On Learning
October 2023
I’m a freshman at Columbia University now. One interesting quirk of this is that my autocorrect is now set to American English. An institutionally flavored curiosity is our Core Curriculum — it’s a selection of ‘general education’ [1] classes that every student here must take. The specifics vary by school: my friends at Columbia College end up doing a lot more literature, and I’ll have to do a great deal more calculus in Columbia Engineering, but the hope is the same. No matter what a Columbia student chooses to specialize in down the line, they’ll be competent in adjacent subjects, and ideally knowledgeable about countless others.
Working through Columbia and its Core Curriculum [2] has made me think about learning. Although our current leader has reform on his mind, the British system is undeniably more narrow. Students in the UK choose three or four subjects to study in depth during their last two years of high school, then apply to specific courses at universities where they will only (with startlingly few exceptions) take classes in those subjects for the following three or four years. There’s no emphasis on broad learning. In contrast, I applied to Columbia as an undecided major student, and I will take both technical and non-technical [3] classes before finally deciding on my field of study in sophomore year.
Learning seems to have different objectives and outcomes in these two systems. The British system expects you to have a fully formed idea of what you want to be and do in your life while putting you on the highway to doing the same. This is not asked of a typical American student in the same sense. Though elite colleges will certainly hope for a narrow extracurricular focus relating to some particular subject that a student might want to study, and many of my peers would agree that their high schools facilitate that environment, there is still a relatively broad range of qualifications and classes undertaken before young Americans head off to college. High school is a place to explore subjects and develop those budding interests. While I delved deep into mathematics, computer science, and physics through my four A Levels, my friends here have taken ten or eleven AP classes over a far wider spectrum of knowledge, and have accomplished this while sacrificing less depth than you might expect. After all, we’ve still placed into the same classes.
The outcomes of these two systems are different too. Britain is perhaps the only country that can conceivably stand up to America in higher education — Oxford, Cambridge [4], Imperial College London, and UCL are a few notable institutions — but this isn’t always apparent in the accomplishments of students that attend them. The United States has about 600 unicorns, while the UK has 90. Heck, the entirety of Europe only has 150. Even adjusted for population size, America clearly exerts outsized influence in entrepreneurship.
It might be unwise to solely attribute this disparity to education — brain drains in Europe, lower taxation, and significantly higher appetite for risk in America also matter — but it’s a large factor. A culture that values broad intellectual exploration will always prevail, because it ferments ambition in curious students who don’t have to shoebox themselves into what they thought they liked at some arbitrary prior age and can instead pick and choose the topics they find especially engaging to work with. I admire Columbia and similar colleges for facilitating this through the sheer abundance of opportunities for growth: when’s the last time you saw a Cambridge dropout build a startup? Unicorn hunting starts with a love of knowledge and domain agnosticism that transcends schooling [5].
A few important questions are raised here. Given the breadth of outcomes, which objective function are we currently maximizing in education? What do we care about most: graduation rate, GPA, job placements, creativity, income, unicorns created, social mobility, papers written, Nobel prizes, or something else entirely? Which objective function should we be maximizing? How can we accomplish this with limited resources across diverse demographics and geographies?
I cannot say I have all the answers. The last question particularly has been on the minds of educators and legislators since time immemorial: it’s ever-present in school district budget meetings across this nation. But I do hope I can provide some insight on the first few, because it is evident that education today does not adequately serve ambitious [6] individuals. Finding the right objective function could produce social change on a national scale and fulfillment on an individual one.
My first thought is that we are currently maximizing graduation rate and GPA. In theory, these are great proxy measures for success: all things held equal, more students graduating with a higher GPA should mean smarter students on average. The unfortunate truth is that all things are decidedly not held equal, however. Such a system creates a perverse incentive for GPA-boosting ‘easy A’ classes, and situations where faculty are incentivised to push forth no-zero grading policies to appease angry parents and frustrated students alike.
My second thought is that we should be maximizing creativity and curiosity. The American collegiate style of learning is a bit like building a start-up. Maybe that’s why the two are so closely and successfully interlinked. Assuming you have a liberal arts experience, there’s no compulsion to stick to a subject for three or four years if you dislike it. Conversely, you’re allowed to dive deeper into topics you do enjoy by taking advanced classes, working on research with your professors, and building projects with your peers. That’s conducive to building deep curiosity about a subject — creativity flows from loving what you do and working concretely on it, and there’s no reason we can’t implement this system in some iteration for high schoolers [7]. The Nobel prizes, job placements, and social mobility will follow. On a personal level, you can adapt this by giving your present self the freedom to decide what you want to do. The opinions of your past self on what you should do now was naturally determined by what you knew at the time. You know more than your past self now, so let the foresight of how your past plans worked out guide where you go next.
