What do the floating bananas and the cultivated bonsai trees illustrate in Life of Pi?

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The reference to floating bananas, which the two Japanese investigators insist couldn't have floated and the bonsai tree, which Pi equally insists is preposterous, as trees are not tiny and cannot be carried, draw attention to the way in which the story challenges our notions of what is possible and impossible. 

A key theme of this story is the way in which Pi's tale clearly challenges our notion of what is reality and what is illusion. Pi presents us, and Mr. Chiba and Mr. Okamoto, with a story that is so incredible it is almost beyond belief. When the two Japanese men challenge the reality of his story, arguing that it is scientifically flawed and that no scientist would believe him, note how Pi responds:

These would be the same who dismissed Copernicus and Darwin. Have scientists finished coming upon new plants? In the Amazon basin, for example?

What started off as a simple exploration into what causes the sinking of the ship becomes a fascinating philosophical and scientific debate about the limits of science and the ways in which we perceive and understand reality. The floating bananas and the bonsai tree illustrate that often reality is something that does not fit into our strictly defined notions of scientific fact. This novel insists that we throw aside our skepticism and embrace the limits of our knowledge through acceptance of what may be beyond our understanding.