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The Dot and the Line Go on a Honeymoon: A Revisionist Romance

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When it came to the matter of the honeymoon, the line had several suggestions for his blushing bride. He had heard that the views at the local Koch curve were beyond compare; perhaps she might like to sunbathe by the ocean while he fed her peeled grapes. Or perhaps they could tour the colorful tiles of a gloriously aperiodic tessellation, or indulge themselves in exploring a Klein bottle's sleek nonorientable surface, or go on safari in the mysterious, ever-changing wildernesses of cellular automata. He had presented her with brochures for various tour packages, each featuring enticing photographs of the possibilities.

"Oh, darling," the dot said, "we have a lifetime ahead of us to explore such mathematical riches. It's part of who you are! But shouldn't we look at things from the other side, too? I've been doing a little research of my own."

And she presented the baffled line with a tour package of her own, put together by one of her numerous sisters. "Trust me, it'll be a blast," she said.

At first, the line hesitated. But he soon realized that the dot had cleverly put together an itinerary that would appeal to both their interests. "Sure, why not," he said. After all, it would be ridiculous to spoil their honeymoon before it even started. He might as well give it a shot.

The first item was an opera. He'd never thought of himself as an opera aficionado, but the dot had obtained a full score in advance, and he came to see that both dots and lines were integral to musical notation. As a point of fact, the music abounded in dotted values, which made him smile fondly.

He was nervous that they wouldn't have any clothes suitable for the opera, but the dot persuaded him that they could afford to indulge just a little bit. He came away with a handsome suit and a silk cravat with a subtle wave motif in gold thread: conservative, it must be admitted, but better to be somber than silly. The dot, for her part, cast longing glances at a deep blue velvet gown trimmed with black lace finer than butterfly wings, but instead contented herself with a more subdued satin dress in shimmering violet. To console her, the line obtained a necklace of silver filigree that added the right degree of sparkle to her outfit.

He wound up enjoying the performance more than he'd anticipated. True, it was difficult to follow the plot's baroque twists and turns at times. He was certain that the thunderous baritone was, at various points of the performance, the jilted young lover, the imprisoned baron, the trickster tomcat, and the head chef. But there was a certain thrill to the melodrama and the way that moments of high passion were sung without any hint of shame. The lyric soprano was especially expressive, and he made a note to himself to pick up a recording at some point.

Next they went to a museum of needlework for tea. There was a guided tour just for the two of them, by a scholar who seemed flattered at the dot's genuine interest. She showed them tapestries that resolved into a sort of pointillism on a grid, and then each point into its constituent stitches. The dot could name every type of stitch by sight. The line was amazed at the subtleties that could be achieved by careful placement of different colors of thread, so that they appeared to blend into each other. His favorite tapestry depicted the queen of birds surrounded by her subjects: pale doves, kestrels captured in the act of bating, quizzical kiwis, owls with eyes like uncanny lanterns. The dot, on the other hand, gravitated toward a storm-tossed sea with dolphins leaping silver-bright alongside a clipper with its sails full-bellied by the wind. The line made a note to himself to investigate the possibility of a cruise on their next vacation.

The tea itself was elegant without being affected. The dot exclaimed over the watercress sandwiches, which had been cut in the shapes of birds and leaves. She took her tea with both sugar and milk, while the line declined the sugar. He expected to go away hungry, as the portions were so delicate, but after several courses of sandwiches and petits fours, he confessed that he was quite full.

Then, just for fun, they spent a weekend at an inn situated at the heart of a left-handed trefoil. "Sometimes you just need to lie in bed for a bit," the dot said confidingly. In practice, she would only sleep in for an extra ten minutes, then wake up to nibble at the breakfast that the line had brought for her--she had a particular fondness for toast with strawberry jam--before heading into the adjoining gardens.

The gardens were a mystery to the line at first. Their paths went this way and that past cunningly arranged dwarf trees and over small brooks, past broad rocks where turtles sunned themselves. Although the walls did not enclose a large area, the illusion of vaster space was created by preventing the casual eye from seeing too far in any one direction. Clearly there was a sense of order and rhythm in their design, even if it couldn't be expressed in strictly Euclidean terms. He said as much to the dot.

The dot smiled coquettishly, but her eyes were earnest. "The world is broad and beautiful," she said. "We'll have to explore it together, won't we? For there's more than one approach to the Truth."

"Always," the line said fervently.

When it came time to go home, the dot sighed over her suitcases and said, "It was over so quickly."

"Nonsense," the line said, pressing her hand. "It's only beginning. We'll make time to show each other such things--that's a promise."

"I'll hold you to that," the dot said. By now he knew that her flirtatious manner in no way meant that she wasn't also serious.

"I wouldn't expect anything less," the line assured her.