[HN Gopher] How to Understand Things
___________________________________________________________________
How to Understand Things
Author : ingve
Score : 320 points
Date : 2020-07-11 14:58 UTC (8 hours ago)
(HTM) web link (nabeelqu.co)
(TXT) w3m dump (nabeelqu.co)
| RedShift1 wrote:
| Heh I get this a lot in my daily sysadmin/developer duties. When
| you need to turn on a knob somewhere you don't just wanna know
| that you have to turn it on, you want to know why you need to
| turn it on and follow the chain up until you get to facts you
| already know. But it's not always possible to get that far,
| there's too many layers of abstraction, the source code is not
| available or you just don't have the time.
| capdeck wrote:
| I can draw a parallel to this in software development. Some
| product features that require development "from scratch", where
| you can get down to the original code and logic - this is where
| "taking time to think" really pays off.
|
| But when you are basically composing a final product from
| components, libraries and features - this is where figuring
| something out may take really long time and a lot of effort. It
| today's world many libraries are open source, so you actually
| can get to the bottom of many issues. But the time and effort
| cost of that is almost never acceptable.
|
| My conclusion is - if you are a "slow" thinker, prefer getting
| to the bottom and figuring stuff out - try and choose the
| "fundamental" type of work. Where you are "done is better than
| perfect" kinda person - you'll thrive in the upper layers of
| development stack where shipping stuff out is of utmost
| importance. Focus on your strengths.
| kasperset wrote:
| Agree on the aspect of time. As we have progressed, we now have
| many levels of abstraction that it is hard to think deeply
| about the problem. Almost a la like a code that has grown too
| deep to understand every "bit" of it. Moreover, I think people
| now work in teams rather than one individual thinking about the
| system holistically.
| sillysaurusx wrote:
| It's possible. It just takes time; very few people are in a
| position to devote that time.
|
| This gives an advantage I haven't seen discussed: when you
| put in the time, you make connections no one else thought of.
| It happens time and again, and it's a clear pattern at this
| point.
|
| It takes months of daily study, often tedious, with no clear
| benefit. But the benefits sometimes come. (I wrote "usually"
| rather than "sometimes," but that's not really true. The
| usual result is that you go to sleep more confused than you
| started. It's not till much, much later that the connections
| even seem relevant.)
| jka wrote:
| I like to imagine that at some point we might collectively
| have a large enough software development population to
| solve most significant problems comprehensively enough --
| and fairly and equitably enough -- for most people that we
| begin to see developers with increasing amounts of free
| time.
|
| At that point I think we could collectively really begin
| digging into some of the huge backlog of software bugs and
| errors that we've built up over time and make everything
| more reliable, seamless and consistent.
|
| It'd be a massive undertaking, especially to solve each
| issue thoroughly and without causing negative externalities
| elsewhere. But it'd also be a great puzzle-solving and
| social challenge, not to mention an educational and useful
| one.
| pandesal wrote:
| Jesus christ that background is distracting.
| samtregar3 wrote:
| Even worse, you can't scale the text. So if you can't read
| small print against some kind of optical illusion you might as
| well give up. I gave up.
| abnercoimbre wrote:
| Wasn't sure whether your comment was relevant, then I
| remembered I closed the article a third of the way through
| because of a deep annoyance with the background.
|
| I'm all for individual expression, but here I think it
| subtracts from the reading experience.
| maximp wrote:
| Sad to say, I had the same reaction :\
| inetsee wrote:
| One of the things I remember quite vividly from my Psychology
| classes in college was the idea of a "satisficing" problem
| solver. Given a (reasonably solvable) problem to solve most
| people can come up with a satisfactory solution. The difficulty
| comes when you ask them to come up with a new solution. Many
| people struggle because their brains say "I already came up with
| a solution, and it was a pretty darn good solution too."
|
| The really creative people are the ones who insist that their
| brains come up with another solution, and another one until they
| can be confident that they've found the best solution within a
| reasonable time investment.
| cmehdy wrote:
| To me this seemed to get easier as I encountered more
| "languages of the mind", i.e. more ways to think about things.
| This, is very much tied to the "nurture" part of our lives, as
| foundational experiences are more by the very definition of
| "experience" subjective and unique.
