Jean-Luc Godard's 1956 film Alphaville makes several references to Jorge Borges's essay, "A New Refutation of Time," in which Borges makes an argument against the existence of time. 


"Every instant is autonomous. Not vengeance nor pardon nor jails nor even oblivion can modify the invulnerable past. No less vain to my mind are hope and fear, for they always refer to future events, that is, to events which will not happen to us, who are the diminutive present. They tell me that the present, the “specious present” of the psychologists, lasts between several seconds and the smallest fraction of a second, which is also how long the history of the universe lasts. O better, there is no such thing as “the life of a man,” nor even “one night in his life.” Each moment we live exists, not the imaginary sum of those moments.
....
Let us consider a life in which repetitions abound: my life, for instance. I never pass the Recoleta cemetary without remembering that my father, my grandparents, and my great-grandparents are buried there, as I shall be; then I remember that I have remembered the same thing many times before; I cannot stroll around the outskirts of my neighborhood in the solitude of night without thinking that night is pleasing to us because, like memory, it erases idle details; I cannot lament the loss of a love or a friendship without reflecting how one loses what one really never had...
These tautologies (and others I shall not disclose) are my whole life. Naturally, they recur without design; they are variations of emphasis, temperature, light, general psychological state. I suspect, nonetheless, that the number of circumstantial variants is not infinite: we can postulate, in the mind of an individual (or of two individuals who do not know each other but in whom the same process is operative), two identical moments. Once this identity is postulated, we may ask: Are not these identical moments the same moment? Is not one single repeated terminal point enough to disrupt and confound the series in time [(or) the history of the world, to reveal that there is no such history]? Are the enthusiasts who devote themselves to a line of Shakespeare not literally Shakespeare?" http://thefloatinglibrary.com/2009/02/13/a-new-refutation-of-time-selections-j-l-borges/

Borges plays with the concept of time and the dichotomy of the individual in two of his short stories: "Borges and I" and "The Other." In the latter, Borges coexists as himself as a young man and an old man. "While the younger man cites his romantic vision about a brotherhood of man, the older Borges reveals his doubt about the existence of a single man. Following incorrect information that the first provides, elder Borges concludes that it is a real episode for him, but a dream for the younger." http://en.wikipedia.org/wiki/The_Other_(short_story)

This duplicity also brought to mind the unusual experiences of Philip K. Dick.
"Throughout February and March 1974, Dick experienced a series of visions, which he referred to as "2-3-74". As the visions increased in length and frequency, Dick claimed he began to live a double life, one as himself, "Philip K. Dick", and one as "Thomas", a Christian persecuted by Romans in the 1st century AD." http://en.wikipedia.org/wiki/Philip_K._Dick