This is quite an interesting discussion. I haven't watched any of the jazz episodes so I can't really comment on them but I do feel that I have some experience with both jazz and irish music.

My first instrument was the trumpet. I played in the concert band in high school and I also played in a jazz trio with some friends. I thought we we pretty good but no one was really interested in three white guys playing jazz back then (at least that was my impression).

I discoved traditional Irish music in the mid-seventies and have been involved in that ever since. Improvising in Irish music is quite different from jazz improvisation but that does not preclude interaction or influence between the two forms. There was certainly a connection in the form of dance. It has been said that slaves took note of Irish step dancing and the result was tap dancing. I also hear similarities in vocal music, say, between scat singing and lilting. And, getting a bit away from jazz, I hear similarities between Irish singing ornamentation and certain styles of black and white singers' ornamentation.

Here's another correlation. The banjo, originally an African instrument, found it's way into both Irish (tenor banjo) and old-timey (5-string) music.

I'll have to catch one of these jazz episodes and judge the series for myself.

Richard