Dissonance of juxtaposed ideas, and particularly those just at the edge of chaos, can be some of the most fruitful places for learning.

Attempting to resolve these frictions can generate new knowledge.

This is what commonplace books are meant to do. Record this knowledge, allow one to juxtapose, and to think and write into new spaces.

It's also important to look more closely at things that don't cause dissonance. Is it general wisdom that makes them true or seem true? Question the assumptions underneath them. Where do they come from? Why do they seem comfortable? How could one make them uncomfortable. Questioning assumptions can lead to new pathways.

An example of this is the questioning the final assumption of Euclid (the "ugly" one) which led mathematicians into different geometry systems.