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Pareto distributions are everywhere, and most learning ends up being one. Recently encountered this while getting into weight training for hypertrophy. The core is good form, diet, and progressive overload. Other than that, learning the basis of a specific exercise is something you can pick up as you expand.

It's so similar to most of the things I've specifically sought to learn as an adult. You get so much bang for your buck, time-wise, when learning something new. The best part is when you don't even need to dig deep past that foundational 80% and you can become pretty knowledgeable about something in a very reasonable amount of time.

Something from Andrej Karpathy on learning that stuck with me [0]:

> Learning is not supposed to be fun. It doesn't have to be actively not fun either, but the primary feeling should be that of effort. It should look a lot less like that "10 minute full body" workout from your local digital media creator and a lot more like a serious session at the gym. You want the mental equivalent of sweating. It's not that the quickie doesn't do anything, it's just that it is wildly suboptimal if you actually care to learn.

[0] https://x.com/karpathy/status/1756380066580455557?lang=en

A counter point, or maybe complementary point (b/c I agree w/ the quote). I killed myself trying to do more than 8 pull ups in a gym for ages; at times I'd be going to the gym 4x a week doing full body workouts, always working hard, always sweating, always gassed at the end; consistently doing pull ups to exhaustion on multiple sets. Yet 8 was a kind of ceiling. At some point I stopped working out, but got a pull up bar at home. I stuck it in my office doorway. I would do occasional pull ups -- never more than 2-3, usually only 1. But just casually a few times a day, nearly every day, when I walked by it. It was never hard, it never felt like work. It became more of a way to briefly relax, an alternative to the cigarettes I used to smoke. Well after a year of that when someone challenged me to a friendly pull up competition, I was shocked that I could do 15 in a row easily, I still had more in the tank even. That always stuck with me because it taught me that while hard work is important, consistency is _more_ important. Working "hard" as such is often not only not required, but perhaps often not actually the thing that will help.

For anyone not familiar with this methodology, it's called 'greasing the groove.'

https://www.youtube.com/watch?v=JmOEgK5o2yg

That’s a reasonably well known strategy to pull-ups. Start at one regularly and slowly build up once it becomes easy enough to do so.

I think learning is more like growing plants, you don’t need to get everything perfect, or even one thing perfect, but a set of things to good enough.

There are a lot of things that interfere with learning so the presence of those will inhibit learning regardless of effort.

how much weight did you loose during that time?

you either lost significant weight, or added significant muscle .. no other way .. the end result here is more significant than how you reached it

for pull up, loosing weight is usually far more important than adding muscle, so i am leaning toward you lost weight

Oh, I'm pretty lightweight / lanky (hover around 165lb, BMI around 20-21). I didn't see any significant weight change at the time, perhaps I transferred muscle if that's a thing since I was doing less general muscle building at that point - just pushups and the casual pull up routine, running (sprints) to blow off steam.

I can see weight loss being a significant factor for heavier people, esp. those that are heavy and strong. I am definitely neither (typical things like bench press / squat etc I used pretty light weights).

Eh, you can also improve your lifts by just not being exhausted every time you go to the gym. With lifting, more is not always more. Fatigue and failure to properly recover is a fairly common reason for plateaus, especially with full body pulls.

This is complete bs.

I've learned 2 languages to fluency by mostly watching movies. I've learned the linux cli by setting up a minecraft server for my friends in high school. I've learned programming by making IRC (and later Discord) bots for communities I was part of.

All of this was fun, and it worked better than staring at a textbook and hoping that my "effort" pays off.

I think there is some conflation in this thread between "learning" and "practice" which are fairly different things.

As an ADHD person, nothing shovels the dopamine into my neural receptors quite like going from zero to "knows enough to be dangerous" in a new hobby or field of knowledge. That's the fun part. But climbing the experience curve much further than that requires some amount of _deliberate_ study and beyond that deliberate _practice_ and experience in order to become something like an expert.

Chasing questions down rabbit-holes is fast and entertaining but only takes you so far. Deliberate practice (studying) is mostly less fun, even when that thing is your life-long passion and/or career. But necessary if you want to be highly skilled in that area.

> nothing shovels the dopamine into my neural receptors quite like going from zero to "knows enough to be dangerous" in a new hobby or field of knowledge.

Man, this describes me to a T. I love that feeling of the "first 75%" (or whatever percentage it is). Then I tend to lose interest in the long tail.

>I've learned the linux cli by setting up a minecraft server for my friends in high school.

What you've learned was "enough to set up a minecraft server", but definitely not as much as "learned the linux cli", and that's without even touching the obvious question "what does someone mean when they claim they learned the linux cli"?

I fell for this trap too: I watched a tutorial by Nick Chapsas, then made my own ASP.NET Core Web API for a personal project, and thought "Wow I know ASP.NET MVC time to get a junior developer job".

After a few resumes (there's .NET demand in my area) I landed an interview with a startup. The interviewer (who happened to be the cofounder and has 15 years of .NET experience, some working directly in Microsoft) started hitting me with questions like "what kind of objects can get constructed in a using block?", "what's the difference between readonly and const", "how can we identify that a payload comes from a mobile client if the endpoints are shared?", etc.

That's when I realized that I knew enough to make me go "woohoo I have a .NET Core web API" but not enough to get a junior job. In fact, he was honest enough to tell me "you're barely entry level, and this wasn't even the technical interview it's just the screener".

Off-topic but related with the event: I obviously didn't get the job, but he left me with an advice I'm actioning: "Stop jumping around and stick to one language, I don't know if that's gonna be C#, TypeScript, Go, Python, whatever. Deep dive something well. You're only hurting yourself in the long run".

Trying to provide a perspective..

