I've learned from Fuller's writings that doing the impossible is the only way for humankind to change and evolve because we have already done what is possible.
To prove this point, read Erik Larson's page-turner "Devil in the White City" as he tells the story of architect and visionary D. J. Burnham as he develops "The White City" (1893 Chicago's World Fair). He did the impossible and topped Paris' previous exposition that introduced the Eiffel Tower and created an aesthetically magnificent, architecturally impossible, catalyst for change in an unthinkable amount of time despite the formation of Unions and the Chicago elements.

Going for the impossible helps us step out of what is known and draws out creative solutions and totally new ways of doing things. Daniel J. Burnham's story is one of intention, but intention toward fulfilling his vision for the impossible which eventually changed the world.