|
| Solving a problem within mathematics in a new way can be made
| much easier if you have grasped multiple fields (for example,
| algebra vs. geometry). I've seen people understanding chemistry
| well because they enjoyed cooking, and could sort of use either
| to get to a given explanation to solve a problem. I've
| definitely started to grasp chemistry only when I reached a
| decent level in theoretical physics.
|
| Here's my assumption: everything has a likelihood of depending
| to some degree on other things (examples: can you do
| mathematics without a language or writing? can you do physics
| without mathematics?). Therefore, "thinking laterally" could
| very well be thought of more as "thinking with an interesting
| combination of previous vectors of thought". Perhaps the
| "genius" is to create nonlinear combinations of previous
| vectors.
|
| So in short, this ability to come up with another solution, and
| another, and another.. I wonder how much it is tied to the
| richness of experiences you've had since your birth, and
| particularly the foundational ones (at the very least I would
| assume to be more testable than later on, if my hypothesis
| about dependency of "thought vectors" is true).
| getpost wrote:
| Not stopping after the first right answer is one metacognitive
| strategy[1] among many. Metacognition is an area of active
| research.
|
| I first heard of metacognition as a distinct discipline in
| connection with the treatment of insecure attachment.[2]
|
| Metarationality[3] is an aspect or extension of metacognition.
|
| [1] https://helpfulprofessor.com/metacognitive-strategies/
|
| [2] https://www.psychologytoday.com/us/blog/the-resilient-
| brain/...
|
| [3] https://meaningness.com/eggplant/introduction
| kevsim wrote:
| As an engineering manager, I love having a mix of people who just
| always need to go deep on whatever they're working on and others
| who are just obsessed with shipping and getting stuff out.
| Particularly great when you pair them off and they push/pull each
| other a bit.
| jonwalch wrote:
| Totally agree with this. I used to be solely in the latter camp
| and my teammates pulled me in the deep direction.
| RichardChu wrote:
| I worry that the way modern society is structured disincentivizes
| deep understanding.
|
| 1. Industry cares more about concrete results, quick execution,
| and bias for action.
|
| 2. Academia cares more about positive results, quantity of
| published papers, and small achievable experiments over big
| experiments that might fail.
|
| Where are the institutions that care about deep understanding?
| catwind7 wrote:
| i agree. I think this is why I find companies like tesla and
| spacex exciting. They seem to have set up incentive structures
| that encourage _both_ quick execution and innovation (which
| requires deep understanding). One thing he's said that really
| struck me is that it's _really_ difficult to produce innovation
| if you tie punishment to failure. People tend to be
| conservative if they are punished / think they will be punished
| harshly for trying and failing. But if you want to innovate,
| failure has to be an acceptable outcome
|
| hopefully we see more companies go in this direction
| jmchuster wrote:
| well that's where the whole mantra of "move fast and break
| things" comes from.
|
| Putting it out there and failing also accelerates you faster
| to the right answers. If you release it today, it'll take 6
| more months of iteration to really get it right. Or maybe you
| spend an extra 2 years of development to get it "right", but
| then once you release, you'll still have to spend 3 more
| months of iteration anyways to get it right.
| catwind7 wrote:
| yeah, this hits home for me because my team just spent a
| couple of years trying to get a product right and now it's
| on the verge of being replaced
| LoathsLights wrote:
| Unfortunately deep understanding doesn't put food on the table,
| concrete actions do.
| sharkjacobs wrote:
| > Understanding something really deeply is connected to our
| physical intuition
|
| This rings true to me.
|
| I think that I "understand" how to start a fire, which I do a
| couple dozen times a year, in a deeper more complete way than I
| understand any of the abstract software development that I spend
| 30 hours a week doing.
| sidpatil wrote:
| I can't scale the text on that page. I tried in both Firefox and
| Edge.
| afarrell wrote:
| > This quality of "not stopping at an unsatisfactory answer"
| deserves some examination.
|
| > This requires a lot of intrinsic motivation, because it's so
| hard; so most people simply don't do it.
|
| It also requires self-confidence, persuasiveness, and social
| power.
|
| Without these traits, your attempts to really understand
| something will be dismissed as "overthinking things" or "trying
| to understand the universe". Those around you will urge you to
| "stop thinking just do the task" or "do the obvious thing" as
| they lose patience with you. If you don't resist them you'll end
| up moving forward despite feeling confused, sometimes completely.
| You'll then end up pissing people off when you execute too slowly
| or fail (in their eyes, intentionally).
|
| > This is a habit. It's easy to pick up.
|
| Not if the people around you are exhausted by you.
| BeetleB wrote:
| There are both extremes, and best not to be at either one of
| them.
|
| Example: I forget the name of the principle, but in mathematics
| the statement "P implies Q" is considered true if P can never
| be true. As an example, let P be "George Washington was a
| woman" and Q be "Queen Elizabeth is a man". Then the statement
| "If GW was a woman, then QE is a man" is considered to be a
| true statement.
|
| I have a friend who refuses to accept that such a statement
| should be considered "true". And he has put off studying real
| analysis until he can learn enough logic theory to convince
| himself on the validity of accepting such statements as true. I
| do not think he'll ever get to study real analysis, because he
| is full of "No! I need to understand this really really well
| before proceeding!" statements.
|
| It's a fine approach if you have an infinite amount of time.
|
| The other issue, as another commenter pointed out: It's very
| difficult to measure progress in thought. The mind is great at
| fooling itself, and not until you try to solve real problems
| (or discuss them with others) will you expose most of the gaps
| in your mind. The same person in the above anecdote does suffer
| from this. He definitely puts in effort to learn a lot (and has
| succeeded), but there are always more things to learn, and he
| moves on to the next topic before really applying what he has
| learned. As someone who talks to him often, it's really hard to
| tell if he understands. He is the classic case of "I'm sure I
| can solve problems when I need to, with a bit of review".
|
| At the other extreme, of course, are people who are not really
| that motivated to understand. They are satisfied if they get
| the answer at the back of the book. You won't get far with just
| that.
|
| > If you don't resist them you'll end up moving forward despite
| feeling confused, sometimes completely. You'll then end up
| pissing people off when you execute too slowly or fail (in
| their eyes, intentionally).
|
| This sounds more like an issue at work, and your experience is
| fairly universal - most jobs I've worked at have it. In my
| experience, understanding things well is sadly not valued on
| the job. They want you to "execute", and want you to minimize
| the time you spend learning. And of course, they would rather
| hire someone else instead of ensuring your proper
| learning/training.
| ssivark wrote:
| It's worth mentioning that this desire to think through things
| deeply often runs contrary to a bias for action, and it's very
| difficult to measure progress in thought. There is a long phase
| of thinking very hard, and a short phase where things suddenly
| become clear. So, thinking through and understanding things
| deeply is often discouraged as a consequence.
| philjr wrote:
| The key is to decouple the two.
|
| When you are required to act, act and act decisively. If you
| are clear that the understanding could be deeper (and it
| usually can), you trigger a work effort to understand more.
| So the next time you need to make a decision you're more
| informed.
| TrackerFF wrote:
| I want to add - habits like that are great to pick up, and fine
| tune, when you're in college.
|
| More so if you're a college student that can focus 100% on your
| academic life/studies, unburdened by things like work.
|
| EVEN more so if you have great mentors, professors, etc. that
| can guide you to the right place.
|
| I'm not saying that one CAN NOT do the things above, if you're
| a busy student with work on the side, and very limited
| resources as far as mentors or professors go...but I do think
| that those lucky enough to find themselves in the right
| positions, are more likely to mature - and quicker.
|
| (And it was no surprise to see that the author is a PPE grad
| from Oxford)
| matt_kantor wrote:
| Your points about social context are great ones and 100% valid,
| but I want to make a case for "stop thinking just do the task":
|
| ---
|
| Often, trying (and potentially failing) to do a task is the
| best way to learn about it. The key is to be very explicit
| about what parts of that task you actually understand and which
| ones you're pulling out of your ass.
|
| This is especially true when creating software. It's super rare
| to have requirements that are concrete and detailed enough to
| form a comprehensive understanding of the final design before
| you start developing it. Instead there are usually parts that
| have clarity and others that are fuzzy. If you can enumerate
| those and keep them separate you can often leverage the parts
| you understand to make progress on those you do not. Writing
| placeholder/obviously-terrible code to stand in for the unknown
| parts just so that you can spin up a running system is a great
| way to do that. Along the way you'll see what patterns emerge,
| where you hit walls, etc, which is not always easy to imagine
| with raw abstract thought. And having "working" software that
| you can play with is a great way to find edge cases and
| otherwise make progress on those unknowns. Once you've gained a
| more complete understanding you can replace the placeholder
| junk with well-designed/actually-thought-out modules.
|
| (Another obvious reason to do this is if your company will
| literally go out of business if you wait until you have a
| perfect understanding to launch a product/service, but I think
| most people here get that.)
|
| I'm not sure how much this generalizes, but it also works well
| for me when writing. I usually start with a vague understanding
| of an idea I hope to communicate, then jot down disjointed
| sentences to capture parts of it. As I do so it gradually
| becomes clear how things are connected, where my reasoning is
| muddy, what I thought I knew but can't express so probably
| don't, etc, and I can use this gained understanding to
| iteratively rewrite and reshape my message until it becomes
| something coherent. Sometimes, anyway; other times I don't end
| up sending/publishing it at all because along the way I learned
| that the thing I was hoping to communicate was based on a
| faulty assumption or is not as straightforward as I thought it
| was. Which is great, because either way I've learned something.
|
| ---
|
| I guess I'd say it differently: " _keep_ thinking _and_ do the
| task ".
| dorkwood wrote:
| > But it's not just energy. You have to be able to motivate
| yourself to spend large quantities of energy on a problem, which
| means on some level that not understanding something -- or having
| a bug in your thinking -- bothers you a lot. You have the drive,
| the will to know.
|
| This resonates with me. Someone once asked me how I decide when
| I'm finished with a particular thing I'm working on. The answer
| is as simple as "when I stop thinking about it". When it stops
| bubbling up in my thoughts. Until then, I'll keep returning, and
| I'll keep chipping away.
| typon wrote:
| Unironically writing about "honesty, integrity, and bravery"
| while working at Palantir
| djohnston wrote:
| Excellent read. So much of this resonates deeply with me based on
| uni experiences. I studied math and was guilty on more than one
| occasion of basically memorizing some theorems and methods of
| manipulation, missing the forest for the trees so to speak.
| skybrian wrote:
| This takes a habit that's sometimes good for some people and some
| subjects, and turns it into a universal recommendation, and then
| claims that's what intelligence is, which is really quite
| dubious.
|
| To work on math, you need time, a peaceful place to think, and
| motivation. Even then, you can't do this for everything, because
| there is too much. Obsessing on something that's not urgent when
| there's more important stuff to do may not be good time
| management, depending on your priorities and other claims on your
| time. But you might do it anyway, depending on your interests.
|
| Also, learning some other subject well may be less about thinking
| by yourself and more about going out and talking to people, or
| playing a lot of games, or challenging yourself in some other
| way. All that takes time too.
|
| But there is a lesson here: knowing something in more than one
| way means you know it better. I see this especially in music,
| where there are multiple ways to memorize a piece and they
| reinforce each other. Auditory memory (being able to hear it in
| your head), muscle memory, knowing the chords, knowing the
| lyrics, even remembering where it is on the page can all help.
| bredren wrote:
| This reminds me of a discussion in the most recent episode of
| Django Chat with Aymeric Augustin on the difference between
| tutorials and reference documentation.
| pstuart wrote:
| Interesting. tl;dr -- we learn by experiencing things, not by
| being told things.
| cloudier wrote:
| I think this is the transmissionism versus constructivist view
| on teaching.[0] This is something that is well-known in
| education and I wish more people knew about it! Lay people
| commonly think of education as transmission of ideas from
| teachers to learners, but educators believe that learners
| construct their own understanding of ideas. So these educators
| try to create situations where the learners can do that
| construction.
|
| [0]: http://nas-
| sites.org/responsiblescience/files/2016/05/Dirks-...
| cosmodisk wrote:
| I catch myself doing this quite often: I read documentation, try
| a couple of things,if it works,I move on. Now this is all good
| when dealing with simple things but the more complex things are
| the less it works. It's like reading learn python in 10 days and
| then going on GitHub with all that newly gained knowledge and
| confidence and trying to understand how a large codebase works.
