Space Invaders: Why you should never, ever use two spaces after a period. (2011)
slate.com
slate.com
In this sentence, the problem of one space after a period vs. two is shown at the start of the following one. Two spaces identifies when a new sentence starts as opposed to where the period character may be used mid sentence.
Go ahead, type that and watch as you have to undo capitalization on the word "two' because there isn't any ability to understand when one is mid sentence without there being two spaces to differentiate that from an otherwise mid sentence use of the period character.
Always two spaces.