Minute Physics decided this issue is important enough to make a video about even though it has nothing to do with physics, so here is why you’re reading ‘Ye Olde Shoppe’ the wrong way: in the olden days, the sound “th” had its own letter, Þ, called thorn. This letter appears in Scandinavian languages and was probably introduced by the Vikings, during numerous invasions of England during the 9th and 10th centuries (Old Norse and Old English were similar languages, both having come from Northern Germany). During this time, words like “this” and “that” would have been written “Þis” and “Þat”, if Old English were anything like Modern English.
Clik here to view.

The first page of the Old English text of Beowulf, with words containing the letter thorn circled
Then the English were conquered for the last time, in 1066 by an entirely different sort of Vikings: Normans, who had settled in the part of northern France now known as Normandy, who spoke French and who instituted it as the language of the aristocracy in England. Over time, the ruling class did adopt English, but it became heavily influenced by French. These French-speaking English didn’t like the letter thorn, so they started using “th” instead of “Þ”, and it obviously caught on. But for centuries after the Norman conquest, thorn was still used.
In fact, it was still in use when the printing press was invented 400 years later, but since printing presses came from continental Europe, the typed alphabets were Latin and didn’t include the letter thorn and other Norse runes. Having to make do with what they had, English writers figured that ‘y’ looked close enough to “Þ” and started using it instead. And that’s how “Þe olde” became “ye olde”. Interestingly “ye“, pronounced like you’d think, actually meant the same thing back in those days as “y’all” does in the South now.
Clik here to view.

This taco house will not put up the French spelling of "þe"
All Scandinavian languages eventually followed suit with English and started using “th” instead of “Þ” — except for Icelandic, who still uses thorn and another Old English letter called eth (ð). As for English, there’s little chance of it going back to “Þ”, especially since words like “thorn” would become “Þorn” and probably be either read as “born” or “porn”. And just for confusion, there’s a letter called sho (Ϸ) that looks very similar to thorn, but comes from the Greek alphabet and has nothing to do with English.