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The joke is simple enough: they took the idea behind Pepsi Points and extrapolated it until it was ridiculous.
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. A trillion seconds from now is after the year 33700CE.
In 46BCE Julius Caesar decided to fix this with a new, predictable calendar. Every year would have 365 days – the closest whole number to the true value – and the bonus quarter days would be saved up until every fourth year, which would have a single bonus day. The leap year with an extra leap day was born!
Despite it being a mathematically better calendar, because this new system was born out of Catholic holidays and promulgated by the pope, anti-Catholic countries were duly anti-Gregorian calendar. England (and, by extension at the time, North America) clung to the old Julian calendar for another century and a half, during which time their calendar not only drifted another day away from the seasons but was also different to the one used in most of Europe.
Through a massive effort, almost everything was updated. But a disaster averted does not mean it was never a threat in the first place.
When looking at humankind’s relationship with engineering disasters, bridges are a perfect example.
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 how engineering progresses. Before the Millennium Bridge, the maths of ‘synchronous lateral excitation’ from pedestrians was not at all well understood. Once the bridge had been fixed, it was a well-investigated area.
Thankfully, it did not take loss of life for humans to learn about the resonance in suspension bridges. To this day, there is a sign on the Albert Bridge in London warning troops not to march in time across it.
much. It was a classic step forward in engineering: take previous successful designs and make them do slightly more while using slightly less building materials. The Dee Bridge fulfilled both these criteria.
Sneaky, huh? From unfortunate names to malicious attacks, running a database is difficult. And that’s even before you have to deal with any legitimate data-entry mistakes.
The European Spreadsheet Risks Interest Group (yes, that is a real organization, one dedicated to examining the moments when spreadsheets go wrong) estimates that over 90 per cent of all spreadsheets contain errors. Around 24 per cent of spreadsheets that use formulas contain a direct maths error in their computations.
Value at Risk (aka VaR) calculation gives traders a sense of how big the current risk is and limits what sorts of trades are allowed within the company’s risk policies. But when that risk is underestimated and the market takes a turn for the worse, a lot of money can be lost.
A spreadsheet has all the outward appearances of making it look as if serious and rigorous calculations have taken place. But they’re only as trustworthy as the formulas below the surface. Collecting and crunching data can be more complicated, and more costly, than people expect.
There is more than one way to make a geometric mistake. To me, the less interesting way is when the geometry theory is solid but someone makes a miscalculation when doing the actual working out – even though that kind of error can lead to some pretty spectacular consequences.
As devastating as a miscalculation like that can be, I’m more interested in geometry mistakes where someone has not properly thought through the shapes involved – situations where the geometry itself is wrong, not just the working out.
I just looked up the Australian postcode where I grew up (6023) and, as of 2011, there were 15,025 people living in 5,646 different dwellings.
Trains in Switzerland are not allowed to have 256 axles. This may be a great obscure fact, but it is not an example of European regulations gone mad.
This is, apparently, easier than fixing the code. There have been plenty of times where a hardware issue has been covered by a software fix, but only in Switzerland have I seen a bug fixed with a bureaucracy patch.
This means that writing computer code involves trying to account for every possible outcome and making sure the computer has been told what to do. Yes, programming requires being numerate, but in my opinion it is the ability to think logically through scenarios which most unites programmers with mathematicians.
The prevalence of military examples of maths going wrong is not because the armed forces are particularly bad at mathematics. It’s partly because the military are big on research and development, so they are at the bleeding edge of what can be done, which tends to invite mistakes.
In 1993 Kate and Chris met while studying at Sheffield University in the north of England and a few years later decided to go on a world trip.
Getting our heads around probabilities is very hard for humans. But in high-stakes cases like this, we have to get it right.
Some of the ancient Sumerian records were written by a person seemingly named Kushim and signed off by their supervisor, Nisa. Some historians have argued that Kushim is the earliest human whose name we know. It seems the first human whose name has been passed down through millennia of history was not a ruler, a warrior or a priest … but an accountant.
Our modern financial systems are now run on computers, which allows humans to make financial mistakes more efficiently and quickly than ever before.
