Well, the French say faire la figue, the Italians fare la figa, and the Spanish dar la higa. (Make or give a fig.) The Elizabethans called it the figo or the fig of Spain; cf. Henry V, III. 6. The OED suggests that it was a poison fig. The fig is a gesture made with the hand in a fist and the thumb between the index and middle fingers. It represents the feamle genitalia, as the digitus impudicus (or bird) represents the male. Both are signs of contempt. It seems a small stretch from that contempt to nothingness. Remember Hamlet and Ophelia:

HAMLET
Lady, shall I lie in your lap?

OPHELIA
No, my lord.

HAMLET
I mean, my head upon your lap?

OPHELIA
Ay, my lord.

HAMLET
Do you think I meant country matters?

OPHELIA
I think nothing, my lord.

HAMLET
That's a fair thought to lie between maids' legs.

OPHELIA
What is, my lord?

HAMLET
Nothing.