| Within about 30 seconds you close the browser and binary tears
| start dripping on your keyboard...
| refrigerator wrote:
| Great post. Personal anecdote:
|
| I don't think I really understood anything in school, but I was
| decent at going through the motions of carrying out certain
| methods and recalling certain facts when I needed to.
|
| I went on to study Maths at university, and for most of my first
| year, I had the same surface level "methods + facts" knowledge
| that got me through school. After some studying, I could recite
| definitions and theorems, I'd memorised some proofs, and I could
| occasionally manipulate a problem to get an answer. I think about
| half of the cohort was in a similar position. But it was clear
| that there were others in a completely different league.
|
| When we were studying for our first year exams, I was struggling
| to remember the proof of a specific theorem (it felt quite long).
| A friend was trying to help me learn it, and he asked me what
| "picture" I had in my head for the theorem. I didn't have any
| pictures in my head for anything.
|
| It turned out that a simple drawing could capture the entire
| statement of the theorem, and from that drawing, the proof was
| trivial to derive. It was long-ish to write out in words, sure,
| but the underlying concept was really simple. This blew my mind
| -- I realised I didn't have a clue what we'd been studying the
| whole year.
|
| The worrying thing is that I actually thought I understood that
| stuff. Before that incident, I didn't know what it feels like to
| actually understand something, and I didn't have an appreciation
| for the layers of depth even within that. I suspect lots of
| people go through the entire education system like this.
| ReactiveJelly wrote:
| And if you got good grades, then the system wasn't testing
| whether you understood it - Bad news.
|
| But it's good news that you were able to understand once he
| drew the picture for you. So there is an effective way to teach
| that theorem - If only the professor knew it.
| nqureshi wrote:
| OP here -- that is a fantastic anecdote!
|
| Do you have an example of a "drawing" of a theorem, in this
| context? (I've seen these for fairly trivial theorems but not
| for more complex ones, so I'm curious.)
| refrigerator wrote:
| Ahh I did a bit of googling but couldn't find anything nice
| -- sorry! Most of the time, the complex stuff is broken down
| into smaller "lemmas" with their own manageable proofs, and
| then the proof of the whole theorem will be something like
| "Follows from Lemma 2.1, Lemma 2.2, and a basic application
| of Theorem 1.4"
|
| This is the theorem I was talking about:
| https://i.imgur.com/1xEH51Z.png (taken from
| https://taimur.me/posts/thinking-at-the-right-level-of-
| abstr... which touches on a similar topic to your post)
| Chris_Newton wrote:
| As someone who very much relates to the GP's anecdote, I
| might suggest determinants as a good example.
|
| As an undergraduate studying maths, I encountered a standard
| theorem in one of my first courses, which says that about 947
| different conditions are equivalent to a matrix having a
| determinant of zero. I dutifully memorised these. I also
| dutifully memorised the algorithm for how to calculate a
| determinant. I might even have remembered some verbatim
| proofs of some of the equivalences.
|
| However, I developed absolutely no intuition about what a
| determinant _is_. I had book knowledge, but no insight. It
| was a long time ago now, but I'm fairly sure that when I
| graduated I still did not truly understand even this very
| basic (by undergraduate standards) subject. I think it was
| probably a few years later, when I came across some of the
| same theory but in a much more practical context at work,
| that most of the connections in that equivalence theorem
| first "clicked".
|
| Meanwhile, here is what a gifted presenter with the right
| illustrations can do in about ten minutes:
|
| https://www.youtube.com/watch?v=Ip3X9LOh2dk
|
| The 2,000 or so substantially identical comments below that
| video are very telling.
|
| Given the understanding you'd get with that quality of
| presentation, the equivalences I mentioned above would have
| been obvious and constructing the proofs from first
| principles would have been straightforward.
| ericjang wrote:
| In the process of learning about a family of algorithms in
| machine learning I also gained some physical intuition of
| determinants (same diagram as 3Blue1Brown, but applied in a
| different context of "squashing and stretching" probability
| mass): https://blog.evjang.com/2018/01/nf1.html
| refrigerator wrote:
| This is awesome, determinants were one of the things that I
| never really understood during my degree
| nqureshi wrote:
| Awesome example, thank you!
