Coincidental re-introductions to established acquaintances suggest that one draws one's acquaintances from a hypothetical, homogeneous ''small world'', not to be confused with an acquaintance chain or an acquaintance volume. The world's size can be estimated from the coincidences, given an estimate of the acquaintance volume. A typical Freeman-Thompson phonebook test score and a dozen coincidental introductions give an estimated ''small world'' of about 1,300,000 persons. Even single cities are much larger, so this result points to the fragmented and insular structure not just of acquaintanceship volumes, but of the milieux from which they are drawn. Conversely, assumptions about the size of the world from which acquaintances are drawn can be combined with information on coincidental introductions to shed light on the size of the acquaintance volume.