For the whole history of handwritten and printed documents in the European Latin languages, with different glyphs having different horizontal widths, one ordinary character space after a full stop has been standard practice. It only changed when that so-limited bastard interloper, the typewriter, came on the scene briefly, with its awful single-width character alphabets, that something had to be done to mark the space between sentences in a different way, otherwise the text became too difficult to read. This was the only reason for two spaces after a period. It's never been the practice in documents produced by scribes or printers, which has a far longer history than the typewriter.
Now that the typewriter has largely been banished to the dustbin of history, there's no justification for putting two spaces after a period, it's a mistake, or an eccentricity, whatever you want to call it. As an earlier poster pointed out, the single space after a period is slightly wider than a normal word space. This follows the scribal tradition.
After I retired from the railway I ran my own business as a typesetter/typographer (going back to my first love!), and have academic qualifications in the field; I love everything about printing, typesetting, its history and conventions. To be asked to put someone's own ideas, research, knowledge, poetry, whatever it is, into print to present them to her audience, to make her text pleasurable to read and easy to find information in it, is the greatest privilege.
For insights into typography and the development of the scribal and printing conventions, Robert Bringhurst's The Elements of Typographic Style is a good read. He's a poet and author as well as a printer, and writes about his subject with a love I really appreciate.