It's not really arbitrary. When do you ever see a professionally-produced newspaper, magazine, or book with two spaces after a period? You don't, because it is technically incorrect and anything that has been professionally typeset will not have two spaces after a period. Of course in today's world of online publishing and blogs, you will see many people using two spaces simply because they don't know the proper way to typeset a document, although (as one poster pointed out) MS Word and other word processing programs should flag the extra space as an error.