An Aphid Named Quintillion

“How can we know for certain what the truth is, unless we seek to find it?” an aphid named Quintillion argued.

She kept her wings respectfully folded as she stood before the Council of Grand Numerators.  But she dared to sweep aside the train of glittering white filaments that plumed from her back, a particular characteristic of her tribe.

“They came out of the primordium, just as we did,” she said.  “They are not beasts.  They are an intelligent species.  They are potential companions.”

“Or rivals,” someone in the gathered assembly muttered.

“Brutes,” another voice chimed in.

Quintillion found it challenging to ignore such distractions.  But the Council members seemed unfazed as they proceeded to ask her questions.

“How could a species so young, and pardon me, so gigantic, possibly obtain even a modicum of intelligence, much less sentience?”

“Agreed,” another councilor chimed in.  “How intelligent can they be if their brains are so massive?  Surely the messages traveling between the separate cells take thousands of times longer than they do in our brains?”

Quintillion tried to keep her antennae from twitching with agitation.  If only the Council would accept evidence proposed from other insect classes, especially the bees, she would have stronger support for her argument.

She turned and swept aside her woolly train again.  “There’s no reason an intelligent species has to be the same size as we are.”

“Why haven’t they tried to speak to us then?”

She was ready for that question.  “Why haven’t we tried to speak to them?  They have encountered us, as have encountered them.  But perhaps they are as unaware of our intelligence as we are of theirs.”

She noted the uncomfortable shuffling among the gathered assembly, and the stern gleam in the eyes of her fellow numerators—most of them.  She knew what they were thinking, what those eyes were accusing her of.  She was placing their new society in danger.  Long had the scholars, the dew-gatherers, the mothers, fathers, and leaders of the aphid colonies struggled to unite their disparate tribes into one.  And they had succeeded.  They had built the modern Multivariate Aphid Colony in which Quintillion and millions upon millions of her people lived, not yet in happy harmony, but in peace.

A delicate peace.


Quintillion and those of her generation had only ever known life within the MAC.

Some aphid tribes had always partnered with certain ant tribes.  But the MAC had only just in her lifetime begun to trade and attempt friendships with other colonial insects, like the bees and even with wandering and solitary insects, like the beetles.  It was from such insects that the aphids first heard about the “two-legs” as anything other than one of the large and lumbering beasts in the world.  The bee societies had the most interaction with the creatures.  That disturbed the aphid leaders, for they deemed the bees to be a troubled and dying society, and they wondered if the cause was that the bees consorted with other creatures, such as the two-legs.  It was from the bees that the aphids first heard accounts and stories that suggested that the two-legs had a level of intelligence that the aphids had not conceived of before.

They were just rumors at first, present-day fairy tales.  The public perception was that the two-legs were not intelligent, but there was private concern that they might be, and that such a discovery would cause unpredictable and irreparable disruption to their delicate new society.

But there were those who longed to know.  Those who were intrigued by the notion that there was another sentient people in their world.  Those who believed they could find out and either put the fears of their people to rest, or advance their people into yet another stage of their society.

And who better to perform the measurements than a numerator? Quintillion had argued.

She had designed what she hoped was a simple experiment.  Not much was known of the two-legs, save that they were a much, much younger people than the insects.  Quintillion wondered if such a young people, even if they were intelligent, would have developed enough intelligence to truly understand one of the most profound concepts in the world, numbers.

She had not ignored the potential effects on her society.  Beside the proposal for her experiment, she had written some theoretical treatises on what it would mean to their society should these rumors and legends be true.  Her new pursuit had caused some stirs in her local life.  Her family, her mother in particular, had been proud of her prior accomplishments as a numerator.  Quint had attained a high enough position to do some interesting research of her own, yet the first subject she had chosen was mired in controversy.

The Grand Council, the gathered assembly of numerators and numerators-in-training, and special invited guests, all listened while Quintillion laid out her proposal.  After she concluded, a recess was called, so that the Council might review her proposal.

Quintillion knew, as everyone who had gathered knew, that she would be denied.  She had seen a gleam of curiosity in more than one councilor’s eyes.  But that curiosity would be outweighed by responsibility.

When next she stood before the Council with folded wings and folded arms, she marked their solemn expressions.

“We are numerators, Quintillion,” the Council’s speaker said.  “Your proposal is insufficient in its rigor and its focus toward our purpose.  As such, we must and do deny your request.  We do so with good will and high hopes that you will bring us another proposal.  One that is suited to your talents and to the Numerator’s Aim, and one that we can approve with our greatest confidence.”

The speaker spoke thus, but another of the councilors was not so gentle.

“If the legends of these giants who walk upon two legs have tickled your antennae,” he said, “then perhaps you are poised to leave our community and join the guild of storytellers.”

“With respect, Councilor,” Quintillion said, “a numerator can love stories and a storyteller can love numbers.  These are new days.”  She clipped her response at that last word.  She longed to say more, but did not want to be dismissed for being a restless youth.

She surveyed the room, her gaze snapping from aphid to aphid, gauging each one’s response to the councilor’s words and to her response.  And she dared herself to go further.

“I ask the Council to allow the assembled numerators to cast their own judgment.”  She waited for a nod from the speaker before she continued.  “My fellows, if you approve of my proposal—whatever the Council may say—wave your arms to me.”

A few daring souls waved their arms to her.  Many more raised but one arm, indicating that they agreed with the Council’s decision.  And there were many, less than half, but many who abstained from taking any kind of position.

One of her supporters came down to the floor and joined her.  Quintillion was only mildly surprised to see that it was her long-time rival, Octillion.

He greeted the Council, the gathered numerators, and Quintillion in the formal fashion.  Quint was eager to leave the floor and perhaps indulge in a round of self-pity alongside a round of stout evening dew.  She knew why old Octi had waved a hand.

“Councilors I entreat you to reconsider,” he said.  “I entreat you to do as we numerators are not wont to do.  To risk.  To dare.”  He turned away from the councilors and toward the assembled aphids.  “To guess.”

This was an old argument from her rival.  Octillion often spoke of how the numerators stood by while others engineered the MAC and the new society in which they lived, which in some ways, was quite similar to the old society.

“We are born and built to obey the ways of our society,” Octillion said.  “And there are many ways in which we should, for we are, after all, civilized.  But if we continue to do everything the way our ancestors did, we will never progress beyond what we are now.  There are many who believe that they would be satisfied with that.  And yet those same people want us to continue developing sweeter nectar funnels.  We can’t have it both ways, can we?  And if we advance only in one direction, we will meet the end of that road and then be stuck.  We must be prepared to travel down roads that seem unseemly.  And anyway, what have we to fear from the lumbering beasts that walk upon two legs?”

“It won’t be as you hope it will be,” the speaker of the Council said.  “The creature will see and swat you.  It’s a reflex.”

“I’m sure that is true, for my colleague is wrong about them.  And so we will be careful.”  Octillion bowed to the Council.  “I offer to join Quintillion’s research team as an honest observer.”

“She does not have a team,” a councilor said, “for she has no reason to gather one.”

The speaker spoke again.

“We recognize Numerator Quintillion’s honorable effort to expand the knowledge of her people, and Numerator Octillion’s support of his colleague.  But our decision stands.  By order of the Grand Council of Numerators, neither you nor any numerator within the MAC will pursue this research.”

With that the councilors rose, and the hearing was ended.


Others had done it before her.  The histories even praised some of those who did.  So it was not outside the realm of reason for Quintillion to consider slyly defying the Council as other numerators had done in past ages.  Octillion had been right.  Numerators were generally not a daring bunch.

She would do the research she proposed—or as much of it as she could manage—without the resources that full Council aid would afford.  She would document her research, and store the records for a time when her people would be ready to revisit them.  Such would be her contribution to the pursuit of truth.

She begged leave of her friends that evening, when they offered to treat her to her favorite leaf.  She was not quite as devastated as they seemed to fear when they reluctantly left her.  But Quintillion wanted to be alone, not in misery, but in thought.

She flew through the night air until she spotted the one friend whose company would be perfect for the mood in which she found herself.

She landed and found the giant water bee nibbling on whatever he had found on the ground.  Diameter, or Diamee as Quint had come to call him, was a creature that should not be.