Let’s say because of your genetics, you can enjoy playing basketball, and you do that, and you have fun doing that, you get better at it… but that’s that, it won’t be that easy for you with other subjects or even get to next level at basketball. Then you need to submit to discipline… or are you willing to wait for things to become fun?

> pays off

That’s why it is important to chase things you are curious about, then you don’t need to wait for some return…

Agreed, consistency is more important than doing a marathon session. Anyone who has learned a musical instrument can tell you this, far better to practice 10 minutes a day everyday than 1 hour once a week.

Yeah, but Andrej is talking about learning much harder things in much more depth. He's a world class research scientist and engineer.

Practically everyone on planet earth learns a language as a child. Learning how to use some commands in linux and and programming a bot are literally child's play. I learned to play soccer the way you speak of - i'm... ok at it. Messi did a different thing.

Judging from his name, he has been struck with post-soviet spirit of doom and gloom.

He's also been struck with 10-100s of millions of dollars, an insanely successful career, and a good nature.

He was born in '86 in Slovakia, so he probably doesn't remember much of the late communist and early post-communist times.

Doesn't make it less true though.

A big hole in this article is that you need to find the very best learning resource there is. This is a must.

Eg: For RL it would be Barto&Sutton book.

Sometimes the best source is not intuitive. Eg: The best way to become a safe driver is to go to performance drivign school - its a bit expensive but they tell you how to sit and stay alert in a car which I have never seen outside of these schools.

One of my most common things nowadays is to ask ChatGPT is to ask to build a curriculum. Creating and understanding what a great curriculum looks like is 20% of the work of understanding a field.

You can LEARN ANYTHING now if you have the time and inclination and elbow grease. Truly nothing is beyond your grasp - NOTHING. Its a magical time.

I'm actually building a tool that will do all this for you and get you started down the learning path faster than what we have now.

And for the curious - the best way to learn medicine is not a textbook. There are solutions out there like Skethcy which work much better for anatomy.

My own learning project - learn Medicine "on the side". It seems ludcirous that we give up the keys to our health to doctors just so we don't have to learn 2 years of courses. Am going to fix that!

As a medical student, perhaps I can give some recommendations on the best free resources to learn medicine. If you like YouTube videos, Ninja Nerd has a great channel for learning the foundations. If you like textbooks, I used Guyton for physiology and Harrison's is probably the standard for clinical medicine. If you just want to look up how to treat a specific condition, look up "<condition> clinical guidelines". You'll always be missing the additional knowledge that comes from years of experience, but there's no harm in increasing your knowledge as long as you maintain the humility to remember that your knowledge is incomplete.

It's similar to how I learned software development as a hobbyist, so I understand a little about headlines like OpenAI switching from Next to Remix, but at a deeper level, I don't really understand what it's like running Next.js at the scale of MAUs. But it's still worth learning so that I have a little more understanding about the world around me.

Thanks for the reply.

Yep I'm ware of Guyton and Nnja.

The marginal information that a doctor has from real life is useful but with so many medical errors, for 80% of people they aren't relevant.

I've caught surgeons literally mentioning the wrong type of incisions right before the surgery.

> My own learning project - learn Medicine "on the side". It seems ludcirous that we give up the keys to our health to doctors just so we don't have to learn 2 years of courses. Am going to fix that!

While I admire the drive to become knowledgeable in the field of medicine outside of a professional curriculum in the disciplines, I’m not aware of any curriculum that proposes competency as a medical doctor in two years. Though I haven’t practiced medicine in many years, I do have a degree in medicine and went through internship, residency and fellowship. Trust me, it was far more than two years. Further, I don’t see how you would be able to (legally) gain experience in any of a range of procedures without following the consensus training path.

The first two years are the scientific part of a medical course.

The next two are more about interacting with a live patient in a variety of settings. Obviously this si useful.

But most of the harm created by the medical system and skewed doctor incentives (only 15 minutes to see you) can be averted by those 2 years. For example: knowing to e able to read a examination report means abiliy to ask questions immediately.

Can you tell me why doctors are totally useless in diagnosing extremely common issues like acid reflux. Why do GI specialists have no freaking clue what is causing acid reflux. Why do they not know what how exactly my a1c is relevant to heart disease instead of just prescribing me a statin.

I personally know couple of doctors who themselves are clueless in fixing their own chronic conditions. Let alone helping someone else.

Sure go to the doctor if you broke your arm but they are totally out of their depths if you have any chronic conditions. Not sure what exactly they study for like a decade if they don't have answers to almost anything.

Asking a doctor to diagnose and treat a chronic condition from a list of symptoms is like asking a detective to solve a crime from a list of evidence.

There is A LOT of additional legwork and investigation required to get to the truth even if you're brilliant Sherlock Holmes (and most won't be).

The best they can practically do in the 10 minutes they spend on your case, is try to treat symptoms.

And this is why you need to study Medicine!

https://meded.ucsf.edu/sites/meded.ucsf.edu/files/inline-fil...

> There is A LOT of additional legwork and investigation required to get to the truth even if you're brilliant Sherlock Holmes (and most won't be).

I got all the additonal tests though. I got upper endoscopy, a appointment with ent who put some sort of scope down my throat, bloodwork, esophagram, barium swallow test. He said he got nothing else and i am on my own and admitted that almost 90% of time they don't find anything.

Mind you this is one of most common conditions not some rare disease that needs sherlock holmes .

Because there are 12 different "causes" that are all very subtle and are highly influenced by your diet and behavior etc.

Doctors also never want to admit they dont know the answer to something

Yikes. No. If you have doctors who aren’t honest with you or honest about when they need to do more research to understand more, get the hell away and find someone else. I know not everyone has that choice, but if you do… please find a doctor who will level with you and you can trust. You do not want to get Dr. Deathed.

