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Musing, Alice, over the linked terms --"species," "special," "specific"--that you found, I went to the OED (a favorite way for me to think about, and through, such patterns). Turns out that all these words derive from the single Latin term "species," meaning "appearance, form, kind, etc.," which derives itself, in turn, from "specere": "to look, behold." Riffing on this connection, I'd  say that it is actually the act of beholding, of looking attentively @ our world, which makes it (or "specific" aspects of it) special. So many examples of this, but one very striking illustration might be the photography of Rosamund Purcell, who can see--in the skull of a hydrocephalic child--a head opening like a flower: