The character known as the Old Man, sometimes called the Mysterious Old Man, is an elderly figure who appears throughout the anime as a quiet, enigmatic presence rather than an active participant in the main events. He appears to be around eighty years old, with white hair and black eyes, and is first glimpsed by Tsukiko Sagi from a bus as he crouches on the ground near what turns out to be a hospital, drawing complex, mathematical-looking equations in chalk. These chalk markings are more than idle scribbles; they relate directly to the attacks carried out by the boy known as Lil' Slugger, and the only calculations clearly shown in the series correspond to the assaults on Tsukiko and on Yuichi Taira. His presence is later explained when he becomes a hospital patient in a wheelchair. The journalist Akio Kawazu caused a traffic accident involving the Old Man, leaving the journalist indebted to the Old Man's son and obliged to pay the man's medical bills, which become a point of contention between the son and Kawazu. For most of the story, the Old Man remains hospitalized.

In personality, the Old Man comes across as senile, cryptic, and detached from ordinary concerns. He rarely speaks in a straightforward way and instead offers puzzling remarks, such as telling someone they must dance with a bunny. In the series opening sequence and in the prophetic segments that close each episode, he appears in a tuxedo, laughing and delivering an ambiguous prophecy connected to the next episode, reinforcing his role as a figure who seems to see beyond the surface of events. Within the fantasy world of the character Makoto Kozuka, he is framed as an ancient master, which fits his generally mysterious and almost oracular quality.

The Old Man does not have conventional motivations in the sense of personal goals or desires. His function is closer to that of an observer and transmitter of the story's underlying pattern. He is able to predict and identify the victims of Lil' Slugger, and his chalk equations operate as a kind of record or blueprint of the delusion spreading through the city. In this way, he acts as a narrative device that signals how the events of the series are deterministic and cyclical, with the paranoia repeating itself in new forms across generations.

His most significant relationship is with the detective Mitsuhiro Maniwa. Maniwa feels a strange connection to the Old Man from their first interaction, and this develops into a bizarre bond. Late in the story, Maniwa's radio begins receiving signals associated with the prophetic Old Man, and in the twelfth episode, just before the Old Man dies, he tells Maniwa where to discover the truth about how Maromi and Lil' Slugger are connected. The Old Man's death coincides with the revelation of Tsukiko's hidden past, and his passing transfers his role to Maniwa, who is shown in the final episode drawing the same kind of equations on the ground that the Old Man drew at the beginning. This succession confirms that the Old Man is part of a repeating cycle, and that the role of the cryptic observer will continue even after he is gone.

As a character, the Old Man shows little personal development, since he functions more as a symbol and a catalyst than as a person with an arc. His significance grows, however, as the story progresses, moving from an odd street figure seen in passing, to a hospitalized patient whose debts tie into another character's story, to a dying prophet whose words and actions set the final revelations in motion. His notable abilities include foreseeing and identifying Lil' Slugger's victims, appearing in the delusional or fantastical spaces of other characters, and existing in a kind of dreamlike realm outside linear time, from which he can observe the larger pattern of the city's collective paranoia. Through these abilities, he stands apart from the other characters as someone who understands the structure of the story unfolding around him, even if he never explains it directly.