The Tanque Dimension is a parallel universe which may be the source of much of the Pilgrim's power.
One Pilgrim theory suggests that Pilgrim is able to tap into another script, into a parallel dimension, the Tanque Dimension. That human brain is able to script information creating realities. The dimension holds all the information for everyone who ever lived, and Pilgrims are able to tap into it. Pilgrims who come near quasars and pulsars are able to tap into these scripts written by other pilgrims who navigated through them. This dimension may be what allows Pilgrims to continue to physically exist (even after others 'perceive' death), and also rewrite reality around them, such as projecting themselves to more than one place or all places at the same time.