| grugagag wrote:
| What happened after this revelation? Did anything change? Did
| you try to intuitively understand the problems you were working
| on? I think this boils down to how you were taught (or self
| taught) to approach the subject and the set of tricks you
| learned along the way that became your toolset.
|
| Did you do a lot of exercises in school? They usually help
| build the intuitive part, the aha moment, that comes through
| repetition.
| refrigerator wrote:
| Yup, definitely changed the game for me, and turned on my
| 'intuition' spidey sense, of whether I actually understood a
| concept.
|
| We did do a lot of exercises in school, but they mostly just
| tested whether you can reliably apply a method that you were
| taught, rather than testing understanding.
| dctoedt wrote:
| > _It turned out that a simple drawing could capture the entire
| statement of the theorem, and from that drawing, the proof was
| trivial to derive._
|
| Excellent point.
|
| 1. A similar example: Feynman diagrams.
|
| 2. Another: Venn diagrams.
|
| 3. Longer example: On Navy nuclear-powered aircraft carriers,
| the officer of the deck underway (OOD) must have at least a
| basic understanding of how the engineering plant works. It's
| second nature for nuclear-trained OODs, of course, but non-
| nukes could sometimes have trouble. Back in the day, it turned
| out that an effective way to help non-nukes learn what they
| needed to know was to have them: (A) memorize a really-simple
| block diagram of the reactor and steam system, and also (B)
| memorize a chant, of modest length, that summarized how things
| worked. During slow periods while standing OOD watch, I'd make
| a non-nuke OOD trainee draw the diagram from memory; then I'd
| quiz him with "what if ..." questions _(back then it was always
| "him")_. If he got hung up on a question, I'd tell him, "chant
| the chant." That usually helped him figure out the answer in
| short order.
|
| (U.S. submarines don't have that problem, AFAIK, because pretty
| much every officer who will stand OOD watches is nuclear-
| trained.)
| johnchristopher wrote:
| Did that realization at the eve of exams bring up a bout of
| anxiety ? (edit: I would have freaked out)
| refrigerator wrote:
| Haha, yeah. Thankfully, the Maths exams were set up such that
| you could always get 60% (the boundary for a "2:1" grade in
| the UK -- an acceptable score for most people) by just
| knowing the 'bookwork', which you could do by memorising
| stuff without understanding it.
| alicemaz wrote:
| >I suspect lots of people go through the entire education
| system like this.
|
| +1. it took me a couple years after getting kicked out of
| college to get my head sorted out to the point where I felt
| like I could "think" again
|
| I think one of the most harmful things about schooling is the
| way it imposes a tracked structure on learning. it demarcates
| knowledge into discrete subjects and sets up a linear
| progression through them and says you need to master each step
| on the track before moving onto the next one. this is poisonous
| and borderline evil, and I've encountered many people who are
| crippled for life by it. a lot of people never pursue things
| they're really interested in and could become extremely
| passionate about because school has convinced them they need to
| stack up prerequisite knowledge before they're even allowed to
| touch it
| knzhou wrote:
| > says you need to master each step on the track before
| moving onto the next one. this is poisonous and borderline
| evil
|
| What's wrong with it? You do need to understand calculus
| before classical mechanics, classical mechanics before
| quantum mechanics, quantum mechanics before quantum field
| theory, and quantum field theory before the Standard Model.
| I've seen tons of people disregard this and the result is
| always confused word salad. People waste years of their lives
| this way, going in circles without ever carefully building
| their understanding from the ground up. The order in school
| was chosen for a reason.
| pc86 wrote:
| It didn't work for the GP. That makes it poisonous and
| evil.
|
| I've seen this sentiment _way_ too much on HN. X didn 't
| work for me, therefore X is a scam, its perpetrators are
| evil sociopaths, and if it worked for you you're a cog in
| the machine, _man_.
| BeetleB wrote:
| I suspect you and GP are talking about slightly different
| things. GP is probably more opposed to artificial
| compartmentalizing of things. As an example:
|
| > You do need to understand calculus before classical
| mechanics
|
| Yes, but how _much_ calculus? Do you need all of Calc I, II
| and III before even attempting classical mechanics? And
| should calculus even be treated independently of classical
| mechanics?
