Actually, speaking as a modern, practicing typographer, it is quite true that most typographers and typesetters nowadays DO practice the "one space after a period" rule whenever setting type with computer software, which for most of us is most of the time. In handset type these days, since it's an artisanal situation rather than a mass-production situation, the only rule you'll get us all to agree on is, What looks most beautiful at the moment?Manjoo is correct about the origin of the two-space rule in typewriters. But he probably already knows that newspaper type on lead-based Linotypes was proportional in some cases and monospace in others. I remember using both kinds of type, as demos, when I was setting type on a Linotype at The Ann Arbor News. And also in the very early days of computer typesetting. (Remember TeX, anyone?) The big change back to one-space came with the advent of the personal computer and the installed fonts. I could pull out back issues of the long-defunct but really important magazine of the times, Desktop Publishing, and show at least one article on this topic, with the consensus agreeing with Mr. Manjoo.
Besides, how cares what doctors and programmers think about setting type? It's not their field of expertise—although since the advent of desktop publishing it does seem that every amateur suddenly thinks they know all there is to know about type and typesetting. They're wrong, of course. LOL