Studied long time ago / studied once and then forgotten / no interest in getting updated / no proper channels for getting updated / ...

Any of those could be a reason.

Since this struck a note - you can find UCSFs list of textbooks here: https://meded.ucsf.edu/sites/meded.ucsf.edu/files/inline-fil...

Start with Anatomy. And the basic anatomical form.

Start with a problem you personally have. (Go to a doc if its serious!)

Figure out your concentric anaotmy of hte issue, the pathology. Everytime you read a textbook it will push you to a new subject.

Do this for at least 5 hours and you'll be able to relate to your doctor much better.

If you want to know what a dcotor looks at for decision support - you can go to uptodate.com - I think they have a free trial for 3 days or something.

The most essential idea is that a doctor is someone whose model of hte human body is much more realistic than yours.

Thus as you learn medicine keep improving the model you have of your own body and how someone elses would be different from yours - for all major body systems - lymph, respiratory, nervous, endocrine , muscular, digestive, integumentary, urinay, excretory, circulatory etc.

>you need to find the very best learning resource there is. This is a must.

I think there's a line around "good enough", unless your goal of course is to be on the road to "become the very best". I think the better metric is making sure you have a accurate resource over a quality one. The 15-20 hour "sprint hard" methodology isn't stopping after that first sprint, just slowing down.

So if you find/can now access a better resource later, just start the sprint again on that. I know from experience (in real time, unfortunately) how easily "find the best resource" can end up becoming "spend weeks collecting resources but not consuming them".

The other problem is: How do you recognize what is "good enough" if you lack the skills/competence required to be able to say "this is good enough"?

For example, I'm a frontend developer who wants to learn backend. And let's say that I chose C# and .NET for this. I can either do tutorials in Microsoft docs and then reach out to Reddit or some other community for resources, to receive the commonsense advice "just build something", and we're back to zero because now the goal is to build something for learning's sake therefore what is "good enough project" to build to maximize gains?

>then reach out to Reddit or some other community for resources, to receive the commonsense advice "just build something"

An expert giving bad advice isn't going to help with your curriculum. To give a charitable interpretaion, forums like Reddit are very used to getting mostly Novices coming to ask questions. To the point where even if an advanced novice is asking about how to reach "Competent" level they will still give novice advice. And the best way to climb from novice to advance beginner is to "just build stuff".

There's definitely an open secret that there's plenty of novice material, and plenty of expert material. But the road to competent and proficient is basically a dead man's land for many subjects. I argue the curve to competent is harder than Proficient and Expert[0]. Such a hard point that you often won't find "best resources" without either education, consulting an expert, or simply work a job in that topic.

I don't have much better advice if you are seeking resources. But the next step up if you get stumped is to put more effort into finding other experts who will help out. try to email those potentially open to give advice on what to find or what's good/bad. Join communities similar to what domains you want to explore and form relationships. If you are getting to that point, offer to help contribute to projects others are working on.

[0]: Expert is steeper, but by that point you have a good sense of judgement to figure out what is a good or bad resource to study from. So it's "easier" to learn how to learn by this point.

Get in front of an expert and ask them what they should have read first.

In most fields the best will know. And the process of getting inf ront of the best will also teach you about the field.

I'm giving a C# class at a university-like institute (for the first time in my life) and I'm glad I had the time to learn the language while it evolved over the last 15 years. Learning nowadays is daunting because of the size of the language and the N ways to do even simple things. You also need to understand the programming landscape before C# (mostly C and Java) to understand some decisions made by language designers.

As much as I like learning by myself, sometimes I have to admit that taking (and paying) for a class is the good solution. The way I organize notions for my students would take them months/years to understand by themselves, if at all.

I ran into this issue when diving into the world of Rust. What ended up getting me to move forward was asking Claude/4o to design a curriculum that would teach me the basics in a way would lead to completion of a project I had in mind.

I ended up dropping 4o and going exclusively with Claude. Claude is amazing at teaching.

I understand the struggle but may not be able to offer an exact solution. People usually expect you to just throw something together without structure, but if you don't have preliminary experience with doing anything similar at all, you are stuck with a blank piece of paper and no ideas, and it feels absolutely terrible.

I don't know what works for you, but what worked for me was finding open-source projects in a domain I'm looking to write an application or a library in and using them as a reference. With time, you become able to determine which ones are of high quality and are a good example, and which ones are not. You could also ask Claude/ChatGPT for references to starting point.

On C# specifically, I can recommend looking at https://github.com/bitwarden/server which is more "traditional" style but does not have much nonsense/bloat you would usually see in an enterprise codebase. That's what I always reference as a style and project layout guide for newcomers that don't already know how they want the project to look. And then as you go through the code, you can always dump the snippets into a chatbot and then cross-reference the replies with documentation if needed. Chatbots also great at quickly sketching up project structure - it can be a terrible one but it's easier to do "hey, I don't like this, let's change it to X" than trying to come up with everything from the scratch.

If you already have experience with writing TS-based applications with e.g. React components, base router, etc., you can more or less translate this onto structuring an ASP.NET Core application with controller/api handlers, model classes, services, ORM layer and similar. There really is no true right or wrong singular way of doing it, and people who claim there is are dogmatics from a cargo cult.

In general, a lot of C# code out there that you will encounter will take more steps to solve its task than strictly necessary, as the generational trauma of ungodly horrors of 666-layer "Clean" architecture DDD-done-badly monoliths still haunts many, manifesting in a milder form of "write a small three file microservice as a 40-file three-project solution". It is highly useful to approach new patterns and anything that seems ceremoneous with "is this abstraction strictly required or can this piece be removed and done in a few lines of code or maybe a method?".

