# Algorithmic Poems

This post was first published in my old blog, hosted at

`blog.neerajadhikari.com.np`

. I have since taken down the old blog and copied some of its posts here.

While there are now algorithms left and right writing poetry (or, depending on your opinion, writing stuff that is not quite poetry), let’s talk about something even more interesting - poetry that describe algorithms. Surprisingly, I couldn’t find more than a few such poems. It is difficult enough to exactly and concisely express most algorithms even in prose, so perhaps it is not so surprising after all. But simpler, elegant algorithms are relatively easier to express in prose and as we shall see, poetry. As we can expect, these poems do not provide a complete specification of algorithms, but nevertheless describe their general working very well. Here I list the ones that I have found, and I’ll keep expanding this list as I hopefully find more in the future.

## Sieve of Eratosthenes

Sift the Two’s and Sift the Three’s,

The Sieve of Eratosthenes.

When the multiples sublime,

The numbers that remain are Prime.

– Anonymous

The sieve of Eratosthenes is an ancient algorithm for finding all primes up to a given limit. It is a simple algorithm, discovered by the Greek mathematician Eratosthenes of Cyrene millennia before there were computers or even the formal study of algorithms. It works by starting with a list of all natural numbers less than a limit and crossing out multiples of discovered primes one by one, starting with two. Once there are no bigger primes to cross out multiples off, the algorithm ends and all numbers that remain unmarked are primes.

## Gradient Descent

Still the fog persists.

Let the incline have its way

and set your compass.

Keep taking footsteps

until that first suspicion

of an uphill slope

then turn left or right,

just one of many zig-zags.

Will it ever end?

This poem by Michael Bartholomew-Biggs appears in his paper titled Algorithms and Poetry, along with other poems describing algorithms for optimization problems. This one describes the gradient descent or steepest descent method of finding the minimum of a function in possibly high-dimensional space. It is the most common method used for optimizing neural network weights. It works by starting at some initial position and gradually moving in the direction (in the input space) of the steepest descent of the function value. The algorithm stops at the “first suspicion of an uphill slope”, or the point from which there is no way downhill. The fog in the poem refers to the fact that at a time we can only ‘observe’ the immediate surroundings of the point we are at, instead of the entire topography.

## Spanning Tree Protocol

I think that I shall never see

A graph more lovely than a tree.

A tree whose crucial property

Is loop-free connectivity.

A tree which must be sure to span

So packets can reach every LAN.

First the root must be selected.

By ID it is elected.

Least cost paths from root are traced.

In the tree these paths are placed.

A mesh is made by folks like me

Then bridges find a spanning tree.

This one by Radia Perlman is my
favorite. It describes the algorithm for the Spanning Tree Protocol, which is used implemented by
layer-2 bridges in a network which may have cycles in the topology which lead
to *broadcast radiation*, the situation when broadcast frames flood the
network. To prevent that, the bridges compute a loop-free subset of the network
topology that spans the entire network, in other words, a spanning tree. The
algorithm runs on each bridge in the network, and they communicate by sending
out configuration messages to their neighboring bridges. First they agree on a
root bridge for the tree based on an ID derived from the MAC address, and keep
the links that provide shortest distance paths to the root bridge in the
spanning tree. The links not in the spanning tree are deactivated.

While working at Digital Equipment Corporation (DEC), Radia Perlman was tasked with developing a constant-memory protocol that enabled bridges to locate loops in a local area network. Legend says that she was given a week to finish the job, but she invented the protocol in a day and spent the rest of the time writing this poem.

*Do you know of, or have yourself written, a poem that describes an algorithm?
If so, send it to me and I’ll add it to the list.*