The Vanishing Point
universe is passive aggressive” were the last words Triglyf Loench
collapsing to cries of “Oh, my God!” from the horrified students
filling the lecture
amphitheater. For nearly three hours, he had scribbled equations across
huge blackboard, beginning slowly like a jazz musician and building to
crescendo of wild ecstatic improvisation, erasing the cascading numbers
room for more, while everyone from math major to PhD candidate took
with their cells and tried to follow the most amazing mathematical
since the publication of the Baklanov Equations in 1937.
a dozen cells called 911, Carolyn Seepers, a thin, driven woman who had
transferred from the College of Nursing after sitting in on one of
held his mouth open to keep him from swallowing his tongue. It took the
emergency squad forever to arrive. Many were weeping, many were nearly
frustration that he had collapsed before completing the most
equations ever written.
His hand still
gripped the chalk stub, his lips quivered, but he could not speak. The
paramedics lifted him gently onto a stretcher and carried him away. No
could complete his work; no one would ever see the vision that struck
Like Shakespeare, like Freud, like Baklanov himself, Triglyf Loench had
now. I am Walter Ecriveur, PhD, one of the last of those golden
acolytes who were
with him when he achieved enlightenment. Except for Carolyn, the others
their novitiates to write algorithms for stock traders or to develop
apps for the selfie public.
is difficult to visit a man in skilled nursing who once embraced the
but now can’t press a call button. Yes, Professor Loench had survived
encounter with the act of creation, but like Fermat, who died before he
his famous proof, was unable to share his vision.
a few days before he collapsed, he had agreed to supervise my
the infuriating Baklanov Equations. I was intrigued by Baklanov’s
Equation, which, as I read it, suggested that Pi was not an infinite
The problem with the equations was Soviet mathematician Dmitri
(1892-1938?) died before he could demonstrate they had any application
real world. During the Great Purge Stalin had him shot for writing a
mathematical parody of the Soviet Union. Like his equations, however,
Baklanov’s death is not well understood. After the collapse of the
Union, documents were uncovered in a secret archive suggesting Stalin
him alive until 1947, when he was shot for refusing to work on the
So after Professor
Loench’s stroke (if it was a stroke), I changed my dissertation topic
Loench’s Blackboard, what the mathematical world now called the
series of equations he had spun in his last wild improvisation. Even if I failed, I would
join a group of
dedicated theorists who would not rest until it was understood. In
as in medicine, it is sometimes necessary to rule out incorrect
determine the correct one. During that dazzling and terrifying last
class, I had
detected threads of Baklanov’s Seventh and Ninth Equations intertwined
Efforts to reach
him through whatever neurological event had robbed him of speech and
hopeless. The best neurologists at City Hospital followed by the best
Mayo Clinic were unable to reach a diagnosis, much less develop a
plan. The closest was a psychiatrist at the Mayo Clinic, who opined it
was an extreme
case of Baklanov’s Syndrome, an amalgamation of bizarre symptoms that
mathematicians who succumbed to the lure of the Baklanov Equations.
no known cure.
was the only one in the department who had the patience and could
anguish of sitting beside a man who had scoured the universe for its
only to be struck dumb before he could reveal them. So as faculty and
to decipher Loench’s Blackboard, I would take their work to the
a lap top on his tray table, and let him watch the equations stream
screen. When his eyes grew dull I knew the writer had failed, much as
generations of mathematicians failed to find a proof for Fermat’s Last
until nearly 400 years after his death. Many, like Carolyn Seepers,
by what they perceived as a personal rejection when he did not affirm
a second he brightened, but then it was like he flared out,” I told
Nevertheless, this was the most positive response anyone had received
But Carolyn was
more than dejected. She was devastated. I tried to console her at
bar favored by math majors in the strip of second hand bookstores and
restaurants across from City University. She thought she recognized a
Baklanov’s seemingly impenetrable Third Equation in the last section he
the blackboard before he collapsed. Like a great poet inventing a word,
Baklanov invented symbols to express concepts necessary to understand
In 1967 Milton
Deupree at the University of Chicago had speculated this particular
represent an algorithm to reduce incomprehensibly large numbers to
segments much as travel to the stars is measured in light years, so
might speak of a number to the power of so many Baklanovs. Until
no one had been able to confirm this because no one could conceive of
so large they called for a Baklanov Compression.
lit up when he saw it, he really did,” I said to console her.
