Admiral Drake
Admiral Drake is a divine figure in the book, a higher self of Mr. Popper who determines Mr. Popper's progress toward maximizing his potential. He gives the unruly, difficult gift of a penguin to Mr. Popper to begin this journey, because Mr. Popper must strengthen his resolve and his sacrificial powers in order to keep the bird alive, and then Drake rewards him with a symbolic adventure, a transcendentalist mission to the North Pole. The quest is a mystic symbolic, referring to self-actualization.
Captain Cook, the penguin
When the first penguin arrives, it is a loaded gift, because the bird is very sick, having been badly cared for. This symbolizes the callous relationship between socialized mankind and nature. The rigid order of society makes Mr. Popper feel trapped, longing for adventure in the wilderness, so the penguin symbolizes his essential connection to nature. It even symbolizes his id.
The penguin family as life
Penguins reproduce, Mr. Popper quickly learns. Admiral Drake's gift has now expanded, because there are 12 penguins when all is said and done, two grown ups and ten little baby penguins that eventually grow up themselves. The penguin family is a symbolic reminder that human families are part of animal nature, and the penguins symbolize blind obedience to instinct, whereas Mr. Popper has his mind to plague him, confusing his instincts. They symbolize the basic purpose of life: To survive and maybe procreate.
The jail sentence
The scenes where Mr. Popper gets put in jail are difficult for him to endure, and they show something symbolic about his experience of life. In another way, Mr. Popper feels trapped already, even when he's not in jail, because he is trapped in melancholy. He is trapped in a small town that doesn't really understand him. He is trapped in fear and regret, and all these things are on his mind when he is arrested for an honest mistake. Fate is symbolized in the jail sentence.
Sacrifice and reward
Through motif, the symbol of sacrifice is depicted. Mr. Popper gives money to build a proper home to the penguins. He gives his comfort to live in the cold. He sacrifices his reputation, and his safety, and aspects of his own family life. He sacrifices freedom by getting arrested by people who don't understand the penguins or their meaning in his life and story. But at the end, the North Pole is a symbolic reminder that his sacrificing was not in vain. He gets to have an adventurous life now.
