Hacker News Reader

Comment by questionr | Hacker News Reader

I often here comments about finishing a mathematical/technical book over the course of a "few" weekends.

But I don't see how thats possible if it includes completing all (or even most of) the given exercises. Especially when you have a full-time job.

View on HN

Some people are able to do it. But most are exaggerating or not doing the exercises. It takes me weeks to properly finish a good technical book due to time constraints. Either way, just do your best and forget about anybody else.

Over the weekend? I can't do it. Even if I forced myself to read for 6 hours Saturday and Sunday I'd forget everything during the weekdays.

An hour or so every day is much better and realistic.

Great point about forgetting the material. If you really want to learn something you need to review it more than once, and you need to encounter it in more than one environment / context (unless you're a genius, maybe). It's science, yo.

https://en.wikipedia.org/wiki/Spaced_repetition

context based learning --> https://www.ted.com/talks/deb_roy_the_birth_of_a_word

I learned that from math literature. To really solidify a topic you need to express it in as many ways and "different angles" as possible. It's related to the more ways you've seen a problem solved the better your understanding.

Depending on the material it is doable over the course of a few weekends. Consider many college courses meet twice a week for one hour each time, so two hours a week. ~14 weeks leaves only 28 hours of in class instruction time. Devote three of your weekends this month to complete study and you'll easily match the hourly total lecture-wise (you could even do it in one weekend if you're hardcore), what can kill you is the exercises, and the time it takes for actually learning the material.

Despite meeting more frequently I don't think college students learn the material any better than an upfront binge learner, because most of them have no clue how to actually learn something. They read and cram exercises enough to match the patterns and pass by (a sort of compressed periodic binge learning), and then they're done. Course interdependence forces some amount of actual learning that lasts but not that much.

Anyway to pull off the weekend study you wouldn't spend 6 hours on each day of your weekends just "reading". You would be reading (not necessarily in order or even every page), doing exercises, creating mnemonics, finding other resources to clear something up, and possibly making some flash cards to take advantage of spaced repetition later, which has an important characteristic that you don't need to review every day for an hour, only at the moment before you'd naturally forget which could be days, months, or years away. Depending on the subject you may also just be "practicing", for whatever that means for the subject. (Writing programs is a common programmer method to supplement in the learning of something.)

Another benefit to the intense approach is that you create many associations up front, instead of living in confusion until (if you don't give up beforehand) your slow and steady schedule advances to the point where learning something new makes enough older things click together. If you're just casually reading for 6 hours a day on Saturday and Sunday, and do no review, and have no intensity of making it an active exercise instead of a passive reading-only one, then yeah, you're not going to learn anything, but I doubt you'd learn much more by converting the same behavior to an hour a day.

I always thought the point of a university was to teach you _how_ to learn, the actual material learned being an added bonus.

Some students might learn how to learn as a side effect of surviving the system, but there are easier ways of surviving the system than actually learning. There are strong incentives against actually learning too -- e.g. when the material to be learned is obsolete or irrelevant in the face of modern technology. In any case I think you're the first I've heard say they thought the point of the system is to learn how to learn, I've never seen that even historically. (And if it were true, the system is an even bigger failure than it already is while addressing its other stated purposes...)

"The aim of the University is a true enlargement of mind... the power of viewing many things at once." [0]

Would very much like to see Cardinal Newman's Ideas around 'liberal' and 'servile' education catch the attention of the HN crowd. We're doing learning and advancement all wrong by focusing on utilitarian outcomes for universities rather than pure development of the mind (whence would flow marvellous creativity).

[0] http://www.newmanreader.org/works/idea/

I cannot find that quote on the site you linked. Do you have an expansion? The closest I found in the text was this paragraph:

"Instances, such as these, confirm, by the contrast, the conclusion I have already drawn from those which preceded them. That only is true enlargement of mind {137} which is the power of viewing many things at once as one whole, of referring them severally to their true place in the universal system, of understanding their respective values, and determining their mutual dependence. Thus is that form of Universal Knowledge, of which I have on a former occasion spoken, set up in the individual intellect, and constitutes its perfection. Possessed of this real illumination, the mind never views any part of the extended subject-matter of Knowledge without recollecting that it is but a part, or without the associations which spring from this recollection. It makes every thing in some sort lead to every thing else; it would communicate the image of the whole to every separate portion, till that whole becomes in imagination like a spirit, every where pervading and penetrating its component parts, and giving them one definite meaning. Just as our bodily organs, when mentioned, recall their function in the body, as the word "creation" suggests the Creator, and "subjects" a sovereign, so, in the mind of the Philosopher, as we are abstractedly conceiving of him, the elements of the physical and moral world, sciences, arts, pursuits, ranks, offices, events, opinions, individualities, are all viewed as one, with correlative functions, and as gradually by successive combinations converging, one and all, to the true centre."