When the aphids first observed the tiny water-dwelling animals, so tiny they were almost invisible, they soon discovered that the puffy eight-legged creatures were the most resilient animals the aphids had ever encountered.  Their girth made them appear somewhat like wingless and antenna-less bees, thus earning them their common names.  To study them more closely and perhaps attempt communicating with them, the aphids developed a means to mathematically magnify the creatures.

There had been no anguish or outcry against the numerators whose researches brought the water bees into the lives and homes of many an aphid, as companions, helpers, and even mounts.

Quintillion settled beside her friend, giving him a playful shove when he leaned against her.  She rewarded him for the affection with a drop of dew.

She managed to enjoy a few moments of peaceful contemplation before she spotted another flying toward her.  When he landed, he gave no greeting, but began speaking as if they’d been in the middle of a conversation.

“Did you hear what that one councilor said to us?  ‘Your dew-gathering days aren’t over.’  I’ll bet he never gathered a drop of dew in his life.”  Octillion brushed pollen from his arms and patted Diamee’s head.

Quintillion twitched an antenna.  “You know he was one of the few numerators who argued for the MAC from the very first.”

“Yes, I know.  I’m just angry.”

“Why are you angry?”

“Because they are letting their fears get the better of them.  Running from flickers that aren’t really there.”

He pulled out a container of nectar and offered her a drop.  “I know what you are sitting here and contemplating, Quint.  And I’m still game.”

Quintillion said nothing.

“That is, if I’m right and you are still planning to go ahead with your full proposal.”

“Even if I dared to defy the Council’s direct orders,” Quintillion said, “I would not be able to perform my research.  I don’t have the resources.”

“I do.”

Quintillion quirked her antennae.

“That is, I have a friend, a distant cousin really, who has the resources, and is enthusiastic for interesting new theories.  She’s rather well-to-do.”

“And what does she think about the two-legs?”

“I don’t know, but I’m sure she would be eager to find out the truth.”

“And how far will we take this discourse before you go and report me to the Council?”

“Only as far as your next insult, Quinty.  Otherwise, I will have nothing to say to the Council until our researches are completed.”

Rivals they might be, and they owed each other no favors, but Quint knew that Octillion would not report her to the Council.  She knew him as well as he knew her.

“You’re confident that they are just beasts?” Quintillion said.  “That my research will prove your theory correct.  You wouldn’t be helping me otherwise.  But what will you do if I’m proven right?”

“You think too little of me, dear colleague.  If you’re proven right, I will first proceed to faint away, too overwhelmed to remain conscious.  And when I come to again, I will demand that we confirm the results with the utmost rigor in our research.  Then after a night drinking the sweetest nectar I have in my pantry, and falling into a dreamless stupor, I will wake, freshen myself, and go with you to the Council, to report your findings.”

Our findings, you mean.”

They were silent then for many moments, as they drank dew and gazed up at the stars.  Then they rose and under the light of a waning moon, the two young aphids clasped arms.


“We will tell everyone that I’ve taken you on a vacation,” Octillion said the next morning as they gathered near the abode of his distant cousin.

It was not unusual for an aphid to treat a rival to a vacation when that rival had failed at some great endeavor.  It was an old custom that had fallen our of favor, but one of the few that many considered worthy of reviving in the new society.

“No one will be suspicious of a lengthy vacation, especially when they hear my cousin is treating us.”

Octillion was right.

Quint’s mother was actually quite pleased to hear that her daughter had made an acquaintance with a well-to-do aphid who might help steer Quint toward more reputable research.  Little does she know that the steering was going in the other direction.

Octillion was right about his cousin’s enthusiasm as well.  Her name was Axiom, and she was one of the wingless alder aphids.  She gushed over Quint’s woolly filaments, asking if Quint ever styled it in any unusual ways, and before Quint could answer, she switched to asking about their expedition and relaying all the rumors and legends about the two-legs that she had heard.  As she spoke, she made the last of the preparations for their travel. For an aphid without wings, she was quite adept at flitting from one thing to another.


They would be traveling a long distance to reach an area where the two-legs were numerous.  Quintillion rode upon Diamee and when he was tired, she would shrink him and let him ride upon her.  As was the way of his kind, this regular shift in size did not seem to cause him any harm.

