Short Guide to Critical Thinking – Part 2

Humans aren’t naturally great at seeing the world statistically.

So, they make up their own reference points.

3/8 – Averages

In statistics, the mean is a numerical value equal to the sum of the observations divided by their number. Erroneously, we assume that average is equal to mean, too. But the average is really defined as the central value in the dataset. That can be also intended as the most typical value (mode), or as the value that divides the dataset into two equal parts (median).

Why this speed lesson on statistics?

Most of us aren’t used to scientific observation or do not work with data. That does not stop us from averaging repeated events. It is another funny work of our brain, which tries to give us a sense of what happens around us and anticipate events.

My experience as a driver seems to suggest that other people who drive Skoda Octavia do not care about speed limits in the city, and are particularly bothersome on the highway. No offense if you are one of them. What I did here, was to sum up my observations of all drivers I faced in few months. I noticed that I am mostly swearing at those with the above-mentioned car and few other circumstances, and I got my average. Of course, my reasoning is flawed.

First of all, my experience as a driver is subjective, and so is the one for the others: it depends a lot on the taste for speed, feeling of safety, anxiety, and so on.

Second, it is a very specific experience: based on my experience driving in Slovakia and for 12 months. So, isn’t that there are more Skoda Octavia than in other countries, and this affects my observation?

Third, the road is a perfectly random place. You never know which car will come after you, and what will you find on your way. Yet, I fail to acknowledge this randomness while I am on the road. It is easier to give myself a plausible story (Octavia’s drivers are a pain in the ass) than think of probability and randomness.

The same happens with the news. Unfortunately, with fake news as well. Reports of certain incidents sound more awful than others because we build a baseline based on our assumptions. That is how certain politicians make their bidding, exploiting simple-minded people, racists, and xenophobes. An immigrant committing a crime in your home country sounds outrageous because the culprit is an immigrant, and not because of the crime itself. When you think of this, you realize how stupid and preposterous we are sometimes.

There is no single antidote to this. We aren’t exempt from biases, but once we are aware of it, we can start working on them. It is all a matter of thinking.

4/8 – Sparsity and Outliers

These two concepts are directly connected to the idea of averaging, specifically for these examples that I shared above.

An outlier is an extraordinary event, something that does not happen often. In terms of numbers, it is something incredibly low or high compared to the rest of the observations. A mean which is calculated including outliers is flawed and may propagate as a systematic error. Therefore, outliers must be handled differently.

On top of that, let’s also consider events that are sparse. These are things that do not happen frequently, yet they happen with some frequency. Think of them as the opportunity to see Halley’s Comet from your window (once every 75 years).

Outliers and sparse events are red herrings and can mislead us, however impressive they may look, sound or feel. Yet, they influence our opinions. If even one dog, out of all the dogs we are going to meet in our life, bites our hand, we are going to develop a fear of being bitten by any future dog.

This is, of course, a natural instinct of self-preservation that is managed by our reptilian brain, the limbic system. But imagine what happens if this kind of fear can be manipulated through other events. We fear the unknown, as it provides no certainty.

When bears and hogs descend the forests to scavenge our towns for food, for the first time we deem it extraordinaire. The second, we begin to be afraid it will become a habit. People begin panicking and suggest even the nastiest solutions.

The same happens for pandemics. Nothing affects us in a century, so we become naturally unprepared. If something similar, let’s say a zoonosis, seems to begin afterward, we are even overprepared.

The whole point is, we do not treat every single event as unique and we do not put them in the bigger perspective, “averaging” using real numbers. We let our emotions and biases talk first, our opinions based on a very subjective, emotionally driven average we made up in our heads.

5/8 – Contradictions

We do love generalizing and simplifying things so that we do not deplete mental energy in deep analysis. It is a good strategy to go through the day, considering that not all things need to be analyzed. Also, not everything catches or even deserves our interest. Our attention span is limited, and so it is the mental energy we can afford on focusing.

However, when we are hit by the generalization, we are eager to explain to others why that does not regard us, and how we are an exception. We find justifications to explain how our situation is specific and why it makes us different from any other person.

This is our attempt to become an “outlier” in front of the others, especially when we do not like the generalization. We don’t want to be averaged. Each of us is unique; hence, being associated with a larger, anonymous group is an emotional trigger. This is one contradiction of the halo effect: a few qualities or events associated with a category of people or things become extended to the whole category. We mentally average qualities of one or few individuals belonging to a category, to the extended category.

All Italians are loud. All immigrants are criminals. All blondes are stupid. The list of stereotypes can continue forever. This is, however, unacceptable when we are part of the category, unless it is (of course) a source of pride.

But either the situations are based on emotions and the sense of belonging, not on rational facts. This is commonly used by media to attract consumers in a negative way (mom becomes astronaut; black guy kills people).

The way we cope with this contradiction is that we immediately feel it when it is used as pejorative if it somehow touches our emotional chord, and less because we have in mind an ethical view on the matter.

It gets complicated since we feel something wrong before we acknowledge if it really is.

Finally, we also are prone to linear stories. We cannot accept that something that for us is bad, can be good for another (unless it regards us personally). It boils down to who is damn right about something, eventually through certain attrition. In many cases though, there is no single answer. Just, we don’t really know how many factors influence an event and to which extent, because there is no apparent correlation (that is why predictive analysis is so important, but more on that later).

It even happens in science. Did you know that mental visualization is not universally acknowledged? There are people that, despite decades of incredibly detailed research, do not believe it exists – simply because they cannot experience it. Their counter-research is driven by this hypothesis, but it’s flawed. A real statement is that not everyone can experience visual memory, though it exists. As you can see, even well-educated scientists are victims of the halo effect, misjudgment, and opinions.

Remember, that what we believe are facts many times are just our opinions, and the same happens for many sources of information out there.

The third part of this article will be published next week.

Published by Andrea Paviglianiti

I practice coaching, I love reading, and I work as a data scientist. I also recharge my batteries with meditation, martial arts, and video games. I perform career and skills coaching – thus I define myself as a “cognitive” coach: I help people improve their learning experience to succeed where they want. My method is based on behavioral analysis, psychology of learning, philosophy of dialogue, and classic literature. I write about how to get better at learning, the best books I read, and my personal philosophy of coaching. And I will not lie to you – I can get verbose at times! I’d be happy if you stick around and read more of what I have to share!

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