I am completely new to the lesswrong site but have read a few of the blogs and think that I could learn a lot from this site. I think it is a good thing to have a basic knowledge of many fields, but I also think that it is important to have a in depth knowledge in the basic principles of science first. For example a person who has a broad knowledge in witch craft and taro cards could be very smart with what they know, but all they really know is fiction and without first having an in depth knowledge of scientific principle to test what they learn against, other wise people can be lead to believe anything.
Related to: The Simple Math of Everything, Your Strength as a Rationalist, Teaching the Unteachable.
Eric Drexler wrote a couple of articles on the importance and methods of obtaining interdisciplinary knowledge:
This topic was discussed intermittently on Overcoming Bias. Basic understanding of many fields allows to recognize how well-understood by science a problem is and to see its place in the structure of scientific knowledge; to develop better intuitive grasp on what's possible and what's not; and to adequately perceive the natural world.
The advice he gives for obtaining general knowledge feels right, even for studying the topics that you intend to eventually understand in depth: