Scientific Observations & Math

Scientific Observations & Math

My last post was about science and newness. Modern science values new information more than existing information and rewards research that pushes forward into new territories. What unites new science in any field with the historical information that the new science rests on, is mathematics. As Yuval Noah Harari writes in his book Sapiens, “mere observations, however, are not knowledge. In order to understand the universe, we need to connect observations into comprehensive theories. Earlier traditions usually formulated their observations into stories. Modern science uses mathematics.”
 
 
Mathematics are used to communicate observations because mathematics can be objective, precise, and evaluated for accuracy.  My experiences of reality and how I may interpret and communicate that reality is not likely to be the same as the way someone in New York City, Tokyo, or Kabul experiences, interprets, and communicates their immediate reality. However, if we chose to measure our worlds through data and agree on the scales to use, we can begin to bring our subjective experiences of reality into a unified and consistent framework. A lot of how we understand the world is subjective. For example, I run a lot and a lot of my friends run, so a three mile run sounds short to me. However, for someone who doesn’t run often and doesn’t have friends who run often, a three mile jog may as well be a 26 mile marathon. Mathematics escapes the subjective, goes beyond stories and narratives that we may develop from our subjective experiences. It ties our collective experiences together into something more objective. Mathematics allows us to go from stories to real theories.
 
 
That still doesn’t mean we all understand and interpret the numbers the same. In his recent book How to Make the World Add Up, Tim Harford shares an example of national statistics in the UK showing that the average rail car has only 100 passengers. However, in Harford’s experience, traveling at rush hour, the average rail car is completely packed with far more than 100 people. The statistics can be viewed through a different reference point, through the average passenger traveling at rush hour, or through the rail car traveling throughout the day. Without mathematics we could never describe this reality in a consistent and unified way. Our descriptions of the world would be based on narrative and story. Mathematics gives us a grounding through which we can understand the universe in a more comprehensive and generalizable manner.
Pollution & Purity

Pollution & Purity

“Throughout history, and in almost all societies, concepts of pollution and purity have played a leading role in enforcing social and political divisions and have been exploited by numerous ruling classes to maintain their privileges,” writes Yuval Noah Harari in his book Sapiens.
 
 
Humans are amazingly good at identifying the in-groups and out-groups to which  they belong or do not belong. We are also capable of incredible acts of in-group kindness and generosity as well as out-group nastiness and unfairness. I think that JK Rowling’s Harry Potter books can be read as an example of our incredibly powerful in-group versus out-group nature, and within those stories we can also see how purity and pollution play a role in how we understand our in-groups relative to our out-groups.
 
 
In the books, an evil and powerful wizard, the son of a magical witch and non-magical (muggle) man, attempts to rule the world on the premise that magical individuals are inherently superior than non-magical individuals. Purebloods, those whose family line is entirely magical rather than half-bloods or mud-bloods, those whose family line includes muggles or is entirely muggle, are seen as superior and more valuable. Mud-bloods and half-bloods are viewed by the evil wizard and his supporters (and tacitly accepted by many characters) as somehow polluted, or at best diluted. That becomes the basis for out-group hostilities, biases, discrimination, and general nastiness.
 
 
Harry Potter may be a fiction, but the books reflect real world struggles that do take place between arbitrary groups and real world discrimination that occurs based on appearance, social class, talent and skill, religion, and other factors. The United States was founded as a country that discriminated against black people because of the color of their skin and their seemingly savage or backward tribal lifestyles in Africa (and also because white plantation owners stood to benefit from the free labor and exploitation of captured Africans). People born with mixed race parents were called mulatto, and were quite literally seen as less pure than people born to white parents. Ability, skill, and intelligence did not differ in a material way between black slaves and white slaveowners, but in-group and out-group dynamics founded a country based on an imagined hierarchy and real world discrimination between white and black people – a hierarchy and system of discrimination that was legally upheld and perpetuated long after slavery ended.
 
 
Other countries have had similar challenges. In India, a caste system was built almost entirely on ideas of purity. A certain segment of the population was referred to (and still is  to some extent) as “untouchables” for fear of contamination. This group was (and still is) isolated and outcast within the larger society and the results of the discrimination shown to such people has later been use to justify the unequal treatment they receive.
 
