Scholars of ancient languages will immediately spot that this word has something to do with a wasp, since sphex is the name of that insect in classical Greek. In more modern times, it has been given to a genus of solitary digger wasps. Therein lies a tale.
When such a wasp returns to its burrow with a paralysed cricket to feed its grubs, it will leave it at the entrance while it checks inside that all is well. It then comes out again and drags its prey inside. This gave a naturalist with a cruel streak an idea for a bit of behavioural research. He moved the cricket a little way away while the wasp was in its burrow. When it surfaced and found its cricket was missing, it searched for it and returned it to the entrance to its burrow. It then repeated its search of the inside. No matter how many times the cricket was moved, the wasp repeated the same steps robotically without working out what was going on.
Douglas Hofstadter recounted the story in one of his Metamagical Themas columns in Scientific American in 1982 and coined sphexish for this unthinking deterministic or pre-programmed behaviour, in which the wasp was at the mercy of its instincts and environment. In a book derived from his columns, Hofstadter later suggested that humans might likewise exhibit such robotic behaviour:
To the extent of having an individual style, any artist is sphexish — trapped within invisible, intangible, but inescapable boundaries of mental space.
Metamagical Themas, by Douglas Hofstadter, 1985.
So far as I know, the term hasn’t appeared in any dictionary, but it has some circulation among behavioural psychologists. Daniel Dennett created the related noun sphexishness in 1984. Hofstadter coined antisphexishness in his book for the opposite state: free will.
Thanks to Barry Rein for telling me about this word.