'Life of Pi' is about psychological and physical survival. It is also about the nature of storytelling. The hero has to deal with a horrific, overwhelming, heart-breaking tragedy. To protect his sanity, he retreats into fantasy, much like the heroine in 'Mulholland Drive'. By detaching himself from his emotions, he can objectify them and deal with them more successfully. He has to control his fear, his anger, and his sorrow. If he does not bring these feelings under control, they will devour him. The Tiger is his own base nature and his higher self must train it, if they are to coexist and survive. Once he returns to society, his base nature recedes back into his unconscious; the Tiger returns to the jungle. Pi is also about storytelling and, in the end, the storyteller prefers the fairy-tale struggle of the soul overcoming Nature, rather than the starker, more brutal reality.
Lord Ganesh, the elephant headed: Is shown in the very first image of the movie, and the rest of the movie is basically a metaphorical representation of the journey of young boy and his own life's struggle with his own "removal of obstacles", of ego (Richard Parker). It's brilliant, and Ang Lee takes courageous liberties from the original novel, but it works, it works! Study, the story of Ganesh, The Remover of Obstacles, just view the beginning image... the elephant head was placed on his head by Shiva, who had decapitated him, but the elephant head (elephants are revered for wisdom, all-knowing of who they really are) and the tools that he carries in his 4 hands: the ax, the harpoon type tool, the om symbol, and the bowl of fruit (the sweetness of self) are all interwoven throughout the movie. The rat which depicts ego, fast, unaware type behavior is what Ganesh rides on and is what Richard Parker ate (his ego). The movie also does a beautiful 'overall' of all religions, going from west to east... Hinduism, Buddhism (happy Buddhist) to the Japanese who just want to know the truth, no epic symbolic animal story (which is a major difference between India (Hinduism) and Japan (Zen/budhhism). they just wanted the facts.. but in the end we like Pi's story better... and so it goes with God, so it goes with religion. religion is full of symbolic metaphors, Christianity is no different, but Hinduism, the tale of all those Gods is beautiful and Ang Lee pulls it off beautifully.
The wonderful thing about Life of Pi is that it can be interpreted to mean many things, depending on the viewer. My personal interpretation is that the main purpose of the story is to confront the question of whether or not there is a God in a unique way. At the end of the story, we are presented with two possible explanations for Pi's journey: a fantastic, almost unbelievable tale with the animals, as well as a grim, unspectacular tale with humans. I believe the animal story represents faith/religion, while the people story represents science/fact. In life, everyone eventually has to decide what they choose to believe in, or not believe in. Yann Martel is trying to make the point that while religion and faith in a God is quite frankly hard to understand and inconceivable to us sometimes, as it is the Japanese men who listen to Pi's story in the hospital, the alternative, a world without God and based on solely science/fact that we can understand may not be as great as we thought it would. Personally, I believe what the audience saw, the story with the tiger, is what really happened. Furthermore, as someone who thinks that story represent faith, I think that Richard Parker represents God. And the reason he never said goodbye on the shore is because although the tiger left Pi, God never did.