If the quote comes from this, it is crucially leaving off the continuation: "...as one whole, of referring them severally to their true place in the universal system, of understanding their respective values, and determining their mutual dependence." This implies that by learning a lot, you enlarge your mind, and then can connect everything. This has nothing to do with learning how to learn, especially as a primary goal of university. Here is a college that supposedly follows his guidance: http://www.thomasmorecollege.edu/academics/true-enlargement-... Again, from that page, "it is plainly both the knowledge of architectonic principles and the familiarity with the substance of the various arts and sciences of which a liberal education is composed, including such pursuits as history, literature, rhetoric, mathematics, and the study of the natural world." So what you learn matters.

Thanks for the link though, should be interesting reading later. I agree it'd be nice if universities embodied some of the purpose they historically set out to be for, and we resurrected utilitarian trade schools with tight integration into what companies want so that those without the inclination or ability to pursue intellectualism can still learn something useful and create a better life for themselves.

Hi Jach,

I'm glad you find the Cardinal's thoughts stimulating. Yes, I pulled that quote from a Google result without sourcing it correctly, but perhaps you would agree they convey the spirit of the discourses? I'd love to hear your remarks on Cardinal's distinction between liberal and servile education[0], or, indeed, your impressions of the essay as a whole.

Addressing your point, it seems that these things are not that different (being able to fit knowledge within a universal system and understanding how to learn), or that in achieving the stated end (being able to fit knowledge within a universal system), one would need to 'learn how to learn.'

If you'd like to continue the discussion offthread, I'm available at myusername at geemayl dawt com

[0] http://www.newmanreader.org/works/idea/discourse5.html

It probably isn't if you're coming at the material for the first time, or after a long break. I took a 15-week course in Linear Algebra a few months ago, and we only covered about half the book in that time. I spent just about every weekend and evening doing those exercises. It's very time consuming.

However, if you gave me my old College Algebra book, I might be able to skim through it in a month of weekends and refresh myself on most of it, because I've used that stuff a lot in various jobs. Same goes for a lot of (but by no means all) programming books. I'm immersed in that stuff daily, so I can get through it pretty quickly.

Well, math really isn't a spectator sport. You have to do the work on your own, reading is only part of the work. A very time consuming hobby indeed.

It depends. I tend to remember a fair amount of material in math classes from just paying attention. I rarely explicitly study at all for math classes and when I do the results are mixed. Example: In calculus 2 there were all those annoying weird trig integral forms. I couldn't remember them all because it was like a new one arrived daily for a while. I set out to do practice problems with them but still didn't remember much and did poorly on parts of tests that required them. Other things like arc length, double integrals, integration by parts or integrating vertically instead of horizontally, all were just intuitive to me and I remembered them without trying to. I'm not sure how typical or not my results are but in general throughout school if I felt the need to study something and practice it, it was bad news, but if something made sense to me it stuck without much further effort.

I'll add on my own anecdote here, I'm a stats major and I've found that in my stats (as opposed to pure math) classes, I find the learning is very much done just by reading the book because every new concept is just an intuitive application of earlier ones, once introduced to the concept I can understand it even without working through the excercises.

In my more pure math classes (and admittedly in some topics like counting problems) I have to spend a lore more time doing exercises to actually have a grasp of the material. It's frustrating but that's just how life goes.

It can be if you make it. It has been about a decade since I finished coursework for my pure math degree, I do not work in mathematics, and I am enjoying mathematics more than ever just from reading books. I do not miss doing textbook exercises (evaluating integrals? computing determinants? I reach for Maxima or Wolfram Alpha), and am content with reading other people's proofs.

I rarely "finish" a technical book. I instead skim over it once or twice and then keep it on hand as a reference. Some books are indeed worth reading front-to-back and in-depth, but usually the use as reference material is more important to me.

Mmm. Besides, I find my programming/work/etc. improves when I read novels in my spare time :)

On the contrary, I find my work/family life improves when I do nothing in my spare time ヅ

I think such books are pointless if you aren't going to use them in your day-to-day work.

