Bowditch's education
Bowditch is forced to forgo a formal education at a fairly early age to help his family financially. Typically, when kids drop out of school so young, their knowledge base stagnates, and they don't become successful. Ironically, despite the challenges he faces, Bowditch breaks the mold and becomes highly educated and incredibly successful.
Logic and rationality
Bowditch approaches all of the problems he deals with logically and rationally, which his math studies taught him. However, this approach (which allowed him to become so successful otherwise) doesn't work for him in the political sphere.
Bowditch's apprenticeship
Bowditch is bound to an apprenticeship as an indentured servant, which is a position that typically enables the apprentice to learn and grow. However, this indentured servitude prevented him from attending Harvard and formal schooling, which would have allowed him to learn quite a bit about the world and other subjects.
The sea
Despite experiencing quite a bit of trouble navigating, many sailors and captains at first do not recognize the value of Bowditch's work. However, they only recognize the value of Bowditch's work after they have experienced troubles at sea or after their voyages.