The Dissidents

THE DISSIDENTS

                              It is better to fail in originality than to succeed    

                                                                  in imitation.

                                                                          HERMAN MELVILLE

Confident in their King, the natural numbers enjoyed at their ease their domain which was so well ordered that they fiercely wanted it to last eternally. Satisfied, King One observed how everyone depended on his goodness.

— Behave well, friend Eleven, and realize that on subtracting or adding me, you simply disappear.

— If you want to be alive, dear Fifteen, pay attention and I will join Fourteen with pleasure.

It was a quiet and happy life. However, as it is our intention to be honest right from the start, we have to admit that deep inside they were not feeling all that happy, and what they called quietude was nothing more but boredom. An odd number neighbored two even ones; an even number surrounded by odd ones felt uneasy. “Everything breathed well established hierarchy, unveiled mystery, endless existence, impossibility of sacrifice, rest and delight”.

This being said, the Cartesian light that once illuminated them, faded away and they ended up imagining that their lives were perfect. Amidst this regulatory harmony King One felt concerned. He thought himself superior, aware of his enormous power, but: what was on his left, perhaps another kingdom with hills and rivers and subjects? Over there a monarch as powerful as he himself could be raising an army!

Lost in such thoughts he was struck by a revelation: “There should not exist other worlds to my left-hand side except for the mirrored image of our world!” Thus came into existence the whole numbers and, in particular, Zero, an apparently neutral character whose absorbing energy would be revealed in due time.

King One’s idea was magnificent. This new world impressed by its abundance and wider collective participation. Now the small numbers had a say in the matter and they could be subtracted from by the greater ones without being punished.

One’s power had but doubled. He kept all his entire relatives in his pocket. The King was so proud-hearted that he did not pay any attention to the rebellious fractions who made their appearance those days.

These unfortunates were not of entire type, nor showed they well-defined principles, but they were everywhere and had started to create division. King One was tormented by the idea that they could serve as intermediaries between the even and odd numbers. And what if the newcomers would succeed in achieving an understanding between those brainless people? On the other hand One’s rule was being questioned by some integers who welcomed the glamorous indefiniteness of those bits of numbers.

The dissension among his subjects poisoned the King. He had done so much for those ungrateful people, and now they began to question his greatness. Since long ago he had been observing the maneuvers of those characters. Some of them had showed the boldness to sneak in between him and Zero. Of course, these wouldn’t worry him because they were tiny and he could control them with his little finger. But, how to handle the others?

One night whilst everybody was asleep, a brilliant idea crossed his mind. From tomorrow on a new law would come into force: “Next to addition and subtraction, two new operations will be incorporated: multiplication and division. The integers own me their lives; thanks to the new law the untamed ones can be conceived through quotients of integers, ergo through me, the Supreme Procreator”.

This new law had its peculiarities. The good-for-nothing Zero could wipe out anyone with a simple multiplicative manoeuver, but One was the closest integer and he was well aware that he was holding the reins. That fractions to his left were taking risks was none of his business. Another side effect of multiplication is that it creates class distinction. The prime numbers would begin to look down on the composite ones. But, in a general sense, the new legislation would bring along more benefit than affliction.

King One's strategy was rewarded with stability that reigned for many years in the extended empire of the natural numbers. The fractions, after some insignificant revolts, lost their hope. Feeling themselves bound by the regulations, they became sheep of the herd which, in due time, came to be known as the Domain of the Rationals, in this way paying tribute to the tameness with which its inhabitants assumed their lives.

No one could foresee that the next rebel would emerge almost under the nose of the King himself. A late afternoon, much warmer than usual, while enjoying a lemonade, One saw him show up. That character, without requesting permission nor greeting anyone, sat down to the right of Seven Fifths. His irreverent appearance put One and, consequently, all rationals on guard. He used a different language and talked about things never heard before.

In an incredibly short period, the Domain of the Rationals was invaded by what the King called “roots of evil.” The solid ground where they had lived until that moment had becoming to crumble. A certain Square Root of Two was the one who started the insurrection.

At that time One lost weight and acquired the physical condition for which he is known. He spent many hours in his chambers, while those “infamous tubers” undermined the stability of his Empire.

The imp of irrationality began to dance about shamelessly in the most unexpected places. However, something worse would happen if a rational was added to, subtracted from or multiplied with one of these zombies. There would be no way of bringing the rational back. The result would inevitably be another zombie. “Things have become very nasty,” the King thought while chewing on the last bit of ice in his lemonade.

But kings sleep one eye closed and one eye open. Anguished by the momentary feeling of helplessness facing the radical hordes, One began to ponder the idea of ordering Zero to exterminate the conspirators through ruthless multiplication. As luck would have it, another brilliant idea crossed his crowned mind before the massacre took place.

He remembered a young woman he had met some time ago at a costume party. Her name was X and she was known for having a changeable personality. In a matter of seconds she could assume any identity. The King would take advantage of those qualities.

So he had her brought in immediately and before the third glass of lemonade he asked her to infiltrate the integers. “Use all your potentials. Do whatever you have to do, but don’t come back without a clear answer. I need to discover the Achilles heel of those damned radicals.”

A few days later X showed up for the monarch bearing excellent news. The crux of the matter was that all those rioters were, in one way or another, implicated in the integers’ family tree. Getting them out of their holes was the final solution.

The King could not hide his joy. “If I am the owner of the children, I will be the master of their parents! Through the veins of my dear Two runs the multiplied blood of that damned Root! “ he shouted.

The next day the offensive began. Although “Inverse Procreation” was the term recorded in the documents, in their conversations X and One called it “Operation Tuber”.

Finding the roots of an integer was nothing else but discovering the totality of his ancestors. That way all those dissidents could be kept down.