The market was already a bit fragile on 6 May 2010, with the Greek debt crisis growing and a General Election taking place in the UK. The sudden, blunt release of the E-Minis slammed into the market and sent high-frequency traders haywire. The futures contracts being sold soon swamped any natural demand and the high-frequency traders began to swap them around among themselves. In the fourteen seconds between 2:45:13 and 2:45:27 over 27,000 contracts were passed between these automatic traders. This alone equalled the volume of all other trading.
In the first half a second after this data is released, more than $40 million worth of trades can already have occurred in a single fund. The chumps who waited to get the data for free at 10 a.m. would find that the market had already adjusted.
It would be remiss of me not to say something about the global financial crisis of 2007–8. It was kicked off with the subprime mortgage crisis in the US then rapidly spread to countries all around the world. And there are some interesting bits of mathematics which fed into it. My personal favourites are collateralized debt obligation (CDO) financial products. A CDO groups a bunch of risky investments together on the assumption that they couldn’t possibly all go wrong.
instead I’ll talk about a more interesting and concrete example of people not understanding maths: company boards giving chief executive officers (CEOs), that is, the people in charge of companies, pay awards.
Boards just kept giving the same number of stock options, seemingly ignoring their value. And during the 1990s and early 2000s that value went up a lot.
The explosion in CEO pay stopped. This is not to say it decreased back to pre-explosion levels: once established, market forces would not let the level drop. The massive CEO pay packages still awarded today are a fossil of when company boards didn’t do the maths.
In the 1992 Schleswig-Holstein election in Germany the Green Party won exactly 5 per cent of the votes.
regulation. It seems that, if the Trump administration couldn’t change the ACA itself, it was going to try to change how it was interpreted. It’s like trying to adhere to the conditions of a court order by changing your dog’s name to Probation Officer.
In January 1982 the Vancouver Stock Exchange launched an index measure of how much the various stocks being traded were worth.
Most real-world salami-slicing scams seem to use amounts greater than fractions of a penny but still operate below the threshold where people will notice and complain.
If humans are going to continue to engineer things beyond what we can perceive, then we need to also use the same intelligence to build systems that allow them to be used and maintained by actual humans. Or, to put it another way, if the bolts are too similar to tell apart, write the product number on them.
I’m not a typical Australian. But then again, no one is.
But the folks who founded OKCupid happened to be mathematicians, and the site is almost as much about data as dates. So they dug into the stats and, along the way, they found something interesting.
Just because something survives does not mean it is significant.
I should make it very clear: in the article I explained that the correlation was because of population size. I explained in great detail that this was an exercise in showing that correlation does not mean causation.
More than one person suggested that expensive neighbourhoods have fewer masts and young families with loads of kids cannot afford to live there, proving once again that there is no topic that Guardian readers cannot make out to be about house prices.
As the saying goes, there are only three things certain in life: death, taxes and people trying to cheat on their taxes.
This goes to show that, even though some sysadmins see themselves as gods on Earth, they still have to obey the laws of physics.
He points out that, in pharmacy, it is illegal to give a patient the wrong drug. This does not promote an environment of admitting and addressing mistakes. Those who do make a slip-up and admit it might lose their job. This survivor bias means that the next generation of pharmacy students are taught by pharmacists who have ‘never made mistakes’. It perpetuates an impression that mistakes are infrequent events. But we all make mistakes.
On reflection, most calculators have no error checks built in at all and should not be used in a life-or-death situation. I mean, I love my Casio fx-39, but I wouldn’t trust my life to it.
I could almost hear the regret in their voice at ever having told me about the mistake in the first place. Showing them my holiday photos of me with the manifestation of their miscalculation did nothing to persuade them.
Humans don’t seem to be good at learning from mistakes. And I don’t have any great solutions: I can totally appreciate that companies don’t want their flaws, or the research they had to fund, to be released freely.
The CHI+MED team who are researching the computer–human interactions with medical devices actually came up with a new version of the Swiss Cheese model which I’m quite partial to: the Hot Cheese model of accident causation.
These systems definitely helped reduce errors where the wrong medication was given, but they also opened up all-new ways for things to go wrong.
