only vaguely familiar with the concept of the fourth dimension, and
your fascinating essay in the January Natural History will encourage
me to investigate it. I believe that you are away of some points that
I would like to make and ignored them for brevity's sake, but let's
the overriding proposals of the essay was that we cannot view both sides
of an object at the same time. Actually there are several ways that
this would be accomplished, the simplest, by the used of a septum and
mirrors. A more easily-understood way would be to use two fiberoptic
endoscopes, each focused on opposite sides of the object, and each viewed
simultaneously by opposite eyes as follows (I'll use a sphere since
my drawings of cubes, viewed on opposite corners, appear confusing).
however, that even though we have provided the brain with the simultaneous
view of each side of the object, we have not enhanced the three-dimensional
view into a fourth dimension. In fact, with no common detail visible
to each eye, the percept is either diplopia if the two sides are too
dissimilar, or fusion to a single, flat, two-dimensional disc.
has many individual tactile sensors, which contribute to the 4-dimensional
mental image of the penknife that the brain is programmed to interpret.
If A-square were a Cyclops, he could not have appreciated the new stereoscopic
view provided by the sphere; there are monocular clues to depth, but
the 3-dimensional appreciation requires binocularity. Similarly, we
are limited by the bilaterality of the visual system to a maximum view
of three dimensions. By my calculation, four eyes, on flexible stalks,
and the necessary brain functions to interpret the images would be the
minimum requirement. (But you know, I really do not have any trouble
visualizing this when I conceive of it this way, with four eyes and
four endoscopes, perhaps because of my training. And I do recognize
that we are minimizing the spatial elements in these examples).
are two issues that I need to investigate regarding the 4th dimension.
First, why is it necessary to understand it in visual terms, particularly
human vision? Is this just a prejudice based on our human emphasis on
vision? Why isn't the hand/penknife example adequate, as it appears
to be to me? Secondly, is this all very simplistic? Do we also have
to incorporate a view from both insides as well as from the outside
of an object to attain appreciation of the fourth dimension?
I better go dig out my old textbooks or hit the library.