Humble Pi: A Comedy of Maths Errors

by Matt Parker

And it was not just a lame ‘tried’. He went all in. The promotion required that people claimed with an original order form from the Pepsi Stuff catalogue, traded a minimum of fifteen original Pepsi Points and included a cheque to cover the cost of any additional points required, plus $10 for shipping and handling. John did all of that. He used an original form, he collected fifteen points from Pepsi products and he put $700,008.50 into escrow with his attorneys

trillion are different sizes, but we often don’t appreciate the staggering increases between them. A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years.

Humans instinctively perceive numbers logarithmically, not linearly. A young child or someone who has not been indoctrinated by education will place three halfway between one and nine. Three is a different

If you have access to a child of kindergarten age or younger with parents who don’t mind you experimenting on them, they will likely do the same

All humans are stupid when it comes to learning formal mathematics. This is the process of taking what evolution has given us and extending our skills beyond what is reasonable. 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.

Camelot, who run the UK lottery, put it down to ‘player confusion’. The card was called Cool Cash and came with a temperature printed on it. If a player’s scratching revealed a temperature lower than the target value, they won. But a lot of players seemed to have an issue with negative numbers …

The Earth is tearing around the sun at a speed of around 30 kilometres every second, so this New Year’s Eve you will be over 650,000 kilometres away from wherever you were last year. So, if your New Year’s resolution was to not be late for things, you’re already way behind.

If you ever have access to a friend’s phone, go into the settings and change their calendar to the Buddhist one. Suddenly, they’re living in the 2560s. Maybe try to convince them they have just woken up from a coma.

The seasons will still reverse once every half a million years. And you will be alarmed

At 3.14 a.m. on Tuesday, 19 January 2038 many of our modern microprocessors and computers are going to stop working. And all because of how they store the current date and time. Individual computers already have enough problems keeping track of how many seconds have passed while they are turned on; things get worse when they

20 Fenchurch Street in London was nearing completion in 2013 when a major design flaw became apparent. It was nothing to do with the structural integrity of the building; it was completed in 2014 and is a perfectly functioning building to this day, and was sold in 2017 for a record-breaking £1.3 billion. By all measures, it’s a successful building. Except, during the summer of 2013, it started setting things on fire.

The exterior of the building was designed by architect Rafael Viñoly to have a sweeping curve, but this meant that all the reflective glass windows accidentally became a massive concave mirror

a kind of giant lens in the sky able to focus sunlight on a tiny area. It’s not often sunny in London, but when a sun-filled day in summer 2013 lined up with the recently completed windows, a death heat-ray swept across London. Okay, it wasn’t that bad. But it was producing temperatures of around 90°C, which was enough to scorch the doormat at a nearby barber’s shop. A parked car was a bit melted and someone claimed it burned their lemon (that’s not cockney rhyming slang; it was an actua...

And it’s not as if this freak alignment of reflective surfaces could have been predicted in advance. It had never happened to a building before. At least, not since the same thing happened at the Vdara Hotel in Las Vegas in 2010. The curved glass front of the hotel focused sunlight and burned the skin of hotel guests lounging by the pool.

Directions to The Onion could involve walking past The Gherkin and going left at The Cheese Grater. (Yes, they are all buildings.) Number 20 Fenchurch Street was The Walkie Talkie – until everyone unanimously switched to The Walkie Scorchie. The Millennium Bridge continues to be The Wobbly Bridge, even though it only wobbled for two days. But I love the way the nickname gets

about two steps per second, which means their body swings side to side once per second. A human walking is, for all bridge intents and purposes, a mass vibrating at 1 Hertz – which was the perfect rate to get the bridge wobbling. It matched one of the bridge’s resonant frequencies.

The same thing works inside any radio receiver (including contactless bank cards). The antenna is receiving a mess of different electromagnetic frequencies from TV signals, wifi networks and even

While resonance is great in some situations, engineers often have to go to a lot of effort to avoid it in machines and buildings. A washing machine is incredibly annoying in that brief moment when the spin frequency matches the resonance of the rest of the machine: it takes on a life of its own and decides to go for a walk.

