Numbers are magical. It would be impossible to even count the ways the world be different without numbers – literally! Stuff just wouldn’t have value. There’s so much information in numbers, and they don’t change. In kindergarten, you’re taught that if you have 5 apple and your friend gives you 3 more, then you have 8 apples. And the five apples you have will always be 5 and three will always be 3 and eight will always be 8. The simplicity and static nature of numbers make them so amazing that some people would say that numbers don’t lie. As it turns out, while numbers are typically seen as infallible, the way they are presented can sometimes be misleading, and we may fool ourselves.
Richard Feynman (scientist extraordinaire and one of my scientific heroes, if you’ve been reading along) is attributed with saying that “the first principle is that you must not fool yourself, and you are the easiest person to fool”. Numbers can be deceiving because we are so easily mislead into believing they are not. Add five and three, and you get eight. Every. Single. Time. There have been a few examples in history where numbers weren’t so straightforward; they let us fool ourselves – sometimes with dire consequences.
NASA’s Mars Climate Orbiter launched in 1998, setting out on its scientific endeavor of exploring the climate of Mars, its atmosphere, and its surface while in orbit. Less than a year later, the craft lowered itself into orbit around the red planet when suddenly all communication was lost. 750 pounds of expensive plastics and metals and composites disintegrated in the Martian atmosphere, turning a chance for new knowledge into an utter and complete failure. So where do numbers come into play? The cause of the error was found to be a calculation error; NASA and the mission’s contractor, Lockheed Martin, had agreed on using standard SI units of momentum (Newtons x seconds), but the computer software had been written to output pounds x seconds. A single Newton is more than four times larger than a pound, and the orbiter was destroyed before the error was even detected.
Speaking of Newton, don’t think that great scientists don’t have their fair share of failures as well. I’ve written about Newton’s sailor’s manual blunder before, but I’ll summarize it again here. Isaac Newton was working on the theory of gravitation in 1679. He referred to an old nautical text to see if his prediction of the Moon’s orbital period was accurate. Sailors had previously used the distance between the Earth and the Moon, along with the time between revolutions, to calculate the speed of the Moon’s orbit. A frustrated Newton found that his value was off by about 15%. As it turned out, the sailor’s manual was actually referencing a nautical mile, which is longer than a normal mile since it accounts for the curvature of Earth. What’s the exact difference between a nautical mile and a mile? It’s about 15%. Newton didn’t realize this at the time though, and it may have delayed his theory of gravitation by a few years. So in both of these cases, the numbers were technically correct, but the units were wrong. When looking at numbers, it’s important to notice what they’re representing. It might be true that if I have 5 apples and you give me 3 apples, I’ll have 8 apples. But what if I have 5 apples and you give me 3? Well, 3 what? Because if you give me 3 oranges, then it’s apples and oranges.
Sometimes though, even when we use the right units we find ourselves in a shipwreck of trouble. Built for Sweden in the 1600s, the 69-feet warship called Vasa hoisted its sails on its maiden voyage and skipped across the Stockholm harbor. It didn’t even traverse one nautical mile. Apparently, ship building in these times was essentially trial-and-error. If your ship worked, people wouldn’t know why, but they would copy your design. If you wanted to make any changes, you were just rolling a die and testing fate. Vasa was built similar to other ships and underwent a standard stability test, where sailors ran back and forth atop the deck to make sure it wouldn’t capsize. Vasa failed the test; ten attempts were planned but the boat nearly keeled over after the fifth, and so the test was stopped.
Still, military firepower seemed more important than what authoritative figures thought might just be a small risk, and the doomed ship set sail. As it turned out, after excavation from the deep sea and lots of tedious measurements, the ship was found to be asymmetric. Historians discovered that the ship builders used four different rulers. One ruler used Swedish feet while the other used Amsterdam feet. The units are both “feet”, but the actually size differs by an inch (like the one we know of today). Across 69 feet, those inches add up and when the wind hit, Vasa tipped portside. So numbers might be represented to mean the same thing when really, they are tricky enough to bring down a massive warship.
I remember in history class hearing about old Goody Osborne, married off at thirteen. It seemed so young, but of course, I thought, she would only live to about age 35. So, getting married at thirteen was almost too late; Goodie was already nearly middle-aged! Except, not quite. It is true that before the 1900s, the average age never rose above 40. However, it’s important to keep in mind what an average is. Sum up all the values, and divide by the number of items that were summed. If I got a 95%, a 92%, an 88%, and a 96% on my Salem Trials homework, I would add them all up (371), divide by the number of homework sets (4), and have my average grade (93%). If I had to turn in one more homework, but I only did half of the assignment and got a 45%, my new average would be 83%. I dropped an entire letter grade from just one poor assignment!
This shouldn’t be news to most people; averages are one of those utilitarian math tools that people actually use in the real world (looking at you, long division). What might be interesting to learn is that in the 13th, 15th, and 16th century, if a man in Britain survived past the age of 21, he could be expected to live well over the age of 60. (The 14th century saw this number drop to 45 due to the bubonic plague.) The total averages were skewed by high infant mortality rates, a problem that was substantially improved with the advent of modern medicine and vaccinations, Germ Theory, and hand-washing. So, sometimes averages can be misleading; only when armed with the right knowledge does an average make sense.
It’s crazy to think how these simple Arabic runes can be so complex. This short reflection doesn’t even cover major statistical elements like the confidence limit, standard deviation, and curve fitting, which can also lead to a misleading presentation of numbers. It’s important to be aware but not paranoid. Instead, paranoia should be replaced with knowledge; knowing what numbers represent and how they can be converted to useful material. Information requires knowledge to be analyzed critically, and numbers are just a form of information. Numbers don’t lie, but a unknowing eye could be duped. Learn from the historical mistakes of NASA engineers, venerated scientists, and Swedish sailors. Understand how averages are calculated and what could possibly makes things seem muddled. And mostly, avoid fooling the easiest person to fool.