If this post is inappropriate, I apologize.

I stumbled upon this site after reading "Harry Potter and the Methods of Rationality".  The story so far has really moved me on multiple levels and sent me here in a quest to learn more about rationality as a philosophy/way of thinking about the world. I have read Ayn Rands published works and loved the stories and most of the message.  The characters always seemed like titans that were far and above me, but now, I've seen a character that is a bit more approachable. 

I've started to go through the "Map and Territory" section of the "Core Sequences" and this whole project and community makes me ecstatic.  I'm currently working my way through the Bayes's Theorem article with some success.  The more I read, the more I realize I may have a problem.

 

I'm pretty dumb.

 

Is higher level reasoning "use it or lose it" ?  I like learning new things and love reading but any new ideas require a ton of thought and re-reading.  I think I have enough interest to keep plugging away at it, but I'm not sure I'm going at things the right way.  Is there a "Kid's Table" for lesswrong.com?

For "Priors":  I'm 28 years old, white male, married, no children, poor economic upbringing, solid emotional upbringing, currently lower to middle class, high school diploma, US Navy, currently a civilian electronics technician, raised Baptist currently Agnostic/Atheist (recently).

I guess that's it.  Thanks!

--John

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[-][anonymous]12y 36

You're probably not dumb. You probably have a lot less formal schooling than the average LW member. Don't worry about it. Just keep self-educating (which is always hard and slow work. It definitely is for me.)

Also, don't let people who sound smart -- much less fictional characters -- intimidate you. Ayn Rand, bless her heart, didn't write the world's most realistic characters. People on LW who talk about "advanced rationalists" and use a lot of jargon aren't necessarily as fancy as they come across. A lot of that is vocab choice and confidence.

What are you interested in learning? (There's a good chance that LW shouldn't be your only source.)

Ah, I'm glad to see that I'm not so horribly stuck in the mud. I don't have many relationships to gauge these things by. Thank you :) I've always wanted to learn how to "think better". To have greater use of my facilities with greater frequency in everyday life. Problem solving, math, social interactions, all of which seem to elude me except in "Spurts" of clear thinking. (I.e. this comment will take quite a while to write, If I was speaking, I would not be able to be as clear in my thoughts.) I think that's why this site excited me so much. Much of what is here seems to get to the root of "thinking".

It should excite you even more then, to know that part of what is on here is a model explaining why this site excites you so much!

I don't know why I'm so excited for you, but I am. It can be easy to feel intimidated by people and comments are sometimes on the blunt side, but if your goal is self improvement people will really respect that (I will at least!)

For what it's worth,I started with the sequences and went from there.

If you're reading through some of the posts in the core sequences and understanding them pretty well then you're not dumb. Even if it requires lots of thinking and re-reading.

There's an idea that being smart means that you can understand anything quickly and easily, but that's not really true (at most, it is sometimes one unreliable sign of intelligence). Being good at something doesn't mean that it's always easy for you, it means that you can work to meet the challenges that you face. With intelligence, a big part of that is being able to recognize when you don't understand something, and to keep thinking it through and investigating it until you've figured it out. Which sounds like what you're doing.

If a new idea comes quickly to someone, a lot of the time that's because it's already relatively familiar to them - they have the necessary background knowledge and know about related concepts, so it's relatively easy for them to add this one new piece of knowledge. (If you've gotten to the posts on inferential distance then this will sound familiar to you.) Your educational background means that a lot of the topics being discussed on LW will be less familiar to you than they are to many other people on LW, so of course it's going to take more work for you to figure them out. The fact that you're putting in that work and figuring them out is a sign of your ability to learn. It doesn't mean that you're dumb.

I'm glad to hear that you've been enjoying your studies and am happy that you're here.

You might find the References & Resources For Less Wrong posting useful.

Aside from the ones mentioned there, one book that I had a favorable impression of upon browsing through it and that looked pretty accessible to me is Carl Sagan's The Demon-Haunted World: Science as a Candle in the Dark.

I concur with the points made by SarahC and Unnamed. My experience has been that with very few exceptions, learning substantive subject for the first time is a struggle. I've often felt bewildered and disoriented for a significant period of time before things started to gel and coalesce.

Quoting from Sections 7 and 8 of William Thurston's Mathematical Education essay :

Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through some process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics.

After mastering mathematical concepts, even after great effort, it becomes very hard to put oneself back in the frame of mind of someone to whom they are mysterious.

I remember as a child, in fifth grade, coming to the amazing (to me) realization that the answer to 134 divided by 29 is 134/29 (and so forth). What a tremendous labor-saving device! To me, ‘134 divided by 29’ meant a certain tedious chore, while 134/29 was an object with no implicit work. I went excitedly to my father to explain my major discovery. He told me that of course this is so, a/b and a divided by b are just synonyms. To him it was just a small variation in notation.

One of my students wrote about visiting an elementary school and being asked to tutor a child in subtracting fractions. He was startled and sobered to see how much is involved in learning this skill for the first time, a skill which had condensed to a triviality in his mind.

