The purest case of an intelligence explosion would be an Artificial Intelligence rewriting its own source code. The key idea is that if you can improve intelligence even a little, the process accelerates. It's a tipping point. Like trying to balance a pen on one end - as soon as it tilts even a little, it quickly falls the rest of the way.
Do not flinch from experiences that might destroy your beliefs. The thought you cannot think controls you more than thoughts you speak aloud. Submit yourself to ordeals and test yourself in fire. Relinquish the emotion which rests upon a mistaken belief, and seek to feel fully that emotion which fits the facts.