This is a common theme in human progress. We make things beyond what we understand, and we always have done. Steam engines worked before we had a theory of thermodynamics; vaccines were developed before we knew how the immune system works; aircraft continue to fly to this day, despite the many gaps in our understanding of aerodynamics. When theory lags behind

application, there will always be mathematical surprises lying in wait. The important thing is that we learn from these inevitable mistakes and don’t repeat them. The twisting

Stephenson went with the creative suggestion that the train had derailed on its own – basically arguing that the train broke the bridge, not the other way around. Nobody bought it. But he did raise the very good point that, in all the previous bridges he had built, the cast-iron girders were fine. None of their theories had hit upon the true cause.

maths and humans go about things. The human brain is an amazing calculation device, but we have evolved to make judgement calls and to estimate outcomes. We are approximation machines. Maths, however, can get straight to the correct answer. It can tease out the exact point where things flip from being right to being wrong; from being correct

Null Island is a small but proud island nation off the west coast of Africa. It’s located about 600 kilometres south of Ghana, and you can find it by putting its latitude and longitude into any mapping software of your choice: 0,0. Fun fact: its coordinates look like the facial expression of anyone deported there. For, you see, outside of databases,

Null Island does not exist. It really does live up to its slogan: ‘Like No Place on Earth!’

For generations, cartographers have been sneaking fictitious places into real maps (often as a way to expose people plagiarizing their work), and it was inevitable that Null Island would take on a life of its own. So, they literally put it on the map.fn2 If you believe their marketing material, Null Island has a thriving population, a flag, a department of tourism and the world’s highest per capita Segway ownership.

I’m as guilty as anyone; many of my small projects that involve a bit of data are kept in spreadsheets. It’s just so easy. Superficially, Excel makes for a great data management system. But so many things can go wrong.

For example: the universe is currently 13.8 billion years old. The important digits are 13.8 and ‘billion’ tells you how big the number is. Much better than writing out 13,800,000,000 and relying on the zeros to indicate the size.

Things like the base-2 binary of computers use a reduced set of digits; binary only needs 0 and 1. A number system needs as many digits as its base, which is why base-10 has the ten digits: 0 to 9. But once you go past base-10, there are no more ‘normal’ digits so letters get called into service.

really easy to convert between binary and base-16 hexadecimal numbers, which is why hexadecimal is used to make computer binary a bit more human-friendly; the hexadecimal 4C47 represents the full binary number 0100110001000111 but is much easier to read.

The gene has the catchy name of MARCH5, and if you think that looks a lot like a date, then you can already see where this is going. Over on your first chromosome, the gene SEP15 is busy making some other important protein. Type

Much like computers having trouble keeping track of time in a 32-digit binary number, Excel has difficulty keeping track of how many rows are in a spreadsheet.

You guessed it: Excel counted its rows as a 16-bit number, so there was a maximum of 2^16= 65,536 rows available. So when the journalists opened the data in Excel, all the data after the first 65,536 entries vanished. New York Times

The European Spreadsheet Risks Interest Group (yes, that is a real organization, one dedicated to examining the moments when spreadsheets go wrong)

love the idea of a spreadsheet lab: columns instead of collimators; if-statements instead of incubators. She was able to analyse one of the biggest corpuses of real-world

find that incredible. Billions of dollars were lost in part because someone added two numbers together instead of averaging them.

find twenty white hexagons and twelve black pentagons. But

My main point was that there is a general feeling in society that maths is not that important; that it’s okay not to be good at it. But so much of our economy and technology requires people who are good at maths. I thought the government acknowledging that there is a difference between hexagons and pentagons would raise awareness of the value we should place on maths and education. Five is a different number to six! And for the record, the signs are

His gesture was both genius and cruel; the socks were simultaneously right and wrong. I’ve not been so conflicted about a pair of sports socks since Year 9 PE lessons.

As a general rule, doors should open in the direction they would need to in an emergency. Because of the location of the hinges, a door opens easily in only one direction; every doorway has a bias one way or the other. A door either loves letting people into the room or is keen to get everyone out of the room.