 
In some ways fears of pollution and desires for purity are rooted in biology. Pigs can carry dangerous parasites that can infect humans. For early Jews – before sanitary cooking methods were developed, dietary restrictions possibly helped ensure there was less parasite and disease transmission. Isolating sick individuals, people with sores, or people who were hired or charged with handling dead bodies, possibly helped reduce disease transmission among early humans. However, from these reasonable precautions came the biases, fears, and unjust discrimination which became part of our in-group and out-group dynamics and ultimately contributed to the ideas of pure ruling classes and polluted lower classes. Something that was biologically prudent took on a narrative that was exploited and abused over time for political ends.
 
 
When we sense ourselves being fearful of ideas of pollution, whether it is genetic, racial, sanitary, or other forms of pollution, we should try to be aware of our thoughts and feelings. We should try to recognize if we are simply acting out in-group versus out-group biases and prejudices, or if we do have real health and sanitary concerns. If the latter is the case, we should find ways to uphold health and safety while minimizing and reducing bias and discrimination as much as possible.
Imagined Orders Versus Natural Orders

Imagined Orders Versus Natural Orders

Imagined orders are myths that we agree upon and uphold through our actions and beliefs. There is no clear or objective basis to an imagined order to which everyone can agree at all times. Often, imagined orders exist on a continuum with numerous caveats and carve-outs as needed to maintain order and stability. They help shape our institutions and societies by creating a sense of common understanding and accepted beliefs and behaviors.
 
 
Natural orders, on the other hand, are the basis of the scientific theories and observations that humans can make. No matter where we are on the planet we can make the same observations of the speed of light, of protons and electrons, or of gravity. An important distinction is that natural orders exist whether we believe in them or want them to exist. Imagined orders only exist when we believe in them and want them to exist. Yuval Noah Harari describes it this way in his book Sapiens,
 
 
“A natural order is a stable order. There is no chance that gravity will cease to function tomorrow, even if people stop believing in it. In contrast, an imagined order is always in danger of collapse, because it depends upon myths, and myths vanish once people stop believing in them.”
 
 
We can ignore natural order, pretend it isn’t there, and abandon trust and belief in the scientific institutions that deliver knowledge regarding natural orders, but that doesn’t make the natural order itself go away. However, this is something that has occurred throughout human history with our imagined orders. The divine right of kings to rule is an institution that has been discredited and largely abandoned across the globe, but at one time was a powerful institution. Similarly, Roman and Greek religions were abandoned and were left for me to study in English class in high school as mythical stories. The myths which held the Soviet Union together also failed and were abandoned. Once a myth is no longer accepted, it is easily rejected as little more than fiction.
 
 
Harari argues that this fragility of myths is what drives us toward constant vigilance and ritual surrounding myths. Our judges wear long robes to appear more wise to help give credibility to their decisions. We hold large official and serious investigations around events such as the January 6th riot at the US Capitol to help preserve our electoral system. We play the national anthem ahead of sporting events to remind everyone of the fiction of our Nation. The reality, however, is that judges only have authority if we all recognize and agree that their words and declarations are important. Determining what was a violent riot and what was an impassioned plea for freedom can depend on perspective (though when it comes to January 6th and how objectively awful Trump was this one doesn’t seem defensible). And the United States isn’t a real thing. There is no clear reason why our country exists in the exact place that it does – indeed at one point the same territory existed but it was not the United States.
 
 
This doesn’t mean that these myths are bad or are not useful. They help us live our lives, cooperate, and coexist. They are useful fictions, even if they are fragile, built on little more than vague concepts and ideas, and require silly rituals like singing a special song before playing sports. 
Should You Be So Confident?

Should You Be So Confident?

Are you pretty confident that your diet is a healthy option for your? Are you confident in the outcome of your upcoming job interview? And how confident are you that you will have enough saved for retirement? Whatever your level of confidence, you might want to reconsider whether you should be as confident as you are, or whether you are just telling yourself a narrative that you like and that makes you feel comfortable with the decisions you have made.

 

In Thinking Fast and Slow, Daniel Kahneman writes the following about confidence:

 

“Confidence is a feeling, which reflects the coherence of the information and the cognitive ease of processing it. It is wise to take admissions of uncertainty seriously, but declarations of high confidence mainly tell you that an individual has constructed a coherent story in his mind, not necessarily that the story is true.”

 

We feel confident in our choices, decisions, and predictions about the future when we can construct a coherent narrative. When we have limited information and experience, it is easy for us to fit that information together in a simplified manner that creates a logical story. The more conflicting and complex information and knowledge we obtain, the more diverse experiences and viewpoints we adopt, the harder it is to construct a simple narrative, and the harder it is for our story about the world to align in a way that makes us confident about anything.

