I wish the author would have spelled out one, concrete, specific abstraction which he knew, which helped him understand Dijkstra's algorithm.
I propose an alternate explanation: The author found it easier to understand Dijkstra's algorithm the second time, because he struggled with it the first time.
And that is because there is no "lowest level." Anything can be explained in terms of something else--every word in the dictionary is defined using other words. We don't learn anything bottom-up like this, it's a more holistic process, a hermaneutic circle.