Mathematics is full of this kind of thing, on all levels. It never stops.

[...]

Similarly, students at more advanced levels know many things which less advanced students don’t yet know. It is very intimidating to hear others casually toss around words and phrases as if any educated person should know them, when you haven’t the foggiest idea what they’re talking about. Less advanced students have trouble realizing that they will (or would) also learn these theories and their associated vocabulary readily when the time comes and afterwards use them casually and naturally. I remember many occasions when I felt intimidated by mathematical words and concepts before I understood them: negative, decimal, long division, infinity, algebra, variable, equation, calculus, integration, differentiation, manifold, vector, tensor, sheaf, spectrum, etc. It took me a long time before I caught on to the pattern and developed some immunity.

My experience has been that with very few exceptions, learning substantive subject for the first time is a struggle. I've often felt bewildered and disoriented for a significant period of time before things started to gel and coalesce.

One of my professors once told me that you only really understand the content of one math course when you're taking the next one that builds upon it...

I have always wondered exactly how this works. Whenever there's some maths area I'm struggling with, I only struggle with it while that area is the focus of study. Eigenvalues were a mildly unspeakable horror when I was learning specifically about Eigenvalues, but they suddenly became trivial when the I was asked to use them on a new unspeakable horror.

I don't remember any progressive improvement. It's as if I was asked to step up my game, and all the prerequisite knowledge just fell into line without any complaint. This pattern has existed throughout my maths education all the way back to basic algebra and I can't really find a satisfactory explanation for it. No other subject of study behaves like this.

[-][anonymous]12y 20

I always said, "I've always been bad at math. I'm just bad at different math every year."

Math divides into "way too hard" and "trivial" -- the good news is that the "trivial" pile grows over time.

I wonder if that's because you're not trying to "understand" something, you're just using it as part of a separate algorithm? You stop caring about what it means to find an eigenvalue, and just think about how to get what the number you need to solve the problem in front of you.

Also, oddly enough, when taking the math course that builds on something, you get a lot more practice at it than when you were taking the original course. In other words, you probably do a lot more algebra in calculus class than in algebra class.

I'm starting to wonder if, when first tackling a troublesome topic, I think of it as an enemy, but when given a different enemy I suddenly start treating it like a reluctant ally. The "falling into place" phenomenon also happens when the New Unspeakable Horror is a real-world issue I need to deal with, like a problem at work, or an exam.

I should have thought of this before, but I can already relate to the vocabulary issue described in the second quote. I often use electronics or computer jargon when talking to my wife, not realizing I'm at home and not in the shop. Her arched eyebrow usually cues me to realize I need to swap my terminology around.

I was always a huge fan of the "Cosmos" series, but it never dawned on me to look for books written by Carl Sagan. Thanks!

I think your post was very appropriate.

Others have adequately addressed your question about learning new things (SarahC and multifoliaterose are doing math in academia, listen to them), but brushed off your question about "feeling dumb". Why ignore this issue when you can solve it? Whenever I need to get sharper and more "toned" for tomorrow, I work through some math problems or some Project Euler tasks. The effect is quite noticeable, and the more I practice the longer it stays afterward. I've found that it's more helpful to solve problems that are slightly below my current limit of ability, but try to do them quickly, switching to the next problem immediately when I finish the last. Getting 'em done makes me feel much more confident about my intelligence. It also carries over to mental agility in conversations, etc.

Reading stuff, on the other hand, doesn't seem to help my mental agility at all, even if it's clever stuff like the Sequences or HP:MoR.

Whenever I need to get sharper and more "toned" for tomorrow, I work through some math problems or some Project Euler tasks. The effect is quite noticeable, and the more I practice the longer it stays afterward. I've found that it's more helpful to solve problems that are slightly below my absolute limit of ability, but try to do them quickly, switching to the next problem immediately when I finish the last. Getting 'em done makes me feel much more confident about my intelligence. It also carries over to mental agility in conversations, etc.

I think this is a good suggestion. When I first got interested in math late in high school I did a lot of problems from old math contests and this made me feel sharper, boosting my confidence. Some things that may be useful to johnbgone here:

  1. The Art of Problem Solving materials. They have a free archive of old AMC problems on their website.

  2. There's a good and accessible book called Mathematical Circles: Russian Experience

  3. I remember having a favorable impression of Alfred Posamentier's Challenging Problems in Algebra.

  4. The Art and Craft of Problem Solving by Paul Zeitz is great (but much of it requires more prerequisites than the aforementioned materials).

You might want to read this PDF: http://www.occampress.com/grades/grmath.pdf

If you read it you'll see that you do not have to be a child prodigy, don't have to start early on, don't need a good formal education and do not need to appear particular smart to work wonders (at least in mathematics). There are dozens of examples.

