This essay was originally published on my website.
“I think, therefore I am” said Rene Descartes. If humans couldn’t think, we wouldn’t be humans. The definition of human beings would not be the same. So much of our lives affects our thinking to a degree that we don’t even know when we are thinking. We think all the time. We spend our lives thinking, even when we sleep. Is all thinking the same? Are there different types of thinking?
Let’s get started.
Let’s dive into a type of thinking that I’m fascinated by: Statistical Thinking.
A lot of our thinking has one purpose: to use past experiences or memories to predict future outcomes. The past is already gone, the future is yet to come, and the present is…The present is a combination of the two. Thinking is a mental game like chess, we capture as many pieces (information) as we can. Each movement (thought) is a model that allows us to foresee the future to achieve a goal.
That is beautiful to be able to describe the power of the mind and even more beautiful to understand just a little bit of it of our consciousness.
Our mind allows us to think and our thinking allows us to see the world. Each type of thinking provides a different way to see the world and our surroundings. Think about it this way: different thinking, different lenses. It’s like putting on expensive sunglasses or using cheap drugstore sunglasses.
We see with our lenses, we see through our lenses, but we don’t see the lenses themselves. What most people don’t know is that we have agency over them. We can build, create, and change our lenses for the ones we desire. How we see the world (our lenses of reality) determine the kind of experience we are going to have.
For example, our perception of reality predicates our success. Ray Dalio’s first life principle is to “Embrace Reality and Deal With It.” The world is not what we wish it is or was. The world simply IS. If we are able to see the world as it is, our decision-making vastly improves due to the fact that we are able to see what is actually TRUE.
A new branch of mathematics that was developed over the last two hundred years to deal with the more complex aspects of reality: statistics. Statistical thinking allows us to explore concepts such as probability, mean (average or typical value), bias, confidence level, among many others. Statistical thinking is like putting on $2000 sunglasses. If you had on before a pair of cheap drugstore sunglasses, you will notice the difference. And of course, your vision will be better.
To me, seeing the world with statistical thinking lenses is like having a superpower. It has allowed me to find the truth and an accurate description of the world. For instance, one of my passions is investing. I’ve been investing and trading in the stock market and adding this type of skill has given me leverage and comparative advantage to not be fooled by randomness or emotions but rather data or approximately accurate information.
Not only statistical thinking can be applied to financial markets. It can be applied to our everyday lives. We live in a constant flood of information that we do not even know what is true anymore. The truth is manipulated by media outlets, politicians, economists, meme-creators, and who knows who anymore? Who knows who and what is true?
Statistical thinking comes into play by helping you look at the situation, giving you the necessary tools to analyze it, and determining what the right strategy or decision could most likely be and even forecast the future.
Statistics is fascinating. Statistics is not facts or boring data. I’m referring to the study of statistics, which involves the collection/manipulation of data and the probability of an event occurring. You don’t need a degree in statistics nor take a class on this subject. You just need a basic understanding and once you do, you will never see the world the same way. That is why most university majors require to take introductory statistics courses, not only in physics and biology, but in fields such as political science, economics, and psychology.
When I first took a college-level statistics class in high school (AP Statistics), I was always confused that no matter how accurate or how sure one could be about a problem, there was always and every single time, the likelihood that everything we did was pointless and that our results were wrong. This was discouraging to many of my classmates, but to me, it described our human nature and how ignorant we are about everything that surrounds us.
I hear the word “ignorance.”I hear the word “probabilities.” I hear the fact that we don’t know enough. This question comes up instantly: How can we use our ignorance and our limited knowledge to our own benefit and have a better perception of the world?
In the 18th century, two Scottish Presbyterian clergymen decided to create a pension fund for widows and orphans of dead clergymen. They proposed that each church’s ministers would pay a small portion of his income into the fund, which would invest the money. When a minister died, his widow would receive dividends on the fund’s profits, allowing her to live comfortably for the rest of her life. The clergyman had an issue, how were they going to determine how much money the ministers had to pay in so that the fund would have enough money to live up to its obligations? The clergyman needed to predict how many ministers would die each year, how many widows and orphans they would leave behind, and by how many years the widows would outlive their husbands.
