Does the novel demonstrate that Fitzgerald himself suffered from Carroway's romantic illusions, and would the novel have been improved by passages that set the author at a distance from his narrator?
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Of course, this type of question is going to come down to personal preference. With this in mind and with full steam ahead, I would suggest that the novel would not have gained anything from Fitzgerald refraining from alluding to what he experienced and what he saw of the times.
Fitzgerald might very well have "suffered from Carroway's romantic illusions." Yet, this is what makes the work so much more poignant. There is a personalization that that is evoked when one reads the text. It becomes clear that Fitzgerald is writing about people he has seen, souls he has known. This helps to make the work more connected to both the time period and the reader. The time period becomes more vibrant in both its ornate elegance and tragic splendor when it is seen through the filter of Fitzgerald's own eyes.
It is difficult for him to turn away and become emotionally detached because he is of the time period, a time period that is so uniquely human in its desire to escape from the past and yet be tethered to it with a paralyzing fear of the future. I think that this poignancy of the time period is lost if Fitzgerald detaches himself from it. The painfully universal condition of Nick's "romantic illusions" are only enhanced when we understand that Fitzgerald suffered from them, himself.
It is this indulgence in the contingent splendor and implicit destruction within "romantic illusions" where the work is enhanced when seen from the characters' and author's points of view. This indulgence becomes something that is universally human, making the work more meaningful to the reader. The reader recognizes what is being offered is a depiction of more than just a time period, but rather of a depiction of what it means to be in the human condition. It is part of the reason that the work is still appreciated and enjoying a resurgence with the release of the new film. Fitzgerald's rendering of the human predicament is enhanced because we recognizes his presence in the drama. To remove that presence for the sake of authorial detachment takes meaning away from the work.