p194
Semicircular canal and spatial dimension (footnote 7)
Although we may conclude that the shape of the semicircular canal furnishes the the basis of 3D space, but whether it is Euclidean or not is not simple. As we know well, our intuitive metric in the vertical direction and that in the horizontal direction are not the same. The following paper suggests that how freely our head moves relative to our body contributes
The orthogonality of the three representative directions.
Michael D. Malinzak et al.,
Locomotor head movements and semicircular canal morphology in primates
PNAS 109 17914 (2012).
What is known before this paper: Most prior research has compared subjective assessments of animal `agility’ with a single determinant of rotational sensitivity: the mean canal radius of curvature (R). In fact, the paired variables of R and body mass are correlated with agility and have been used to infer locomotion in extinct species.
Morphologic features of the canals influence rotational sensitivity, and so it is hypothesized that locomotion and canal morphology are functionally related. This paper introduced a new canal metric variables (the variance from 90\deg among angles between
canals of one side of the head (90var),) that are highly correlated with head rotation (weighted mean of angular velocity magnitude) and independent of body size.
Animals with fast head rotations have semicircular canals oriented more nearly at right angles to one another within each ear (i.e., they possess a low value of 90var).