Pepsi launched a promotion in 1995 in which people could score points and then exchange them for company items. A shirt cost 75 points; sunglasses, 175; and there was even a leather jacket that could be exchanged for 1,450 points. (...)
But the people who made the announcement wanted to end it with something surreal. So, wearing the shirt, glasses and leather jacket, the protagonist goes to his school flying with his Harrier reactor. According to the announcement, this military aircraft could be yours for seven million Pepsi points.
(...) Pepsi allowed anyone to buy additional points at ten cents a point. I am not familiar with the second-hand market of military aircraft, but a price of $ 700,000 for a 20 million aircraft seems like a good investment. And that's what John Leonard did, who tried to take advantage of it.
(...) At first, Pepsi rejected his request: "The Harrier reactor that appears in the Pepsi ad is not real and we include it simply to create a funny ad." But Leonard had already been advised by lawyers and was prepared to fight. His lawyers counterattacked: "We formally ask you to fulfill your commitment and immediately carry out the necessary arrangements to send the new Harrier reactor to our client." Pepsi did not yield. Leonard sued them and went to trial.
(...) Leonard never obtained his reactor, and the Leonard trial against Pepsico, Inc. is already part of the history of Law. (...)
Pepsi took the necessary steps to protect itself from future problems and relaunched the campaign by changing the value of the Harrier to 700 million Pepsi points. I find it incredible that they did not choose this high amount in the first place. Not that seven million sounded more fun; The company simply did not worry about doing the mathematical calculations when choosing an arbitrary high amount.
As humans, we are not good at judging the size of the high figures. And even when we know that one is greater than the other, we are not aware of the size of the difference. In 2012 I had to appear on the BBC news to explain how big a billion was. The debt of the United Kingdom had surpassed the trillion pounds sterling and came to me to explain that this is a very large number. Apparently, shouting "It's really great, we return the connection to the studio!" It was insufficient, so I had to give an example.
I used my favorite method of comparing large numbers over time. We know that one million, one billion and one billion are different amounts, but we often do not appreciate the sharp increase between them. A million seconds counted from now are only eleven days and fourteen hours. Not bad. I could wait all that time. It's less than two weeks. A billion seconds is over thirty-one years old. A billion seconds counted from this moment would place us in the year 33700 ec (it was common).
'Mathematical Pifias: Misunderstanding has never been so much fun'
Author: Matt Parker (Pedro Pacheco González, Translator)
Publisher: Editorial Crítica (Collection : Drakontos)
Pages: 352
Price: 18.90 euros
Those amazing numbers make sense if we think only for a moment. Millions, billions and billions are each one thousand times more than the previous one. One million seconds is about a third of a month, so a billion seconds is about 330 (a third of 1,000) months. And if a billion is thirty-one years or so, then it is clear that one billion is about 31,000 years.
During our lives, we learn that numbers are linear, that the spaces between them are all the same. If we count from one to nine, each number is one more unit than the previous one. If we ask anyone what number is halfway between one and nine, he will answer five, but only because that is what they have taught him. Open your eyes! Instinctively, humans perceive numbers logarithmically, not linearly. A young child or someone who has not been indoctrinated by existing education will say that the number that is halfway between one and nine is three.
Three is a different kind of midpoint. It is the logarithmic midpoint, which means that it is the midpoint with respect to multiplication rather than sum. 1 × 3 = 3. 3 × 3 = 9. You can go from 1 to 9 either by adding two equal steps of four, or multiplying by two equal steps of three. So the "midpoint using multiplication" is three, and that is what humans do by default until they teach us to do it differently.
When some members of the Munduruku indigenous group of the Amazon were asked to place some points in the group to which they belonged, between one point and ten points, they placed groups of three points in the center. If the reader has access to a preschooler or younger child whose parents do not mind experimenting with them, they will do something similar when asked to distribute numbers.
Even after a lifetime with an education that deals with small numbers, there is a vestigial instinct that drives us to see large numbers as logarithmic; to understand that the gap between a billion and a billion is roughly the same as the existing jump between a million and a billion, because both are a thousand times larger than the previous one. In reality, the leap that leads to the billion is much greater: the difference between living up to thirty-one and reaching a time when perhaps humanity no longer exists.
Our human brains are not wired to be good at math by default
Our human brains are not wired to be good at math by default. Don't get me wrong: we are good at a fantastic range of numerical and spatial skills; Even babies can calculate the number of points on a page and perform basic arithmetic with them. We also appear in a world that is equipped for language and symbolic thinking. But the skills that allow us to survive and form communities do not necessarily encompass academic mathematics. A logarithmic scale is a valid way of arranging and comparing numbers, but mathematics also uses the linear number line.
All humans are foolish when it comes to learning academic mathematics. It is a process by which we take what evolution has endowed us with and extend our capabilities beyond what is reasonable. We were not born with any kind of ability or ability to intuitively understand what fractions, negative numbers or many other strange concepts developed by mathematics are, but, over time, our brain can slowly learn to deal with them. Currently, we have educational systems that force students to study mathematics and, with enough training, our brains can learn to think mathematically. But, if those skills cease to be practiced, the human brain quickly returns to factory settings.
A type of British lottery scratch coupon had to be recalled the same week it was launched. Camelot, the company responsible for the British lottery, eliminated it because it "confused the player." The coupon was called "Fresh Money" and was presented with a temperature printed on it. If after scratching, the coupon showed a temperature below the target value, it won. But it seems that many players had a problem with negative numbers ...
One of my coupons said I had to find temperatures below –8. The numbers I uncovered were –6 and –7, so I thought I had won, and the woman in the store thought the same. But when he scanned the coupon, the machine said it wasn't. I called Camelot and I came up with the story that –6 is older, not smaller, than –8, but I don't see it the same.
Which shows that the amount of math we use in our modern society is amazing and scary. As a species, we have learned to explore and use mathematics to do things that exceed what our brains can process naturally. They allow us to achieve objectives that go beyond what our hardware was designed for. When we are operating beyond intuition we can do the most interesting things, but it is also when we are most vulnerable. A simple mathematical mistake can go unnoticed and then have terrible consequences.
The current world is based on mathematics: computer programming, economics, engineering ..., everything is mathematics with different appearances. So all kinds of seemingly innocuous mathematical mistakes can have very strange consequences. This book is a collection of my favorite mathematical mistakes of all time. Errors like those that appear on the following pages are not only funny, they are revealing. Briefly draw the curtain to reveal the mathematics that, as a rule, go unnoticed behind the scenes. It is as if, after our modern witchcraft, it turns out that Oz does overtime working with an abacus and a calculation rule. It is only when something goes wrong that we suddenly realize how far mathematics has made us get and how long the fall could be. My intention is in no way to laugh at the people responsible for these mistakes. There is no doubt that I have made many mistakes myself. We have all done it. As an additional challenge, and for pure fun, I have deliberately made three mistakes in this book. Let me know if you have found them all!
Matthew Parker is an Australian recreational mathematician, author and comedian
/cloudfront-eu-central-1.images.arcpublishing.com/prisa/PVGW65ZK4PGIEFX6PIHO7GCBHU.jpg)
