Albert Einstein's theory of general relativity is concerned with the
structure, or the geometry, of the universe. In order to describe the
universe, Einstein discovered that he needed four variables: three variables
to locate an object in space and a fourth variable describing time. This
system is known as space-time.
Because we are three-dimensional beings, how can we imagine four dimensions?
One interesting approach to visualizing four dimensions is to consider an
analogy of a twodimensional being struggling to understand three dimensions.
This approach first appeared in a book called Flatland by Edwin Abbott,
written around \(1884 .\)
Flatland describes an entire civilization of beings who are two dimensional,
living on a flat plane, unaware of the existence of anything outside their
universe. A house in Flatland would look like a blueprint or a line drawing to
us. If we were to draw a closed circle around Flatlanders, they would be
imprisoned in a cell with no way to see out or escape because there is no way
to move up and over the circle. For a two-dimensional being moving only on a
plane, the idea of up would be incomprehensible. We could explain that up
means moving in a new direction, perpendicular to the two dimensions they
know, but it would be similar to telling us we can move in the fourth
dimension by traveling perpendicular to our three dimensions.
Group members should obtain copies of or excerpts from Edwin Abbott's
Flatland. We especially recommend The Annotated Flatland, Perseus Publishing,
2002, with fascinating commentary by mathematician and author Ian Stewart.
Once all group members have read the story, the following questions are
offered for group discussion.
a. How does the sphere, the visitor from the third dimension, reflect the same
narrow perspective as the Flatlanders?
b. What are some of the sociological problems raised in the story?
c. What happens when we have a certain way of seeing the world that is
challenged by coming into contact with something quite different? Be as
specific as possible, citing either personal examples or historical examples.
d. How are A. Square's difficulties in visualizing three dimensions similar to
those of a three-dimensional dweller trying to visualize four dimensions?
e. How does the author reflect the overt sexism of his time?
f. What "upward not northward" ideas do you hold that, if shared, would result
in criticism, rejection, or a fate similar to that of the narrator of
Flatland?
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