  • “[Isaac] Newton (1642-1727) ... was educated at local schools of low educational standards and as a youth showed no special flair, except for an interest in mechanical devices.”
  • “Before Newton and Leibniz, the man who did most to introduce analytical methods in the calculus was John Wallis (1616-1703). ... he did not begin to learn mathematics until he was about twenty — his university education at Cambridge was devoted to theology...”
  • Gottfried Wilhelm Leibniz (1646-1716), co-discoverer of the calculus and a pioneer logician, “knew almost no mathematics up to 1672 [when he was 26].”
  • “Hermann Günther Grassmann (1809-77) [discoverer of vector algebra], ... showed no talent for mathematics as a youth and ... had no university education in mathematics, but later became a teacher of mathematics in the gymnasium (high school) at Stettin, Germany...”
  • Francois Viète (1540-1603), who laid the foundations for the algebraic approach to geometry, spent most of his life in high public office; “it was only during the time he had free from official duties that he was able to devote himself to mathematics.”
  • Gerard Desargues (1591-1661), one of the pioneers of projective geometry, was self-educated. Yet “Desargues was one of the most original mathematicians in a century rich in genius.”
  • Gottfried Wilhelm Leibniz (1646-1716), co-discoverer of the calculus, was selftaught in mathematics.
  • James Bernoulli (1655-1705), a member of the remarkable Bernoulli family that made so many contributions to the early development of the calculus, was self-taught.

I like learning new things and love reading but any new ideas require a ton of thought and re-reading.

Don't be intimidated by most of the people on LW. They largely are not smarter but much more educated. A lot of the people here on LW have the best formal education in the world so they came across a lot of concepts before. Things are not obvious to them either, they just learnt to accept them. Is 1 + 1 = 2 really obvious? No! The last page of Russel and Whitehead's proof that 1+1=2 could be found on page 378 of the Principia Mathematica. The complete proof of 2 + 2 = 4 involves 2,452 subtheorems in a total of 25,933 steps!

How is the educational level of the participants of this forum, by the way?

Just to continue your list of spectacular infos from math history: Newton probably suffered from microcephalia (as was speculated upon at Leibniz) by alcohol abuse of his mother during pregnancy.

If someone wants to walk in the footsteps of Ramanujan, here the textbook he used as teenager for autodidactism. Unfortunately I do not know if anyone tried that book with teenagers. Here someone's collection of basic math texts by which Gauß, Euler and other math geniusses learned to make their first steps.

Practice, practice, practice. No, wait, hold your rotten fruit, I'm serious.

It's a bit hard to articulate, but I've been thinking a lot lately about the interaction between two human abilities: the ability to do whatever you want, and the ability to get better at something by doing it over and over. The second one sounds like the hard one, but really the first one is--most people never realize that they really do have full agency over their own lives. They're too used to ruling out possibilities according to someone else's heuristics, and never stop to examine those heuristics. If you haven't yet fully internalized the fact that you really can do whatever you want, I'm not sure what words would inspire that, but think about it.

As for the practice bit, again, people have this artificial division between "people who can do x" and "me." But all it really takes to be able to do most things is to try to do it a lot, ideally in a structured sort of way. The catch is that you have to be willing to do something you're really bad at for a while--as Go players say, lose your first 100 games as fast as you can. Or play 100 twangy horrible chords before you play a pretty one. Or screw up 100 math problems before the concept makes sense. But if you decide you'd like to have a certain skill, and have a good attitude about the necessary period of sucking at it, there's nothing stopping you from acquiring the skill.

The synthesis of those two ideas is quite liberating. As it applies to your case, you can learn as much as you like about whatever you like, including ways of reasoning and discrete facts and abstract concepts. There are also exercises that'll improve your brain's capacity to learn, understand, and remember. (I don't know a lot about that, but there are other people here that do.) And you can have as much of all of this as you want, limited only by how much time you can find for it. In short, yes. You have all the power you need to be as intelligent as you aspire to be; you just have to choose to use it.

On a side note, you should know you're not alone on the low-level-of-formal-education front. I'm a high school dropout and just started college a couple of months ago, in my 20s. A lot of the technical stuff on LW goes over my head--but, per the above, that's mostly because I haven't chosen to dedicate time to learning it yet. :) It's lower priority than schoolwork and other projects of mine, and knowing that makes me feel totally fine about not understanding.

(ETA: Okay, so this is my 2:30am level of eloquence. If it still seems like a good idea in the morning, I'll think about drafting an essay explaining the point in more depth, since, as I said, I've been thinking about it a lot lately.)

But if you decide you'd like to have a certain skill, and have a good attitude about the necessary period of sucking at it, there's nothing stopping you from acquiring the skill.

Not only this, but if you find a skill intimidatingly impressive, you're probably overestimating how difficult it is.

Indeed. It's more useful to know what the curve of difficulty is like. A guitar teacher friend once warned me that, unlike the piano (on which it's easy to make a pretty sound at all and hard to make a complicated one), on the guitar it's hard to make a nice noise at all but once you can do that it gets much easier. Knowing that, or at least having been told that, has done a lot to keep me from being frustrated while learning the guitar. "It's okay ... it's supposed to still be difficult and sound weird. I'm still new at this."

