In exhibitions held since the 1960s this painting has usually appeared with the simple descriptive title Two heads (Zwei Köpfe). However, the painting was originally titled Imaginary bridge (Imaginaire Brücke) when it was first exhibited at the Grosse Berliner Kunstausstellung, Berlin, in 1926, and in Hoch's first solo exhibition at Galerie de Bron, The Hague, in 1929. The original title seems far more appropriate to the personal imagery of the painting.
The two heads in Imaginary bridge have the appearance of anonymous wooden mannequins. There are certain peculiarities about these heads, however, such as the brow of the male head folding over the long, straight nose, and the bobbed haircut of the female head, which invite us to identify them as caricatures of the artist herself and Raoul Hausmann (1886-1971), with whom she had a stormy personal relationship from 1915 until 1922-23.
Hausmann made the mannequin head a central image of his own work. In his sculpture The spirit of our times 1919 (Musée National d'art Moderne, Centre Georges Pompidou, Paris) Hausmann attached various gadgets to a real wooden mannequin head to express the robotic existence he perceived in contemporary city-dwellers. In his drawing Portrait of Felixmüller 1920 (Nationalgalerie, Berlin), he drew the head of the artist as if reduced to mannequin impersonality, sitting on a square base exactly like those seen in Imaginary bridge. For Hausmann the mannequin head was a vehicle for satire. In Imaginary bridge Höch seems to have taken over Hausmann's satirical image and turned it back on its author, perhaps to describe an uneasy personal confrontation.
According to the artist's niece, Eva-Maria Rossner:
The meaning of the painting clearly points to Hannah Höch's unfulfilled wish to have a child by Raoul Hausmann [a wish apparently thwarted by the fact that Hausmann was already married]. On Hausmann's neck in the painting we see the image of a naked woman who stands screaming at a man who moves hastily away. This refers to Hausmann's wife who is openly outraged that he is fleeing from her to go to Hannah Höch. The question mark [also painted on Hausmann's head] presumably points to the fact that Hausmann does not know what to do. Between the heads is seen the longed for child across the imaginary bridge; the sun's rays emanating from Hausmann penetrate deeply into Höch's head. From the head of Hannah Höch, fir trees emerge, a symbol of her birthplace, the Thüringer Wald.1
Michael Lloyd & Michael Desmond European and American Paintings and Sculptures 1870-1970 in the Australian National Gallery 1992 p.155.