Indeed, in 1920, an article titled “Euclid, Newton, and Einstein,” published in the prestigious scientific journal Nature, referred to Flatland at some length. Einstein’s recent theory of General Relativity (1917), based in part on his earlier Special Relativity (1905), treats time as a fourth dimension. Time is not absolute. This fourth dimension is not rigidly marked out like ticks on a ruler but instead can expand and contract depending on gravity and on the motion of the observer through the three spatial dimensions. The Nature article compares the motion of our three-dimensional space against a hypothetical fourth dimension to Abbott’s description of motion of his two-dimensional Flatland relative to a three-dimensional sphere: If the latter passes through Flatland, it will be witnessed by the two-dimensional creatures as a circle (the intersection of a sphere with a plane) whose diameter starts as a point when the sphere first touches the plane, grows larger and larger to a maximum size, then contracts down to a point and disappears. The analogy between Einstein’s relativity and Abbott’s Flatland description is striking although not quite exact, since Einstein’s fourth dimension of time behaves very differently from an additional dimension of space. Nevertheless, the writer, signing him or herself only as “W.G.,” recognized a point of modern scientific significance in Abbott’s little book.

For me, the importance of the second part of Flatland lies not in its literal geometrical and dimensional discussion, but in its more shrouded warning of too much complacency in the scientific enterprise—and, by extension, all of life. At the time Flatland was published, in 1884, much of science, and especially physics, hummed along in a state of self-satisfaction. Newton’s celebrated laws of mechanics and gravity were unchallenged. Dalton’s and Avogadro’s modern concept of the atom provided a good working basis for the understanding of matter and chemical composition. The nature of heat and the laws of thermodynamics had become well established earlier that century by Rumford, joule, Clausius, Kelvin, and others. In 1865, Maxwell brilliantly elucidated the complete theory of electricity and magnetism, including a fundamental understanding of the properties of light. Soon after, Mendel published his laws for biological heredity; Mendeleyev put into place the periodic table and was successfully predicting new chemical elements. The theory of natural selection, although not unanimously endorsed, offered a scientific explanation of the specialized diversity of species. Science was indeed content with itself.

In an ironical dream, the two-dimensional narrator of Flatland visits Lineland, where the pitifully ignorant Monarch “was persuaded that the Straight Line, which he called his Kingdom and in which he passed his existence, constituted the whole of the world, and indeed the whole of Space.”

“Behold me—I am a Line,” said the Monarch of Lineland, “the longest in Lineland, over six inches of Space.”

“Of Length,” responded the narrator.

“Fool,” said the Monarch. “Space is Length. Interrupt me again and I have done.”

The first interruption of nineteenth-century science came with Roentgen’s discoveries of X rays, barely a decade after the publication of Flatland. X for unknown. Nothing had ever been seen like the highly energetic and penetrating radiations that streamed from an electrified gas. Then, the next year, powerful radiations emerged from uranium and radium, which were apparently spitting out tiny pieces of themselves. To the astonishment of scientists, the immortal and indestructible atom could disintegrate of its own accord. In 1905, the twenty-six-year-old Einstein proposed his new theory of time, contradicting all our intuition and experience with the physical world. Two events that are simultaneous to a man on a bench are not simultaneous to a man in a passing train. To Einstein’s theory of relativity, W. F. Maggie, Professor of Physics at Princeton (Monarch of Lineland), responded in 1911:

I do not believe that there is any man now living who can assert with truth that he can conceive of time which is a function of velocity or is willing to go to the stake for the conviction that his “now” is another man’s “future” or still another man’s “past.”

The final insult to all common sense was delivered by Heisenberg and Schrödinger’s quantum theory, which decreed that the position and velocity of an individual particle cannot be completely specified, even in principle. As a result, one cannot predict with certainty the future position and velocity of a particle; such predictions can be done only in terms of probabilities, which apply only to the average behavior of a large number of particles. In short, the world hovers in a state of uncertainty. Einstein, once the pioneer of revolutionary scientific ideas, now resisted the new ones and opposed the indeterminancy inherent in quantum physics. In a letter to fellow physicist Max Born, Einstein wrote:

The idea that an electron exposed to a ray by its own free decision chooses the moment and the direction in which it wants to eject is intolerable to me. If that is so, I’d rather be a cobbler or a clerk in a gambling casino than a physicist.

Back in 1884, the narrator of Flatland, who has had his worldview shattered by a visit from a three-dimensional Sphere, launches on a personal mission to “arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity.” The flatlander begs the Sphere to take him to the “blessed region of the Fourth Dimension.” And the Sphere, who has previously scoffed at the flatlander’s small worldview, replies: “There is no such land.