Intelligence isn't what you know, it's how you know it. Anybody can memorize facts, but not everybody make an inference resulting in a valid conclusion.
I view the the pattern of one's thinking as layers and in each layer, all thoughts are connected like a web. The topmost layer is our most present thoughts. It is these we make the little voice in our heads vocalize. The deeper we delve, the more subconscious and analytical the thoughts become. Our brain is like a computer, it's constantly processing information. It's how much of this information one can access which determines their intelligence. Particularly ignorant people are only able to access the uppermost, and thus most obvious, layers of their thinking, while incredibly intelligent people can access their layers to a great depth. Thus, the process of "deep thinking" results in very different conclusions when comparing one to the other.