A Mathematical Fable

There was once a man who built a tower.

He didn’t have any particular reason. “I figure,” he thought, “I like towers, and building them sounds fun, so I’ll just go ahead and build one.”

And so he began. Stone by stone, floor by floor, up and up he went. But he forgot to tell anybody about it, and the surrounding folk only realized about the erection once the still unfinished building poked its head through the treetops.

“What are you doing?” asked one of the peasants.

“Building a tower,” replied the builder.

The tower was narrow and damp, and its height was still rather unremarkable. You see, the builder was inexperienced. This was his first tower.

“But why? Isn’t it high enough now?”

“Is it? I have been building ever higher, and yet I am still standing on a floor — I don’t feel very elevated at all!”

Some time passed. The tower now rivaled the surrounding hills in height. The villagers came back to inquire about his progress.

The builder now had to shout to be heard. “I have made marvelous discoveries about stonelaying! While the lower levels of this tower are inhospitable, I have begun to perfect my craft, and the higher levels are rather beautiful if I may say so myself!”

“Pray, tell us about the techniques!” said the villagers.

“I’m afraid I can’t explain them like this, you’ll have to come see for yourselves.”

This intrigued the villagers, and some of them set out to climb the tower.

As the few explorers climbed up, the builder kept adding more floors — by now, it reached so high into the sky that on cloudy days its crest was hidden from view. He was building so quickly that the rest of the villagers thought no one could ever reach the top.

It had been so long, now, that the explorers were presumed dead, perhaps from exhaustion, or perhaps from falling down the endless stairs.

But one of them came back.

“I didn’t get that far up, but it was already getting quite nice,” he said.

One could only imagine how beautiful the top levels must be, now. As the villagers pondered this, to everyone’s surprise, they saw another of the explorers emerge from the very crown of the tower. The explorer waved, and appeared to shout something, but nothing was heard. A while later, he dropped a roll of parchment to the onlookers below.

I will be staying here to help the Master, he’d written. I have seen Beauty and I cannot forsake it.

It has been generations since the Builder started building.

Legend has it the gods had asked Him to build the tower so that he may reach the heavens.

Another legend says He built it because He wished to fly, but no matter how high He got, He was still stuck on His two feet; and so He’d kept building.

Climbing up the tower must take a lifetime now. In fact, there are now entire families living atop the tower, studying the methods, and laying more and more stones, building ever higher. We know this, because every now and then the builders throw down a scroll of parchment, giving news about births and marriages and trying to explain some of their discoveries. Unfortunately, without practical examples, the texts are gibberish, and the tower is now so high that stones dropped down disintegrate as they hit the ground.

A rare few pieces survived the impact. They are barely recognizable as stone, more like an abstraction of the idea of a stone, carved in stone itself; doubtless they must be beautiful once one figures out how to even gaze at them.

The tower rises so high that it seems endless.


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