When a person externalises an idea on a piece of paper, those concretised aspects of the thought can be used as a foothold from which to advance in a chain of thought. There is a limit on how many elements can be held in a mind at once, but if a piece of paper is leveraged as a storage or even calculation system, far more complexity can be reached by the thinker. This models a process of contemplation and writing, the thinker switching between modes to reach an entirely new position.