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by ADITHYA SRINIVASAN
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So a bit of background about me before I go into the question.So I am sophomore studying Mechanical Engineering in India.

I have noticed that I have forgotten about 80-90% of the course-work that I did during the first year.Don't get me wrong,I studied the courses properly and not for the test.Still,if you were to ask me how much of the course I remember now, I would at the very best remember the general idea of the stuff I read.

This is very startling from a long time perspective.College-work in India is generally more overloaded than other countries(from what I have observed),so what this means is people consume a lot of knowledge in a very short amount of time and forget it before they can make any use of it at all(leaving aside the question whether the knowledge is useful in the first place).This occurs despite the best intentions to learn and especially so with complicated stuff.I am not just talking about the facts here but whole concepts and ideas of the subject tend to be forgotten sooner than we can find any use for them.I am pretty confident this applies in most colleges(India or not).

This throws up a host of questions for me.The major premise/reason for attending college is to gain knowledge that I can further apply to job/life.The other touted premise is "Learning to Learn or Solve Problems".If that were the objective,I fell college apparatus is a very ineffective way of achieving it(will elaborate on this if required).Assuming that the former premise is the actual one,I do not think the college system accounts for my forgetting curve.Even if you were to take proactive steps and learn the material properly,you are still likely to forget it before you use it.It is impractical to practice spaced repetition for multiple semesters worth of course work.And if you were to do it,the question here(which I will go into detail further),is it worth to put this much effort into pre-learning it,effort into remembering it and then finally using some small portion of it later on in your lives?

All this is I feel part of a bigger question:

What utility do I gain from pre-learning any knowledge at all that I am not going to use in my near future ?

This question is asked presupposing that you are not learning out of pure curiosity and rather with the hope of using it later on.Basically you expect that this knowledge will help you meaningfully constrain your anticipation and help you make your decisions.

This question I feel has multiple sub-questions to it,which I only partially have found an answer(hence the post/question).

1.How exactly do I quantify my forgetting curve?

2.How much of what I am pre-learning is going to be useful?(This differs on a individual basis)

3.Assuming that what I have learnt is useful,how much extra effort do I have to put in to make sure that my knowledge stays intact at the time of use?This may the effort through spaced repetition or any other retention method that you use.I feel a useful parameter to define ,in addition to the forgetting curve,is "time/effort required to reach 50%,80% of knowledge at start" at any point in time.I would highly appreciate if you give me any paper on this(hopefully where the subject learns undergrad math-level concepts).

4.What should be the exponential(negative) scaling factor of the utility when you finally do end up using it?(This also might differ on an individual basis).

5.Finally answering the previous 4,is it worth to invest your time on something to pre-learn?We can debate on the degree of pre-learning here.I feel the amount that we generally do in college is waaaay off.


PS:This is the first time I am posting on LessWrong. So I am not exactly sure whether this qualifies as a question or as a post.So forgive me if the post itself is a bit rough.

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What is the point of College? Specifically is it worth investing time to gain knowledge?
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johnswentworth

130

First, the standard answer: Bryan Caplan's The Case Against Education. Short version: education is about signalling to future employers how smart/diligent/willing-to-jump-through-hoops/etc you are. Skill acquisition is mostly irrelevant. This is basically true for most people most of the time.

That said... I personally have gotten a lot of value out of things I learned in courses. This is not something that happens by default; the vast majority of my classmates did not get nearly as much value out of courses as I did. I'll list a few things I did differently which may help.

Avoid nontechnical classes: this one is kind of a "well duh" thing, but there are some subtleties. "Technical" should be interpreted in a broad sense - things like e.g. law or languages aren't technical in the sense of STEM, but they're technical in the sense that the things they teach are intended to be directly useful. By contrast, subjects which are primarily about aesthetics or history or critical theory are not really intended to be directly useful.

Decreasing marginal returns: the first course in any particular field/subfield is far more valuable than the second course, the second course is more valuable than the third, etc. This suggests going for breadth over depth. In particular, I recommend taking one or two courses in many different fields so that you can talk to specialists in those fields without being completely lost. You don't need to become an expert yourself; much of the value is in being able to quickly and easily work with specialists in many different fields. You can translate jargon and act as a human interface, and you can easily jump into many different areas.

General-purpose tools: focus on fields which provide tools applicable to many different domains. Most of applied math qualifies, as well as computer science, economics, and law. Ideally, you take one or two courses in some general-purpose subject, then run into applications of that subject while sampling other fields. By seeing it come up in different contexts, you're more likely to remember and use it.

Summary of this point and previous: go for depth in general purpose tools, and practice those tools while gaining breadth in other areas.

Use available resources: I've covered about as much material in open courseware as I have in in-person classes. I've watched online lectures, I've read textbooks, and I've audited courses. (I've even audited classes at universities where I'm not registered - professors are usually happy with people just showing up.) In college, I'd often watch a semester's worth of online lectures on a subject before taking a class on the subject; material is a lot easier to follow when you already have a general idea of where things are headed and how it all slots together..

