The Interpunct reference article from the English Wikipedia on 24-Apr-2004
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Interpunct

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Interpunct is a small middle dot used for interword separation in ancient Latin script. The dot was vertically centered, e.g. "DONA·NOBIS·REQVIEM".

Interpuncts were perhaps the first consistent visual representation of word boundaries in a written language. (Ancient Greek, by contrast, had not developed interpuncts; all the letters ran together.)

When a wave of enthusiasm for all things Greek swept ancient Rome, the use of interpuncts died out, presumably being inadequately fashionable.

The use of spaces for interword separation didn't appear until much later, roughly 600-800 AD.