We hear copy editors, but more often typesetters whining about the two spaces contributing to the vertical river thing. Look. If you want the reader to logically follow your argument on the page and you respect your own thought process enough to trust the reader to come back and reread your sentences, then use the the two spaces. Individual sentences are easier to find that way. If all you care about is achieving a uniformly gray page, then try the single space.
I can still picture the side of the page (left or right) and approximate position on the page of passages of text I read as an undergraduate in certain books. I looked up just now two such passages I could think of and still have the books and both were from books with extra space between sentences. The pages of such books have distinct features. If all pages just look evenly gray memory is destroyed or not created to begin with in the reader. Either way two spaces is better.
The issue at hand has been with us for a very long time, but at the core it has nothing to do with keyboards or quantities of "spaces." It has to do with the display of symbols on printed pages. And in particular the failure to adequately include display information into the logical encoding of the symbols as distinct from their appearance on a page.
If we are just looking at words on a page, the question might be simply, should the white space between words be equal to the white space between sentences? If both sentences and words are demarcated only by space, then the answer must be no, for some method is needed to distinguish the logical structure of a sentence from a mere grouping of words. Given that we have additional sentence ending symbols, the answer should be effortless, but the symbols are vague. Ages ago, someone fucked up and used a period to indicate an abbreviated series of characters. Because of this, the character series period-space cannot sufficiently mark the logical ending of a sentence.
To restate the original question: "What character (or series of characters) is correctly used to indicate the end of a sentence structure within a series of symbols?" The correct answer is, and must by necessity always be, "The end-of-sentence-character(s)." Unfortunately we are confronted with an Adamsian Total Existence Failure with respect to such a standard.
Should the white space between an abbreviation ending in a period and the following word be equal to the white space between the end of a sentence and the following sentence? I think the answer is clearly no. Why would they be? The ending of a sentence indicates the end of a logical construct. The ending of an abbreviation is something wholly of a different character. If you must choose between ending a sentence in one or two spaces, use two.
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