As for the practice bit, again, people have this artificial division between "people who can do x" and "me." But all it really takes to be able to do most things is to try to do it a lot, ideally in a structured sort of way.

I often don't think in terms of intelligence or talent. Until you start getting to the limits of human performance, there are simply skills that some people have learned and that others haven't. It's not that I can't draw, it's that I haven't learned how to draw. There also seem to be meta-skills that make a difference: for example, the skill of translating "word problems" into mathematical equations. When trying to help classmates with high school physics, this was often their stumbling block.

Well put. There's a page in the Usual Error about this--basically, that almost every "can't" can be expressed more precisely as "haven't chosen to spend time learning to," or "haven't prioritized." And making a point of acknowledging those explicitly to yourself is empowering. When you actively reword statements like that, you're reminding yourself of your own agency instead of denying it.

You should distinguish between intelligence and being rational. One can be very intelligent without being very rational and vice versa. Intelligence is about how fast you think and how many abstract concepts you can juggle at once, that sort of thing. Rationality is about having good heuristics, making good decisions, that sort of thing. This site is primarily about being more rational rather than being more intelligent.

Ah, I think that I have been using the words as near synonyms. I understand the distinction, (now, I think) but what of increasing intelligence? Will study in general rationality help improve cognitive speed/capacity through the "compression effect" described above by multifoliaterose?

Obviously, I can't say for sure, but I personally think that increased rationality probably won't make you more intelligent in the speed sense. I do suspect that since both intelligence and rationality, being more rational does help you solve problems faster in a sense similar to how being more intelligent would. I also suspect being more rational is more helpful than being more intelligent; it's easy to use your big brain to shoot yourself in the foot.

What do you mean by intelligent? What are the specific things you'd like to do better or more easily?

Possibly annoying: Can you set aside your concerns about being intelligent? It's at least possible that they're taking up some of your attention which could be better spent on the things you'd like to be intelligent about?

I'm sorry if I came across as wanting to be "smart" for some sort of status reason. I just have become remarkably aware of how often I tend to "zone out" how long it takes me to solve problems or make decisions.
I guess the initial intent of the post was to see if anybody has been where I've been and found a way out. A slow decline into cognitive stagnation, followed by, hopefully, a renewed passion for learning.
My interests are usually focused on electronics and engineering, but I get distracted by music, fictional literature, movies, and computer games. I bounce around so much that I don't really gain much expertise in anything not related to work. My father always said that you should shoot for the moon so that you will at least hit something. I guess my "Moon" goal would be to learn enough to become a great inventor.

My apologies-- after I posted, I realized that what I'd said sounded unfriendly, but I wasn't sure what to change.

I didn't think you wanted to be more intelligent for reasons of status. That literally never occurred to me-- I tend to think of being intelligent as fun and useful, and probably tend to underestimate the status aspect.

What I had in mind was that "being intelligent" is a vague goal, and it might be useful for you to be more clear about the details so that you could pursue it more effectively. It also seemed to me that the other posters, though they came off as friendlier than me, were guessing about what you meant, and you could get better advice if you asked a less general question.

And part of being intelligent is knowing what you mean, so it seemed as though asking you for more precision might lead to good practice.

Here's one of Eliezer's essays that might be useful-- you don't need to be a magical person to have great achievements.

Two possible angles on your situation: Refuse to Choose by Barbara Sher-- I've just started reading this, but it looks promising. The premise is that the whole culture is oriented towards having single specialties, but some people's minds don't work that way, and they're happier and more effective pursuing the interests they've got. I haven't gotten to the parts about how not to be paralyzed by indecision and how to make a living, though.

Another possibility is that you're mildly depressed, and should be looking at getting more sunlight and exercise and such. Please note that I'm guessing from not very much information.

I don't think inventors start by learning huge amounts. They mix tinkering and learning.

I'm realizing that what looked like status issues wasn't so much that it looked as though you were trying to get high status by being intelligent as that it looked as though you were trying to avoid low status, and the low status issue was self-imposed.

At that point, I was twitching pretty hard, because while this may or may not be what's going on with you, I've got similar issues around competence-- again, conceived as a single lump of a trait. And if I hadn't been for this discussion, I wouldn't have realized that this is a big chunk of what I've been beating myself up about.

One common advice is that you shouldn't just passively read nonfiction, you should argue with it and try to push whatever it presents further or try to come up with counterexamples.

Keeping a private journal about stuff you read and think about might help. Writing things down forces you to make your ideas more explicit. Trying to summarize what a book or an article says will make you engage with it more. Exactly how much engagement a given text warrants is a hard problem.

Get comfortable with frustration. Deep learning something is much slower than reading about it, and you will be confused about it in the meantime. Assume that everyone goes through this but doesn't talk about it much. People who seem to know something very well have had a compulsion to keep digging at it even though it was initially confusing.

