Explorers who went to the South Pole but got the calories wrong, a warship and a spaceship that were lost because the builders got their feet mixed up, a missile that missed the target by a few bits… when it comes to math, you have to have a lot carefully.
You know when you make a small mistake and the damage is colossal? That’s precisely what I’m going to talk about today: disasters that were caused by mathematical errors.
I laugh at some of these things, even though they’re not funny and they’re kind of sad. But there are mistakes that are so ridiculous, so bad, that it actually makes a person want to laugh.
Okay, let’s start with the first misadventure.
Calorie-free shipping
During one of the first expeditions to the South Pole, between 1910 and 1912, the group leader, Robert Falcon Scottwrongly calculated the amount of calories that the explorers’ rations should contain.
They were ingest about 4,400 kilocalories per day. However, due to the cold and the efforts they had to make, spent around 7,000 kilocalories daily. Therefore, they created a calorie deficit.
This miscalculation in calories meant that, when they arrived at the South Pole, the explorers had already lost about 25 kg weight — and, on the return trip, they lost so much weight that they ended up starving.
Swap feet… for meters
In the second mathematical disaster, in 1628, expressions of horror appeared on the faces of the Swedes as they saw their new Vasa warship sinks less than a mile from the coast.
And what was the problem? The ship was asymmetrical, it was thicker on the port side than on the starboard side. And, probably, this was due to the fact that the builders worked with different measurement systems.
The archaeologists who explored the wreck found four rulers that had been used in the construction of the ship. Two of these rulers were calibrated in Swedish feet, which corresponded to about 30 centimeters. And the other two, in Dutch feet — about 28 centimeters.
A similar error occurred a few centuries later, when the space probe Mars Climate Orbiterfrom NASA, which was going to orbit Mars, came to life.
The engineering team made the calculations with the British imperial systemwhile the staff of the Jet Propulsion Lab used the metric system.
It was rubbish.
Sheet with calculation error
This isn’t really a disaster, it’s more of a bizarre detail. Apparently, in 2007 version of the Microsoft Excel spreadsheetmultiply numbers whose result was 65.535 resulted in an error.
For example, 850 x 77.1 supposedly gives 65,535but in Excel the result presented was 100,000. And the same happened with 10.2 x 6,425, that is, when calculating numbers whose product was 65,535, Excel said it was something else — those 100,000.
But what is special about this number 65,535? Could this be the true number of the beast? Well, it’s nothing more or less than the biggest number that can be represented using 16 bitstaking into account that it is 216-1.
0.010111000011 seconds count
Fourth disaster: in 1991, during the Gulf War, a North American missile was unable to intercept an Iraqi missile, which resulted in the death of 28 soldiers.
The cause was a inaccurate calculation of time since missile launchdue to arithmetic errors on the part of the computer. More specifically, the missile’s internal clock measures the time in tenths of a second and calculations were carried out using 24-bit numbers.
The problem is that, in the binary system, the number 1/10 (i.e., 0.1) does not admit a finite representation and your binary expansion was cut off after 24 bits.
It is truncation error was propagating over 100 hours, which caused the errors to accumulate and increase, and in the end the error ended up being 0.34 seconds.
Now, as the Iraqi missile had a speed of about 1.676 m/sthis meant that in this space of time, in 0.34 secondshad traveled more than half a kilometer: 569.84 meters. The North American missile was unable to predict this behavior and no longer had the range to intercept it.
This is what we can call a typical rounding error…
The bridges sway. Often!
Finally, the fifth and final disaster has to do with the Tacoma Bridge is leftin Washington, in 1940. This bridge was made of steel and, strange as it may seem, This material has high elasticity and therefore oscillates with a certain natural frequency.
Now, on November 7, 1940, due to winds of about 60 km/hthe periodic external force acting on the bridge had a frequency that coincided with the natural frequency of the bridge, and this caused a phenomenon called mechanical resonance.
The bridge then began to sway more and more.because these frequencies coincided precisely, and the result turned out to be completely destructive.
A similar phenomenon occurred in 1831, at Broughton Bridgein England, when a column of soldiers marched through it, because, by the work of Satan, the frequency of soldiers’ march coincided with the natural frequency of the bridge and then there was this resonance phenomenon again.
The bridge began to sway—and away it went.
This is the reason why, if a military column cross the D. Luís I bridgeno Porto, soldiers cannot march. On the other hand, we can rest assured: on Saint John’s night, when thousands of people cross the bridge, there is no danger — because their steps are out of sync.
And that’s it, these 5 cases show us that you need to be very careful with regard to mathematics; we have to do things very rigorouslytry to predict what could happen… and of course, do tests.
