I find philosophy dense and difficult to understand ... if you could recommend a book or webpage
In that case I'd suggest starting with:
(try it and see if the style/approach appeals to you, if not no worries) or
http://www.amazon.com/Popper-Modern-masters-Bryan-Magee/dp/0670019674
(This summary book on Popper is only 115 pages. The easiest to read book option.)
Open-mindedness and curiosity are one thing. Raw native intelligence is something different. I might be above average on the first two, but I expect I have less of the second that the average LWer. For example, I would love to understand the math of quantum mechanics, but it's hard for me and really learning it, if I decided to, would likely be a multi-year endevour. Same with computer programming...I would love to actually be able to do it, but it doesn't come super easily.
I think you're mistaking subject specific skills for raw native intelligence. Being good at math and programming isn't what intelligence is about. They are specific skills.
BTW I believe most educational material is quite bad and makes stuff far harder and more confusing than necessary. And for quantum physics in particular the situation is pretty terrible (if you want to learn it in depth; there's OK popular science books for a lower level of detail). The situation with programming is better: there's way more self taught programmers and more non-academic efforts to try to create material to help people learn programming, which I think are often more successful than the stuff schools put out.
I would equate intelligence with basically how good one is at learning in general, without giving priority to some fields. I think open mindedness and curiosity are crucial traits for that. A lot of people aren't much good at learning in general, but have a specific field or two where they do OK. They can be impressive because in the area where they are rational they gain a lot of expertise and detailed knowledge. But I don't regard them as more intelligent than more broad people.
You find math hard to learn. But most mathematicians find various things hard to learn too, such as (commonly) social skills. Most people are more impressed by math knowledge than social knowledge because it's more common. Most people learn social skills, it's nothing special. Yet that doesn't really imply math is harder. More people try hard to learn social skills. And more people are alienated from learning math, at a young age, by their teachers (especially females).
Whatever topics one is bad at learning, I don't think it's normally caused by intelligence itself. I think raw native intelligence is itself a misconception and that the hardware capabilities of people's brains don't vary a lot and the variance doesn't have much practical consequence. Rather, I think what people call "intelligence" is actually a matter of their philosophical theories and rationality, especially either general purpose ideas (which allow one to be good at many things) or ideas in specific fields people are impressed by (e.g. math).
What I think causes people to have trouble with math, or social skills, or other things, besides the inherent difficulty of the subjects, is irrationalities, caused largely by external pressure and cruelty. Those people who have trouble learning social skills were teased as children, or had trouble finding friends, or something. They did not try to learn to interact with others in an environment where everyone was nice to them, and they could fail a bunch of times with no harm coming to them, and keep trying new things until they got it. With math, people are forced to do things they don't want to like unpleasant math homework and math tests. They don't get to learn at their own pace for their own intrinsic motivations. This commonly alienates people from the subject. Causes like these are cultural.
I would equate intelligence with basically how good one is at learning in general, without giving priority to some fields. I think open mindedness and curiosity are crucial traits for that.
Maybe I was above average in, say, my high school graduating class, but I doubt that is true of the Less Wrong community. People wouldn't be here if they lacked that degree of open-mindedness and curiosity.
...They don't get to learn at their own pace for their own intrinsic motivations. This commonly alienates people from the subject. Causes like these are cultural.
http://vimeo.com/22099396
What do people think of this, from a Bayesian perspective?
It is a talk given to the Oxford Transhumanists. Their previous speaker was Eliezer Yudkowsky. Audio version and past talks here: http://groupspaces.com/oxfordtranshumanists/pages/past-talks