| Contributed by
Mythili Vutukuru
This poem by Vijay Fafat is a metaphysical reflection on the nature and philosophy of mathematics, explored through a parable of a battle for supremacy between the constants of mathematics. The poem begins with the narrator, an “Inquiring Mind”, recounting arguments between various mathematical constants, in a fictional mathematical universe, about who is more important. The goddess of the realm, Euclidia, then admonishes them for their narrow-minded thoughts, and urges them to go out and explore the universe, in order to understand its beauty and oneness. The narrator is then transported into a mathematical Eden where he meets several constants in exotic mathematical landscapes. The narrator briefly perceives the beauty and interconnectedness of mathematics, but this joy soon morphs into a feeling of despair about the inconstancy and incompleteness of mathematics. He recovers from this gloom when he realizes how mathematicians over the ages have overcome paradoxes to expand the boundaries of mathematical thought. The poem ends with deep questions about the nature of mathematics itself, its connection to reality, and profound contemplations about how mathematics would appear to transfinite minds that transcend human limitations.
The poem stands out both for its rich mathematical and philosophical content, as well as its beautiful lyrical verses. The first half of the poem introduces the reader to a large number of mathematical concepts through poetic descriptions of a mathematical universe, clever metaphors, and vivid imagery, while the second half tickles the brain with deep philosophical questions about the nature of mathematics itself. That said, the poem is a heavy read, and one requires some patience to fully appreciate all that it has to offer. While the large number of footnotes are very helpful to readers not familiar with the entire math, flitting back and forth between the main text and the footnotes can break the flow sometimes. However, for anyone that enjoys poetry or mathematics or philosophy, this poem is a rewarding journey, and well worth the effort required to read it.
Below is a detailed summary of the poem’s seven acts.
The first act starts with reflections on the beauty of mathematics by the narrator, who stands on a metaphorical mathematical beach…
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“Waves of theorems and postulates
washed over the mathematical sands around me.”
… and loses himself in the “shiny pebbles” of mathematical thoughts he sees.
“I felt the bliss of their mere existence,
as the remote thoughts of lost lovers.
They enveloped me,
as warm sunshine cradles you in its embrace.”
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The narrator uses well-crafted mathematical metaphors to describe an oceanic landscape.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“A tiny whirlpool formed near my feet.
The shoal-fish of Feigenbaum swam in its swirling chaos,
strangely attracted to its Lorenzian curves”
...
The Bridges of Langlands and Erlangen,
they arch over this ocean as magical wormholes;”
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In Act 2, as the narrator reflects on the majesty of mathematics, he recalls a mythological battle “The Battle of Constantopylae” between the various mathematical “constants” that inhabit the mathematical universe ruled by Goddess Euclidia. (The mythological origins of Euclidia’s world are narrated in an earlier poem “Discordium Mathematica - A Symphony in Aleph Minor” by the same author.) During a recounting of this battle, the reader is introduced to a number of mathematical constants, some well-known (like π and the Planck’s constant) and some obscure (like the “Euler–Mascheroni” constant). The constants quarrel with each other on who is more important, and we hear detailed arguments by the three important constants – π, Napier’s constant “e”, and the unit imaginary number “i”.
The constant π begins with:
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“Do I not control
the destinies of smooth curves,
tiny arcs to command in every neighborhood?”
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The verses contain several references to mathematical concepts, and the interested readers can learn more about them from the copious footnotes and endnotes. For example, when π asks: “Who ties integers in binds of co-prime brotherhood, eh?”, the footnote explains: “The probability that two randomly chosen positive integers are co-prime—have no common factors—is 6/π2”
These constants indulge in some light-hearted banter during the battle as well!
“Are not Einstein’s equations my general relatives (ha ha!)?”
After π comes “e” to argue its case.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“It is I who tames additively the might of multiplication;
It is I who assays the beauty of logarithm’s curves.
…
Prays the Prime Number Theorem at my temple;
Stands the giant of Euler’s formula on my shoulders!”
Finally, we hear from “i”.
“Surely one can observe. . . and feel collegial,
adds i as magic a new dimension to the real!
..
Of Complex Analysis indubitably i be the father!
Quantum Mechanics a ghost without me to mother!”
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Beyond lessons in mathematics, the poem forces us to introspect, once we see that this battle is really an allegory for the narrow-minded fights and echo chambers we encounter in the real world.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“For this Myth of Constantopylae recounted
minor tales of braggadocio;
curious stories of reflected strength;
a mite’s reach for the mountain-top;
an all-too-human conceit of narrow thought. . .”
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After the constants put forth their arguments, the goddess Euclidia chides them and puts them in their place in Act 3. She reminds them: “Not a single number governs these spheres of music, not a single principle holds them overall”. She talks to them about the vastness of mathematics, and its interconnectedness. “Does not Master Euler put you in a single stable with his symbolic imagery?” she asks, referring to the famous equation eπ i + 1 = 0. She exhorts them to go explore the boundless reality, and tells them not to come back until they have toured her kingdom fully, and feel the “wondrous oneness with your own true self”.