Choosing which confusing thing to keep engaging with and which to discard as nonsense is not easy beyond some commonly recognized nonsense clusters, but peer reviewed mathematicians and physicists tend to have a better than average track record in producing confusing but useful stuff.

Being able to get really interested in some big questions that have some meaningful scientific approach to them, like "how can living things do all the stuff they do if they're just built from atoms" or "what kind of Earth-based creatures could keep living and where after the sun has gone out in a couple of billion years" will help you get some direction at looking into a large amount of stuff with some purpose in what you want to get out of it. Reading things just for general erudition is great too, but the choice of things to start studying can get quite overwhelming. Reading more will also help you come up with more interesting questions, so try to make this a cycle instead of trying to come up with the perfect objective all at once.

Dude. You're not "pretty dumb." You're clearly (a) quite reasonably intelligent (b) good at hard work with a goal, given your achievements.

And frankly, you only need a moderate amount of (a) for (b) to be the deciding factor that will make you a success in life. Look how many posts there are here on how not to procrastinate, for example.

You know how to work to a goal, so what you need is not IQ, but a big goal.

You also have a very powerful correct instinct: find people smarter than yourself to hang around with. There's not much that enables complacency more than finding oneself the most interesting and successful person one knows. You know people like that. I sure know people like that. They're rather less interesting to anyone who isn't themselves.

(I'm definitely in the "moderately bright" rather than "searing genius" box. I still don't understand EY's "simple" explanation of Bayes. Somehow I muddle through with a facility with words.)

Is higher level reasoning "use it or lose it" ?

In some sense I think the answer to this is yes. This is, of course, all the reason you need to start learning now. I have no evidence for this, but in my experience learning becomes easier the more you do it (as in many things...).

Might I recommend Eric Drexler's guidelines for learning "about everything"? He suggests:

  1. Read and skim journals and textbooks that (at the moment) you only half understand. Include Science and Nature.
  2. Don’t halt, dig a hole, and study a particular subject as if you had to pass a test on it.
  3. Don’t avoid a subject because it seems beyond you — instead, read other half-understandable journals and textbooks to absorb more vocabulary, perspective, and context, then circle back.
  4. Notice that concepts make more sense when you revisit a topic.
  5. Notice which topics link in all directions, and provide keys to many others. Consider taking a class.
  6. Continue until almost everything you encounter in Science and Nature makes sense as a contribution to a field you know something about.

This type of learning is probably essential to understanding nature from a rationalist (=scientific) viewpoint, and you will be surprised how naturally the transition from "understanding little but knowing the words" to "partially understanding the words" to "understanding the words" occurs.

A good collection of hints, fits to my experiences in autodidactism. But you need a very good library at hand for such browsing (I used as teenager what a mathematician had designed as "Bibliothekskontinuum" ). "Don’t ... study ... as if you had to pass a test on it" is IMO very good too. Skimming connects with the subconscious procedures of memory and learning and works much better that one usually expects. In a similar way, I would suggest to take interesting looking books at home, laying them aside your bed and browsing like you please each evening before sleeping. That helps very much in identifying fitting themes and texts. But then one should stick on one issue and dig deeper, learn and think about a specific topic. After that, the cycle starts again, but on a higher level. Making notices is simplified by having a small paper notebook all the time around.

And, of course, it helps not to be frightened by sensing how small one's knowledge is. When I first entered the math library, I took a book by chance, and understood nothing, not even what the author told about. Then I tried an other one, with the same result. This continued until I came across a "Basic Number Theory" (by A. Weil) and could not believe that I even did not understand the first page. That was a bit too much for my taste - I stopped browsing then, sat down and worked systematically until I found out what to understand in which order for digesting that "Basic Number Theory" - a really tough job for me then. Some more than a few months later I happily finished it's last page and asked some professor lurking in the library for "the 2nd volume". He barely could supress laughter, as there was no "2nd volume", I already was in some sense at the top of the mountain.

But you need a very good library at hand for such browsing

The internet is basically all you need. Anyone with that has access to a whole bunch of resources, including Wikipedia, OpenCourseWare and Khan Academy. Journal articles are often less available, but it is increasingly easy to gain access to journal articles through a combination of Google Scholar, the researchers' websites, and open access journals.

No, for several reasons (drawn from experiences in math, I am sure in physics and other sciences it is even worse):

  1. Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount. The contents of an advanced level are only insufficient there, even some of the decades old and basic ones.

  2. Suitable and really good existing texts on the web can be found only if one knows very precisely what one is looking for. But someone who wants to learn needs to find the better stuff, which is in part outside his/her mental frame. In contrast, good texts, even if found, still become hard to detect because of the noise by shallow pseudo-substitutes.