She looked so
sad and helpless I wanted to touch her, but graduate students rarely
other the probing questions such actions now require.
then he drifted off,” I lied. In fact his features relapsed into
despair. “At least for a moment you spoke to him.”
felt like a long term care nurse telling a patient’s daughter her
father lit up
when he heard “I’m Nothin’ but a Hound Dog” on an iPhone but slipped
senility the instant the song ended. She sniffed and tried courageously
her beer. This was as much encouragement as mathematicians ever give or
from one another.
don’t drink much beer,” she said pushing the glass away.
have some Bach CDs at my apartment,” I said, as amazed at my temerity
Next only to Baklanov, Bach intoxicated mathematicians by his
exposition of every conceivable aspect of a theme with a mathematical
almost beyond human capacity.
would be nice,” she said.
we walked back across campus to my apartment and sat on the floor
listening to a
recording of The Art of Fugue.
Carolyn was slowly reviving until it stopped abruptly with the
died before he finished it,” she sobbed. “Just like Professor
isn’t dead,” I said and suddenly I understood.
Carolyn, Bach knew how that was going to end the same as Fermat knew
for his Last Theorem before he died. Every mathematician is always
equations ahead of his writing. Loench knew exactly where he was going.
Something stopped him from completing it.”
crying and looked at me as if I were a genius.
“So when he said
‘the universe is passive aggressive,’ he was talking about something he
but hadn’t written,” she said.
“Yes. And when
he froze up looking at your work, it’s because he was afraid you were
find out why the universe is passive aggressive.”
We just looked
at each other, and then we made love. I think the only time either of
think of anything besides the Baklanov Equations and Loench’s
when we climaxed. And then she sat up and reached for her clothes.
happening?” I asked.
“I have to get home
I was as stunned
as when Professor Loench collapsed. Mathematicians don’t usually share
their lives, but I thought we had shared everything.
“Can I walk you
back to your apartment?”
“Yes. Maybe we
can talk some more.”
That’s how I
learned about an unexpected pregnancy, a failed marriage, and four
to be a mother and a graduate student while working part time as a
“This has really
helped, Walt,” she said pecking me on the cheek at the door. “We’d been
about perfect numbers, and then something set him off.”
“What could set him
off about perfect numbers?”
thesis on Baklanov’s Ninth. No one has ever found an
uneven perfect number, and no one has developed a proof to show one
could not exist.”
about the Ninth suggests it’s about perfect
numbers. I told him I’d like to try.”
are you alright?” a female voice called from behind
the baby sitter,” she laughed. “Yes, Beth, I’m alright.
on. Don’t stop,” I pleaded as the door opened to reveal a
startled undergraduate expecting the worst.
this is Walt,”
she introduced me and went on about
her thesis. “We were going to do it with the Baklanov Equations.”
Beth froze. She
must have thought she was saying that to her.
“The Seventh and
the Ninth are related,” I gasped, suddenly realizing expressions or
parts of Baklanov’s
Seventh and Ninth recurred again and again on Loench’s Blackboard.
tomorrow,” she said, pressing my hand and stepping inside.
I floated back
to my apartment. We were beginning to untangle something as infuriating
Baklanov Equations themselves.
one way to test it,” I said the next day. “Let’s tell Professor Loench
how he responds.”
When she found a
babysitter, we took the bus to his nursing home. He was lying
motionless on his
back, staring at the ceiling as intently as Descartes watching the fly
inspired him to invent calculus to measure its progress.
Loench, you remember Carolyn Seepers,” I introduced her. His eyes
softly, but he kept staring at the ceiling.
you remember our conversation about
perfect numbers, Professor?” she began.
His eyes were
brimming with tears.
working on a proof for an uneven perfect number?” she asked.
My breath nearly
stopped. His eyes turned to her.
Ninth?” I asked.
Now he was
looking directly at me.
“Is Baklanov’s Third
part of it, too?” she followed up.
He looked at her
as proudly as if he were hooding her for her degree.
“And his Seventh?”
“But what is the
Seventh about?” I nearly screamed.
were burning, but he did not speak. Carolyn gripped my hand.
“My nerves are
at the vanishing point,” she said.
point,” Loench repeated, a look of inexpressible anguish contorting his
We were both as surprised
as if the statue in the Lincoln Memorial had spoken. Recovering, I ran
hall for the nurse. When we returned to his room, his eyes were closed.
died that night. A teaching assistant called to tell me the next
Carolyn and I were sitting in her kitchen trying to keep Carla amused
talking about the Google definition of the vanishing point.
“My God,” she
said. “I killed him.”
She broke down,
and Carla started to cry along with her.
alright?” the TA asked over the phone.
“We’ll be OK,” I
said and ended the call.
How could a term
from art criticism cause a man’s death? I wondered. And then I saw it.
listen,” I said gripping her hand. “The vanishing point is where two
lines converge in a painting.”
in non-Euclidean geometry,” she sniffed.
“It must have
something to do with Baklanov’s Seventh,” I said.