 

A high level of confidence doesn’t represent reality, and it may actually reflect a lack of understanding of reality and all of its complexities. We are confident that our diet is good when we cut out ice cream and cookies, but we don’t really know that we are getting sufficient nutrients for our bodies and our lifestyles. We don’t really know how we perform in a job interview, but if we left feeling that we really connected and remembered to say the things we prepared, then we might be confident that we will land the job. And if we have a good retirement savings program through our job and also contribute to an IRA, we might feel that we are doing enough for retirement and be confident that we will be able to retire at 65, but few of us really do the calculations to ensure we are contributing what we need, and none of us can predict what housing or stock markets will look like as we get closer to retirement. Confidence is necessary for us to function in the world without being paralyzed by fear and never-ending cycles of analysis, but we shouldn’t mistake confidence in ourselves or in other people for actual certainty and knowledge.
Extreme Outcomes

Extreme Outcomes

Large sample sizes are important. At this moment, the world is racing as quickly as possible toward a vaccine to allow us to move forward from the COVID-19 Pandemic. People across the globe are anxious for a way to resume normal life and to reduce the risk of death from the new virus and disease. One thing standing in the way of the super quick solution that everyone wants is basic statistics. For any vaccine or treatment, we need a large sample size to be certain of the effects of anything we offer to people as a cure or for prevention of COVID-19. We want to make sure we don’t make decisions based on extreme outcomes, and that what we produce is safe and effective.

 

Statistics and probability are frequent parts of our lives, and many of us probably feel as though we have a basic and sufficient grasp of both. The reality, however, is that we are often terrible with thinking statistically. We are much better at thinking in narrative, and often we substitute a narrative interpretation for a statistical interpretation of the world without even recognizing it. It is easy to change our behavior based on anecdote and narrative, but not always so easy to change our behavior based on statistics. This is why we have the saying often attributed to Stalin: One death is a tragedy, a million deaths is a statistic.

 

The danger with anecdotal and narrative interpretations of the world is that they are drawn from small sample sizes. Daniel Kahneman explains the danger of small sample sizes in his book Thinking Fast and Slow, “extreme outcomes (both high and low) are more likely to be found in small than in large samples. This explanation is not causal.”

 

In his book, Kahneman explains that when you look at counties in the United States with the highest rates of cancer, you find that some of the smallest counties in the nation have the highest rates of cancer. However, if you look at which counties have the lowest rates of cancer, you will also find that it is the smallest counties in the nation that have the lowest rates. While you could drive across the nation looking for explanations to the high and low cancer rates in rural and small counties, you likely wouldn’t find a compelling causal explanation. You might be able to string a narrative together and if you try really hard you might start to see a causal chain, but your interpretation is likely to be biased and based on flimsy evidence. The fact that our small counties are the ones that have the highest and lowest rates of cancer is an artifact of small sample sizes. When you have small sample sizes, as Kahneman explains, you are likely to see more extreme outcomes. A few random chance events can dramatically change the rate of cancer per thousand residents when you only have a few thousand residents in small counties. In larger more populated counties, you find a reversion to the mean, and few extreme chance outcomes outcomes are less likely to influence the overall statistics.

 

To prevent our decision-making from being overly influenced by extreme outcomes we have to move past our narrative and anecdotal thinking. To ensure that a vaccine for the coronavirus or a cure for COVID-19 is safe and effective, we must allow the statistics to play out. We have to have large sample sizes, so that we are not influenced by extreme outcomes, either positive or negative, that we see when a few patients are treated successfully. We need the data to ensure that the outcomes we see are statistically sound, and not an artifact of chance within a small sample.
Narrative Confidence

Narrative Confidence

We like to believe that having more information will make us more confident in our decisions and opinions. The opposite, however, may be true. I have written in the past about a jam study, where participants who selected jam from a sample of a few jams were more happy with their choice than participants who selected jam from a sample of several dozen jam options. More information and more choices seems like it would help make us more happy and make us more confident with our decision, but those who selected jam from the small sample were happier than those who had several dozen jam options.

 

We like simple stories. They are easy for our brain to construct a narrative around and easy for us to have confidence in. The stories we tell ourselves and the conclusions we reach are often simplistic, often built on incomplete information, and often lack the nuance that is necessary to truly reflect reality. Our brains don’t want to work too hard, and don’t want to hold conflicting information that forces an unpleasant compromise. We don’t want to constantly wonder if we made the right choice, if we should do something different, if we need to try another option. We just want to make a decision and have someone tell us it was a good decision, regardless of the actual outcome or impact on our lives, the lives of others, or the planet.