In Act 4, the narrator is transported into a beautiful magical realm, an “Eden of Mathematical Constants”. The reader is introduced to a dizzying array of mathematical constants via beautiful metaphors, and accompanying footnotes.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“In a small hut downstream lived ‘The Tarski Family’:
The Banach-Tarski twins, 4 and 5.
The avuncular Constant of Laczkovich, 1050
The body-building cousin, the Marks-Unger Constant, 10200”
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On the journey in this mathematical paradise, we also get to meet the eponymous mysterious constant.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“And high above this numinous constellation of rising stars,
as a beacon of ‘riddle wrapped in an enigma’,
blazed the audacious spectacle
of Cantor and Godel’s Constanto Mysterio…”
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The exploration ends with the lesson that all constants are important in their own unique way, another one of those lessons for real life.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“For truth be told,
every number is a mathematical constant,
every constant one of arithmetic interest,
(for not being one would trigger Berry’s Paradox)
and it is only our favoritism and small reach,
which makes some constants more equal than others…”
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From Act 5 onwards, the story moves on from the mathematical constants towards philosophical cogitations of the narrator. While in the magical realm, the narrator experiences a great clarity of mathematical thought for some brief moments.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“For the briefest of moments,
the most glorious secrets of Creation were mine;
-an explicit well-ordering of real numbers;
-an elementary proof of Fermat’s Last Theorem
…
In that blink of the cosmic eye,
every path to every theorem
was a tautology in my eyes;”
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But in Act 5, the unearned vision dissipates quickly, and comes crashing down in the form of despair over the “inconstancy” of the paradigm of mathematics. The narrator finds that the “termites” of paradoxes, anomalies, and incompleteness erode the foundations of mathematics. Once again, the reader is introduced to a plethora of mathematical concepts via beautiful poetry and generous footnotes.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“My mind’s unsettled voice susurrated in growing bedlam,
not just of the inconstancy of Thought,
not just of the uncertain constituents and domains of logic,
but of the inconstancy of Foundations,
of the quagmire at the feet of lofty castles we had raised;
…
In that bewildering melee of congeries swirled:
Cantor’s elucidation of the nature of size
and his brazen assault on Infinity.”
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However, the narrator recovers from this state quickly in Act 6, as mathematicians have done in the past, and moves on to contemplate on some very fundamental questions on the nature of mathematics itself.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“Do we create mathematics?
Do we fashion our own illusions of concluding deductions?
Does all mathematics flow from impersonal logic,
or is it experiential?
Is mathematics the decryption key
to the encoded messages of our Reality?
Or a mere abstraction from concretized reality,
a rhythmic ritual of pencil, paper, proof?”
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These brilliant set of questions will nudge the reader to pause and think, on what mathematics really is, and what connection it bears to the real world.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“Would it matter to the universe,
if our set theories turned out to be inconsistent?
Surely the bridges would not collapse,
nor oceanic tides reverse
if we proved 1 = 0,
(though men might go mad). . .”
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The narrator finds that after his mind goes through this intense questioning, it arrives at a state of unlearning. The profound introspective journey in Act 6 ends with these beautiful lines, which bear an uncanny resemblance to descriptions on how spiritual awakenings unfold.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“To decipher the universe,
one must first become an unknowing child.”
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In Act 7, the narrator finally finds peace in the realization that perhaps the limitations we see in mathematics are due to our shortcomings…
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“The fallibility of our mathematics represents
the sequestered ambit of human thought,
not nature’s design.”
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… and goes on to say….
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“For “our Mathematics” is an abbreviated hymn
hummed by our bounded minds.
The amphiline of the unbounded ocean of proto-Creation
lies far beyond our perception."
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He exhorts us to imagine how mathematics would look like to super-beings without human limitations.
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“For creatures blessed with transfinite, non-local minds,
there would be no Godelian constraints.
They would have no doubts about the Axiom of Choice.
…
Large Cardinals would be their playthings
as integers are for us."
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This beautiful exposition about how mathematics would look like to transfinite beings asks the interesting question…
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“Would Man even be Man amongst these Gods?”
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… and if the path to a cosmic “God” runs through mathematics ….
| (quoted from Constanto Mysterium - A Paradise of Shifting Constants)
“If there is a Cosmic Mind of such power
as to house all truths of All-Mathematics
as a constant pole star,
written in a Book of Infinite Visions,
in perfect calligraphy,
then perhaps we shall unite with that Overmind some day
through metamathematics
and not the blood-thirsty meanderings of all our religions…”
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… suggesting that perhaps the pursuit of mathematical knowledge is a journey of self-discovery for the human race itself.
This very long poem ends with a hopeful coda, where the narrator exhorts readers to explore the uncharted territories of the mathematical cosmos without hubris, reminding us that this beautiful journey to the frontiers of mathematics is the only constant of mathematics.
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