Along their way, Octillion had reviewed the details of Quint’s proposed experiment, making suggestions and objections.  The Council would have done so, had they approved the experiment.  They tried to encourage Axiom to review the details as well, but she was more interested in observing the changing environment and meeting the odd wayfaring bug.

She joked with Quint about getting shrunken along with Diamee, so she too could ride on the winged aphids’ backs and know what it felt like to fly.

Quint was mortified when she thought she was being rude to her generous patron.  She tried to explain why Ax was too complex for the shrinking and magnifying procedure.  But the alder aphid merely laughed and assured Quint that she was only teasing and she had no desire to fly.

“She’s afraid to,” Octillion later explained.  “She got caught on a sparrow’s back once and went for a wild flight.  Never complained about not having wings after that.”


There was one morning when Quint was afraid that Diamee had run off.  They searched all morning until finally, Quint remembered that the water bee was still shrunken, and she found the creature sleeping under her mandible.

Then one evening, Octillion revived in her a memory that she had completely forgotten.  It was when they were very young, before either of them had decided upon numeration, the course that sparked their rivalry.

One day, on a lark, Octillion challenged Quint to wrestle arms.  Quintillion, being slightly older, and at the time, slightly bigger and stronger, refused the challenge at first.  But egged on by a gathering crowd, she relented, and they began.  And it became clear to the two of them that Octillion was outmatched.  He still remembered the current of fear that jolted through him when he realized how humiliated he would be upon his defeat.

“Only, I wasn’t defeated,” he said.

He’d felt her resistance weaken, and he’d felt that it was not from exhaustion or surrender, but by her own will that her arms fell back before the force of his.  She suffered teasing for a while, but none as bad as he would have, being the challenger.  Perhaps she’d known that.

They were not friends, nor allies.  Quint had no reason to surrender as she did.  Octillion could not fathom why Quint had conceded such an easy victory, when victories were so rare at their age.  It bothered him so much that he confronted her, told her that he knew she had let him win.  And he demanded to know why she had done so.  He had half begun to imagine that it was part of some grander scheme of vengeance or torment that she had planned.  He imagined that she would smirk at him and say nothing, or bat him away as an annoyance.  He did not expect for her to answer as she did.

Octillion smiled.  “You said, ‘There’s no victory here.  You’re due for a growth and when it comes, you will be at least as strong as I am.  Stronger perhaps.  Wrestle me then and you’ll truly beat me.  Then see if you feel victorious.’”

Quintillion remembered then.  When the growth came and greater strength with it, Octillion challenged her to a rematch, which she accepted.  And the game became not herself against Octillion, but the two of them against those who were watching.  They pretended to be evenly matched, though Octillion could have beaten her any moment.  Wordlessly, they exchanged a look and an understanding.  A question.  How long could they keep it up before the spectators began to walk away?  Would they be left alone after everyone else grew tired of watching the stalemate?

“As I recall it,” she said.  “We won.”

Octillion laughed.  “Yes, we did.”


As adventurous as it was just to venture so far outside of the colony’s borders, the true adventure began when they finally arrived in the territories of the two-legs.

Quintillion had tried and failed to recruit a bee or an ant to her team, an insect who had lived close to the two-legs and could advise her of the best subject to choose.  Absent such expertise, they had to spend some time observing.

All three aphids had seen two-legs before, but never so close.  The two-legs were so big that it was difficult to gauge their age.  And Quint did not know if their size even changed with age, or if they went through moltings.  They made sounds and gestures that certainly served as modes of communication, but the aphids could not decipher the communications.  They had heard from other insects that the two-legs released chemicals that some, like the mosquitoes, found appealing, for they fed upon the large creatures.  But again, the aphids could not sense any such chemicals.

At last, Quintillion chose one of the two-legs.  It was not the smallest they observed, nor the largest, but somewhere in between.  So they jokingly named it “Half.”

And they realized that Half was still quite large, and they would have to make their message large enough for it to see.


With Diamee’s help, the aphids pushed a specific number of twigs into a lined formation in a corner of the walled region where their selected subject seemed to reside.  They hid and took shifts observing, and waiting for the two-legs to appear.