On tooling - can strongly recommend using .NET CLI which will be very familiar after using NPM and co.:

Create new projects/solutions with 'dotnet new {template name}' (e.g. console, classlib, sln, gitignore).

Add/remove projects to/from a solution with dotnet sln add/remove

Add dependencies with 'dotnet add package PackageName' or 'dotnet add reference path/to/project' if you want to combine multiple projects.

Run projects with 'dotnet run' (-C release). Hot-reload for most scenarios is possible with 'dotnet watch'. Publish into a final complete application with 'dotnet publish -o {path}'. There are many ways to do the last one, but for simple back-ends doing the default output and then copying it to a "runtime" image in a dockerfile will suffice.

^ This is exactly it. It's Dunning-Kruger.

By the very fact that the resource is "good enough" implies that it won't have the holistic and beginner-tolerance required of a good instruction set.

A great text will get you upto beinngin in 2 weeks - month. A "good enough" will mean a year if it isn't your primary focus.

Try learning RL from any other text than Barto-Sutton.

It's not foolproof, but some universities publish their course textbook lists online (and in some cases recommended readings too). As a bonus, textbooks often have recommendations for further readings.

Yep ... UCSF does this.

Weidly its the only good one I Found.

Would love to hear more about your thoughts on learning medicine! Why would you recommend an online program over textbooks?

When I’ve gotten deep into a topic I’ve actually almost ALWAYS learned that textbooks are the best way to learn things.

The internet is full of information. Sometimes it’s too much, unstructured or tangential to the goal at hand. Textbooks, in my experience, are truly written by the experts. It’s been vetted, rigorously reviewed and fact checked. It’s not inspired by influencers or clickbait.

Obviously YMMV, but when you find a top recommended textbook, it’s usually miles beyond a YouTube video or medium blog for deeper level content. It usually flows better and makes more sense as you study consistently.

Realize I didn't answer your qeustion.

Online courses aren't really holistic enough and not fundamental enough. They are usually dertivatives which are a translation of sorts from source documents.

For medicine you want the source documents which you can really trust.

Meidicine isn't static - it'll keep changing but its important to know source mateiral and tracking how outlooks and fixes for diseases change from there.

UptoDate.com has the best deciison science -newest knowlege. Thye are about 18 months old from cutting edge research. (Which is a good thing).

U=I bought more or less every book on this.

https://meded.ucsf.edu/sites/meded.ucsf.edu/files/inline-fil...

Start with Anatomy.

Start with a problem you HAve personally. And understand the anatomy and physiology. Use that to learn every abstraction you bump into. Example you'll definitely need to learn about the skin for example

Also go to uptodate.com for your condition. Thats basically what a doc uses anyways.

For inspiration go to r/medicalschool .

Constantly use

> One of my most common things nowadays is to ask ChatGPT is to ask to build a curriculum.

I've been trying to do this for some rabbit hole I decided to go through. It's great for generating a list of topics but good luck getting actual existing books or papers. In some instances it would generate a paper title and link it to some other paper that might be slightly relevant.

Posts like this that talk about learning "efficiency" always come off as soulless and dystopian to me. I think learning should be fun and that fun learning is the most effective---that's the only thing I optimize for and I certainly don't think about efficiency percentages. What a drag that would be.

I studied mathematics and I think this subject illustrates my feelings on this perfectly. Coding, just as well.

When it comes to learning maths, or a new programming language, there's all this tedious boilerplate you need to know. The rules, or syntax, the names of everything, how it all fits together.

There's ways to make learning this stuff more fun, but ultimately, not that much more fun. And anyway, the learning part is not the good part, it's the things you can do once you reach a certain knowledge level that are incredible, beautiful, even sublime.

On the other hand, take something like learning to paint, or taking dancing lessons. Unless you're hoping to become a member of an international ballet company, learning to dance is the fun part.

As another point, if you're a knowledge worker and you're likely to have situations in your life where someone basically says to you "right mate, you've got the job, here's a huge body of deep technical knowledge to learn, get up to speed, see you Monday" then a certain amount of skill in knowing how to absorb that quickly is a good thing.

> Unless you're hoping to become a member of an international ballet company, learning to dance is the fun part.

I think this really depends on the dance.

With most relatively technical partner dances, such as argentine tango and west coast swing, being a beginner sucks and it's especially rough if you're a lead.

There's this fairly long period when you're not going to be very fun to dance with, and you're not going to have fun dancing because too much of it is still in your head and not in your body. At the same time you need to dance with lots of people in order to improve, and people will throw you a bone once in a while for the sake of letting you practice, but at the same time they're not really having fun.

It's only if you stick with it for a year or two and get through this rough patch, it becomes very fun and rewarding.

I would say "fun" is overrated. We have become so focused on everything being fun that everything including fun itself has become tepid and mediocre. It is important to slog through the hard parts to cross the barrier of expert beginner. We are over downplaying the value of hard work and grit.

In many ways I agree with your opening sentence---maybe I shouldn't have written "fun". I think I was trying to get at something more like that the experience of learning itself is itself a good thing (even if it's not fun, even if it's suffering, even if it's hard) and I think mechanical and stoic recipes to optimize the process fail to adequately appreciate that fact.

The best part of learning piano isn't getting good at piano---it's learning piano. And sure there are some things we have to learn that we aren't that interested in learning, but I think even those things have the capacity to be worthwhile experiences if properly framed.

I think applying the word "efficient" to this area is suggestive of urgency and greater purpose---I don't buy into either.

I think 'fun' is a prerequisite for optimal learning, you can definitely have both.

