Last night Ruth asked about how the various senses of words like organ, organism, and organize are related. It turns out that they go back through French and Latin to a Greek root organon, which also had a variety of meanings; the OED lists "tool, instrument, engine of war, musical instrument, surgical instrument, also bodily organ esp. as instrument of sense or faculty." The original sense in Greek was "that with which one works."
This root, in turn, is an ablaut variant of ergon, meaning "work," which shows up in words like energy and ergonomics. This word is cognate with the English work, and both it and ergon go back to the Proto-Indo-European *werg.
It seems that organize was originally used in the sense of "to give organic structure to" or "to arrange or form into an organ or body" and then generalized into its current sense of arranging or systematizing.
