The phrase "man the world" means to take charge and assume responsibility for the world around us. There are various synonyms that can be used to express this idea, such as "take control", "lead", "govern", "direct", "manage", "take charge", "oversee", "shoulder responsibility", "command", "dominate", "guide", "supervise", "assure", and "keep in check". Each of these words conveys a similar sense of power and duty to improve the state of the world and its inhabitants. It is up to each individual to decide how they will man the world and make a meaningful difference in the lives of others.