And I think greater purpose is definitely a thing if you subscribe to a utilitarian moral framework

There is a big difference between learning something to become a skilled professional versus just a hobby. A lot of things I learned are for myself. I want them to be fun. There is no end goal. I don't want to compete with anyone, I don't want to prove anyone I am very good at this. I am learning new skills for fun and I intend to get enjoyment from practicing them. Throwing at a hobbyist "now repeat this 1000 times to get it perfect" is how you kill motivation.

This is exactly why drills exist: to make reasoning mechanic. The same as in the military... You can only decide (know) if you have the basics memorized to the core, and this requires... boredom in most of us.

I graduated in mathematics. Proving that Projective Space is a noetherian scheme is not exactly a thrilling challenge. But you have to go through the motions if you want to be able to "think" about algebraic varieties.

Same in any other field of "knowledge".

> We are over downplaying the value of hard work and grit.

Who is doing that?

> Posts like this that talk about learning "efficiency" always come off as soulless and dystopian to me. I think learning should be fun and that fun learning is the most effective

I don't disagree, but maybe the author is making do with what they have. Maybe they only have 30 minutes ~ 1 hour of free time per day (which is dystopian on its own), and need to think about efficiency if they want to achieve a certain degree of proficiency in whatever they're learning.

Another interpretation is that they are only trying to optimize their learning process if it's work related, because they need to. Or maybe they have an engineer mindset, and make the process more efficient is a fun thing to do by itself.

I so much agree with you. I understand and remember the things I learn more when I am having fun or it piqued my curiosity. But I guess shortness of time needs us to focus on the efficiency aspect of it too.

The steps here are fairly generic and can fit into whatever regimen you have. It simply comes down to "find your learning path and grind hard in the beginning. Then you can slow down and relax after that first burst".

Seems like decent enough advice if you ever have trouble getting started. It's actually not unlike cramming for a test, except you keep study afterwards and don't dump that knowledge the day after. "fun learning" or not, just make sure to really dive in in the beginning.

I somewhat disagree. Although having fun is important, I also want to make the most of my time. further, I think some aspects of learning can be a real slog, but when you get through it you find it rewarding.

If I'm not having fun learning something I can't stick with it. Efficiency without tenacity/grit is useless. It's kind of a tautology that "more efficient is better", but I agree it's pointless without fun. Being less "efficient" but having fun will yield better results imo

Yeah, I agree. Also, I don't think there is an ideal way to learn something. Different people absorb lessons best in different ways.

The people I've thought were most successful were not grinding their way through learning but enjoying it, letting new questions arise and pursuing them. Is that efficient? It might not seem so. But the learning tends to be more transformative; they grok the lessons more deeply.

A work colleague once told me that it's like reading textbooks in graduate school -- you read it once just to get a general sense of the vocabulary. They you start over, concentrating on the meaning. New ideas take a lot of study to learn well. "Efficient" learning strikes me as a compromise where you get a superficial understanding for the sake of speed.

I cannot recommend reading A Mathematician's Apology enough. It was written by GH Hardy and I think it's one of the best non-math texts out there to understand how a mathematician's brain works.

https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

Fairly short and beautifully written.

I also like mathematician's apology and would recommend it for understanding now a mathematician's brain works and in particular a mathematician's perspective and mindset on being a mathematician.

But I'm curious what prompted you to bring that up in this thread? I don't see how it's connected to the blog post.

Oops! Thought I was in this thread: https://news.ycombinator.com/item?id=41909564

Thank you friend!

Contra to a lot of what's being said in this thread, I think a lot of smart people get stuck in the trap of overvaluing quality of input relative to quantity of input. Put another way: the bitter lesson applies to the AI inside your skull too.

Relatedly, it took me a while to appreciate that seeking out and organizing the best knowledge on a topic is, for me, just a form a procrastination. Its ok if I'm doing it for fun. But if I want to learn, the key seems to be that every single day I start the day learning or reinforcing something, and do no other activity until that one is completed. A somewhat related thing I learned in medical school, is that many people have an internal cue for when you've really learned something. When you have re-visited something for the nth time, and the feeling you have is a deep level of annoyance that you are rehashing the same thing again, that is usually the signal that it will stick. May not work for all but worked well for me and the folks I shared it with.

Hmm. Given that Textbooks are all you need, I’m not sure this holds.

Maybe “don’t focus so much on organizing your inputs, instead focus on many quality input reps”?

This is something I have personally struggled with, so I wish the author elaborated more. If you are a novice, how do you quickly identify what the foundational knowledge is? How do you know what makes you an expert and not an "expert beginner" as the author says to the extent that you can build a personal curriculum about it?

>If you are a novice, how do you quickly identify what the foundational knowledge is?

You probably can't. You need to rely on knowledge of others to identify good resources. And then lean that against how you learn in order to pick the best resource for you.Same for verifying being an "expert beginner". Never be the smartest person in the room if your goal is to grow.

In a crude way: google it. You'll probably get a generic (maybe even horrible AI slop) on top. But you're not looking for a perfect guide on first Google (not unless you have a very popular topic). Look for terms used and start googling those to narrow down to a more specific place. Maybe a forum post full of (hopefully) competent+ people answering your question. Maybe you find a quality guide to follow. Maybe you find you're on a completely wrong rabbit hole and figure out better terms to Google.

That's basically half my learning while on the job. Usually works pretty well in my personal time too.

I tried to think about this and came to a personal realisation that perhaps there is no strict "foundational knowledge" for most topics.

Pick programming, is knowing binary operations foundational? Is knowing compilers? Is it knowing bubble sort? Or perhaps knowing data structures?

I believe that if you have been using/working in a field, whatever you touch for your own goals that's enough.

