiful abstractions? Wouldn’t these students be not just fully capable but actually driven, by an intuitive understanding of the romantic beauty of the abstractions, towards study that truly furthers human understanding (i.e., by the creation of more subjectively beautiful and therefore practically useful abstractions)?

And most importantly for the great masses of college students: Among average students, who would not be capable of at least critically analyzing abstractions and appreciating their value?

Conclusion

Only by placing reason in a larger context, analyzing the value of reason, and understanding why reason was created can we value life as more than a series of milestones, people as more than objects whose labor government or capital can exploit, and undergraduate education in technical fields as more than a four-year journey of rote (interspersed, if the student is lucky, with a touch of ethics unconnected to the rational tools that constitute the primary focus of study).

Riemann didn’t formalize the integral because he was an automaton with a reservoir of methodological knowledge. I feel that he must have had a full appreciation for the power of abstractions. Clearly, he needed methods to inform his thinking, and rigorous technical training to guide his work. He wasn’t guided by romantic notions of abstractions. But I beg you to tell me how many undergraduate students can even tell you what an equation is - what its power is, what its creation did for humanity, and suggest a couple directions for new abstractions.

And while not everyone can be a Riemann or Newton or whoever, at least give bright students the chance to ask “why” questions before they become completely disillusioned because of a missing-the-forest-for-the-trees curriculum.

Addendum: Related Observations and Predictions

Stanford, MIT and a few others already do what I am talking about. Most seem to do it using Solution 2. With the rise of MOOCs, colleges that take the vocational approach will fade away unless they go beyond mere vocational training via the approximately the way (instilling a sense of Quality) described above.

Addendum: Request for Comments

This essay could be completely wrong, and maybe college students should blindly study methods, because the world is so complicated that the ability to develop abstractions or at least appreciate others’ abstractions is beyond your average college student. I see things differently, which is why I wrote this.

This essay would be nothing without critical analysis, refinement, counter-examples and other critical discussion. Send your thoughts my way - please.

Addendum: What this essay is not

This essay is not a call for a new Great Books curriculum. It is true that the Great Books curriculum is dead. I think this is for good reason: The Great Books were written in another time, and I think their advice just isn’t applicable or great anymore.

This essay is also not a call for students to study philosophy only. One can argue that philosophy as a field is failing to make an impact on our world in the way it could. Philosophy as a study should be kept, but integrated into each technical subject. The equations ultimately come from a sense of what is valuable in the world, from a sense of what “it is to be part of the world, and not an enemy of it.”

Addendum: The three courses

What is X: The power of reason in your field, and the big picture

Introduction to Linguistics and Computation

Introduction to Symbolic Logic: Romantically-inspired rational-tool production*

* - This course must also teach Quality itself, and not just symbolic logic methods. That is, the ethos and open-minded didactic methods (yes, I think it is okay to use methods to teach non-methodical things) of the first two courses must be embedded in it.