Finally, towards evening, the two-legs appeared, along with two others.  The others seemed to frolic about while their subject walked toward the corner where they had arranged the twigs.  Quint had selected the corner after observing that their subject often visited there.  It was protected from wind, and few other creatures, including the four-legged beasts that also roamed about, approached the spot.

Their subject found the twigs and knelt down to observe them.  The two-legs, Half, lingered on the twigs for a while.  Quint believed that meant the two-legs was interested, perhaps intrigued.  Half left the twigs where they lay.

Next the aphids removed two of the arrayed twigs and made two furrows in the ground in their place.  It was meant to represent the subtraction of those twigs.  Quint wondered if the arrangement was too complex, too abstract.

When next Half returned, it lingered even more, signaling to the aphids that there was some awareness in its mind.

They repeated the pattern twice more, and observed Half as Half observed the twig formation, never touching it.


“I’m not convinced,” Octillion said over their dinner the same night.  “Curiosity does not equal intelligence.”

Quintillion crossed her arms.  “Agreed. There’s no victory here.  So let’s proceed with the next phase.”

Axiom’s antennae and her flat body quivered with excitement.

“Let’s see if Half can do some simple math.”


Quintillion looked at the three piles of twigs.  She wished Half luck before retreating to what she now referred to as their “field office,” a hospitable bush that grew nearby.

She had let Axiom borrow Diamee for a swim in a puddle that had formed after some nightly rains.  The weather was growing colder.  And they would have to end this round of experiments soon, until fairer, calmer weather prevailed.

The three piles that Quint and Octillion made contained different numbers of twigs.  They placed two piles next to each other, and one pile below the others.  When the twigs in the two neighboring piles were added, they equaled the number of twigs in the pile below them.

Neither Quint nor Octillion had seen when Half had come.  They had rested little since beginning of their experiment and both had dozed off.

But from their vantage, when they woke, they could see that the piles of twigs had been disturbed.

The two piles that were next to each other had been combined.  Perhaps that meant that Half understood addition.  But it might also mean that some other creature had come and disturbed the piles.  Since they had not observed Half manipulating the twigs, that particular trial could not be included in their research.

They repeated it again.

This time, they watched Half as it found the twigs.  This time, instead of combining the two piles that added up to the pile below, Half separated all the twigs and lined them up.  Each twig in the combined pile, had a partner twig from the pile below.

“Is it trying to demonstrate that it understands the one-to-one correlation between each twig in the combined pile and each twig in the totals pile?” Octillion asked.

“I think so,” Quint said, riveted by the two-leg’s movements.

Next they tested Half’s understanding of subtraction.  They placed two piles together, one below the other, and one containing less twigs than the other.

They observed Half counting the twigs in the piles, and then setting aside the “extra” twigs from the pile that contained more, until both original piles contained the same number of twigs.


They next tested Half’s understanding of division.  They placed twelve twigs in one pile.  Below it they placed six twigs.  Next to this pair, they placed a pile containing twenty-four twigs.  Below it they placed six again.

When Half came, it seemed to ponder over the twigs for some time, and Quint began to worry that they had reached the limits of the two-leg’s intelligence.

But perhaps the creature was merely trying to understand the way the problem was set up.

While Quint, Octillion, and even Ax watched, Half manipulated the piles.  Quint’s heart began to soar when she saw the two-legs dividing the pile of twelve twigs into two piles of six, and dividing the pile of twenty-four twigs into four piles of six.

But her soaring heart faltered, glided lower, and settled on the earth, when she saw that Half was not moving from the spot.  Other two-legs approached Half and handed it items.  Perhaps it was food.  Quint only thought so because she recognized a container full of water.  Such a vast and deep lake of water.  Half drunk it as if it were only three drops deep.

Night came, and the two-legs stilled sat where it was.

Quint perched upon a leaf and crossed her arms.  “She’s waiting for us to come out,” she said.  “I wonder if we should.”

“The safer course is to stay hidden,” Octillion said, “while we continue observing.”

“And in the meantime,” Quint said, turning to him, “do you concede defeat?”

“Let’s wait until we gather a bit more data on division,” he said.  “And since it seems to be camped out here for the night, I say we take our rest and gather that data in the morning.”