 

Daniel Kahneman writes about this in his book Thinking Fast and Slow. He describes a study (not the jam study) where participants were presented with either one side or two sides of an argument. They had to chose which side they agreed with, and rate their confidence. “Participants who saw one-sided evidence were more confident of their judgments than those who saw both sides,” writes Kahneman, “This is just what you would expect if the confidence that people experience is determined by the coherence of the story they manage to construct from available information. It is the consistency of the information that matters for a good story, not its completeness. Indeed, you will often find that knowing little makes it easier to fit everything you know into a coherent pattern.”

 

Learning a lot and truly understanding any given issue is challenging because it means we must build a complex picture of the world. We can’t rely on simple arguments and outlooks on life when we start to get into the weeds of an issue or topic. We will see that admirable people have tragic flaws. We will see that policies which benefit us may exploit others. We will find that things we wish to be true about who we are and the world we live in are only semi-true. Ignorance is bliss in the sense that knowing only a little bit about the world will allow you to paint a picture that makes sense to you, but it won’t be accurate about the world and it won’t acknowledge the negative externalities that the story may create. Simplistic narratives may help us come together as sports fans, or as consumers, or as a nation, but we should all be worried about what happens when we have to accept the inaccuracies of our stories. How we do we weave a complex narrative that will bring people across the world together in a meaningful and peaceful way without driving inequality and negative externalities? That is the challenge of the age, and unfortunately, the better we try to be at accurately depicting the world we inhabit, the less confident any of us will be about the conclusions and decisions for how we should move forward.
System 1 Success

System 1 Success

“The measure of success for System 1 is the coherence of the story it manages to create.”

 

Daniel Kahneman writes that in his book Thinking Fast and Slow when discussing the quick conclusions of our System 1, the mental processing part of our brain that is fast, intuitive, and operates based on simple associations and heuristics.

 

System 1 stitches together a picture of the world and environment around us with incomplete information. It makes assumptions and quick estimates about what we are seeing and compiles a coherent story for us. And what is important for System 1 is that the story be coherent, not that the story be accurate.

 

System 2, the part of our brain which is more rational, calculating, and slower, is the part of the brain that is required for making detailed assessments on the information that System 1 takes in. But normally we don’t activate System 2 unless we really need to. If we judge that System 1 is making coherent connections and associations, then we don’t give it more attention and scrutiny from System 2.

 

It is important that we understand this about our minds. We can go about acting intuitively and believing that our simple narrative is correct, but we risk believing our own thoughts simply because they feel true and coherent to us and in line with our past experiences. Our thoughts will necessarily be inadequate, however, to fully encompass the reality around us. Other people will have different backgrounds, different histories, and different narratives knitted together in their own minds. It’s important that we find a way to engage System 2 when the stakes are high to make more thoughtful considerations than System 1 can generate. Simply because a narrative feels intuitively correct doesn’t mean that it accurately reflects the world around us, or creates a picture of the world that will work within the narrative frameworks that other people create.

The Process of Writing

I listen to lots of podcasts and have a handful of authors whose output I follow fairly closely. Those authors frequently discuss the importance of writing, their process, and what they gain from trying to write each day. One thing is clear from these authors, the process of writing helps with the process of thinking.

 

At the end of his book When Dan Pink writes, “the product or writing – this book – contains more answers than questions. But the process of writing is the opposite. Writing is an act of discovering what you think and what you believe.”

 

I have heard this a lot. That writing is something that helps take nebulous thoughts and organize them together. That writing is not taking the thoughts one already has and putting them down on paper, but that writing pulls disparate pieces that we didn’t always realize we were thinking, and combines them in a logical and coherent manner. We discover through research and close assessment of our mind what we think, and present that to the world.

 

For me, writing is a way to connect with the books that I read. It is a chance for me to revisit them and remember the lessons I learned and think again about the pieces of books that I thought were most important when I originally read them. For me, writing is as much re-discovery as it is discovery. I don’t pretend  that my writing is genuine and unique inspirations from my own mind, but rather reflections on why I found what someone else said to be important.

