Through the Mathemalchemy Looking Glass
A deeper incursion in the Tortoise Story
On waking up, Tess the Tortoise felt this was going to be a special day – a day to have an adventure. As always, she made a careful plan, and started her list. Breakfast first, of course – a nice leisurely breakfast; nothing good was ever accomplished on an empty stomach. But then, she wanted to have a nice walk, really far–she still is going strong, despite what her nephew Raphael says. Even if her days of racing Harry the Hare lie behind her, she still does have what it takes.
Where would she go? Hadn’t she read the other day that a new meditation path had been inaugurated? Zen’s Path—no, that was not quite right—Zeno’s Path! Yes, Zeno’s Path—“all the way to infinity”, if she remembers the silly slogan correctly.
Of course it didn’t go to infinity; the nice little drawing on the flyer had made more sense, showing that the walk did indeed cover infinitely many consecutive bits of path. Didn’t the path go from Downtown to the bottom of Integral Hill? Then, after the walk, she could climb to the top of Integral Hill, to the highest of the Lebesgue terraces, and look around. Look down on the Riemann cliffs, and maybe have her lunch there.
Lunch–what would she have for lunch? A lettuce of course, some berries, and a nice roll of bread. It would surely fit in the dainty little bag that had come in the accessory kit of her kite—there was a bit of a breeze, so it was a nice day to try out the kite she had received for her birthday from Wacław. So, there it is, all on the list: breakfast, Zeno’s walk, Integral Hill, lunch. And then a nap. Of course.
And here is Tess, trundling along on Zeno’s path, with the Riemann wall on her right. She will have an even nicer time than she imagines, because it is one of those rare days where the weather conditions are just right, and there will be a flurry of Koch snowflakes on Integral Hill to greet her.