A small aside — I think that gifted education is severely lacking in secondary education. Wherever you go, it always seems to fall into the pitfall of “just do more”. I remember finishing my workbook in second grade math and being told to do harder sums, then geometry, then algebra, but in any case it never seemed to end. There was just a deluge of knowledge that threatened to confuse and terrify. The benefit of this approach was that I learned a lot more than I would have in ordinary class, but it seemed to be at the expense of breadth. When you don’t stop to smell the flowers every once in a while, you don’t have time to appreciate the subject for what it is and form wider mental links between disciplines. ‘Move fast and break things’ at least implies you had time to build something in the first place. Learning shouldn’t be taken at breakneck speed in a straight direction nor at a leisurely pace — think of your intellectual journey as water flowing down a steep hill. It moves quickly but traces contours near and far [8].
My last thought on the education system is that of accountability and oversight. Secondary education is scripted and top-down: students do what teachers say, teachers do what principals say, and principals do what superintendents say. Needless to say, this chain of command is extremely unhelpful for getting anything of substance done: every request goes up and down the hierarchy before it can be approved, with a single ‘no’ at any stage killing the proposal entirely. It’s a great system for balancing books and coordinating action across public schools, but this neglects the variation between each institution — even each classroom — which is so nuanced that one superintendent could not possibly know the ins and outs of every single circumstance under their remit. Ambitious students are harmed by initiatives which do not recognize and sustain their rapidly changing needs. On the flip side, students do need to take more initiative in developing their own love of learning outside of rigid schooling; having gone through the process myself, I can say that the hypercompetitive nature of American college admissions is terrible both for wellbeing and curiosity. Knowledge for a fixed endpoint, be it admissions or achievement, is unsustainable in that its utility diminishes as soon as that milestone is reached. Knowledge that results in innovation has no fixed endpoint by nature — it sustains itself through the constant iteration and refinement of new ideas that spring from exploring the steep hill on whose surface we flow. Love of knowledge without externalities is a powerful driver.
We can now wonder how to adopt this better perspective on knowledge. I presume you want to build great things and make the most of your talents, so we can shift that paradigm to be a little bit more practical and consider how we can develop our perspective on learning. The natural answer might seem to be ‘go to an American high school/college’, but that’s not exactly accurate or easy either. There are only a few schools with such diversity of talent and innate drive as Stanford and MIT, and they take very few students relative to the sizable applicant pool. Only a few private colleges in the United States follow this true liberal arts model in the first place: many still require you to at least indicate the majors you are considering or apply to a school which restricts you to a certain selection, from which internal transfers can range from fairly straightforward to downright impossible. Your environment does, for better and worse, greatly influence your chances of exposure to different knowledge domains and therefore success.
In light of that reality, think of this loosely as a Java interface: I’ll show you some methods and attributes that I believe a good learner should have, and you can implement them as you see fit. The key part of this analogy is that any class which implements an interface in Java must implement all of its attributes and methods — there’s no picking and choosing here.
Let curiosity guide you. There will always be things you must do — file taxes, eat, drink, sleep, and so on — and there will probably be things you should do, like completing your assignments or walking your dog. A lot of people seem to think that great work comes from forcing it into your ‘must do’ pile — to sustain this, they advocate for cold showers, timetables, and habits of work in order to build consistency. Consistency trumps motivation, they say. While it is true that being consistent is important in general, this discounts the fact that humans (much like everything else) are disinclined to do things which are hard, painful, or boring. Consistency might get you to an MVP, but it’s not going to incentivize you to put in extra hours when it counts. It won’t lead the way to your Next Big Thing to Work On and it certainly won’t make you love what you do. For that, you need passion, which brings us to my next point.
Find your intellectual passion. Not a passion for intellect — that’s just curiosity, which I hope you have by now. Find a specific topic or subject that excites you and makes you feel as though you could spend a day reading about it in a library, flicking through and diving deep into texts to your heart’s content. Just a day for now, your life’s work will come later. Paul Graham would say this is the first part of superlinear returns — you don’t need to commit your entire world and soul to this yet, but the most dangerous part is that this might end up going that way if you genuinely fall in love with what you do. It’s dangerous in the sense of dangerously exciting, because you don’t know where this will go, but it might just change your life.
Once you’ve found this passion, explore it. Be the water flowing down a steep hill — pool your knowledge in places where it sticks, but weave through the grass quickly, moving to and fro on your way. Perhaps you’ll encounter some other problems to set store by. Maybe you’ll be accompanied on your journey, for which some tortured water analogy probably exists. In any case, finding something you love working on will trump both consistency and motivation. Don’t be afraid to pivot away if you see greener pastures elsewhere, but finding that first intellectual love — even if it doesn’t end up sticking — will do more for your development than a thousand cold showers. Hating or even tolerating what you do will never get you anywhere. You must learn to love what you do or go and find something else entirely.
My final reflection is on arrogance. I believe there are two broad types of it. The kind that makes you think you can do anything, and the kind that makes you think that you don’t need anyone else to do anything. Call those internal arrogance and external arrogance, or weak and strong arrogance if you will. Weak arrogance is extremely helpful for anyone who wants to learn and build [9]. Problems are always a lot harder than they seem — the benefit of this youthful sort of arrogance is that you naively believe you can do it all, just because you’ve never been told you can’t do it all. That’s unorthodoxy in a nutshell. Strong arrogance on the other hand is fatal. Very few great things have come out of unbridled individualism and hubris. I advise against embodying strong arrogance, because you will fail and it will probably be quite embarrassing. Weak arrogance will make you a better learner and a better person. It will give you the tenacity to work hard but tolerate the humility to ask for help from those who have seen more than you when you need it. Ambition moderated by humility is all you need.