Quint agreed.

The next morning, when they saw that Half had gone, they flew down to set up another problem, and they found a surprise waiting for them.


They found the solution to the last problem they set before Half.  And next to it, they found a few more piles of twigs.  Half had left a problem for them to solve.  And it was far more complex than what they had been setting before Half.

Octillion marveled.  “Half has put a variable in the problem.  How unexpected.”

“Perhaps Half is Whole after all,” Quint quipped.

But she was overthrown, so much so that she almost could not solve the simple problem.

They had been observing and gathering evidence of Half’s intelligence for days upon days.  It was enough to conclude that Quint was right.  And yet, it was all so calm and controlled.

Quint understood that for some aphids, their lives would be shaken by the revelation that the lumbering two-legs who shared the world with them were indeed intelligence beings.

But she had only been fascinated by her observations of Half.  She had not been shaken by every correct solution that Half produced.  She had not feared the giant’s approach.

But looking at the problem that Half had devised, the leap in logic that it had taken, the visible evidence lying in the dirt, of a mind truly possessed of sentience…Quint was overthrown.

And she felt exposed after rearranging the twigs to solve Half’s problem.  Before, she had not been sure how she felt about showing themselves to Half.

Now…she and her team debated what they should do next.

“Half is our subject, not our friend,” Octillion said.  “Having intelligence does not save one from barbarism.  It might swat us out of some primitive reflex.”

Axiom glanced between them.  “We are speaking with it.  Now what?”

“Now…”  Quint was still recovering herself.  She knew what came next.  She had planned it.  But she just couldn’t remember in the moment.

“Now, diplomacy must follow discovery,” she said.

Octillion turned to her, raising his antennae. “Do you mean—I thought you were going to lock your notes away in some vault until our people had grown sufficiently open-minded enough to consider that these giants might have some sense, that they might even have math.”

“The Council will condemn us for disobedience, perhaps eveneheresy,” Quint said.  “But we can’t un-know what we now know.”

“Can’t we?” Ax said.  “I do it all the time.  Re-discovery can be so thrilling.”

Octillion looked at Quint.  “This is your expedition, Numerator Quintillion.  We leave the final decision to you.”

“You must be sure you both agree to that.  Your futures are at stake as well.”

“Are we blind fools to have followed you?  I knew there was a slim chance you might be right.  And if you were…ah, the delicious disruption.  The horror and the wonder.  I consider it a victory either way.”

“I wasn’t aiming to disrupt, Octi.  I was aiming to…”  Quintillion could not remember what her aim had been.

“We’ll all need more than a moment to digest what we have observed,” Octillion said.  “But I believe Quint is starting her moment early.”

While they stood debating, while Diamee lingered nearby dozing on a leaf, while Quintillion understood at last all the fears and worries of those who had opposed her, the two-legs they had named Half returned to the scene of their experiment.

“We can leave now,” Quintillion said.  “We can be a mystery that Half will almost certainly never solve.  And we can agree to never speak of what we have seen or what we know.  Or…we can be as great a revelation to Half as Half is to us.  As great a disruption to Half’s society, as Half will be to ours.  I was reckless to decide this for our people.  And foolish to believe that I could have just hidden it until our people were ready.  This may be that kind of truth for which no one can ever be ready.  Truth comes with a price.  Not all will be willing to pay.”

“There’s a price to living in ignorance, too,” Octillion said.

“Who are we to decide?” Quintillion mused.  And she answered her own question.  “We are numerators.”

“How can we know for certain what the truth is, unless we seek to find it?” Octillion said, echoing her own words to the Council.

“I wonder,” Quint said, watching Half bend down and look at the solution they had presented to the problem that Half had given them.  “I wonder if we can devise an experiment to find out if Half here is a friend.”

The aphids remained silent and simply gazed up, all of them wondering what, if anything, the two-legged creature would do.

And while they wondered what the two-legged creature would do, Quintillion realized what she would do next.  She had sought the truth about the two-legs.  And she had found it.  She threw back her arms, sweeping the woolly filaments of her mane back, and she raised her wings in preparation for flight.

Copyright © 2018  Nila L. Patel

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