And perhaps the difference between being an expert beginner and an expert is whether you still care about such a distinction? If you can achieve your current and future goals and can eventually learn new concepts then you're good.

I'd say a beginner might be someone who wouldn't even know where to begin.

Let's pick chemistry for myself: sure, I could follow some video but without the video I wouldn't even conceive how to get started with anything.

While, say woodworking, I wouldn't call myself an expert but I would be able to imagine starting a random project from scratch and eventually figure out all the parts.

So, maybe: - beginner: can't complete a project without help/support - mid: can complete but is unsure whether that's the best way - expert: has completed it before somehow

I'd argue the principles Turing and Wolfram lay out in regards to universal computation and computational equivalence are the most foundational, and then various systems or architectures (flow vs stack, etc), etc, are important as there needs to be concrete examples implementing the fundamentals. If you really want to get esoteric, programming goes all the way back with society and religion. Just like how a machine can compute so too can a group of people through their actions, if they adhere as religiously to their tasks as the fablic of reality seems to adhere to its laws in governing the motions of matter. Programming is the building abstract structures which, when represented with matter in the right ways that can take advantage of the moment-by-moment Gets Things Done™ nature of the fabric of reality itself, produces useful transformations of its initial states. Very complex behavior arises from the simplest of mechanistic rulesets, and it's found universally in biology and in places all over reality. Computation is so foundationally fundamental to this place and your (dear reader) existence here, it is shameful it's not in standard middle/high schools' curricula right next to the fundamental theorems of arithmetic and algebra!

It is an iterative process. One would move forward with a baseline foundation and pay attention to the difficulties and inefficiencies in the learning process to triangulate the additional foundation needed.

This is something that can be tricky for sure. Depending on the subject you might not need to start diving deep into every topic. Sometimes you'll have to first ask some high level questions like how do I get this data from this table and convert it to this format. Once you identify what problem you're trying to solve go and learn what's needed to solve it.

You won't always have an optimal solution but that's okay. The most important is to try and use the thing you're learning in some real way or with practice.

> The most important is to try and use the thing you're learning in some real way or with practice.

In my experience, that's a necessary first step to learning. I need to get my hands dirty, get a feel for what I'm working with. An experience is worth a thousand pictures, which are worth a thousand words - you can't gain that basic understanding and instinct by reading, only by having all the sensory inputs of doing it.

Then it's time to read. Now you must find an expert to guide you. First, you'll have too many blind spots - you can't possibly find all that's current, you can't find the best sources efficiently, and much won't be in books yet. And without expertise yourself, you can't distinguish the worn-out theories from the evergreen standards from the unproven innovations; the promising from the unlikely from the absurd; you won't know the consensus from the fringe; the guy advocating their personal theory - maybe even a credible one - from the balanced survey of established ideas. You won't recognize when you're reading just a side of a well-known debate.

You don’t. That is what you will build as you learn a topic, it makes no sense to “identify” it first.

Do the thing you want to learn.

I learnt data analytics and SQL for MIS/BI purposes on-the-job as a sales manager. Got pretty good at it too, built several dashboards and long-standing capabilities for my team.

Now, if I say I want to get into this scene for good, I am immediately daunted with a mountain of diverging learning paths to take. Should I take to Python and its massive library ecosystem, or should focus on database fundamentals? In every choice taken there are seemingly infinite branches, and it is rather hard to focus if you aren't even sure you're on the right track.

Last time I sat in an analytics/consulting interview they grilled me on highly specific technical questions on data pipelines and warehousing and testing and other topics that I've never had to worry about before at work. In another assessment, I was grilled on some AWS/Redshift-specific things. In yet another I was expected to know deep learning. It is all too hard for someone not originally with an engineering (or adjacent) background.

Yeah learning to actually use in practice is different from preparing for interviews. I would say continue where you already built some knowledge and branch out when you realize you have to, and then work on learning one branch as you go.

For interviews you may need to lookup what type of questions to expect and memorize details on that, unfortunately. That is not useful in practice but can be necessary for interviews.

I'm also wondering this. Two possibilities. One, find the first principles/root node/glue that holds many disparate concepts together in some causative way. Two, the specific procedure/step/concept that you keep reusing across multiple problems.

I'm surprised the course by the name of this post isn't here.

The post covers a great mindset, but the math really is one thing, and learning how you learn and how you can learn is invaluable.

This is a great course to start learning about your learning.

https://www.coursera.org/learn/learning-how-to-learn

After/with this, there is a slew of adult learning knowledge that will likely make you feel better.

One key is learning to understand something, before learning to memorize it.

Another is creating your own mind map of how the concepts you are learning fits together.

Farnham street has some great books on mental models as well that was recommended to me as helping

An expert is someone who can often explain complex things in very simple ways. being an innocent beginner is one of the best mindsets to cultivate - you learn what you do and don't know pretty quick, and also a sense of known vs unknown, and size and number of unknowns.

I checked these out but couldn't find the answer to the questions I am asking. It tells you how to maximize efficiency while learning, but doesn't tell you how to identify what you should be learning in the first place and what the sequence of your focus should be when you start.

What do you specifically want to learn? What you need to learn will generally make itself known, if you have some general goal? Just starting at all is the best way to start.

Say I want to learn web scraping. Now if I try to start, I see there are several layers of fundamentals and several potential paths, all of which seem equally important. Where do I start? What platform should I use? Should I start from the DOM and HTML parsing and go ahead from there, or should I start from learning Python libraries built for it as so many books and tutorials advise? Going one layer deeper, do I need to learn data structures before anything else? JavaScript and APIs? The fundamentals of TCP networking? Regex?

It's all too overwhelming at times.