 

Generally, I believe that Pink is correct. I also think that writing is more than just a discovery of our thoughts, but a creation of our thoughts. Give students an assignment to write from a particular point of view, and even if they previously did not hold such a point of view, afterward they are likely to adopt that point of view. This is not so much idea and belief discovery, but belief formation. Part of our brains are rationalizing the words we put on the page, so to defend ourselves for writing those words. We may create new thoughts through writing just as we may discover thoughts and ideas that had already been bouncing through our mind. What is clear, however, is that writing forces the brain to be more considerate of the ideas that fly through it, and to create narrative and coherence between those ideas, organizing thought in new and more profound ways.

Make Up Your Own Fiction

I am really fascinated by ideas of our personal narratives and how powerful the stories we tell ourselves can be. On some level I think we all understand this, and recently I have been thinking about the power of our narrative within political ideology. The Democratic Party seems to be criticized for creating a narrative where where people are hopeless and can’t make it without a little help. Conversely, the Republican Party seems to operate in a narrative where people can always pull themselves up by their bootstraps if they just try harder. I don’t think either of these simple narratives about how the parties treat people is really accurate, and it is not what I am actually writing about today, just a quick example of how narratives can drive so much of our beliefs and ideas.

 

A quote from Fernando Pessoa in his book The Book of Disquiet translated by Margaret Jull Costa shows the power of narrative, “The truly superior (and the happiest) men are those who, perceiving that everything is a fiction, make up their own novel before someone else does it for them…” What Pessoa is saying is that we can all recognize the power of narratives in our own lives, and create our own stories rather than try to live up to stories that other people have made for us. His ideas in this quote align with a lot of the Stoic ideas and thoughts that I try to live by. His quote acknowledges that we are under pressure from other people to be the person that other people want us to be and to achieve a picture of success created by someone else. Writing our own story, however, gives us the chance to be our own person and to pursue a life on our own terms.

 

“Since life is essentially a mental state and everything we do or think is only as valuable as we think it is, it depends on us for any value that it may have.” A painting is only as valuable as we decide it is. A car is only valuable if we all recognize it as such. Any given activity is only valuable if we decide it is a valuable way to spend our time. There are certainly things we can all recognize as more valuable than others based on the use, form, and function of the thing, but at the end of the day, nothing has inherent value just on its own unless we decide that there is a value attached to it. We should all be aware of the value we place in ourselves, the things in our lives, and how we live so that we can craft a story about who we are that creates meaningful value in our lives and in the lives of others.

Longing for Impossible Things

I currently have Fernando Pessoa’s book The Book of Disquiet (translated by Margaret Jull Costa) on my headboard for a little bit of reading before bed. The book was not published during Pessoa’s lifetime, but was compiled and published after his death. It is a collection of Pessoa’s inner thoughts existing as diary entries, reflections on his life, disjointed feelings, and a set of observations about the world. The book includes incredibly written and translated passages like the following:

 

“The most painful feelings, the most piercing emotions are also the most absurd ones – the longing for impossible things precisely because they are impossible, the nostalgia for what never was, the desire for what might have been, one’s bitterness that one is not someone else, or one’s dissatisfaction with the very existence of the world.”

 

Pessoa is incredibly honest with himself through his writing and he seems to be able to interrogate every emotion and every thought he has. He is so good at it that it painfully tears him apart as he is unable to distinguish between himself, the natural world, the stories he creates of how it all ties together, and his unending awareness of everything inside and outside of himself.

 

His quote above stands out to me because I find such incredible inspiration and power in dreaming of large and almost unattainable things. At the same time, giant and ambitious goals terrify me, and leave me almost paralyzed, too afraid to take action but afraid not to dream. I constantly dream of things could have been different, of the steps and actions I could have taken to truly be on a path toward the greatness I desire, and dissatisfaction seems to lurk around every corner if I look for it. But like Pessoa, I recognize how vain and fruitless this way of thinking can be. There is a fine balance in life between believing in the potential of the future, and being paralyzed between the danger, fear, and monotony of every day life. Understanding how absurd our thinking is and recognizing the fallacies of our stories seems like a way to navigate between our ambitious goals and our defeating self doubt.

 

Greater awareness of who we are and the stories we tell ourselves can help us understand if our goals meaningful enough to make great sacrifices for. Recognizing how our narrative drives us gives us the ability to push back against our self doubt and allows us to craft a new framework that is not as limiting for who we are and who we want to be. We can even get outside the story of our goals and see what small actions we can take to begin to make progress toward our goals, defeating the paralysis we may feel. The recognition of the power of our inner narrative is the one thing that Pessoa seemed to be missing, and it also seems like the one thing that could have helped to change his fear and paralysis.