★★★★★
[First Watch]
By one of the universe's simple, mad coincidences, shortly before plonking this on I consumed probably two of the most ideal pieces of media needed in order to form a really specific interpretation that I don't think that I could have cooked up any other way; the first, Chunk Palahniuk's audio commentary for Fight Club, and the second? A timelapse video of a tarantula shedding its skin.
I was so engrossed throughout, but the last minute of the film just crashed into my brain reminding me that THIS is why I watch movies.
In my interpretation, Adam and Anthony need to be the same person. His mother is the main indication. She mentions him trying to be an actor and his troubles with women, neither of which are things that are shown to be relevant to "Adam". She also mentions his new apartment in her voicemail message at the beginning, and I believe that is in reference to the "Adam" apartment where he takes women; his mother knows about it and disapproves. Importantly, I think a hint to the audience is her insistence that she has one son and he has one mother.
Also, the matter of the scar. It would have a different implication if they had a birthmark in the same place, but the scar indicates that they led a shared life at least up until a certain point, that they may have diverged after receiving the scar but I don't think so. Otherwise, how much of a coincidence would it be that even though they have very different professions, they have the same hair cut and beard also?
The wild thing is, his mind is so warped that invents a scenario that he is cheating on his affair partner in a way that makes sleeping with his own wife illicit and exciting.