I think there are several different ways to look at Joyce’s use of the fugue in the “Sirens” episode. Perhaps it is because I had the idea of movement and paralysis on the brain, because of my paper, but I saw this theme playing out and I grasped on to that idea. In a fugue, the original melody is stated, and then is restated again and again throughout the piece in different voices, with variations. There is a lot of movement in it, but it remains centered for the entirety of the piece on that originally stated melody, which is often quite simple. Therefore, it can be questioned whether or not there is any real progress made throughout the piece, because it all goes back to that original idea. Given that this is a major point of concern for Joyce in Ulysses, I think that he might be using the fugal technique as yet another way to call into question the nature of progress.
The text itself is much like a fugue, in that at the beginning we are given fragments that later come up in the narrative. The words and phrases themselves work like a fugue. We are given a name or phrase, and that is added on to and played with often as pops up again and again in the text. Although the word or phrase is repeated often, it usually has been changed in some way. Just like a fugue, there is movement in this, but there is also a return to that original idea. This is much like the idea of the mythic method. Ulysses is a retelling of The Odyssey. Although there are many obvious differences, there is a sense in which everything is being repeated in a way. Everything seems to be caught in the cycle of history.
Questioning whether or not progress is being made has been a major part of the novel so far, and I think by using this fugal technique in the episode of the sirens, Joyce is warning against getting caught in the cycle. In the myth of the sirens, the siren song serves to lead men astray. The repetition of the past, being caught in the same cycles of history, is dangerous in Joyce’s mind, and can lead men astray in the same way. Although I am not sure that he offers any sort of remedy, I did get the sense that Joyce was warning against getting caught up in those cycles. Or he is at least attempting to make us aware of the danger.