From David Ricardo making a fortune buying British government bonds on the eve of the Battle of Waterloo to Warren Buffett selling insurance to the California earthquake authority, the wisest investors have earned extraordinary returns by investing in the unknown and the unknowable (UU). But they have done so on a reasoned, sensible basis. This essay explains some of the central principles that such investors employ. It starts by discussing "ignorance," a widespread situation in the real world of investing, where even the possible states of the world are not known. Traditional finance theory does not apply in UU situations.