You don't believe in knowledge for the sake of enjoying the perspective that more knowledge gives you?

I do, but with a kid my time is now limited. Unused knowledge has this habit of being forgotten. It turns out to be a terrible waste, at least from my POV.

Baseball players waste 9 of every 10 swings on misses. It's a terrible waste.

>Baseball players waste 9 of every 10 swings on misses.

And swinging a bat is one of the skills baseball players need to use for their job. The comment you replied to was talking about skills that are not going to be used every day. So I don't think your analogy is very useful.

Also, people who get paid to play baseball never have a batting average that low

Batting average will be higher than the percentage of swings that don't miss.

Yep, we don't use our brains every day.

That is indeed a perfectly valid trade-off, and not one the grandparent was mentioning. One thing worth mentioning is that if you don't read those books, you will probably not get a job that involves reading those books, nor will you turn your job into something that involves reading those books and applying their content.

If you are a software engineer, you can pretty much use linear algebra, calculus, algorithms in your dayjob, right there! Even if you write CRUD apps or the xth tower defense on android. It's all bytes and numbers and numbers stored in bytes and asymptotic behaviour and relational algebra and type systems and transistors, it just depends on how deep you want to look.

There is a good video from Niel deGrasse Tyson talking about learning.

https://m.youtube.com/watch?v=utedyJ7QRBs

His argument is learning is never a waste of time, even if you don't ever use and forget everything you studied. The simple act of learning is beneficial, it helps build connections in your brain. You develop skills that can be applied to other problems.

It's always beneficial but is it always more beneficial than going to the gym, being with your kids/SO, sleeping more, etc?

Everything has a cost.

I'm very heavy on learning for learnings sake but I don't like the way it's framed as the correct thing to do.

Learn with your kinds/SO. Let's be honest, a lot of your time with them is spent watching TV or something like that anyway. Turn it off and read together.

FWIW, I read a lot and while I often find it difficult to "recall on demand" particular things I've read, I have often experienced that I'll recall what I read in a relevant situation. I first experienced this when I did engineering calculus in college which covered a lot of (for me) obscure parts of calculus. And frankly I couldn't recall much of it at all, but when I took electromagnetic field theory and needed it to answer a question, it would bubble up to the surface.

That experience lead me to keep reading interesting things even if I couldn't recall them a week later on the assumption that when the need arose, if it was relevant, my brain might somehow surface the information for me.

I'm currently a stay-at-home twin dad, and I absolutely crave to learn something new in my spare time (which varies from none to even two hours a day if I'm lucky). I don't care if I forget, but for me life just becomes too stressful without constant learning.

Of course, if I was working, I'd probably have enough to learn at work.

Here here, constant learning is the only thing to save our sanity.

Regarding work, I do have a fulltime job, yet one has to fight hard to ensure any amount of learning, constant or otherwise.

https://www.google.com/search?q=hear+hear&ie=utf-8&oe=utf-8

Whoops, thanks, how did that slip past my brain filter ;-)

So what you meant to say was with your current situation it is useless to you.

it nice being reminded how boring and simple my job is...

I've actually ended up having to let go almost every person working for me that takes your view.

Learning such things expands what you can do at work, no matter what it is. We no longer live in a world where you can punch a clock and do the same thing for decades until you get the gold watch and are send home to wait to die watching TV on your barcolounger (I don't think I've seen one of those in 30 years). Things are changing so fast that the only way to stay ahead is to learn, learn deep and actively practice your art or craft.

"Mr. Potter, one of the requisites for becoming a powerful wizard is an excellent memory. The key to a puzzle is often something you read twenty years ago in an old scroll"

I skim technical books that are not immediately useful to i) build a mental index and ii) fill the gap of my unknown unknowns.

When I hit a problem, sometimes much later, I won't remember the details, but I'll remember that there is a concept that could help me, and know where to look to find more information.

For example, I've read much more about low level networking and messaging than was immediately useful at the time. Months later, a messaging pattern I read about turned out to be a good solution to a problem I was facing. If I hadn't read the book I wouldn't even have known what to search for.

(I also read about some technical topics more deeply for my own enjoyment/future career prospects, but the value of that is more uncertain.)

created a thread asking just this https://news.ycombinator.com/item?id=12718444

Reply on news.ycombinator.com