Yeah, start from any point A. A suggestion is where you can progress in some way. Don’t make too many decisions. There’s so many viable ways to learn that, just start where it is natural for you. You don’t have to figure everything out or have answers to everything.

https://www.coursera.org/learn/learning-how-to-learn

>What’s something you’ve learned that you believe gives you an edge - something that you’re almost surprised more people don’t know about?

I don't know if it's just me but I would not be stoked to be asked this question during an interview. During interviews you're implicitly trying to differentiate yourself from others vying for the position. You usually do this by talking about your experience in different ways. I find it annoying when the interviewer explicitly asks you to differentiate yourself from others vying for the position. In part it annoys me because I think that should be the job of the interviewer to determine based on how I've answered their concrete questions about my experience. But also explicit questions like this one give such an opportunity for bs that I do not think they give a lot of signal. I guess I could be wrong though and don't spend enough time thinking about what makes me better than other people.

I agree with the blog post that learning how to learn is an important skill. But the post offers very little beyond a few tips on how to actually achieve that. For people interested in actually learning how to learn I'd recommend the book "Make It Stick: The Science of Successful Learning", which offers a lot of details on this topic based on actual scientific research.

that book seems to be very inline with cutting edge research on learning, thanks

book summary

"Make It Stick: The Science of Successful Learning" Summary:

Key Premise: Effective learning strategies differ from common study methods like rereading and cramming, which provide an illusion of mastery but lead to poor retention.

Main Learning Principles:

Retrieval Practice: Actively recalling information strengthens memory and makes learning more durable. Self-quizzing is more effective than passive review.

Spaced Repetition: Spacing out learning sessions over time leads to better retention than cramming.

Interleaved Practice: Mixing different types of problems or subjects during study sessions improves learning compared to studying one topic in blocks.

Elaboration: Explaining ideas in your own words and connecting them to existing knowledge improves understanding.

Generation: Attempting to solve a problem before being shown the solution enhances learning.

Reflection: Reviewing what you’ve learned and considering how it applies to your life strengthens learning.

Varied Learning: Learning in different contexts and environments makes the knowledge more adaptable and versatile.

Key Takeaways:

Rethink study habits: Active learning techniques outperform passive ones.

Learning is more effective when it's effortful—embrace challenges.

Long-term retention relies on consistent, spaced, and active engagement with material.

That summary is pretty good based on what I remember from the book. I think the second to last point, _effort_, deserves a bit more of an emphasis though. It's actually a common theme through all the effective learning methods that they require more effort and that more effort generally implies more effective learning. As an example, simply rereading a text takes little effort compared to doing flash cards, and the later is more effective.

I've been wanting to try this approach for learning a language.

In English for example, learning the 800 most common words, you can understand 75% of the language: https://www.bbc.com/news/world-44569277.

I'd love to start fresh on a new language, take 800 new words, try to learn 10 a day, and see where I get after 3 months. Can I really understand 75% of text if I have perfect recall of those 800 words?

> Can I really understand 75% of text if I have perfect recall of those 800 words?

This thing you're talking about is called 'word coverage'. It's the percentage of words you know in a given text. I've created lots of word coverage graphs in the past, and, as research has shown, you won't really be understanding much until you reach the high 90s in terms of word coverage. The famous number for being able to read English texts extensively requires a word coverage of around 98%. And while it depends on the text, in order to reach 98%, you generally need to know around the top 5k words in a language.

Funny enough, when you understand 75% of the words in a text, you subjectively feel like you're understanding like 10% of what's going on.

Yep, 75% coverage is too low for significant comprehension. You normally need 95% for decent comprehension and 98% for comfortable reading.

The coverage required in Japanese (my target language) seems something like the most frequent 15,000 words (depending on the definition of word) are required for 98% coverage. At 12,000 words it becomes viable to read with some comprehension and semi-frequent dictionary lookups.

Also, interestingly, you need about 2x the number of words in Japanese as English to reach 87% coverage:

"It has been reported that 2,000 high-frequent English words cover 87% of tokens (Nation, 1990). In case of Japanese, 4,024 SUWs are required to cover 87% of tokens." (Text Readability and Word Distribution in Japanese, Satoshi Sato)

This is exactly correct.

With graded readers, thou, you can have good reading experiences with around 3k words (ofc depending on language, book, etc).

While the answer to your question is "no", there is still something you'll be able to do: to express yourself and to understand spoken language.

Like other people said here, understanding will probably still be limited, esp. in writing. But expressing even complex things becomes easier.

E.g. instead of saying "Do you have medication against migraine" at a pharmacy you could say "Do you have something for pain here" while pointing at your head.

This is what we call fluency, and starting at 800 words I would argue you have basic fluency in the language. And also regarding understanding spoken language – those words might be enough to express that you haven't understood something and ask people to simplify.

Words are not enough, though – pronunciation and grammar also play their part.

This post will give you a sense of what understanding 80% of the text looks likes https://www.sinosplice.com/life/archives/2016/08/25/what-80-...

800 is definitely too little. I'm building a language learning app based around this exact strategy. Right now, I've around 7000 German lemmas tracked in the app and still regularly encounter sentences which I don't understand, because I lack the vocabulary.

In my experience, the words that carry the most information in a sentence are the less common ones. Here's what understanding 80% of a sentence is like:

"I went to the sdjfkdsh and got a new ghjsakgfh."

The missing words could be "dealership" and "truck" or "embassy" and "passport" or quite a lot of other pairs that change the topic entirely, so reading or listening to something with 80% understanding generally requires a dictionary in one hand to get you up to a reasonable level of comprehension. That said, I personally think language learning is enjoyable and rewarding, and tackling the most common word list is a good first step.

No. Apart from grammar etc. you‘re missing, you might understand nothing while knowing 80% of the words.