“So what’s Baklanov’s
“If it has
Baklanov Compressors in it, it must be the largest number in the
happening?” Carla asked.
“The divisor of Pi!”
Carolyn exclaimed. “It goes out to so many places everyone thinks it’s
So while the
math faculty planned a memorial service for Professor Loench, Carolyn
and I untangled
Baklanov Seven and Ninth Equations from Loench’s Blackboard using the
compress the numbers. If the faculty allowed her to use the same
for her dissertation, we would receive our degrees together. We were so
we failed to ask why Professor Loench had intertwined them like strands
to make their solutions nearly impossible.
My new thesis
advisor called to ask me to give a remembrance at the memorial. I said
I would as
long as Carolyn could speak with me. I didn’t think I could get through
alone. When he called back to say the memorial committee had agreed, we
confronted with one of the greatest problem mathematicians can face:
“So let’s not
speak,” Carolyn said. We were in her kitchen with Carla, trying to
Blackboard while the little girl offered us wooden delicacies from her
oven. “We’ll write the solution on the blackboard and let them see for
themselves who he was.”
The service was
going to be in the largest lecture room on campus. She was so brilliant
she said softly.
My tears had
dropped onto the page with the solution, and the last numbers ran
then I saw it.
point,” I whispered.
She saw it at
the same time. Pi was not infinite, and there was an uneven perfect
Both had the same number of integers. When they were expressed side by
Loench’s Blackboard, they touched like parallel lines in a painting
to the horizon. According to Baklanov’s non Euclidean proof, the
the outermost point in the universe where creation was still bursting
exclaimed so loud that Carla put her hands over her ears.
scribbled the segment Loench dared not disclose on the tear stained
these numbers touched, the Baklanov Equations showed the universe would
impossible,” I said.
Theory of General Relativity predicts it,” Carolyn said.
I said. “And the point the numbers
converge is the same point where relativity and the uncertainty
She looked like the world was ending.
what’s the matter?” Carla said.
her up and held her on her lap.
the uncertainty principle, we can’t know the position and momentum of
at the same time,” she began.
“Because the act
of measuring alters its position,” I continued.
“So when we
determined Pi and the uneven perfect number, we stopped the expansion
universe. That’s why Professor Loench stopped writing.”
“I had never
thought the universe was so sensitive to a human touch,” I said.
“Walt, what have
we done?” she whispered horrified. “Does truth change when you reach
She set Carla on
the floor and went to the stove.
Mommy?” Carla asked as she turned on a burner.
“No, Carla. No
She moved her
hand toward the flame and back quickly, turned off the burner, and
her chair. Carla handed her a wooden cookie, but she did not pretend to
about everything,” she said. I
seen her so dejected. “If the universe had stopped expanding, the
Second Law of
Thermodynamics would not exist anymore, because the same law of
energy on earth applies to the dispersion of energy everywhere in the
But heat still flows from hot to cold. So what did Loench see? That
it’s all a
ridiculous charade and we’re fools to chase it? That everything
Baklanov and he
had written was wrong?”
We did not know
it, but she had just conducted what would become the most famous
the 21st century. But I looked away from her,
because she had the
same expression of frustration and anguish as Professor Loench when he
“The universe is passive aggressive” and collapsed. If Loench was
lures us to discover its secrets only to drive us mad.
My eyes dropped
to the last segment of Loench’s Blackboard, stained by my tears. So
the end. But no. I suddenly realized the Blackboard was incomplete. The
equation of the universe was unbalanced. So
I took the pencil and continued to write to
see if anything lay beyond Triglyf Loench’s annihilating vision. And
was. Because the Second Law of Thermodynamics still applied, the
continuing its expansion in another dimension predicted in the last
impenetrable segment of Baklanov’s Seventh.
When we wrote the
results on the blackboard at Loench’s memorial, it took the mourners
minutes to realize what we were doing. Then they took out their phones
pictures of what would be known the Seepers-Ecriveur Blackboard. After
finished, I stepped to the microphone.
Loench did not leave us in despair,” I said. “He led us to the edge of
People would not
leave after the service until Carolyn and I returned to the podium.
shouting questions about the new universe. Finally we held up our hands
“The new universe
is there for us to discover,” Carolyn said. “There are twelve Baklanov
Equations. We only know three.”
That’s how we
will spend our lives, reaching into a universe we helped to create.
Fred McGavran retired from practicing law in June 2010 and was ordained a deacon in the Diocese of Southern Ohio. Black Lawrence Press published The Butterfly Collector, his award-winning collection of short stories, and Glass Lyre Press published Recycled Glass and Other Stories, his second collection, in April 2017. He is a frequent contributor to Spank the Carp. Find more about him at www.fredmcgavran.com.
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