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.)

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.

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.

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!

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.)

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.

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?

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.

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.

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.