Complete Stories (35 page)

I obtained the typescript of this story in a roundabout way. My friend, Gregory Gibson, was in London last year, looking for rare books. A dealer in Cheapside Street showed Gibson a copy of an early edition of Edwin Abbott’s 1884 fiction,
Flatland
. The copy Gibson saw was remarkable for the fact that someone had handwritten a whole story in the margins of the book’s pages. The dealer told Gibson that the volume was brought in by a cook’s helper, who had found the book in the basement of a Pakistani restaurant where he once worked.

Gibson could not afford the book’s very steep purchase price, but he did obtain the dealer’s permission to copy out the story written in the volume’s margins. Here, without further ado, it is: the singular adventure of Robert Ackley.

All my attempts to get back through the tunnel have proven fruitless. It will be necessary for me to move on and seek another way out. Before departing, however, I will write out an account of my adventures thus far.

Until last year I had always believed Edwin Abbott’s
Flatland
to be a work of fiction. Now I know better. Flatland is real. I can look up and see it as I write.

For those of my readers familiar with the book in whose margins I write, this will be startling news: for
Flatland
tells the adventures of A Square, a two-dimensional being living in a two-dimensional world. How, you may ask, could such a filmy world really exist? How could there be intelligent creatures with length and width, yet without thickness? If Flatland is real, then why am I the only living man who has touched it? Patience, dear readers. All this, and much more, will be revealed.

The scientific justification for Flatland is that it helps us better to understand the fourth dimension. “The fourth dimension” is a concept peculiarly linked to the late nineteenth century. In those years, mathematicians had just laid the foundations for a comprehensive theory of higher-dimensional space. Physicists were beginning to work with the notion of four-dimensional spacetime. Philosophers were using the idea of a fourth dimension to solve some of their oldest riddles. And mediums throughout Europe were coming to the conclusion that the spirits of the dead consist of four-dimensional ectoplasm. There was an immense popular interest in the fourth dimension, and
Flatland
, subtitled, “A Romance of Many Dimensions,” was an immediate success.

Abbott’s method was to describe a two-dimensional square’s difficulties in imagining a third dimension of space. As we read of A Square’s struggles, we become better able to understand our own difficulties in imagining a fourth dimension. The fourth dimension is to us what the third dimension is to the Flatlanders.

This powerful analogy is the rarest of things: a truly new idea. I often used to ask myself where Abbott might have gotten such an idea. When Gray University granted me my sabbatical last year, I determined to go to London and look through Abbott’s papers and publications. Could
Flatland
have been inspired by A. F. Möbius’s
Barycentric Calculus
of 1827? Might Abbott have corresponded with C. H. Hinton, eccentric author of the 1880 essay, “What Is The Fourth Dimension?” Or is
Flatland
nothing more than the inspired reworking of certain ideas in Plato’s
Republic
?

Abbott wrote many other books in his lifetime, all crashingly dull:
How to Parse
,
The Kernel and the Husk—Letters on Spiritual Christianity
,
English Lessons for English People
,
A Shakespearian Grammar
,
Parables for Children
, and so on. Except for
Flatland
, all of Abbott’s books are just what one would expect from a Victorian clergyman, headmaster of the City of London School. Where did Abbott find his inspiration for
Flatland
? The answer is stranger than I could ever have imagined.

It was an unnaturally hot day in July. The London papers were full of stories about the heat-wave. One man reported that three golf-balls had exploded in the heat of his parked car. All the blackboards in a local school had cracked. Numerous pigeons had died and fallen to the sidewalks. I finished my greasy breakfast and set forth from my hotel, an unprepossessing structure not far from St. Paul’s Cathedral.

My plan for the day was to visit the site of the old City of London School on Cheapside at Milk Street. Abbott attended the school himself, and then returned as headmaster for the years 1865-1889. Under Abbott’s leadership the school moved to a new building in 1882, but I had a feeling that some valuable clue to his psychology might still be found in the older building.

