[zackmorris]

This is why abstraction is so important (came here to say the same thing).

Wikipedia is factually correct but often lacks insight. It puts the learner at the wrong level of abstraction, limiting how much more can be learned.

For example, a sine wave looks complex, and has a great deal of inherent complexity around stuff like transcendental functions. But it's just a spiral, the side view of a radius arm turning through time along the x axis with a period of 2 pi radians and a radius of 1.

But if readers don't know that, they get stuck at the abstraction of trigonometry instead of the far deeper relations between things like complex numbers and higher dimensions.

That's why I think it's difficult to learn quantum mechanics without a teacher. It just ends of being a bunch of matrices and handwaving that makes little sense intuitively.

This is why the debate around higher education is silly IMHO. Sure, someone can avoid college and get hands-on experience in application. But they'll miss out on the theory and abstraction that allows them to transcend their area of expertise. That's good enough for most people, but most likely won't result in true mastery. No schooling is not better than schooling if one wants to do important work.