  3. Browsing a real library makes your brain detect very quickly much more information and orientation, e.g. experiments (by friends who tutor at the local university) with beginning university students who were grouped and then asked to look for literature (in physics) by web/library only, for an hour, showed a very huge difference. An other experiment with students showed that students using a library have much better learning techniques that the other, but the later don't notice. Maybe it is a special case of this. On the interesting ways of how subconscious learning and "active" memory gets connected by seemingly irrelevant sensory inputs may play a role then, a famous extreme case here.

I haven't found my library particularly useful for the most part and I've bought very few books, but I've still largely managed to get up to speed.

University libraries are usually very good and have good long distance services. Have you looked for one? I would not buy books, as most of them one reads only once and science books are expensive. But one can suggest university libraries to buy them, I use those opportunities as the cheapest and fastest way to get them.

I'm in London - how does one get access to a University library as a non-student? Surely they'd want money for that?

If you're in London, and want access to some book that you don't otherwise have access to, you can can apply for a reader's card at the British Library. I don't know if this is useful, as you can then only access the works while in the Reading Rooms (and so, while the library is open), but I find the Reading Rooms in there are a good place to get work done.

They're also probably the only place that you'll be able to access recent journals without being at a university (or asking people who are at a university to get them for you, but that doesn't suit the "browsing" style of learning).

On the other hand, I pretty much agree that you don't really need access to physical books. In CS areas of maths, at least, most people tend to make a draft of their textbook available for free online.

I never had a problem with free access as non-student to a university library (and usually to it's computing center). I would suggest to contact the people and to try it. And are there no good other libraries in London?

£220/year. I can get books on inter-library loan, but it's slow and time-consuming.

Partly though it's that I'm still not convinced I need physical books enough to hurdle these barriers - what sort of books do you have in mind?

I find it hard to believe that there are no better solutions, esp. in London - do you really think London offers it's inhabitants so little? By far less than remote districts in Germany or the US?

Conc. books: A good way to orient is to define the field of one's interests and to look at the websites of seminars and workshops in good universities on those and related topics. This helps to formulate a few possible learning routes and with some luck you find the sources free online. But if you want to avoid to crash (because low altitude flights of learning always crash into dead ends) , you need to follow Ravi Vakil's advise: "(mathematics) is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning "forwards". (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)" BTW, here is a good collection of math related reading tips.

Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount.

How advanced are you referring to? There are many resources at the advanced undergraduate or beginning graduate level (this is biased towards computer science and math, so maybe this is not true for the sciences):

This is a link to a freely available 4-volume set on measure theory

Here is a book on information-theoretic approaches to machine learning and inference

Here is one on statistical learning theory

Here is one on a "computational" approach to classical mechanics (Hamiltonians and Lagrangians abound)

To get to the research level you certainly need journal access, which, as far as I know, is pricy for an individual, hence unrealistic. Hopefully more journals switch to open acccess.

In mathematics, I would call "advanced" roughly what is above the average of "Springer Graduate Text" book series level. Of course, I do not say that one finds nothing, e.g. the Bourbaki seminar series is very good for autodidacts, or this site. It is a bit like the difference between a complex organism and the bunch of isolated cells.

Also, regardless of how much raw intelligence you actually have, it may be better to try to maintain the attitude that successfully figuring out stuff is primarily about effort, not smarts. This psychology thing that's been floating around in various forms basically describes people as more eager to go at new challenges when they think their success is due to hard work, and people who define themselves by some idea of innate intelligence tend to get stuck at one challenge level.

Concentration, patience and determination that help with effortful study can also be trained, while it apparently isn't very easy to increase raw intelligence. The meditation stuff people are doing over at the other thread is a somewhat unorthodox approach, but it could help with concentration, noticing subtleties and being patient with obtuse material.

I have read Ayn Rands published works and loved the stories and most of the message. The characters always seemed like titans that were far and above me, but now, I've seen a character that is a bit more approachable.

I can't comment on your intelligence but as a general rationality issue this sets off warning bells. Fictional characters exist in fictional worlds. Their authors often construct those worlds and those characters to portray their worldviews most favorably. In general, relying on fictional characters to either interest one in any idea is potentially dangerous and taking ideas seriously primarily due to associated fictional characters is a good way to have a set of worldviews that reflect who happens to write well. Determining truth by who writes well is not a good epistemological system.

I completely agree with you that fiction should neither be a primary source of information and philosophy nor should it be my only source of inspiration. I don't like to think of myself as delusional, but I do like to be inspired by the works of others. I'm hoping to eventually develop my learning "tastes" so that I won't use fiction as such a crutch. What do you think?

I like to be inspired by the works of others as well. I just have to remember what isn't real about them!

When you find yourself impressed by fiction, it might be interesting to try to consciously think about what the author has glossed over, or the unrealistic leaps they take. Other commenters have mentioned that authors construct their works to be most favorable to presenting their worldviews--you might also note that, for example, Ayn Rand does not exactly include many technological details in her works on fiction: she doesn't know, the characters don't know. Much less impressive that way. What else are you impressed by that isn't real? And then--what's left that is real?

Not enough detail to make an assessment. I've only seen a single warning sign so I don't have enough data to see any general patterns. But I would suggest that in might help to pay particular attention to Sarah's comment and Jsalv's comments which seem relevant.

The tone of this comment seems to me unnecessarily caustic - the points that you make therein can be made in a more friendly and welcoming way.

The tone of this comment seems to me unnecessarily caustic - the points that you make therein can be made in a more friendly and welcoming way.

Can you point out specific aspects that seem overly caustic? I'm having trouble seeing that.

I can't comment on your intelligence but as a general rationality issue this sets off warning bells.

As written sounds like: No offense, but the fact you said this makes me think you're dumb.

Better: Fictional characters (especially those in works of propaganda) are designed to seem super smart, super rational, super moral and so on. Don't make yourself feel stupid by comparing yourself to impossible ideals - even Einstein didn't do things as impressive as Galt, the fact you feel inferior to them doesn't tell you much about how smart you are.

Interesting. I'm a bit confused as how it does that especially given that I specifically am talking about rationality not intelligence (and those are very much not the same thing). I can see that your rewrite is fine but I can't see what is bad about the original.

Sure.

The author asked "Do I have a chance at becoming intelligent?" It appears as though he's interested in becoming a stronger thinker/rationalist and that he's worried that he might not be capable. With this as context, the comment

I can't comment on your intelligence but as a general rationality issue this sets off warning bells.

could be read as "I have doubts as to your ability to be rational" which is both potentially misleading and potentially discouraging. I know that you may not have meant your comment with this connotation - just explaining how it initially came across to me.

A sample rephrasing that would have avoided this issue is:

"It's possible to improve as a rationalist and I think that your posting here asking for suggestions is a move in the right direction. While I'm glad that the works of Ayn Rand and Eliezer have gotten you interested in rationality, one initial suggestion that I have is to avoid placing too much stock in the appeal of fictional characters in informing your beliefs about the world. Fictional characters exist in fictional worlds. Their authors often construct those worlds and those characters to portray their worldviews most favorably, and an author's ability to do so has little to do with whether or not his or her worldview is correct."

Thanks. That makes sense.

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I agree with the other commenters, and I want to add that something like correspondence bias is probably making your judgments of LWers' intelligence higher than they should be.

From your perspective, a smart comment or post is a fait accompli - it's just handed to you with no clue as to its origin in the writer's mind. That origin is probably pretty damned humble. Behind most smart comments and posts on LW are, likely, several occasions of saying something dumb (here or elsewhere), being called on it (hopefully in a friendly way), and growing that wee bit smarter.

By the way, I think I recognize in your post the same exhilaration I remember feeling when I was first exposed to the rationality/science/philosophy corpus.

If I'm right about that, your concerns about your intelligence & educational background are probably irrelevant anyway. You, sir, are hooked. You can check out anytime you like, but you can never leave. ;)

As you are already inclined to read texts you expect to broaden your mental scope, I would recommend to move to real literature, e.g. a few novels by Dostoyevsky. Or this excellent and beautifull to read history of civilization. This, a study-in-a-novel used like a textbook in french history seminars, on the mindsets and times when modern science was born, may be a bit complex, but recommendable. Russel's History of Western Philosophy is a very good and usefull book too. Among the smaller texts, I found some of Putnam's Essays good here. Plato's dialogues are directly focussed on your question, as they are much more about igniting a process of thinking in the reader, than specific contents or statements they discuss. I would suggest his "Parmenides". But perhaps Descartes is more accessible for you. As you mention sci-tech interests, here finally a very good book relating to that.

I strongly disagree with those recommendations. Those are all old books. Old books are more prestigious, but they're significantly less educational and more confusing than new books on the same topics would be. Reading old books forces you to deal with the errors and confusions that later writers corrected, plus a culture gap and in some cases also a language gap.

Hmm... do you mean that for all the books mentioned, or do you make an exception for fiction like Dostoevsky & Plato? It seems to me that there aren't really good fiction textbooks to bring you up to speed quickly, the way there are in technical disciplines.

With a few exceptions, I think of fiction as being meant to entertain, not to educate, so there is no impartial criteria like "accuracy" to apply. How entertaining a class of books is depends heavily on the reader, so I don't expect my preferences to generalize.

No, that is wrong. E.g. Proust, Flaubert, Balzac, the Mann's, etc. had a very strong focus on the cognitive content of their writings. Weil, Grothendieck, B. Mazur, Y. Manin and many other science writers (I am pretty sure that it fits to Dirac too, but lack precise infos) spend much thoughts on literature, language and poetics. The idea you express fit only to low level texts of both sorts (lit/sci). But the question was about good texts which help to improve the reader's mind.

