“Gotta be a song left to sing, ’cause everybody can’t have thought of everything” -Gillian Welch “One Little Song”
The field of a chessboard is divided evenly into 64 squares, and on that 8x8 grid the 32 pieces are mathematically capable of bearing out more unique games than there are atoms in the observable universe. The first time I heard this I scoffed at it. Considering that just one average grain of sand alone contains 50 quintillion atoms (that’s a 50 followed by 12 zeros) the idea that a handful of pawns and some miniature royalty are going to play through enough different sequences to outnumber the atomic totals strewn across 14 billion light years is unthinkable. On its surface it seems like a preposterous claim hardly worth serious consideration- that is until one seriously considers it.
According to cosmologists the observable universe contains some one-hundred thousand quadrillion vigintillion atoms. That is a 10 with 80 zerosbehind it. Now, my proficiency with higher math reaches its threshold somewhere near the end of a 25 foot tape measure, so I have to trust the calculations of mathletes like cryptographer and “Father of Information Theory” Claude Shannon who has estimated the game-tree complexity of chess to be at least 10 to the 120th power- a 10 with 120 zeros behind it. It is a number so incomprehensibly large that we cannot visualize it with any real sense of scale. If every living human were to play 1 billion games per second it would still take 615 billion years (or 47 times the age of the universe) to complete every possible outcome. So, how can something so limiting as a chessboard be the proving ground for such seemingly limitless variance? The same way 12 little notes have written every song you’ve ever heard.
I can remember a time in my childhood when I worried that all of the possible melodies would one day be recorded, a once trackless frontier mapped and domesticated. We would be left as the heirs to a musical dust bowl where any new works were only tired forgeries of the past, no anthems of our own. Now, the classic rock stations do their best to foster that vision of an eternal hellscape where Ronnie Van Zant is reborn daily, and the world sings, “Big wheels keep on turnin’…” in unison. But the musical frontier is a vast plain, and while not mathematically limitless its borders are far too distant to even consider. It has been calculated that using the 12 notes within one octave over just one measure there are
unique combinations. Vsauce unpacks this fact brilliantly in their video Will We Ever Run Out of New Music? This of course only considers the instrumental side of the song. The numbers behind the letters are no less staggering.
The Sumerians developed the first written language sometime around 3,300 BC. Their writing system was pictographic, and was composed of over 1,000 glyphs each representing a different word. By contrast there are over 1 million words in the English language each of them made up from a small sampling of our own alphabet, itself it just 26 letters. Hell, even if we reduce our dictionary to only rhymes we are still left with a pretty generous inventory. arthur johnston made a recent calculation putting the number at 10,726, and that’s not even counting Steve Miller rhyming “Texas” with “what the facts is” in “Take the Money and Run”, which might stand as either the most genius or possibly criminal use of a near rhyme to date. When Gillian Welch opines in her ode to writer’s block that there must be “One little note that ain’t been used, one little rhyme ain’t been abused a thousand times in a thousand rhymes.” she’s right. We have mixed and remixed every metaphor and melody. We have used and reused every rhythm and rhyme, and yet there are over 28 million songs on iTunes today, and more every hour.
There is an algorithm in the radio being endlessly shuffled. 12 notes. 26 letters. Those sound like pretty restrictive parameters until you see that they aren’t limitations, but a framework. So, with every summer single shot up the charts we find new ways to remix those 12 simple notes into something equally infectious. And with every clever turn of phrase laid down on paper we find new ways to say something significant- even if our near rhymes sometimes miss.