Pi and the Seductions of Infinity

This essay and poem are part of the Universe in Verse book.

“My business is circumference,” Emily Dickinson wrote in one of her most cryptic letters.

Since ancient times, human beings have been enchanted by the immutable
relationship between the circumference of a circle and its diameter, no matter the circle’s size. Today, we have a symbolic form for that mathematical relationship: π — an ancient Greek letter conferred upon it by a Welsh mathematician in the first years of the eighteenth century, though it was the ancient Greeks themselves who first began thinking mathematically about the mysterious number. The longest number in nature and possibly the most powerful, π factors into our understanding of fractals and eclipses, of cosmology and thermodynamics, yet it remains ever elusive in its totality.

In the third century BCE, a millennium after Babylonian and Egyptian scholars tried to discern its exact value with fractions, Archimedes devised a geometrical approach that contoured its first few digits. Eight centuries later, ancient Chinese and Indian mathematicians approximated it to seven digits. The invention of calculus in the seventeenth century bloomed hundreds of digits, with Newton himself computing the first fifteen. Modern supercomputers can calculate with perfect precision 1.4 trillion digits. We need only the first thirty-two to compute the size of the known universe with a margin of error a single proton wide.

Art by Ofra Amit for The Universe in Verse: 15 Portals to Wonder through Science & Poetry

An irrational number — a number that cannot be expressed as a fraction, the ratio between two whole numbers — π unmoors our basic intuitions about reality with its disquieting whisper of an infinity beyond the grasp of reason. There are no known infinities in nature — as transient creatures suspended in space between the scale of atoms and the scale of stars, suspended in time between not yet and no more, we simply cannot conceive of infinity.

And yet the decimal point of π taunts us like the gun barrel of the unimaginable. If we ever reach the last digit of π, we will have known the universe.

Meanwhile, its assuring constancy goes hedging against our own transience, slaking our yearning for permanence in a cosmos governed by incessant change.

PI
by Wisława Szymborska

The admirable number pi:
three point one four one.
All the following digits are also initial,
five nine two because it never ends.
It can’t be comprehended six five three five at a glance,
eight nine by calculation,
seven nine or imagination,
not even three two three eight by wit, that is, by comparison
four six to anything else
two six four three in the world.
The longest snake on earth calls it quits at about forty feet.
Likewise, snakes of myth and legend, though they may hold out a bit longer.
The pageant of digits comprising the number pi
doesn’t stop at the page’s edge.
It goes on across the table, through the air,
over a wall, a leaf, a bird’s nest, clouds, straight into the sky,
through all the bottomless, bloated heavens.
Oh how brief — a mouse tail, a pigtail — is the tail of a comet!
How feeble the star’s ray, bent by bumping up against space!
While here we have two three fifteen three hundred nineteen
my phone number your shirt size the year
nineteen hundred and seventy-three the sixth floor
the number of inhabitants sixty-five cents
hip measurement two fingers a charade, a code,
in which we find hail to thee, blithe spirit, bird thou never wert
alongside ladies and gentlemen, no cause for alarm,
as well as heaven and earth shall pass away,
but not the number pi, oh no, nothing doing,
it keeps right on with its rather remarkable five,
its uncommonly fine eight,
its far from final seven,
nudging, always nudging a sluggish eternity
to continue.

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