No one, to my knowledge, has suggested that the image must accelerate and decelerate or that the relation among torque, angular momentum, and angular velocity has a,1 analogue in the mental rotation case. Of course it may tum our that it takes subjects longer to rotate an object that they imagine to be heavier, thus increasing the predictive value of the metaphor. But in that case it seems clearer that, even if it was predictive, the metaphor could nor be explanatory (surely, no one believes that some images are heavier than others and the heavier ones accelerate more slowly).

Nor do such theories provide a ready account for the equivalence of the slopes of the reaction-time functions for the picture-plane and depth pairs. For, in order to explain the dependence of reaction time on angular difference, we must suppose that the features that are being compared are the features of the two-dimensional drawings, which differ more and more with angular departure, and not the features of the three-dimensional objects, which are the same regardless of orientation.

Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.

:5) In mental process, the effects of difference are to be regarded as transforms (i.e., coded versions) of events which proceeded them. The rules of such transformation must be comparatively stable (i.e., more stable than the content), but are in themselves subject to transformation.

In spite of some unresolved issues, the close match we have found between mental rotation and their counterparts in the physical world leads inevitably to speculations about the functions and origin of human spatial imagination. It may not be premature to propose that spatial imagination has evolved as a reflection of the physics and geometry of the external world. The rules that govern structures and motions in the physical world may, over evolutionary history, have been incorporated into human perceptual machinery, giving rise to demonstrable correspondences between mental imagery and its physical analogues.

But after a while, some higher brain-center cut in, and I began being mentally able to fit the wildly changing scenery into a coherent four-dimensional whole. The process was really no more devious than the process by which one integrates the two hundred lines of a TV screen into a single two-dimensional image . . . which in turn is interpreted as a three-dimensional scene. It's just a matter of processing information. Impossible? I saw.

Rotations in 3-dimensional Euclidean space ... form the poster child of group theory and are almost indispensable in physics. Think of rotating a rigid object, such as a bust of Newton. After two rotations in succession, the bust, being rigid, has not been deformed in any way; it merely has a different orientation. Thus, the composition of two rotations is another rotation.

People seen by the mind are exactly different to things seen by the eye. They grow smaller and smaller as you come nearer down to them, whereas things become bigger.

Two normal observers viewing the same object from the same place under the same physical circumstances do not necessarily have identical visual experiences, even though the images on their respective retinas may be virtually identical.

The subject detects the presence and interrelationships of the basic components of one of the two-dimensional drawings - particularly, the variously oriented straight lines, the several types of vertices by which they are connected and, presumably, something of the structural relationships among these components within the two-dimensional pattern. Then, on the basis of some higher-level processing of these extracted features and their interrelationships, an internal representation, code, or verbal description is generated for each picture separately that captures the intrinsic structure of the three-dimensional object in a form that is independent of the particular orientation in which that object happens to be displayed.

[W]e saw that mental representation is about percepts, mental simulations, conceptual representations... [C]onceptual representations give us concept spaces, and... these concept spaces... give us an interface for our mental representations we can use to address and manipulate them, and we can share them in cultures. [T]hese concepts are compositional. We can put them together to create new concepts. ...[T]hey can be described using higher dimensional vector spaces. They [vectors] don't do mental simulation and prediction, and so on, but we can capture regularity in our concepts with them.

Rotation through a fourth dimension can’t affect a three-dimensional figure any more than you can shake letters off a printed page.

The subject of a gestalt demonstration knows that his perception has shifted because he can make it shift back and forth repeatedly while he holds the same book or piece of paper in his hands. Aware that nothing in his environment has changed, he directs his attention increasingly not to the figure (duck or rabbit) but to the lines of the paper he is looking at. Ultimately he may even learn to see those lines without seeing either of the figures, and he may then say (what he could not legitimately have said earlier) that it is these lines that he really sees but that he sees them alternately as a duck and as a rabbit. ...As in all similar psychological experiments, the effectiveness of the demonstration depends upon its being analyzable in this way. Unless there were an external standard with respect to which a switch of vision could be demonstrated, no conclusion about alternate perceptual possibilities could be drawn.

We live in a three-dimensional world, and our brains are organized in three dimensions, so we might as well compute in three dimensions. ...Right now, chips, even though they're very dense, are flat.