The Love Song of J. Alfred Prufrock

This is probably the longest and the most confusing poem I have ever read. Thankfully, in this post, I will only focus on a few things I noted while reading this detailed and complex poem. One line that stood out to me was line 120: "I grow old...I grow old...I shall wear the bottoms of my trousers rolled." This line was remembered because I found it to be amusing and a little ramdom. However, when I started to think of reasons why the author used these words, I finally understood what was meant by them. As one grows old and elderly, the physical structure tends to weaken and shrink. SInce this happens often, the trousers worn for years by a woman or man who is growing old suddenly seem wider and longer. Therefore, an old man or woman must "wear the bottoms of [the] trousers rolled." I have yet to figure out exactly why this line is in the poem, but hopefully it is a critical point in the work of literature.
Additionally, in lines 37-48, the speaker seems to be comparing himself to Prince Hamlet of William Shakespeare's play, Hamlet. The speaker is very indecisive and does not know whether to act and "show himself" to the "universe," or to take his time without rushing into things. In Shakespeare's play, Hamlet is also very indecisive about an issue concerning his father's death. Hamlet wants to act and avenge the death, but he is unable to take any action and instead lets time pass by. This comparison and part of the poem is a very interesting passage that may give one insight as to who or what the speaker is.
Furthermore, in lines 111 - 119, the author alludes to the play Hamlet, written by Shakespeare. However, the speaker says that he is not Hamlet, but "an attendant lord." He will "advise the prince, an easy tool...glad to be of use." In lines 118-199, the speaker says: "At times, indeed, almost ridiculous- Almost, at times, the Fool." I believe the speaker thinks that he is foolish like Polonius in the play Hamlet. Polonius also tries to give advice to the prince and is glad to be of use by the king and queen in the play. Polonius is an extremely ridiculous man whom Hamlet calls a "fool." This leads me to believe that the speaker is comparing himself to Polonius. I will soon find out!