Set in 1960s Dublin, a fatherless eight-year-old boy who feels alienated by his family, escapes his reality by deciding he's been sent from Mercury to study life on Earth. His fantasies mirror the life of his hero, Flash Gordon, from the serial he watches each week at the local cinema. His escapades result in dilemmas that drive his mother to such distraction that she turns to the boy's strange uncle for help.

Barney Snow (Wood) wakes up in a hospital with no memory of why he is there. All he has is his name and some vague recollections of a car crash. He assumes that he is in the hospital for his amnesia and settles in to try to recover. He quickly realizes that all of the other residents of the youth clinic are all suffering from terminal conditions. Everyone except him. Mazzo, another patient (played by Joseph Perrino), asks Barney to play host for his visiting twin sister, Cassie. Barney immediately falls for Cassie (played by Rachel Leigh Cook), and strives to get better, if only to be able to see her in a setting outside the hospital. He is determined to learn about his past so that he can make her a part of his future. In his explorations, both inside his shattered memories and through the physical rooms of the hospital, Barney starts to realize that there was no car crash. Doctor Harriman (known as The Handyman to her patients), induced amnesia in Barney to make him forget everything in his past. Barney demands to know why and Harriman tells him he has cancer. The experimental procedure that Barney is undergoing is attempting to test the power of the mind in fighting cancer. Barney had volunteered for the treatment, hoping for a miracle cure. The theory was that if Barney didn’t know he had cancer, if his entire memory of it was eliminated, the body might stop creating the cancer cells. The explanation Dr. Harriman gives comes from an old urban legend that bumblebees are aerodynamically incapable of flying. Based on weight ratios to wing power and wind resistance, the bumblebee should be incapable of flight, yet, the theory says, the bumblebee doesn’t know that, so it flies anyway. This statement also gives the film its name. Torn between his hope for a cure and his desire to continue his budding relationship with Cassie, Barney is forced to choose whether to go through the amnesia procedure again or remain with the memories and knowledge he has thus far acquired.