Grandparents were Cousins?

John Hickman shares a larger than usual segment of identical DNA with my father, David.  The comparison at 23andMe looks like this:

23andMe autosomal DNA comparison

John caught my interest because the segment is three times larger than most of the segments that are shared with the hundreds of other DNA cousins.  In addition, he resembles my father and he is a lawyer who teaches politics- some of my (other) interests.

John Hickman is exploring whether his Hale line is related to Nathan Hale (1755-1776).  Nathan Hale is believed to not have had issue before dying at age 21, so if John's Hale is related to Nathan, it is through one of Nathan's ancestors.

My paternal grandmother, Beulah Cook, was descended from Solomon Brewer (1746-1824).  Nathan Hale was the second cousin, twice removed of Solomon Brewer.  Their common ancestors were John Strong (1610-1699) and Abigail Ford (1619-1688):  Great grandparents of Solomon Brewer and 3X great grandparents of Nathan Hale.

We need a paper trail connecting John Hickman's Hale line to Nathan Hale's line.

In the meantime, I tested my some more relatives.  Surprise!!!  A first cousin of my paternal grandfather shares a segment of DNA with a first cousin of my paternal grandmother.

23andMe autosomal DNA comparison
between my father's paternal cousin and his maternal cousin.
They match.  The question is HOW.

This is the same segment of DNA where John Hickman matches my father, so we compare John against my father and my father's maternal and paternal cousins.  John matches all of them.  The comparison at 23andMe looks like this:

23andMe autosomal DNA comparison.
John shares an ancestral line with David, David's paternal cousin, and David's maternal cousin.
The question:  which line?

This gives us some options: 

---The connection is still the Strong/Ford/Hale/Brewer ancestors- and unknown to us at this time, both of my father's parents are descended from these lines; OR

---The connection is through a different line- but still indicates that my grandparents were their own cousins; OR

---The connection is through lines of the maternal lines of the first cousins, which are not related to my father.

The common ancestor is someone I have not uncovered- someone waiting behind a brick wall.  Many of these ancestral lines lived in the same geographical area, so it is entirely possible and perhaps likely that the lines linked up in the past, split, and then rejoined when my grandparents married.

This is why I say that DNA testing gives us the answer first; we have to figure out the equation.

And it is John Hickman's DNA- a cousin of unknown relation- that provides us with the link between the families.

John is also a published author with his recent book, Selling Guantanamo: Exploding the Propaganda Surrounding America's Most Notorious Military Prison.  I find it fascinating how so many relatives are also researchers and authors.  John is especially fascinating because our potential common ancestors were deeply involved in the politics of their day.  Their actions created the records we use today to document our genealogies.