The story follows a Dutch anthropologist and his wife and child who are invited to the house of a communist millionaire in Patagonia (an area located in Chile and Argentina) to study the last two surviving Yachanes Indians.

[2][3][4][1] The film unfolds as an ethnography and starts in the Netherlands at the beach, where Jean (a Dutch anthropologist) and his wife Eva meet a communist millionaire (Narciso), who later invites them over to his house in Patagonia to study the last two surviving Yachanes Indians.

The language seems to be reinvented daily and Jean struggles with his comprehension of it, reading its structure in a complex mathematical sense.

Other subplots in the story involve a love triangle between Jean, Eva and Narciso and the addressing of fluid gender identity of Anita, who is clearly struggling whether they should identify as male or female.

It seems calculated to increase the sense of cultural dislocation, perhaps evoking Ruiz's feelings as a Chilean exile in Europe.

The cinematography (done by Henri Alekan) of On Top of the Whale can be classified as typically Ruizian; the use of chromatic colored filters, unusual composition and framing and tableau vivant images.

The film scholar Michael Godard describes it as "the oft-noted visual excess of the film, the use of artificial coloured filters and other trick devices seemingly unnecessary for a film about language can perhaps best be situated; in the sense that the anthropologist's attempts at comprehending the 'world-view' of the Indians by deciphering their language will inevitably fail since not only is their language untranslatable from its original context but also any such encounter is inevitably a game in which the 'objects' of ethnographic inquire are dissimulating themselves and this dissimulation is inevitably subject to further distortions in its interpretations".

[7]Several themes that come forth in On Top of the Whale include Life, Survival, Love, Reality, Illusion, Marxism and Civilization.