Several years ago, my brother-in-law challenged me and my wife to answer a series of trivia questions with numerical answers (dates, measurements, etc.) The twist to these questions was that we weren’t supposed to come up with an exact answer; instead, we would provide a range that we were 90% sure included the correct answer (for example, between 10 and 1,000). I don’t remember the exact questions my brother-in-law posed, but I’d like to try a similar quiz with you, our readers. For each question below, write down a minimum and a maximum; you should be 90% confident that the correct answer falls somewhere between those two numbers.
- How high above sea level is Mount Kilimanjaro, in feet?
- To the nearest thousand, how many people lived in the Greater Tokyo Area in 2018?
- How many (24-hour) days does it take Mars to complete an orbit around the sun?
- In what year was Mahatma Gandhi born?
- How many full-length novels did Jane Austen complete?
- What is the total height in feet of the Burj Khalifa tower in Dubai?
- How many independent nations are there in the Caribbean Sea?
- How many tribes were in the Iroquois Confederacy at the beginning of the American Revolution?
- In what year did Mansa Musa begin his Hajj to Mecca?
- In miles per hour, what is the airspeed velocity of an unladen swallow? (I’m sorry, I couldn’t resist—and before you ask, a European swallow.)
Now that you’ve finished answering the questions, let’s take a look at the answers:
How many did you get correct? Was it nine out of ten, or close to it?
I don’t remember what my result was the first time I did this type of quiz, but I do remember being shocked at how few I answered correctly. In writing this article, I did one of these quizzes again and got only four out of ten right. My wife, doing the same quiz I did, got eight out of ten by giving much larger ranges when she felt uncertain. If we were correctly estimating our knowledge, we would each have a very high likelihood of getting between 8 and 10 answers correct. It seems that I was overconfident in my estimates.
This phenomenon was first demonstrated in a 1969 study of Harvard graduate students. Each was asked to provide five values as possible answers to each question, including a maximum that they were 99% confident was greater than or equal to the answer, and a minimum that they felt only 1% confident was greater than or equal to the answer. If the students were correctly evaluating their confidence, we would expect that only 1% of the correct answers would be greater than their 99% guesses, and another 1% would be less than their 1% guesses. In fact an incredible 46% fell into these two categories! In other words, they were asked to give a range of answers just like you were, but that they were 98% confident in, and they only got 54% correct. Talk about overconfidence!
This reminds me of a bumper sticker on a car in my childhood neighborhood which read, “Don’t believe everything you think.” Growing up, this felt like a distinction without a difference. However, as an adult, I have come to understand it as an admonition to slow down my thinking and examine my assumptions and thought processes. When I encounter a false assumption or logical fallacy, I try to figure out where it came from and avoid it in the future. I frequently find fallacies in my thinking when I examine it retroactively.
A good example of a logical fallacy happened when I took the quiz as research for this article. One of the questions I answered incorrectly was the diameter of the Moon. I remembered that the circumference of the Earth was about 14,000 miles, so I did some mental math to determine that Earth’s diameter was somewhere around 4,700 miles. Knowing that the Moon’s radius is about a quarter the Earth’s, I calculated its diameter at about 1,200 miles. In order to increase my confidence in my calculation, I added a pretty significant buffer of 600 miles in either direction. Do you see where I messed up?
The true diameter of the moon is over 2,000 miles. My calculations were fine, if a bit rough; my problem was my initial assumption of the Earth’s circumference. I started with a vague memory of the Earth’s circumference and just assumed that it was correct. In my desire to have any kind of anchoring point to help me answer the question, my brain grabbed onto an incorrect number and I never even questioned it. Because I thought it, I believed it.
One of the benefits to examining our assumptions and thought processes is the ability to think scientifically. Many great scientific discoveries have happened when someone looked at a commonplace phenomenon and, instead of just accepting it, asked “why?” or “what if?” It would be easy to see a leaf or feather fall slowly from a tree and conclude that its leisurely descent is because of its light weight. Indeed, Aristotle taught that the speed of an object’s fall was proportional to its weight. By examining that assumption, Galileo was able to conduct a series of “what if” experiments. These experiments demonstrated that things fall at the same rate independent of their weight, overturning Aristotle’s teachings and paving the way for Newton’s law of universal gravitation. Galileo may even have initially thought Aristotle was correct, but he didn’t believe it until he tested it himself.
Great scientific discoveries are not the only benefit to slowing down our thinking. If you’re like me (and your presence on the Exploratorium blog suggests you are), the joy of discovering or learning even a small new thing is a special feeling. Normally, the Exploratorium is a space devoted to the pursuit of this joy. Now, with our doors closed to the public, we must all make our own opportunities for discovery. You can find some on our website in other blog posts or in the Science Snacks, or on any of the myriad science blogs and Youtube channels the internet has to offer. But I think the best place is still the physical world, where we can wonder at the full moon (or the rare comet), the incredible detail of a tiny flower or insect, or the way Karl the Fog always seems to inhabit the same areas. Keep checking back with us, though, and we’ll continue sharing our discoveries.