This resulted in the aircraft taking off with approximately half as much fuel as it required to make it to Edmonton. The amount of fuel required was in kilograms, but they filled the aircraft using pounds, and 1 pound equals only 0.45 kilograms. Except that both the ground maintenance personnel and the flight crew performed their calculations using pounds instead of kilograms. There was still some fuel left from the flight in to Montreal, and this was measured to check how much fuel needed to be added for the next flight. So when Air Canada flight 143 was taking off from Montreal on July 23, 1983, to fly to Edmonton, it had been calculated to need at least 22,300 kilograms of fuel (plus an extra 300 kilograms for taxiing, and so on). Temperature changes can cause things to expand and contract the actual volume fuel takes up depends on its temperature, so it’s an unreliable measurement of quantity. Take the story of the Gimli Glider.Īircraft fuel is calculated in terms of its weight, not its volume. It’s only when something goes wrong that we suddenly have a sense of how far mathematics has let us climb-and how long the drop below might be. They briefly pull back the curtain to reveal the math that is normally being performed unnoticed behind the scenes. The mistakes aren’t just amusing, they’re revealing. My book Humble Pi: When Math Goes Wrong in the Real World is a collection of my favorite mathematical mistakes of all time. So all sorts of seemingly innocuous mathematical mistakes can have bizarre consequences. Today’s world is built on mathematics: computer programming, finance, engineering. A simple math mistake can slip by unnoticed but then have terrifying consequences. When we are operating beyond intuition, we can do the most interesting things, but this is also where we are at our most vulnerable. They allow us to achieve things well beyond what our internal hardware was designed for. As a species, we have learned to explore and exploit mathematics to do things beyond what our brains can process naturally. Which makes the amount of mathematics we use in our modern society both incredible and terrifying. But if those skills cease to be used, the human brain will quickly return to factory settings. We now have school systems that force students to study math, and through enough exposure, our brains can learn to think mathematically. We were not born with any kind of ability to intuitively understand fractions, negative numbers, or the many other strange concepts developed by mathematics, but over time, your brain can slowly learn how to deal with them. But the skills that allow us to survive and form communities do not necessarily match formal mathematics. We also emerge into the world equipped for language and symbolic thought. Don’t get me wrong, we are born with a fantastic range of number and spatial skills even infants can estimate the number of dots on a page and perform basic arithmetic on them. Our human brains are simply not wired to be good at mathematics out of the box. Which brings me to the larger point: As humans, we are not good at judging the size of large numbers. It’s not like 7 million was funnier the company just didn’t bother to do the math when choosing an arbitrary large number. I find it amazing that they did not choose this big number in the first place. Pepsi took active steps to protect itself from future problems and re‑released the ad with the Harrier value at 700 million Pepsi Points.
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