I would suggest that fiction does have some epistemic value too. The best novels/poems/etc. help you understand your own motivation and more easily put you in the shoes of others. Again, I'm only talking about the very best stuff, but for example Austen and especially late Frost have help me become noticeably wiser about interpersonal matters, and I'd estimate that it saved me about 10 years' worth of lived experience and mistakes. Maybe more, since I'm not an especially sociable person by inclination.

Of course, even if we agreed on this, that wouldn't establish whether you feel you need more of that sort of wisdom, and whether you have the prereqs to benefit from it,.

"novels/poems/etc. help you understand your own motivation and more easily put you in the shoes of others" That is only a very late and somewhat restricted idea. E.g. ancient greek science of history used novels etc. as epistomological tool, because the core of the things, that what really happened shows not in the surface of the facts, but has to be found and by poetic/artistic work (re)constructed. That was the reason, why their statues were colored like pop art, and why Thukydides' history book contains poetic inventions as quotes . It is a bit as if in a documentary on e.g. the cold war, suddenly Thatcher, Reagan and Gorbatchev would sing an opera. In contemporary american literature you have this e.g. in Tim O'Brien's The Things They Carried . Or in Reed's "Naming of Parts.". A friend (a great mathematician AND great intellectual ) allowed to illustrate that point by the poem there, scroll down.

Dear jimr..., your confusion could be cured by "reading" and "thinking". Books and other texts should be taken with respect of their content, nor their age, cover design, typeset, or other features. However, if you want a more recent one, I'd recommend this, as a kind of emergency aid in cases of acute confusion.

My recommendations are entirely caused by the quality of the texts and by their fitting to the question above. That some were written between the beginning and the middle of the 20th century is not quite an accident: That was the time of the science and university revolution in the US: The huge and sudden growth of science education then caused a strong demand on easy to read, unpretentious, well written and high quality introductory texts for the many students from rural, underdeveloped regions and equally undereducated kids from (then, when few and simple machines were in use) unskilled industrial workers.

Dear jimr..., your confusion could be cured by "reading" and "thinking".

This comes across as extremely condescending. I didn't say that I was confused, I said that old books in general tend to be confused. Particularly in philosophy, where clarity, accuracy and academic prestige don't seem to be well aligned.

Did I write that you said that you are confused? The books I recommended were written for the general readership, and I do not see how your remarks should apply to them. Which books would you recommend?

For Plato, I would discourage most people from beginning with the Parmenides. It's something of a difficult work, and a lot of people will find it much easier to begin with one of the dialogues that's about something in particular - best if it's a topic they already are curious about.

[-][anonymous]12y 0

Scott Adams has some words of wisdom on the subject:

I proudly include myself in the idiot category. Idiocy in the modern age isn’t an all-encompassing, twenty-four-hour situation for most people. It’s a condition that everybody slips into many times a day. Life is just too complicated to be smart all the time.

The other day I brought my pager to the repair center because it wouldn’t work after I changed the battery. The repairman took the pager out of my hand, flipped open the battery door, turned the battery around, and handed the now functional pager back to me in one well-practiced motion. This took much of the joy out of my righteous indignation over the quality of their product. But the repairman seemed quite amused. And so did every other customer in the lobby.

On that day, in that situation, I was a complete idiot. Yet somehow I managed to operate a motor vehicle to the repair shop and back. It is a wondrous human characteristic to be able to slip into and out of idiocy many times a day without noticing the change or accidentally killing innocent bystanders in the process.

[-][anonymous]12y 0

Quoting from Sections 7 and 8 of William Thurston's Mathematical Education essay titled "Mystery and Mastery" and "Competence and Intimidation"

Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through some process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics.

After mastering mathematical concepts, even after great effort, it becomes very hard to put oneself back in the frame of mind of someone to whom they are mysterious.

I remember as a child, in fifth grade, coming to the amazing (to me) realization that the answer to 134 divided by 29 is 134/29 (and so forth). What a tremendous labor-saving device! To me, ‘134 divided by 29’ meant a certain tedious chore, while 134/29 was an object with no implicit work. I went excitedly to my father to explain my major discovery. He told me that of course this is so, a/b and a divided by b are just synonyms. To him it was just a small variation in notation.

One of my students wrote about visiting an elementary school and being asked to tutor a child in subtracting fractions. He was startled and sobered to see how much is involved in learning this skill for the first time, a skill which had condensed to a triviality in his mind.

Mathematics is full of this kind of thing, on all levels. It never stops.

[...]

Similarly, students at more advanced levels know many things which less advanced students don’t yet know. It is very intimidating to hear others casually toss around words and phrases as if any educated person should know them, when you haven’t the foggiest idea what they’re talking about. Less advanced students have trouble realizing that they will (or would) also learn these theories and their associated vocabulary readily when the time comes and afterwards use them casually and naturally. I remember many occasions when I felt intimidated by mathematical words and concepts before I understood them: negative, decimal, long division, infinity, algebra, variable, equation, calculus, integration, differentiation, manifold, vector, tensor, sheaf, spectrum, etc. It took me a long time before I caught on to the pattern and developed some immunity.