Around that time the term algebra became fashionable. “Algebra” was used to hide what happened between X and the integers. And from repeating the word that much, the citizens of the nascent empire ended up calling themselves algebraic.

Many things had changed. Activities that had always been prohibited were beginning to become part of the daily routine. Radicals, formerly rejected for their irrationality, were now requested by One to intervene in complicated operations, tasks that otherwise would have been impossible to solve.

Many alterations had to be implemented for the common good. Society was beginning to function along different procedures. The only person exempt from complying the reforms was, of course, the one who had devised them. Pleased with his talent, he couldn’t imagine that an extraordinary individual was about to enter the scene.

It was Three who first noticed his presence. He saw him exercising somersaults with a skateboard close to his house. Small in stature he attracted attention by his hat which seemed to be screwed to his head. X was making her usual rounds, when Three informed her that some new bloke was prowling in the neighborhood. X, overestimating her abilities, tried herself to clarify the situation before bringing the matter to the attention of the King. On several occasions she tried to elicit information from the stranger, until she realized that the guy didn't like the algebraic ones, or was up to something else, who knows what he had in mind.

It was very early in the morning when X showed up at the Royal Palace. She knew the sovereign's bad temper and hurried up to clarify the seriousness of the situation..

— An intruder threatens the peace in your kingdom —, she said in a low voice.

—An intruder? —asked the King— Get done with that problem as soon as possible. It's not the first time that a smart character shows up, I've had enough with those irrational ones...

—My King, this one seems to be irrational...

—All the more reason!— One burst out— I order you to reprimand that nobody.

—But my King, I have been at this for weeks without finding a solution...

—Well, well, well—, the King grumbled. — Convene an Extraordinary Meeting for tomorrow and make sure the composite ones do not attend. Just admit the primes and some trustworthy irrationals to the meeting. Now get out of my sight!

The next day those who were summoned took their seats in the Board Room. Three was among the first to arrive, taking advantage of his prime status. Happy to feel he had an important role in the meeting, he proudly looked at his neighbors. He always

had envied Two who bragged about being the only even prime and the monarch's first-born.

The King began the meeting. On his face one could read that he hadn't slept all night. He had thought that he would wake up with a solution that would leave them all stunned. The Board had always been a perfect scenery for him to show off. However, this time he failed to find an argument that would make evaporate the “small problem” raised by Three.

He was aware that the radicals formed a group of protesters, but he also knew how to subdue them. Even the most recalcitrant person kneels for the one pulling the trump ace out of his sleeve.

It was the first time the King solicited the Board’s opinion. It was something never seen before, the great opportunity, but, instead of being happy that they could decide about their future, those dull minded individuals felt overwhelmed.

Fifty-nine proposed to take strong action using Zero to eliminate the “shorty”. It certainly was a drastic solution. X murmured something to One, whose expression underwent a change that did not go unnoticed.

X was used to moving among people of all kinds. She knew how dangerous it was to move Zero to that region between Three and Four. Zero was always branded “a necessary evil”. Everybody knew his resentment about the many restrictions to which he was subjected. Zero, to put it simply, was too a dangerous option.

In the midst of the confusion a benign chubby man entered and installed himself comfortably in the first unoccupied chair he found. He threw a quick glance at the audience and began to speak in that characteristic voice of benign chubby men.

— Hello, my name is Pi and I am irrational to the bone.

Everyone laughed out loud. So, you are irrational? We all have been irrationals since long ago!

—You reinvented the wheel! —another voice screamed and they all burst out laughing again.

Square Root of Two made a puppy face when his gaze crossed One’s, silently pleading for forgiveness.

—I am irrational— Pi continued—, but I am not algebraic.

This time a deep silence spread over the room.

— Do you dare to deny the characteristic feature that best identifies us? The essence of this people that builds its future day by day?— the King questioned him, with a voice that sounded somewhat broken at the end.

— It is not the law of the people that I deny, but your law. I have observed you for a long time, every step you take is to magnify yourself. You confabulated with her — he pointed at X with a corner of his hat — with the sole intention of subduing my radical brothers. You are spending infinite sums for fear of prosperity of your children. You can't stand the idea of an irrational exponent. People like me will never have the least opportunity in a world governed by your outdated rules...

—What are you saying, insolent?— One interrupted him—. You are nothing more than an isolated point and of no importance in this infinitely prosperous universe. I am sure that you are the only specimen of your lineage, a vermin that does not solve any problem. Continue your miserable existence between the brothers Three and Four. Life will you be forgiven, but you will have to stay quiet if you want to be in the picture.

—You are completely wrong, Omnipotent Majesty, I do not speak only for myself. For each one of you all there are millions like me. We also deserve to live with dignity and to be heard.

Pi spoke with equanimity. At the end of his speech shouting came in through the high windows. Uncountable nonconformists expressed their truth at the top of their voices.

The algebraic ones and their King had a notion of infinity which was so restrictive that Pi had to make an effort to not burst into laughter. The infinity that had manifested himself this time was much larger than they could imagine. Recruiting the composite ones in order to balance the different tendencies was a foolish enterprise.

The King decided that time had come to risk everything. It was a decision with unforeseeable consequences, but there was no other option.

Without much thinking he ordered X to lead the Supreme Annihilator in front of him. Terrified the girl listened to One's command, but at the same time she imagined her life surrounded by a multitude of new admirers. Ignoring the royal mandate and camouflaged among the crowd, she moved away from the King who -with no other alternative - was forced to accept checkmate.

This transcendent event was celebrated in every corner of the empire. This is why Pi's followers are known as transcendentals. The algebraic ones would join them very soon. Much has been written about their historic alliance. We will only add that, from that moment on, the name they adopted without reference to origin nor affiliation, would be that of the reals.

From then on, royalty was no longer the exclusivity of a despot.