Nowadays we tend to think of the stream of thoughts inside each person as being composed of discrete units, which we call "thoughts". In the book The Information, the author suggests that prior to the invention of writing, we (people) may have not thought about thinking in this way, as having discrete parts. Considering the flipside of this, then, the author is suggesting that we may have thought of one's stream of thoughts as being continuous.
It feels weird to me to think about either situation being always and exclusively the case (only composed of discrete units or fully continuous). It feels more likely that our streams of thoughts may be both in the way that a rope is composed of many overlapping strands (discrete units) of varying lengths that hold each other in a continuous unit. This also attests to that there can be layers of thoughts, or multiple dimensions (or levels of abstraction).