By Tomasz Piotr Sidewicz
Let me start with a very subjective statement. From my observations and business experience, 95% of clients I deal with cannot think logically. The nature of my job allows me to check their mathematical and logical abilities. As a rule, I give all my clients a short test with a few mathematical and logical tasks. I do it because success in business is a proper combination of the ability to make rational decisions and excellent risk management. Both involve mathematics as an essential tool. On average, I carry out over 1,000 such tests a year, and I have been doing it for at least five years. Calculations of correct versus incorrect answers from 5,000 tests show that, so far, only 250 managers I have met over the last five years have no problems with mathematics and logical thinking. What’s interesting is that my quasi-scientific study doesn’t differ from professional research, which I will refer to later.
Perhaps it has already crossed your mind how you would handle such a test. Well, let’s see. Below you will read three questions developed by Shane Frederick, of the Yale School of Management. His test determines people’s predisposition to make rational decisions and override the gut feeling. This cognitive reflection test is also called the shortest intelligence test. Ready?
- A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?
- If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
- In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
According to research by TNS Poland, only 6% of Poles answered all three questions correctly. My study conducted with a different test suggests the results are even worse, by an extra 1%, but I have to admit that my study probably differs since it is performed under time pressure and some kind of stress. I guess that if the participants of my test had had more time and freedom, their results would have been better.
Why do both statistics show that only one person out of roughly 20 can think logically? The problem with the statistics is that if half of the population eats only buns and the other half eats grilled minced meat, it can be assumed that all of humanity dines at Burger King. Before I answer this question, let me ask you a question. Which group of people do you think you belong to? Perhaps you believe that if you are educated with some degree, and you have already achieved something in your life, you don’t succumb to this so-called cognitive laziness. Well, you do. Everyone does. Me too. This is because our brain works in two modes. One, called System 1, according to researcher Daniel Kahneman, who first used this term, doesn’t put too much energy into what it does. It sort of flies on autopilot and is guided by intuition, emotions, stereotypes and statistical heuristics.
The second mode, named System 2, requires concentration, oxygenation, energy resources, which are commonly called the focus. The thing is that System 1 works 95% of the time, and that’s why you could answer the first question that the ball costs 10 cents. The correct answer is five cents. Surprised? Maybe you are even angry now that you know you belong to the vast majority with the illogical approach? How come 10? If the bat is more expensive than the ball and together it costs 1.10, then… well… Count it yourself on a piece of paper, and you must get the price of the ball is five cents, the bat costs $1.05 and, together (0.05 + 1.05), they cost $1.10. The answer to the second question is five minutes, and the third is 47.
Without contrast, we cannot see
Another fundamental rule of our cognitive perception of the world is what we call the contrast effect. Its influence on shaping our perception of our world and our well-being is significant because in our herd mechanism we have a constant need to compare ourselves to others. This is due to the atavism of survival and fear that we may not be able to cope as well as others do. For example, imagine that each of us work the same number of hours a day and no matter what we do, we are paid the same amount of X. The rule of contrast will make blue-collar workers think that white-collar workers do not work as hard as they should. I’m professionally involved in negotiating with unions, so I’ve been facing similar accusations for years, but I haven’t done any research in this area yet. Fortunately, a similar study was carried out on monkeys by Sarah F. Brosnan and Frans B. M. de Waal. The monkeys were divided into two categories and were supposed to do a simple task. As a reward, some of them got a piece of cucumber for their work, whereas other monkeys got a grape. What do you think? When did the rewarded monkeys with the cucumber rebel? Very quickly. The contrast effect as a mechanism of social inequality and survival fired off soon enough.
Is 567 more than 21,000?
Now, let’s tie these two mechanisms together and add statistical information on the coronavirus situation. There are about 2,500,000 inhabitants in the Łódź voivodeship provincial region. By April 14, there were 567 registered positive cases of coronavirus. This comes out to about one case per 4,409 inhabitants in the region. Let me now play with your imagination and say what the situation with coronavirus in the voivodeship looks like if you were sitting among 4,408 ŁKS football fans (ŁKS stadium has about 5,000 spectator seats) and knew that one of them is infected that day. You will probably look around and assess intuitively (your statistical heuristics would take care of this) whether there were no coughs, sneezing or other symptoms of the virus around you. Then you would return home, and if you did not meet a single person around you who was infected with the virus, the contrast effect would be the primary source of such information. One person per circa 4,500 is rather difficult to imagine as a real danger. Over time, as long as the number of new cases would not increase, but would remain at the same level, your brain would undergo so-called habituation. You would get used to this information and then ignore it.
Let’s change your perspective of numbers a bit and assume you have heard or read that there were already 567 infected people in the City of Łódź with 728,000 inhabitants. This amounts to one case of coronavirus per 1,283 inhabitants. Fast statistical heuristics gives a four times higher risk of getting positive because the contrast effect is smaller. The question how it is easy to confuse the City of Łódż with the entire voivodeship is just a matter of concentration of your System 2.
Why do we succumb to the self-manipulation by statistical numbers? Firstly, the number itself rarely tells us anything concrete. Our primitive brains with their System 1 need an emotional point of reference. In fact, our survival instinct needs such a stimulus. This instinct is dormant every day. If you have something to eat and drink, a bunk to sleep, are completely safe, and you can enjoy full access to Wi-Fi and hot water, your survival instinct has nothing to do. Probably while reading this article, your heart rate is around 60-70 beats per minute. If you had to fight for your life, you wouldn’t be reading this article, and your heart rate would be between 115 and 150 beats per minute. Now that we’ve established that you’re safe, my question is: does the number 21,000 tell you anything? Perhaps you’ll juxtapose it with your earnings or something else that you can measure. Let me tell you, 14 and a half days off is circa 21,000 minutes. The number 21,000 is also the average daily number of deaths of children under the age of five worldwide. That’s what ŁKS and Widzew stadiums can accommodate together. Can you imagine every day both of Łódź’s stadiums filled with dying children under five disappearing all over the world? If you stay close to these places, you will see for yourself that your brain will make sure to remind you of this fact, especially when you are a caring parent and you are more sensitive to children by nature. There’s a good chance that it’ll be embedded in your emotional memory for a longer period of time. If you want to check it out, ask yourself the next day, what you remember from this article?
Even if data is presented objectively, each of us perceive it differently due to our emotional contrast points. Just ask yourself a question about what is possible when the communication specialists are behind the data presentation. Then it gets more exciting and terrifying, but this is material for the next article.
Tomasz Piotr Sidewicz is a student at Społeczna Akademia Nauk.