To my disappointment, nothing of the old building remained…at least nothing that I could see. Much of Cheapside was destroyed during the Blitz. Flimsy concrete and metal structures have replaced what stood there before. I came to a halt at the corner of Cheapside and Milk, utterly discouraged.

Sweat trickled down my sides. A red double-decker labored past, fouling the heavy air with its exhaust. Ugly, alien music drifted out of the little food-shops. I was jostled by men and women of every caste and color: masses of people, hot and impatient, inescapable as the flow of time.

I pushed into a wretched Pakistani snack-bar and ordered a beer. They had none. I settled for a Coke. I tried to imagine Edwin Abbott walking through this dingy space one hundred years ago.

The girl behind the counter handed me my Coke. Her skin had a fine coppery color, and her lips were like chocolate ice cream. She didn’t smile, but neither did she frown. Desperate with loneliness and disorientation, I struck up a conversation.

“Have you been here long?”

“I was born in London.” Her impeccable accent came as a rebuke. “My father owns this shop now for five years.”

“Did you know I came all the way from America just to visit this shop?”

She laughed and looked away. A girl in a big city learns to ignore madmen.

“No, no,” I insisted. “It’s really true. Look …” I took out my dog-eared first edition of
Flatland
, this very copy in whose margins I now write. “The man who wrote this book was headmaster of a school that stood near this spot.”

“What school?”

“The City School of London. They moved it to the Victoria Embankment in 1882.”

“Then you should go there. Here we have only food.” For some reason the sight of Abbot’s book had caused her cheeks to flush an even darker hue.

“I’ll save that trip for another day. Don’t you want to know what the book is about?”

“I do know. It is about flat creatures who slide around in a plane.”

The readiness of her response astonished me. But before I could pose another question, the girl had turned to serve another customer, a turbaned Sikh with a pockmarked face. I scanned the menu, looking for something else to order.

“Could I have some of the spicy meatballs, please?”

“Certainly.”

“What’s your name?”

“Deela.”

She failed to ask mine, so I volunteered the information. “I’m Bob. Professor Robert Ackley of Gray University.”

“And what do you profess?” She set the plate of meatballs down with an encouraging click.

“Mathematics. I study the fourth dimension, just as Abbott did. Have you really read
Flatland
?”

Deela glanced down the counter, as if fearful of being overheard. “I have not
read
it. I …”

The Sikh interrupted then, calling for butter on his rice. I sampled one of the meatballs. It was hot and dry as desert sand.

“Could I have another Coke, please?”

“Are you rich?” Deela whispered unexpectedly.

Was she hoping for a date with me? Well, why not? This was the longest conversation I’d had with anyone since coming to London. “I’m well-off,” I said, hoping to make myself attractive. “I have a good position, and I am unmarried. Would you like to have dinner with me?”

This proposal seemed to surprise Deela. She covered her mouth with one hand and burst into high laughter. Admittedly I am no ladies’ man, but this really seemed too rude to bear. I put away my book and rose to my feet.

“What do I owe you?”

“I’m sorry I laughed, Robert. You surprised me. Perhaps I will have dinner with you someday.” She lowered her voice and leaned closer. “Downstairs here there is something you should see. I was hoping that you might pay to see it.”

It seemed very hot and close in this little restaurant. The inclination of the Sikh’s turban indicated that he was listening to our conversation. I had made a fool of myself. It was time to go. Stiffly I paid the bill and left. Only when I stepped out on the street and looked at my change did I realize that Deela had given me a note.

-----

Robert—

Flatland is in the basement of our shop. Come back at closing time and I will show it to you. Please bring one hundred pounds. My father is ill.

Deela.

-----

I turned and started back into the shop. But Deela made a worried face and placed her fingers on her lips. Very well, I could wait. Closing time, I noted, was ten P. M.

I spent the rest of the day in the British Museum, ferreting out obscure books on the fourth dimension. For the first time I was able to hold in my hands a copy of J. K. F. Zöllner’s 1878 book,
Transcendental Physics
. Here I read how a spirit from hyperspace would be able to enter a closed room by coming in, not through walls or ceiling, but through the “side” of the room lying open to the fourth dimension.

