A pantheistic society on a remote island in the Pacific find themselves in desperate need of fresh water. They invite Tokyo engineer Kariya to find the best sources of water on the island in order to pump it. As the story begins to unfold, Imamura lays out contrasting aspects of human nature by comparing Kariya's rational, scientific thought and the islanders' intuitive, spiritual vision of the world. (According to something said in one of the dvd's extra features, the island in the story was inspired by Okinawa, whose culture at the time still preserved some aboriginal characteristics and was different from most of Japan.)
Things begin to get more interesting when, to his utmost surprise, engineer Kariya is faced with some very primal needs of his own. At the same time, some of the island residents seem ready to put behind their adoration of the gods (sometimes dismissed as 'superstition') in order to concentrate on more practical matters. Others, like the Futori - an incestuous family regarded as beastly even by their neighbors' standards - prove to be particularly resistant to any change.
I believe the Japanese director is addressing some of psychiatrist Carl Jung's ideas regarding the unconscious and man's innate need for myth. In his book, `Man and His Symbols', Jung explains that in prehistoric times, man used to be completely intuitive and animalistic. Through a process of thousands of years, we've become more civilized and scientifically advanced. Yet, the primitive, emotional, non-rational aspect remains perfectly alive in our unconscious and cannot be fully tamed. This interior wilderness manifests itself in different ways, sometimes to our embarrasment, despite our best efforts to control it (a recurring theme in Imamura's films). It also surfaces in myth and dreams, in the form of a cryptic, archetypical language of symbols. Because our very existence and such a substantial part of who we are remain such a mystery to us, we use myth and a variety of symbols in an attempt to deal with these powerful, numinous forces within and without.
On a historical note, Imamura was allowed to work with a relatively large budget, but the film proved perhaps too strange and intellectual to please large crowds. This resulted in financial losses and the director vowed to never work with a large studio again.
Surreal and comical (although not outrageously so, like Imamura's last feature film, 'Warm Bridge Under the Red Bridge') 'Profound Desire of the Gods' leaves you with what could be described as a strong sense of psychic intensity.