A sober exploration. How did we come up with the word "cocktail" for a, well, for a cocktail?

Great question. But no one knows. The origin of the word cocktail is a mystery.

What we do know, is that the earliest known printed use of the word in the context of a drink was in The Farmer's Cabinet on April 28, 1803:

The Balance & Columbian Repository

"Drank a glass of cocktail—excellent for the head...Call'd at the Doct's. found Burnham—he looked very wise—drank another glass of cocktail."

Three years later, we find the earliest definition of the word in the May 13, 1806, edition of The Balance and Columbian Repository, a publication in Hudson, New York. A reader posed the question, "What is a cocktail?" The witty answer:

"Cocktail is a stimulating liquor composed of spirits of any kind, sugar, water, and bitters—it is vulgarly called a bittered sling and is supposed to be an excellent electioneering potion, inasmuch as it renders the heart stout and bold, at the same time that it fuddles the head. It is said, also to be of great use to a democratic candidate: because a person, having swallowed a glass of it, is ready to swallow any thing else."

Clearly, whatever the exact recipe, the effect was very similar to our cocktails today. Huzzah for that.