The Parable of the Rod and the Rope
How the stiff get stiffer and the bendy get bendier
There once was a man who sold rods for a living. His name, naturally, was Rod. Rod loved selling rods and he was good at it too. He especially loved to demonstrate the strength of his rods for his customers. He would bridge a rod across two barrels and stand on it and revel in its strength. Even when there were no customers around, he would stand on his rod with his hands on his hips and glare across the street at his archrival.
This archrival across the street sold rope for a living. His name, naturally, was Jedidiah. Whenever Rod stood with his hands on his hips and stared, Jedidiah would be there -- standing with his hands on his hips and staring right back -- an exact mirror of Rod. The only difference was that Jedidiah stood on a length of rope that was stretched across his two barrels.
Day after day, they stood. Rod on his rod and Jedidiah on his rope.
In the early years, they would hurl insults across the street at each other. “Rope is nothing but a bundle of tiny rods.” “Rods are just fat, inflexible ropes.” But as time wore on, and gray overtook black, they mellowed and even became friendly. Age made them harmonious, and it also made them fat.
In those days, wealth was measured around the waist and both men had done very well for themselves. So much so that, one evening, Jedidiah admitted that he was afraid that his demonstration rope would soon snap. Rod, relieved, admitted the same for his rod. They both agreed that it was time to upgrade their demonstrations, but added a condition as a challenge. They could only change the stiffness.
Rod and Jedidiah came out the next morning with their new demonstrations in hand. Jedidiah asked Rod, “What’s different about your new rod?”
“It’s stiffer than the old one,” said Rod.
“Well, think of a rod as a bunch of springs,” explained Rod as he drew in the dirt.
“When I stand on the rod, the top spring compresses and the bottom spring stretches. The stiffer I can make the rod, the less the springs stretch and compress. And, as you know, the less you push or pull on a spring the less force there is in the spring. So a stiffer rod means the material stretches less and experiences less force as a result. Us rod guys are brought up hearing ‘Stiffness is strength’. Did you make your rope stiffer too, Jedidiah?”
“No, I actually got a more flexible rope.”
“Huh, is that right? Why’s that?”
“To show you why I went with flexibility, I need to explain how the rope supports me first. Unlike your rods, my ropes can’t take compression. The rope is all pulling in one direction, so to speak. ”
Jedidiah paused to draw.
“When I stand on my rope, it sags. You can imagine the sagging rope as two triangles. And the triangle shows you a lot about the forces the rope is experiencing if you know what you’re looking for. The hypotenuse is the tension in the rope. The vertical side of the triangle is the vertical force that’s supporting my weight. The horizontal side is the rope essentially pulling against itself to satisfy the laws of physics, because the sum of the forces has to lie along the rope.”
Rod interjected, “I don’t get it.”
Jedidiah puzzled for a second and then asked Rod to bring him a mug and a piece of string or floss roughly a foot long. When Rod returned, Jedidiah threaded the string through the handle of the mug and handed the ends of the string to Rod. (Feel free to follow along at home.)
“To start, the strings are vertical so all of the tension is going towards supporting the cup. Move your hands apart. As your hands move further, you should be able to feel yourself pulling harder and harder. Feel that?”
Rod nodded and moved his hands back and forth a few more times.
“Try making the string perfectly horizontal.”
Rod pulled as hard as he could but still the string had a dip.
“Huh,” he said.
“You get it now? The string has to angle upwards on each side to provide a force upwards. As the string gets closer to vertical, more of the tension in it can be used to support the weight of the mug. The closer it gets to horizontal, more of its tension is used to just pull against itself.”
“I get it. That’s why you went more flexible on your new rope. The rope will have more of its strength aligned vertically and so there’ll be less tension overall.”
“Exactly,” said Jedidiah as they parted company for the day.
Their new upgrades in place, they resumed their demonstrations. For years, they were fixtures on their street -- Rod standing on his rod and Jedidiah on his rope. And both had a new appreciation for the stiff and the flexible. All was good and bright. That is, until Home Depot came to town and put them both out of business.
Moral: We often think of engineering as converging on an optimal solution. This parable shows how two different approaches can diverge rapidly. If you start out with stiffness in mind, the solution improves by adding more and more stiffness. If you start out with flexibility in mind, the solution improves by adding more and more flexibility. That seems to be a point in favor of the idea I’ve written about before that stiffness might be more cultural than technical.
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Drawing exercise #35. If you missed it, here’s why I’m learning to draw.