Why do we say "It's a small world"?

Meaning:

For such a big place, you run into people you know surprisingly often

Background:

In English, this saying has been traced to 1886 but, based on the fact that the expression can be found in any number of different languages, it seems likely that it predates the 19th century.

For example, according to the nice people at omniglot.com, all these expressions translate broadly the same:

French: le monde est petit
Arabic: al'aalam sagheer (phonetic)
Croatian: Svijet je mali
Kurdish: donyayeeki bechuka (phonetic)
Welsh: Mae'r byd yn fach

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