Give learning Japanese a try. It's a meta-learning adventure! There are 3 distinct classes of characters (two syllabaries that each have a perfect matching pair with the other, 46 each plus some compounds) and the third are (mostly) chinese Kanji characters. Fun stuff!

I wonder if there is a similar "Pareto priciple"-esque approach that one could use to learn Japanese.

There are the "radicals" which can help you to interpret a new kanji, since they're the kanji building blocks.

I highly recommend this site for that. https://kanji.koohii.com/ which goes along with the book "Remembering the Kanji" by James Heisig (strictly speaking, you don't need the book, but I think it will help understand the idea behind the process). But the stories (mnemonics) on the website are better than the ones in the book, but also let you put in your own stories. You can also vote and choose existing stories, so there are crowd sourced mnemonics that other people have said work for them. One interesting side effect of that is a lot of people decided to use Spider Man whenever there is a "thread" radical, for more memorable stories. I did it around 15 years ago and learned how to write all the 2000+ commonly used kanji in a few months (9 months for me; 2-3 months for a more diligent person). It uses a spaced repetition system (Lietner box method).

Kinda!

The frequency of words in every human language follows the Zipf distribution, which is a power law, like the pareto distribution.

Some learners create what are called frequency lists, which are lists of the most common words, and learn those words first. In general, you get (disproportionately) more bang for your buck from learning the most common words than the rarer words when it comes to understanding.

However, due to the very long tail of word frequency distributions, you eventually need to just start learning words as they come and stop trying to over-optimize with a frequency list.

Depending on your definition of "understanding".

If it means you can at least take an educated guess on what a sentence means, then yes.

If it means to understand a sentence like a native speaker does (just slower), then no.

I think the best learning resource for something is being really interested in it.

The initial cram is an interesting concept. If you insert new things to learn at a constant rate, the repetition burden grows logarithmically. Assuming you have some fixed amount of time you can devote everyday optimally your repetition burden should be constant. So the solution is making new things to learn not constant, but front loading a lot of it.

I have a related question: Is learning interlinked with writing?

PG tweeted:-

    You can't replace reading with other sources of information like videos, 
    because you need to read in order to write well, and 
    you need to write in order to think well.

Neel Nanda did it better: https://www.neelnanda.io/blog/34-learning

Identifying what the foundational knowledge is isn't easy for an absolute begginer.

Building an efficient path to expertise is hard for a beginner.

I think the fastest way to learn is asking an expert to build a learning path for you, starting from what you know and what you don't know.

IMO, how to learn depends greatly on why to learn and what constraints do you have.

If you need to pass an exam, obtain a certificate, etc. you will need a different approach than if you are just curious about a subject and explore what it is about.

There are commonalities, however. Much of the advice on deliberate practice (From the book Peak Performance) is valid even if you don't try to be a top expert.

> Very quickly identify what the foundational knowledge is.

This seems to be the most important part but also has the hidden and problematic dependency of... already knowing (i.e. already having learned) what the foundational stuff is?

For me, there’s always an early social element to learning: trying to figure out who the experts are; getting them to point you toward the best resources; and if you’re lucky, bouncing your mental models off them to be corrected. A good LLM can take you part of the way on many subjects, which removes some of the initial friction.

Not every field is like that though.

Some problems are wicked and new, lots of knowledge is basically enacted more than known, and the solutions one seeks often require several disciplines.

I dont think it's going to be that important. Different people have different learning styles but also vastly different capacities making this really difficult to research accurately. People claim to find the secret sauce from time to time. They're most likely wrong.

> “What’s something you’ve learned that you believe gives you an edge - something that you’re almost surprised more people don’t know about?”

My response: Nice try.

It's true.

Learning depends on the environment and whether it is pursued in an auto-didactic sense (Even for a job, say) or whether you are learning for an exam/part of a cohort.

It's not wrong to say Curriculum does not matter. But the level of curriculum is also something that needs to adjust to your current level and related fields you have knowledge within, to prevent you becoming overwhelmed.

Most people stop learning being motivation dries up as Test Anxiety rises to the point where they are at a "low-performance" place in the eustress curve. A few days there and people pause until it becomes urgent. A lot of this is a lack of momentum, but also not dedicating or having access to judgements of learning about your own progress.

In other words, if you judge your learning at all, it helps you manage.

There is a natural tradeoff between the flow-state of "just one flashcard with one information principle at a time, endlessly" and the longer term state influencing your time in flow-state of "am I progressing, what don't I know, how do I feel about my learning and mistakes?"

Think about learning databases, or CSS. When did you really takeoff? Probably A) Practically copying others examples (existing queries ran in PhpMyAdmin, or codepen code) And then later B) Once you overcame a big mistake and saw progress - suddenly what "Display" did clicked for you, and you saw how useful it could be to use the "fixed" option, it unlocked your understanding of the items in A and confirmed or disconfirmed your understanding of how it works.

Again it all depends. Self-motivated learning, even for a job, is easier to work with than compulsory learning. Because there, you don't even have the motivation to gaze up to the horizon and gather any excitement or understanding for what the learning might later lead to. It doesn't feel like a path, it feels like a brick wall. In this regard, a list of subjects is somewhat skin to someone stacking bricks, rather than elucidating a path. Overwhelming anxiety while learning is a real thing. The context really matters as to whether this approach is always the wisest.

Piano piano si va lontano

Crypto Data Live-Streamed. One article. Wisdom all around.

The biggest challenge in learning is identifying gaps in your knowledge. Dunning-Kruger is a real thing and you want to avoid that.

Part of learning to learn, is learning how to identify the things you don't know. Then learning how to structure your 'personal curriculum' them in a rational way - you don't need to know everything up front to be effective.