Have a stock of problems: as you learn new tools, it's useful to have a handful of problems to try them out on. Hard open algorithmic problems like integer factorization or P vs NP or graph isomorphism are great for testing out all sorts of applied math/CS tricks. "How could I use this to start a company and make a gazillion dollars?" is a problem which applies to practically anything. The problems should be things you're interested in and enjoy thinking about, so that you'll find it worthwhile to try out new tools on them even though most of the tools don't actually yield breakthroughs on most of the problems.

This point and the previous one help a lot with actually remembering things and being able to apply them in-the-wild.

Optimize: at my college (Harvey Mudd), it was very easy to tell who had actually tried to optimize their course choices - it was the people who used the "build your own major" option. We only had half a dozen majors, and the course requirements always included things which weren't really what any particular person was interested in. If you wanted to cram in more courses you were actually interested in, while avoiding irrelevant courses, a build-your-own major was the way to go.

More generally, you'll get more out of classes if you read through the whole course catalog, mark the classes which sound interesting, and then optimize your schedule to focus on those classes. Sounds obvious, yet most people don't do it.

Be comprehensive: you're not going to know everything, but you can learn enough that nothing is very far from the things you do know. You can learn enough that you at least have some idea of which things you don't know. You can learn enough that, even if you don't know something, you've probably heard of it, and you have some idea of where to learn about it if you need to. The key is to aim for comprehensive knowledge of the world - you don't need to know every little detail, but at least get the broad strokes of the big things. Anytime you don't have a clue about something, pay attention to it, and look for the most general subject which would give you some background about that thing.

Math, physics and economics are particularly useful for comprehensive foundations - they give you the tools to solve practically anything in principle, though you'll often need more specialized tools in practice.

[-]technicalities30

Caplan puts the signalling share of the college income premium at 50%-80%, leaving (say) 20% for the human capital share. So your sentence calling HC "mostly irrelevant" is technically true, but I wouldn't use the word 'irrelevant' for a feature explaining ~ a fifth of the variance.

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[-]ADITHYA SRINIVASAN20

Thanks. That's a really nice list.I have not seen a lot of these ideas previously.Especially general purpose tool-idea and stock of problems-idea is very good.These ideas are really nice to ensure in-built spaced repetition.

But can you give me some ideas about the second question I asked.I cant do this because I am still undergrad.So pick a topic that you learned about say 4-5 years ago(or any time-frame for that matter),make sure that you haven't used that particular knowledge for the past 4-5 years,try to get back to the same knowledge-level th... (read more)

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6johnswentworth
I graduated 7 years ago. During that time, I've actually used most of the subjects I studied in college - partly at work (as a data scientist), partly in my own research, and partly just when they happen to come up in conversation or day-to-day life. On the occasions when I've needed to return to a topic I haven't used in a while, it's typically been very fast. But the question "how long does it take to get back up to speed on something I learned a while ago?" kind of misses the point. Most of the value doesn't come from being able to quickly get back up to speed on fluid mechanics or materials science or inorganic chemistry. Rather, the value comes knowing which pieces I actually need to get back up to speed on. What matters is remembering what questions to ask, how to formulate them, and what the important pieces usually are. Details are easy to find on wikipedia or in papers if you're familiar with the high-level structure. To put it differently: you want to already have an idea of what kinds of things are usually important for problems in some field, and what kinds of things usually aren't important. If you have that, then it's fast and easy to look up the parts which are important for any particular problem, and double-check that you're not missing anything crucial.

Dagon

50

A few thoughts, none of which are actually answers:

a) Knowledge and forgetting is tricky. There's a very good chance that even most of what you've forgotten is still there, and you'll learn it again much more quickly should you ever need it at a later time. Your class didn't give you knowledge, but it gave you the way to (re)acquire that knowledge when you need it.

b) Both the value of knowledge and the ability to use it is highly variable. the way it worked for me could be completely different than the way it will work for you. College is great for some subset, suboptimal but still positive for others, and negative for still others.

c) (perhaps most important) there's a pretty strong argument that knowledge isn't the primary value of college. The people you meet and/or the credentials you gain could well be the more important things, with (temporary) knowledge as a gateway to both - good (temporary) learning leads to hanging with smarter people and with better grades/degrees.

d) when asking "is it worth it", you must always include "compared to what"? What's your next best activity? Can you get a good engineering-related job without a degree? If so, maybe that IS better for you.

ErickBall

30

I agree with Dagon and johnswentworth's answers, and I would like to particularly emphasize one point. For me, as a mechanical engineer, most of the time I do not use most of the things I learned in school (and indeed I have forgotten most of them). Learning to do my job took months of studying field-specific stuff that most engineering schools don't teach. But if I had tried to learn it without first taking a lot of engineering courses, it would have taken years instead--and almost no company is willing to train someone for years. Think of education as turning yourself into a minimum viable product. It might be better in principle to intersperse work and school--either work as an engineer and then take time off to study, or do some study on the side. But you can't do either of those until you're skilled enough for someone to want to pay you.

