There is a moment early in the series (I've never been able to find it when looking, but I have a clear memory of it; perhaps from an "alternate take") where the Doctor answers, "Caligari." But, since William Hartnell had a way of laughing even while he was serious, it's not entirely clear -- "in-universe" -- how much he was joking.
If one attempts to comprehend the series as a whole, the very insignificance of this extemporaneous muttered quip, forgotten in the selenium past, suggests (to my mind, at least) an eerie significance.
If the Doctor were a sleeper, lucid, avatar of his own larger self, all of his powers are explained. The recurrence of themes like dream-weaving, virtual reality, perception filters, charactes like Daleks, Cybermen, Dominators (Sontarans). Mathematically, all infinities are equal to each other. As Yoda says, "No difference; only different in your mind." Dimensions are relative, right? But relative to what? To the synthetic unity of apperception, subject to the receptual conditions of time and space (thus spake Kant). In a fiction, the apperception of the auditor is functionally projected upon the protagonist (one "identifies" with the hero). The quest of the dreamer is always to discover his or her "true name," upon recollection of which one instantly awakes.
Also, the relativity of time allows one to return to any point just after they last left (as Farscape tells us, "It's going backward that screws the pooch."). So just as soon as the Doctor remembers what he came for, what he's supposed to do, he may yet return home to the Time Lords (they existed then, right? and he remembers them. It has been shown to us that these are the necessary ingredients to "bring something back"), perhaps picking up Susan Foreman (named after the scrap-yard in Ep. 1) along the way; And then, of course, becoming the Valeyard.
So what I'd like to see as the crowning of the series is the real backstory. The Prequel, Prologue, Intro. What's he running from?