Four-dimensional spirits…long sought, but never found! Smiling a bit at Zöllner’s gullibility, I set his book down and reread Deela’s note.
Flatland is in the basement of our shop
. What could she mean by this? Had they perhaps found Abbott’s original manuscript in the ruined foundations of the old City School? Or did she mean something more literal, something more incredible, something more bizarre than spirits from the fourth dimension?

The whole time in the library, I had the feeling that someone was watching me. When I stepped back onto the street, I realized that I was indeed being followed. It was the Sikh, his obstinate turban always half a block behind me. Finally I lost him by going into a movie theater, leaving by the rear exit, and dashing into the nearest pub.

I passed a bland few hours there, drinking the warm beer and eating the stodgy food. Finally it was ten P. M.

Deela was waiting for me in the darkened shop. She let me in and locked the door behind me.

“Did you bring the money?”

The empty shop felt very private. Deela’s breath was spicy and close. What had I really come for?

“Flatland,” stated Deela, “is in the basement. Did you bring the money?”

I gave her a fifty-pound note. She flattened it out and held it up to examine it by the street-light. Suddenly there was a rapping on the door. The Sikh!

“Quick!” Deela took me by the arm and rushed me behind the counter and down a narrow hallway. “Down there,” she said, indicating a door. “I’ll get rid of him.” She trotted back out to the front of the shop.

Breathless with fear and excitement, I opened the shabby door and stepped down onto the dark stairs.

The door swung closed behind me, muffling the sound of Deela’s voice. She was arguing with the Sikh, though without letting him in. I moved my head this way and that, trying to make out what lay in the basement. Deela’s faint voice grew shriller. There was what looked like a ball of light floating at the foot of the stairs. An oddly patterned ball of light some three feet across. I went down a few more steps to have a closer look. The thing was sort of like a huge lens, a lens looking onto …

Just then there came the sound of shattering glass. The Sikh had smashed his way in! The clangor of the shop’s burglar alarm drowned out Deela’s wild screams. Footsteps pounded close by and the door at the head of the stairs flew open.

“Come back up, Professor Ackley,” called the Sikh. His voice was high and desperate. “You are in great danger.”

But I couldn’t tear myself away from the glowing sphere. It appeared to be an Einstein-Rosen bridge, a space-tunnel leading into another universe. The other universe seemed to contain only one thing: an endless glowing plane filled with moving forms. Flatland.

The Sikh came clattering down the stairs. My legs made a decision. I leaped forward, through the space-tunnel and into another world.

I landed on all fours…there was a sort of floor about a yard below the plane of Flatland. When I stood up, it was as if I were standing waist-deep in an endless, shiny lake. My fall through the Flatlanders’ space had smashed up one of their houses. Several of them were nosing at my waist, wondering what I was. To my surprise, I could feel their touch quite distinctly. They seemed to have a thickness of several millimeters.

The mouth of the space-tunnel was right overhead, a dark sphere framing the Sikh’s excited little face. He reached down as if to grab me. I quickly squatted down beneath the plane of Flatland and crawled away across the firm, smooth floor. The hazy, bright space shimmered overhead like an endless soap-film, effectively shielding me from the Sikh.

I could hear the sound of more footsteps on the stairs. Deela? There were cries, a gunshot, and then silence. I poked my head back up, being careful not to bump any Flatlanders. The dark opening of the space-tunnel was empty. I was safe, safe in Flatland. I rose up to my full height and surveyed the region around me.

I was standing in the middle of a “street,” that is to say, in the middle of a clear path lined with Flatland houses on either side. The houses had the form of large squares and rectangles, three to five feet on a side. The Flatlanders themselves were as Abbott has described them: women are short Lines with a bright eye at one end, the soldiers are very sharp isosceles Triangles, and there are Squares, Pentagons and other Polygons as well. The adults are, on the average, about twelve inches across.