|
| There are various traditions when it comes to teaching
| these subjects, and the tradition in the US involves
| keeping a strict distinction between these things, in
| addition to a "theory first" approach. Other people have
| studied things in a different manner. Some of my physics
| professors from the UK had studied most of the math they
| knew only as needed when they would get to relevant topics
| in physics - including differential equations, all of
| analysis (complex or real), some of Calc III, etc.
|
| Even amongst mathematicians, it was common in parts of
| Eastern Europe to focus on a problem, and learn whatever
| theory is needed to solve that problem. They didn't learn
| theory and apply to problems - they took a problem, and
| learned whatever theory is needed to solve them. I recall
| picking up a Kolmogorov textbook on analysis and being
| surprised by seeing this approach, along with the
| informality with which everything is discussed.
|
| And just a minor quibble:
|
| > classical mechanics before quantum mechanics,
|
| You don't really need to know much except the basics. I
| think the classical mechanics we covered in our typical
| "Engineering Physics" courses was sufficient to dive into
| proper quantum mechanics. It's nice to have been exposed to
| Hamiltonians in classical physics prior to taking QM, but
| really not needed. There's a reason neither schools I
| attended made the classical mechanics courses as prereqs to
| QM. In fact, I would argue we should split things up a bit:
| Have a course to teach the very basics of energy, momentum,
| etc. Then make it a prerequisite to both classical
| mechanics and quantum mechanics.
| drorco wrote:
| Some people like to work their way in reverse. I'd often
| pick a really complicated subject I'm after like "stellar
| fusion" and then work my way downwards and learn whatever I
| need to learn in order to understand it. If I had to start
| from differential mathematics, without knowing why I need
| it, I'd probably give up.
| Heyso wrote:
| Our school is poisonous (can tell for France), if not evil.
| It become crystal clear after reading Celine Alvarez. Not
| sure if she got translated yet. In english, but older you
| also have Alfie Kohn, but I haven't read him.
|
| When reading Celine, one understand that children are natural
| born learner, and there is no effort needed to make them
| learn stuff. Our school model is industrial production of
| objects. Thinking human machines. We are way more than that.
| Sadly Pink Floyd description of the school still echo to our
| modern school. Some peoples don't feel that way about school.
| I don't really know why. Maybe they never imagined how better
| it could have been, so they found it great.
| GuiA wrote:
| Check out Celestin Freinet too (also untranslated in
| English AFAIK)
| leafboi wrote:
| The university I went to offered open book/note exams for
| almost all courses. It literally didn't even matter how much
| you memorized... open book tests didn't make anything easier.
| you need to understand or fail.
|
| I'm not into showing off ranking or pedigree but I do genuinely
| believe that the higher the pedigree your school the more
| likely the exams will be harder and require total understanding
| and even creativity over rote memorization.
|
| The reason is because memorization is trivial. Students able to
| get into any top school will likely all easily achieve full
| score on an ordinary tests. The professors at top schools need
| to make these tests brutally hard in order to produce a bell
| curve.
|
| I literally had one new professor at my school actually give a
| mid term that was what would ordinarily be called fair in any
| other school or college... but the entire class ended up
| getting nearly full score.
|
| He realized his mistake and the final was way, way harder.
| aaron695 wrote:
| Is this consciousness?
|
| IQ being the biggest life changer.
|
| Consciousness is considered second and more importantly is
| considered trainable.
| [deleted]
| abdullahkhalids wrote:
| How would you create a training program to teach all of lessons?
|
| I thought of creating a workshop at my uni, titled "how to ask
| stupid questions?" Essentially, do group activities where someone
| presents on some topic, and the goal of the audience is to ask
| genuine "stupid questions" - questions about the fundamentals,
| which most people are embarrassed to ask, but which play a big
| part in understanding.
| musicale wrote:
| Interesting; for the chain rule proof he cites, it would seem at
| first glance that if you rewrite the leibniz notation as its
| equivalent limit notation, then the y terms cancel. It has been a
| while since I learned differential calculus, so perhaps that is
| why I don't immediately recall why this is wrong?
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