The clergymen contacted a mathematics professor from the University of Edinburgh, Colin Maclaurin. The three of them collected data on the ages at which people died and used these to calculate how many ministers were likely to pass away in any given year.
Their work was founded on magnificent discoveries in the fields of statistics and probability. For instance, Bernoulli’s Law of Large Numbers, which found that while it might be nearly impossible to predict with certainty a single event, such as the death of a person, it was possible to predict with great accuracy the average outcome of many similar events. Maclaurin could not predict whether the clergymen would die next year. However, he could predict and tell the clergymen how many Presbyterian ministers would die in Scotland with almost 100% accuracy.
Fortunately, they had data they could use that recorded more than 1000 births and deaths. This data made it possible to see that a twenty-year-old person has a 1:100 chance of dying in a given year, but a fifty-year-old has a 1:39. After processing these numbers, the two clergymen concluded that, on average, there would be 930 living Scottish Presbyterian ministers at any given moment, and an average of 27 ministers would die each year, 18 of whom would be survived by widows. 5 of those did not leave widows would leave orphaned children, and two of those survived by widows would also be outlived by children from previous marriages who had not yet reached the age of 16. Then, they calculated how much time was likely to go before the widows’ death or remarriage (in both cases, payment of the pension would cease). These calculations allowed the two clergymen to determine how much money each minister would need to contribute in order to provide for their loved ones. By contributing £2 a year, a minister could guarantee that his widow would receive a pretty comfortable sum of £10 a year.
According to their calculations, by the year 1765, the Fund for a Provision for the Widows and Children of the Ministers of the Church of Scotland would have accumulated a sum of £58,348. Their calculations turned out to be unbelievably accurate, just £1 less than the prediction. Today, the clergymen’s fund, known as Scottish Widows, is one the largest pension and insurance companies in the world, with assets worth more than £100 billion.
Probability calculations such as those by the two clergymen became the solid foundation of many other fields such as demography by Robert Malthus, evolution theories by Charles Darwin, economics, political science and many other social and natural sciences. Even Newton relied on probabilities when coming up with the probability of clouds in quantum mechanics.
“I only know that I know nothing,” said Socrates once and it reflected that in order to make better decisions, you need to be humble enough to realize that you know nothing. That is the backbone of the scientific method, understanding the limits of our knowledge is how we are able to explore new frontiers. Statistics requires you to be modest to embrace your ignorance. In fact, the smartest people embrace their ignorance. They are intimately familiar with the limitations of their models, and they are excited when they discover that they’re wrong about something.
Another field that I’m fascinated by is physics and coming up with equations that describe reality and our world. Believe it or not, this is a field that has improved my statistical thinking like nothing else. I remember a Saturday morning when I went to Fermilab (America’s particle physics and accelerator laboratory) and the scientist talked about an idea that changed how I approached my decision-making. I learned that when testing our hypotheses, you shouldn’t try to prove it right but rather try to prove it wrong over and over again.
Tesla’s Elon Musk describes his everyday stance as, “You should take the approach that you’re wrong. Your goal is to be less wrong.” The physicist James Clerk Maxwell described it as a “thoroughly conscious ignorance — the prelude to every real advance in science.”
Another reason why I’m so fascinated by statistics is that it can be combined with any other subject matter to create pioneering projects. There are so many opportunities and really interesting projects that can be developed to help people. At the moment, I’m thinking of creating a stock market software that could predict prices using historical data. I’m also learning about the possible uses and businesses that can be created using statistics with coding, machine learning, and data science.
Just as the story of the two clergymen, Musk’s approach, or Maxwell’s quote. The beginning of better decision-making, having a better perception of reality and seeing the world for what it is. It’s necessary that we take this into account and consider these 3 steps.
The first step is to realize that we know nothing and embrace our ignorance. The second step is understanding how statistical thinking helps you see more clearly and accurately to reach new frontiers.
And the third and last step is to recognize that we may never have 100% accuracy or be completely certain but it is by humble enough to recognize your lack of knowledge and putting on your statistical thinking lenses that we might achieve results and make decisions just as impressive as the two clergymen by only being £1 off.