How many dimensions is this?
In the past couple of weeks, I’ve been posting about seemingly simple mathematical problems that defy intuition, and where the answers we find on the internet turn out to be shallow or hard to parse. For a taste, you might enjoy the articles on Gödel’s beavers or on infinite decimals. Today, let’s continue by asking a simple question: how many dimensions does a line have? A trained mathematician might blurt out an answer involving vector spaces or open set coverings, but there’s no fun in that.