@Article{Hinton1979,
author = {Hinton, Geoffrey},
title = {Some demonstrations of the effects of structural descriptions in mental imagery},
journal = {Cognitive Science},
year = {1979},
key = {},
volume = {3},
number = {},
pages = {231--250},
month = {},
note = {},
annote = {}
}
The rotations findings of Shepard and his co-workers show that "there is a changing internal representation whose intermediate states correspond to intermediate orientations of the object." [232] They show this with reaction times, and it is not proven that this means they are spatially isomorphic.
This paper uses the following methods: 1) asking questions about the relationships between parts of the images and 2) making subjects point out, in 3D space, locations for the structure's parts. This is better than making them draw because they cannot use the drawing being created to help them in producing the rest. (Summary author's note: the gesturing might give the same benefit.)
The hard imagery task in this paper involves imagining a cube facing you, putting a diagonal line through it, standing the cube up so that the diagonal line is vertical, and pointing out the positions of the corners in 3d space of the cube, which is now resting on one of its points. People tend to make two mistakes: They forget about 4 of the corners and they think they are oriented horizontally, rather than in a zigzag. [233]
Why is it so hard? 1) the diagonal has "components in all three mutually orthogonal directions defined by the initial position of the cube". 2) Subjects cannot look at an actual cube before doing it, and 3) it requires knowledge of the cube having eight corners connected by twelve edges. This paper proves this by doing experiments that isolate these three sources of difficulty. [234]
This paper argues that there may be several different ways of representing the spatial structure of an object, but only one can be thought of at a time. [235]
Since a reasoner can use symmetries to avoid duplicate data structures (Leeuwenberg 1971; Shneier 1978) the psychologically relevant measure of complexity would be based on the representation of the object rather than on the objective properties alone. [236]
Rock (1973) shows evidence that 2d represented objects have top-bottom directions, and spatial understanding of them depends on this. This paper suggests that this could also be true of 3d objects like cubes.
Spatial structures are represented as a hierarchy of parts, as argued in (Minsky and Papert 1972, Turner 1974, Palmer 1975, Marr and Nishihara 1978). [237] The face, for example, has a top-bottom orientation relative to the body, so that it remains constant even when the person represented is lying on his or her side.