For rebels who are not afraid of being who they are

−CALM DOWN! Everything's going to be fine. It's got to be in here somewhere.

I tried to look as if everything was under control, but even I didn't believe that everything was going to be fine. Damned explorer backpack! I'd told her that we didn't need such a sophisticated piece of junk. There were so many pockets and compartments I couldn't find anything. I decided to dump all the contents on the ground. She looked at me absent-mindedly, her pupils so dilated that the charming blue of her eyes was barely noticeable. At last I found it, between my boots and half hidden by the dry leaves of the plants all around us. The box was quite small, but the text was printed in bright red letters.

I opened the box and desperately looked for the leaflet. As usual, it was right at the bottom and I had difficulty getting it out. When I finally managed it, I had to unfold it God knows how many times. I ended up with an enormous sheet, packed with information and printed in such a small typeface that it looked like the paper was black. I scanned it as fast as possible looking for the administration instructions. I couldn't find them! How was that possible? Then I realized that I hadn't fully opened it yet: there was one last fold that doubled the amount I had to read. I took a deep breath and dived back into that sea of letters. Finally, I found what I was looking for. I wiped the sweat from my forehead with my forearm, while I tried to concentrate on what I was reading.


Shake the canister, place the mouthpiece between your lips and press the button once. Keep the mouthpiece in your mouth and inhale three times. Then immediately remove. Under no circumstances should you inhale more than three times. Failure to follow these instructions can be fatal.

−All right, I've got it. Put it in your mouth and breathe in −I said−. Count to three and then take it out.

I wanted to hold it while she inhaled, but she can't stand anyone putting anything in her mouth. She grabbed it out of my hands and did it herself.

−Count out loud so I can hear you −I wanted to be sure she did it right.

−Zero, one, ...

Exhausted by the long walk and the excess of adrenaline, I lay down while I listened to her counting beside me. It may not have been safe to lie down like that, but I was all in and didn't have the energy to do anything else. Her voice was muffled by the echo caused by the canister. If truth be told I hadn't wanted to go. What the hell were we doing all alone in the jungle? But, of course, we had to do everything just as she wanted. It's not as if they hadn't made it perfectly clear to us: "Keep your mitts off them plants 'cos at this time of year deadly spiders get in behind the leaves. They're small little buggers but they'll be the death of you, no mistake." She'd laughed at the little man who told us that. At him and at his mouth that was already missing its teeth.

−Two, ...

And, of course, Mrs Know-it-all had had to pick a leaf for her collection, hadn't she? Just a moment! What did she say? Zero? Why zero? What did she mean zero? I launched myself at her in an attempt to take the container out of her mouth just as she said three and her head rolled back, her eyes glazed over and her beautiful pupils dilated, COMPLETELY AND FOREVER.

Mathematical note

Nowadays we can't even begin to understand maths without the number zero. However, this has not always been the case. For example, Greek mathematicians, who were interested in geometry, ignored it. To understand their point of view about a number that represents null quantity, imagine that you measure someone's height and you tell them that they are zero inches tall. If they are zero inches tall, who are you talking to? There is no one there. From this point of view, zero is not a possible numerical value and, therefore, cannot be a number.

The Greeks' disregard for the number zero is still present in our subconscious. If you ask someone to count up to three, most people (except maybe the real rebels) will start from one, though they could decide to start from any number before three (zero, for example). It is interesting to note that in a countdown, things change. If you ask someone to count down from three, most people will not end until they say zero. In this case, our brain understands that a countdown is like emptying a list of numbers: every time you say a number it is removed from the list. It is like having a basket full of apples and every time you say a number you take an apple out. It's not until you say zero that your brain perceives the empty basket, so it feels as if the counting has not finished.

Although zero can be understood simply as just another number in the numerical sequence, it is actually much more important than it seems at first glance. Like the Greeks, the Romans did not have zero either, and their mathematics was not at all innovative.

About 4,000 years ago, the Sumerians were already using a positional number system, that is to say, a system in which the numerical value of a symbol depends on its position relative to other symbols. In their system, they included the positional zero as a way to differentiate 10 from 100, or to show that the number 13,013 had no value in the hundreds column. The Sumerian system was taken up by the Babylonians around the year 300. Independently, the Chinese mathematicians in Asia (in the early days of our era) and then the Mayans in America (around the year 350) also developed a zero as a placeholder. Despite being good mathematicians, neither the Chinese nor the Mayans used zero as an arithmetic operator. The Mayans only used it to calculate their calendar systems.

George Gheverghese Joseph recently said that the concept of zero as an indicator of the absence of quantity first emerged in India around the year 400. Joseph suggests that the Sanskrit word for zero, śūnya, meaning empty, comes from the Buddhist doctrine Śūnyata, which practises emptying the mind of thoughts. The use of zero as a number to indicate the absence of quantity is therefore the application of a philosophical concept to the field of mathematics.

The number zero and its arithmetic operations were defined by Brahmagupta, a Hindu astronomer and mathematician, in the year 628. He used a little dot to represent the number. The Persian mathematician Mohammed ibn-Musa al-Khowarizmi suggested using a small circle instead of a dot if there were no numbers in the tens column: this is the first reference to using the symbol 0 to represent the zero in the writing. The Arabs called this circle sifr (meaning empty).

The zero came to Europe via the Muslim conquest of the Iberian Peninsula. The Italian mathematician Fibonacci was the first to use it to calculate equations without an abacus which, until then, had been the arithmetic tool par excellence. This development was welcomed by Italian traders, who soon adopted the Fibonacci zero equations in their accounting books.

The use of zero in Renaissance Europe, however, came up against the Church. "God is in everything that is. Everything that is not is the devil", religious leaders said. The Italian government distrusted Arabic numbers and banned zero. Even so, traders continued to use it illegally and secretly. From the Arabic word for zero, sifr, comes the word cipher, which means coded.

By 1600 the number zero was already common in Europe. It played a crucial role in René Descartes' Cartesian coordinate system, the origin of which is the point (0,0). The developers of calculus, Sir Isaac Newton and Gottfried Wilhem Leibniz, were to take the final step in our understanding of zero. They found a solution to problems such as this one. Imagine you want to know the speed at which the ball moves during a football game. Sometimes it moves very fast (for example, when Messi takes a direct free kick), and sometimes it stops suddenly (for example, when the ball kicked by Messi hits the back of the net). As you see, the speed of the ball is constantly changing during a game. But how can you estimate its speed at a given instant? This is where zero and calculus play a crucial role: you need to measure the change in speed over a period of time. If you then make the period shorter and shorter, you can make a reasonable estimate of the speed at a particular instant. As the period of time approaches zero, the relationship between the change in speed and the change in time is a very small number above zero. This is just one example of the kind of problem that intrigued Brahmagupta about a thousand years ago and which Newton and Leibniz solved with their calculus. Calculus paved the way for today's physics and technological development. For example, computers could not have been conceived without the existence of zero.

Zero's story is the tale of a number who refused to bow to the injustice of being condemned to oblivion. To claim his rightful place, however, he needed the help of rebellious minds who did not meekly accept what they had been taught at school, and understood that between positive and negative numbers there was another number that had been denied its numerical rights.

Although it may seem to you that zero is a matter of little substance, even a nullity, just remember that you could never have read this text without it!

Urbano Lorenzo Seva, Reus 2019

Translation by John F. Bates and Urbano Lorenzo Seva

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