"I'm very much afraid of being mad - that's my one fear"

The quote is most likely referencing the fear of losing one's sense of reality or rationality. Sting, like lots of others, most likely worries the possibility of losing control of his mind and ending up being outrageous. This worry might come from the stigma connected with mental illness or the worry of losing oneself completely. Seething or ridiculous often carries negative connotations, leading one to believe that they may be turned down or ostracized if they show such behavior. Maybe Sting is likewise mindful of the truth that he relies heavily on his mind and creativity, making the possibility of losing his mental professors specifically intimidating.