A "strange" physician who wore a "hat of Afric" was a character in an alternative draft of William Shakespeare's play The Winter's Tale. He was clearly based upon the Eleventh Doctor and his inclusion was the reason that an extract from the draft appeared in the Shakespeare Notebooks.
He appeared in Act V Scene III, set in the chapel at Paulina's house, when Paulina and Leontes examined the statue of Hermione, who was actually the real Hermione. The physician believed it to be a "good job" he arrived in time and described Paulina as "as bad as Julius Grayle" in that she kept curtained statues hidden from view. He then called upon everyone else present to "keep looking on the scene", warning them that their lives depended on not turning away or even blinking.
In response, Leontes expressed his thoughts that "the fellow is sore vexed at heart" which caused the physician to lose confidence. He questioned if the current year was 1904 or if his watch had stopped and realised Hermione was not a real statue at all. He asked what was going on, giving "jolly japes" or party games as potential options, before apologising for spoiling the big surprise and the climactic reveal. He apologised again, especially to "Miss Statue" and for the abandonment of his iambic pentameters, and then awkwardly shuffled away, departing the scene. (PROSE: The Winter's Tale)