Notes
[1] I place ‘general education’ here in quotes because it is very much a misnomer. Exposure to various subjects spurns innovation just as much as practicing math problems makes you better at math. I would wager a not-insignificant amount that a good amount of new development comes from people applying discoveries from other subjects to their own fields of expertise.
Don’t let that fool you into thinking that you should only study the sciences if you’re a scientist, or the great works of Plato and Aristotle if you’re considering anthropology. As scientists need to communicate well with legislators and private entities to get their ideas heard and scaled, writers must be logical and true to the world they wish to portray. Perhaps the latter is a somewhat weaker sounding assertion, but I would hold that it’s correct nonetheless. Non-fiction books must be factual by nature for the most part, but fiction is only as believable as it can conceivably be tied to some phenomenon or behavioral mechanism that humans can identify with. The framework within which the story operates need not be true — it certainly must be consistent. That’s why Harry Potter works.
[2] I’m only doing one Core class this semester — the venerable Art of Engineering, often thought of as the keystone of the Columbia Engineering freshman experience. Think practical projects, lectures from faculty and external speakers on contemporary science and futurism, and a little introductory data science thrown in for good measure. Friday sleep schedule permitting, I always enjoy these lectures. Our professor politely requested we bring our resumes to the first one, where he promptly shredded them in a proclamation that ‘none of this really matters!’. I’d like to say I agree. Too much store is set by abstract lists of achievements. I see it with my peers scouting for internships when they should be exploring what intrigues them. I see it with myself when I apply to a myriad of clubs because I know they’ll put me in good stead for applying to the same next year. Maybe I’ll take this summer off*, as a form of counter-protest against the dark and mysterious forces in higher education that cause this almost unbearable desire to head immediately into the workforce.
*Off doesn’t mean off. More precisely, off doesn’t mean switching off completely. There’s a difference between wasting time and choosing to do something a little less browbeating. I’d like to get into entrepreneurship this summer — I’ve already been working on a few things, mostly in biotech and AI, but I’m constrained by (a) my F-1 visa which prevents work and (b) a lack of pre-seed funding which would allow me to work and study in the United States under the International Entrepreneur Rule. On that note, if you’re an angel investor or know one, let me know.
[3] Columbia effectively means the humanities. Given [1] I’m sure you’ll appreciate that I don’t necessarily consider these courses to be non-technical in the sense of easy.
[4] Often shortened to Oxbridge. I read a book once which christened their union Camberford. That was both amusing and terrible.
[5] It’s therefore a little ironic that this same mindset is cultivated by schools themselves. I find that it doesn’t occur at the institutional level — professors and deans are still concerned with making sure students pass classes and graduate. That’s probably for the better, in fact.
This mindset actually stems from the students around you, and that’s where I believe the real value of an Ivy League or comparable education lies. There’s no real benefit in taking a math class at Harvard versus School X, where the latter isn’t as closely associated with prestige — sure, Harvard might cover content a little more rigorously, and you’ll probably have access to better TAs, but fundamentally you’re learning virtually identical material anyways. The same student would do just as well in a Harvard math class as in a math class at School X nine times out of ten, I’d imagine.
The difference comes when you examine what that same student might do outside of class. School X might not have much in the way of clubs, or start-up accelerators, or peers who are just as hungry to innovate and build new products. Harvard is bursting at the seams with all of the above. The resources and networks that an elite college facilitates justifies the sticker price to ambitious individuals. They might be able to do just as well elsewhere through their own tenacity, but it’s a lot easier when you’re starting out in the right environment. That’s why a lot of successful founders went to a relatively unknown school for their undergraduate education, but generally ended up either dropping out, transferring to a better college, or going to an elite university for their graduate studies.
[6] Note that I intentionally did not specify the type of ambition. That might include founders, entrepreneurs, programmers, scientists, artists, painters, actors, musicians, writers, mathematicians, philosophers, or underwater basket weavers. Their particular interests are not of importance. What’s important is that they are supported to realize their goals. Far too often that is restricted to ‘STEM nerds’.
[7] This is why I like Khan Academy. A broad selection of subjects with the depth to back them up. Pivot at will.
[8] Sometimes you’ll see pools forming in little dips. Keep knowledge in domains that are interesting to you but move forward and explore widely.
[9] I had a friend who once told me his goal was to become the first trillionaire. That caught me off-guard, but I heard him out and thought he had some nice ideas. He ended up closing a seed round deal for the start-up he co-founded for about $2.5m a few weeks ago. Weak arrogance was his ambition to become a trillionaire, but his tenacity and humility in working extremely hard, finding co-founders who were just as talented, and asking for help from investors and academics alike were what brought him that deal. I have a lot to learn from him and admire him greatly.
