"How smart is the essay reader? If I include some puns and literary references, will they go over the reader's head?"
Your essay idea sounds clever, but it actually might be too clever. If your essay has 10 of these literary references and puns, and if the reader needs to get all of them for your essay to work, then you might be asking too much. What percentage of readers will get all of them? It's like swinging for a home run. Though the essay readers might all be smart and experienced, that's not to say they have the background they might need to fully appreciate your essay.
My main question for you, however, is whether this type of essay is the most effective way to reveal your personality. If you write this essay well, your wordplay and references will show the reader you're smart - but is that the main thing you want to communicate? From what you've written, it seems like the real question is how to convey your humor/creativity. Maybe exploring a smaller subset of these references/puns would be a better way to do that.
How did you think of these references/puns? Why did you think of them? How does that thought process make you different from other people? How does this wordplay reveal a different perspective/philosophy on life? You might add depth to your essay by making your puns/references do double work: showing you're clever and showing how you're creative/funny.
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Jon Perkins holds a B.A. in English from Stanford University and a J.D. from Harvard Law School. He helps students with their college, law school, and medical school applications.