A colleague wrote to me as a comment on my paper
A. Borovik, A mathematician’s view of the unreasonable ineffectiveness of mathematics in biology. Biosystems 205, July 2021, 104410, https://doi.org/10.1016/j.biosystems.2021.104410 :
On the subject of unreasonable ineffectiveness, here’s a hilarious problem that might have a mathematical solution, but seems well outside the scope of current mathematics. […]
The Centipede Segmentation Problem: Prove that it is impossible to have a centipede that has an even number of pairs of legs, or 17 or 19 pairs of legs.
Apparently, there are fairly good datasets in biology which suggest that this is the case: https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-3113.2003.00217.x
This reminds me one of the greatest mysteries of the Forest in Strugatsky Brothers‘ novel “The snail on the slope” from 1960s: the number of pups in a brood is always a prime number.
Their novel is admittedly the greatest book of Russian sci-fi, fantastically multifaceted; in particular, it is a vicious satire of the Soviet system, Soviet society, and Soviet science. The Forest is a symbol of many things, and one of them is unreasonable ineffectiveness of not only mathematics, but also any kind of science in comprehension of Life.
You may skip most of the fragment from the novel that I included — I highlighted a few key lines at the end of the fragment.
The pups had already gone quite a way, but Stoyan, driving with great skill, keeping the offside wheels on the path and the nearside on the dusty moss, soon overtook them and crawled slowly behind carefully using the clutch to adjust his speed. […]
Pepper stroked his swollen finger and looked at the pups. The children of the forest. Or perhaps its servants. Or maybe its experiments. They were proceeding slowly and tirelessly one after the other in line ahead, as if flowing along the ground; they oozed across rotting tree stumps, crossed ruts, pools of stagnant water in the tall grass, through prickly bushes. The track kept disappearing, diving into evil-smelling mud, hiding itself under layers of tough gray mushrooms that crunched under the wheels, then again appearing, while the pups held their direction and stayed white, clean, smooth; not a blade of grass stuck to them, not a thorn wounded them, they were unstained by the sticky black mud. They oozed along with a kind of stupid unthinking confidence, as if along a road long-known and habitual. There were forty-three of them.
I was dying to get here and now I’ve arrived, at least I’m seeing theforest from inside and I’m seeing nothing. I could have imagined all this sitting in my bare hostel room with its three empty bunks; late night insomnia, everything quiet all about, then right on midnight the piledriver starts thumping on the construction site. I could have thought it all up: mermaids, walking trees and these pups, turning into pathfinder Selivan–the most absurd things, the holiest. And everything there is in the Directorate I can imagine and bring to mind. I could have stayed at home and dreamed this all up, lying on my sofa listening to symphojazz or voices talking unfamiliar languages on the radio. […] But that doesn’t mean a thing. To see and not understand is the same as making it up. I’m alive, I can see and I don’t understand. I’m living in a world someone has thought up without bothering to tell me, or maybe even himself. A yearning for understanding–that’s my sickness, thought Pepper suddenly, a yearning for understanding.
He stuck his hand out of the window and held his aching finger against the cool car-body. The pups were paying the landrover no attention. They probably had no suspicion of its existence. They gave off a sharp unpleasant smell; their membrane now seemed transparent and it was as if wave-like shadows moved beneath.
“Let’s catch one,” suggested Quentin. “It’s simple enough, we’ll wrap it in my jerkin and take it to the lab.”
“Not worth it,” said Stoyan.
“Why not?” Quentin asked. “We’ll have to catch one sooner or later.”
“Doesn’t seem right, somehow,” Stoyan said. “In the first place, God help us, the thing’ll die on us and I’ll have to write a report for Hausbotcher.”
“We’ve had them boiled,” Acey announced suddenly. “I didn’t like the taste, but the boys said it was all right. Bit like rabbit, I can’t touch rabbit, to me a cat and a rabbit’s just the same; can’t bear the stuff… .”
“I’ve noticed one thing,” said Quentin. “the number of pups is always asimple number: thirteen, forty-three, forty-seven… .”
“Nonsense,” objected Stoyan. “I’ve come across groups of six or twelve.”
“That’s in the forest,” said Quentin, “after that groups scatter in different directions. the cesspit always produces a simple number, you can check the log, I’ve put all my conclusions down.”
“Well all right, write an article then,” said Stoyan.
“I already have,” said Quentin.
Translation from Russian by by Alan Meyers, 1980.