Also, every now and then, some piece of knowledge from a course turns out to be useful, but you can't know in advance what it will be. If you haven't already studied it, then when the situation arises where you could use it you won't be able to tell; and you can't look something up unless you already know it's important.

[-]ADITHYA SRINIVASAN10

Hey,nice to meet a Mechanical engineer here.I have heard this told to me a lot.But I think as John has pointed out,education is mostly used as a signalling device.From what I understand,even if you were to were do a post-grad in Mechanical and work in research field,you would still NOT be using 90% of your education.If you ask that is a huge waste of time.Contrary to John,if you take a Mechanical Engineering degree,you will mostly end up studying/reading a lot of stuff that you surely know that you will not use in the future.We have to finish some specific... (read more)

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3ErickBall
I think 90% is an exaggeration, but even if you get a research job in the same sub-field as your graduate degree, it's true you probably will not be using the majority of your engineering course work. The problem is that you can't pick out the 20-30% you will benefit from and learn that in isolation. And I don't think judging on the basis of which courses you did or didn't like is a very good indicator (though admittedly there were some I disliked so much that I did badly and learned next to nothing). The way an engineering curriculum is structured is to let each topic build on past knowledge. Consider the class on statics that you probably took or are taking. Could you have understood bending moments and deflection of beams without first learning the concepts of derivatives and integrals? How about trigonometry? If you're like me, you've forgotten 90% of your high school trigonometry class, but if you hadn't taken it at all you'd really be struggling with the more advanced material. I do think a lot of courses could be condensed down to a much smaller kernel of key concepts, which could be taught in far less than a semester and then retained with spaced repetition. If you have the impetus and self-discipline to design a system like that for yourself then it might be worth trying, with a couple of caveats. First, the credential of a degree is pretty important--more so in mechanical engineering than in computer science. Second, you want to choose a curriculum designed by someone who has already learned this stuff--you can't pick the topics yourself. And third, part of what you're doing when you take an engineering class is practicing application of key ideas. To return to trigonometry--we did lots and lots of proofs using trig identities. I have forgotten most of them, other than sin^2+cos^2=1. But I don't think it was all wasted, because I still derive formulas from geometric relationships sometimes, and I think it would be much more difficult and error-prone if I
2ADITHYA SRINIVASAN
I see your point and this is what I have more or less been repeatedly told.I think like you told,the best thing to do would be to condense a lot of courses down to their key concepts that can be kept refreshed through spaced repetition. I think 90% may be an underestimate(you could probably tell me more about it).Like, over the course of your career,you would have used less than 10% of the info you collected through your college(including all the nitty-gritties of various topics-the derivations,the special cases etc..).These contribute immensely to your understanding of the topic,but my question is do the nitty-gritties stay after a long time? This is my main question. I'm quite alarmed at the possibility that I might not remember something that I had understood so well when I need to use it and like you told generally people seem to be getting on well without it. For example,lets take the situation you mentioned, a preliminary understanding of Control Theory had helped you identify the problem and correlate it with your existing problem.Even if the problem demanded a more in-depth and a rigorous analysis using Control theory(one that you would have easily done just after finishing the course), you would have not been able to do it and would probably have to spend time reading up on it(the time may be lower than if you were reading it completely new).But mostly you benefitted from the preliminary/broad understanding of the course than the full blown one.It would have been much more efficient(as in you could've done a lotta other stuff),if you had instead initially spent your time just getting upto speed on the very broad view of the topic and used spaced repetition to strengthen it.of course we can debate on the exact amount of content,but we can agree that the full blown one is probably waaay off. I also agree with what Kaj said.But "Control Systems" is a course that you know, you wont use in anywhere near full capacity when you become a Mechanical engineer.And
2ErickBall
I guess I wasn't counting every little derivation or example or even formula that comes up in a class against that 90%. Those are things you see in lecture, but you don't "learn" them. The stuff you actually learn is concepts and techniques, like what you would need to answer the test questions. Even that stuff, of course, you'll mostly forget if you don't review it regularly. But... I'm not very confident that you can strip out all the stuff you're going to forget and still learn the stuff you would have remembered. I don't know of any real examples of this working. It seems like maybe the academic system of "present a whole bunch of info rapidly and then force students to study key ideas from it for homework and tests" might have become entrenched over time because it performs better than the obvious alternatives. I would love to see evidence of something better, though. It seems like good use of spaced repetition is a non-obvious candidate to replace the lecture-homework-test system. If you haven't seen quantum.country, that's the kind of thing I'm thinking of and my initial experience with it is promising.
2Kaj_Sotala
I'm not sure that this is the right way of thinking about it. It's hard to know in advance which parts of your education are going to be useful. If each unit of learning only has a 10% chance of being useful, studying 10 units worth of learning rather than just 1 unit gives you much higher chances of at least 1 of those units being what you need. In that case, the "unused" 9 still weren't wasted, because they increased your odds of knowing something valuable. You ask but this assumes that you know in advance which of the courses are going to help you with your job. If you've never taken them and don't understand their contents, you might not be able to know this.
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