The head cloth, the Sudarium, exists. It is kept in the Cathedral at Oviedo Spain. The blood stains on the Sudarium of Oviedo match the blood stains on the Shroud of Turin. Patterns of other stains also match the Shroud. The provenance of the Sudarium is known all the way back to 600AD or there about. There is a distinct handprint matching a semi-faceprint (not an image) on the Sudarium where someone placed a hand seemingly carrying a body in a prone, face-down position with the hand reaching to support the head, covering the face, from the top toward the mouth and over the nose.
The Sudarium of Oviedo
The Sudarium shows signs of then being twirled from opposite corners into a kerchief to form a long binding, then used to perhaps tie the jaws closed, passing under the chin and beard, behind the ears, then over the crown of the head, where it was tied to keep the jaw closed in death—a known requirement of Jewish burial practices.
In other words a cloth that was wrapped "about" or "around" the "head"/"face" (also words that are proper translations for the Greek word being translated), both of which are alternative meanings of the Greek word being translated. . . and would have been pulled off and discarded in a separate place as a resurrected Jesus walks away from the Shroud and other cloths, left lying in place.
The ONLY cloth that meets the Jewish traditional burial practice would be the kerchief rolled cloth for the binding of the JAW, not a separate face covering. . . which was only used if there were no other body covering according to the writings of the period. The other othonia, plural for burial cloths, would be other bindings used to keep the arms and legs from flopping out from the body, tied at the wrists and ankles, as the rigor mortis passed, and also as the processes of decomposition progressed. It was important to keep the bones as compact as possible for later collection, either to be placed in a separate bone box, an ossuary, if the family could afford one, or to be "gathered unto one's ancestors" by being tossed into a central ossuary in the middle of a family tomb with all of the previous ancestors' bones.
There is a huge gap between "reasonable representation of the Greek" and an accurate translation of the actual meaning of the Greek words with subtle understanding of what they meant in context of cultural usage.
For example, consider the following sentence:
"Thousands of Robin Williams' fans were slain in the aisles with his rapid fire improvisational ripostès to the quick jabs of the straight lines that came at him from left and right."
A future translator would be hard pressed to come to a proper interpretation without knowing
- Who Robin Williams was,
- That hyperbole could exaggerate numbers in news reports or reviews of performances for effect
- That it was from a review of a performance.
- What the slang term "fan" meant in the milieu,
- The idiom of "slaying in the aisles" was not meant to be taken literally, but was a tongue and cheek reference to the hysterical swooning reaction of teenage girls popular performers from period approximately forty years earlier,
- That "jabs" could refer to verbal assaults as well as fisticuffs,
- That ripostès could also be used in the translation of English phrases as well as French, and were not necessarily limited to the archaic sport of fencing, or the more serious art of swordplay,
- And, finally, that "straight lines" do not necessarily have to do with geometry, but were the lead-in set-ups for verbal humor.
All of this would have been culturally NECESSARY for our hypothetical future translator to even begin to attempt to decipher that sentence into anything culturally comprehensible to his future society.