A fascinating book. Mind boggling, intriguing- brings up a horde of questions...
There's something problematic about the whole idea of Flatland. When the two-dimensional narrator is conversing with the sphere, the sphere states that the inhabitants of Flatland are actually not 2-dimensional- for if a line were mere length without "height" it would cease to occupy space and would become invisible. So the sphere argues, that the "very fact that a line is visible implies that it possesses yet another dimension. But the narrator explains this 2-dimensional vision in terms of length and BRIGHTNESS
What I don't understand is how can something be truly a line or a point, or a configuration of lines and points- all in one plane- and still be visible? I remember the difficulty I had in 2nd grade or so, accepting the definition of a point. A point, by definition, was infinitely small, pin-pointed a locus but held no spatial dimension. So in fact, it didn't really exist. You couldn't shine a light on this theoretical perfect point and see it reflect back to you, no matter how greatly magnified the projection was- because carrying no real existence, it could not have the qualities of real existence. Of reflection, of visibility. What do the inhabitants of Flatland see? What does their light shine down upon?
So is Flatland an imperfect 2-dimensional world?
Is there this kind of irregularity in our own 3-dimensional world?
Also... if Flatland is just one plane in space, are there an infinite number of Flatlands in existence? In what manner do they overlap?
Why do voices and light- but not the sense of vision- surpass the dimensional boundaries?
Who are we to say that the fourth dimension, time, is not spatial???
These are among some many questions that reading Flatland stirred in my thoughts.