From this Slate article:
Hundreds of years ago some typesetters would end sentences with a double space, others would use a single space, and a few renegades would use three or four spaces. Inconsistency reigned in all facets of written communication; there were few conventions regarding spelling, punctuation, character design, and ways to add emphasis to type.
Every modern typographer agrees on the one-space rule. It's one of the canonical rules of the profession, in the same way that waiters know that the salad fork goes to the left of the dinner fork and fashion designers know to put men's shirt buttons on the right and women's on the left. Every major style guide—including the Modern Language Association Style Manual and the Chicago Manual of Style—prescribes a single space after a period. (The Publications Manual of the American Psychological Association, used widely in the social sciences, allows for two spaces in draft manuscripts but recommends one space in published work.) Most ordinary people would know the one-space rule, too, if it weren't for a quirk of history.
However, a double-space after period rule is still the default in some software, and most famously in TeX. This implies that the transition may not be as “complete” as the Slate article implies. So, my question is: can we somehow date the end of the double-space?