Causal Illusions - The Book of Why

Causal Illusions

In The Book of Why Judea Pearl writes, “our brains are not wired to do probability problems, but they are wired to do causal problems. And this causal wiring produces systematic probabilistic mistakes, like optical illusions.” This can create problems for us when no causal link exists and when data correlate without any causal connections between outcomes.  According to Pearl, our causal thinking, “neglects to account for the process by which observations are selected.”  We don’t always realize that we are taking a sample, that our sample could be biased, and that structural factors independent of the phenomenon we are trying to observe could greatly impact the observations we actually make.
Pearl continues, “We live our lives as if the common cause principle were true. Whenever we see patterns, we look for a causal explanation. In fact, we hunger for an explanation, in terms of stable mechanisms that lie outside the data.” When we see a correlation our brains instantly start looking for a causal mechanism that can explain the correlation and the data we see. We don’t often look at the data itself to ask if there was some type of process in the data collection that lead to the outcomes we observed. Instead, we assume the data is correct and  that the data reflects an outside, real-world phenomenon. This is the cause of many causal illusions that Pearl describes in the book. Our minds are wired for causal thinking, and we will invent causality when we see patterns, even if there truly isn’t a causal structure linking the patterns we see.
It is in this spirit that we attribute negative personality traits to people who cut us off on the freeway. We assume they don’t like us, that they are terrible people, or that they are rushing to the hospital with a sick child so that our being cut off has a satisfying causal explanation. When a particular type of car stands out and we start seeing that car everywhere, we misattribute our increased attention to the type of car and assume that there really are more of those cars on the road now. We assume that people find them more reliable or more appealing and that people purposely bought those cars as a causal mechanism to explain why we now see them everywhere. In both of these cases we are creating causal pathways in our mind that in reality are little more than causal illusions, but we want to find a cause to everything and we don’t always realize that we are doing so. It is important that we be aware of these causal illusions when making important decisions, that we think about how the data came to mind, and whether there is a possibility of a causal illusion or cognitive error at play.
Stories from Bid Data

Stories from Big Data

Dictionary.com describes datum (the singular of data) as “a single piece of information; any fact assumed to be a matter of direct observation.” So when we think about big data, we are thinking about massive amounts of individual pieces of information or individual facts from direct observation. Data simply are what they are, facts and individual observations in isolation.
On the other hand Dictionary.com defines information as “knowledge communicated or received concerning a particular fact or circumstance.” Information is the knowledge, story, and ideas we have about the data. These two definitions are important for thinking about big data. We never talk about big information, but the reality is that big data is less important than the knowledge we generate from the data, and that isn’t as objective as the individual datum.
In The Book of Why Judea Pearl writes, “a generation ago, a marine biologist might have spent months doing a census of his or her favorite species. Now the same biologist has immediate access online to millions of data points on fish, eggs, stomach contents, or anything else he or she wants. Instead of just doing a census, the biologist can tell a story.” Science has become contentious and polarizing recently, and part of the reason has to do with the stories that we are generating based on the big data we are collecting. We can see new patterns, new associations, new correlations, and new trends in data from across the globe. As we have collected this information, our impact on the planet, our understanding of reality, and how we think about ourselves in the universe has changed. Science is not simply facts, that is to say it is not just data. Science is information, it is knowledge and stories that have continued to challenge the narratives we have held onto as a species for thousands of years.
Judea Pearl thinks it is important to recognize the story aspect of big data. He thinks it is crucial that we understand the difference between data and information, because without doing so we turn to the data blindly and can generate an inaccurate story based on what we see. He writes,
“In certain circles there is an almost religious faith that we can find the answers to … questions in the data itself, if only we are sufficiently clever at data mining. However, readers of this book will know that this hype is likely to be misguided. The questions I have just asked are all causal, and causal questions can never be answered from data alone.”
Big data presents us with huge numbers of observations and facts, but those facts alone don’t represent causal structures or deeper interactions within reality. We have to generate information from the data and combine that new knowledge with existing knowledge and causal hypothesis to truly learn something new from big data. If we don’t then we will simply be identifying meaningless correlations without truly understanding what they mean or imply.
Complex Causation Continued

Complex Causation Continued

Our brains are good at interpreting and detecting causal structures, but often, the real causal structures at play are more complicated than what we can easily see. A causal chain may include a mediator, such as citrus fruit providing vitamin C to prevent scurvy. A causal chain may have a complex mediator interaction, as in the example of my last post where a drug leads to the body creating an enzyme that then works with the drug to be effective. Additionally, causal chains can be long-term affairs.
In The Book of Why Judea Pearl discusses long-term causal chains writing, “how can you sort out the causal effect of treatment when it may occur in many stages and the intermediate variables (which you might want to use as controls) depend on earlier stages of treatment?”
This is an important question within medicine and occupational safety. Pearl writes about the fact that factory workers are often exposed to chemicals over a long period, not just in a single instance. If it was repeated exposure to chemicals that caused cancer or another disease, how do you pin that on the individual exposures themselves? Was the individual safe with 50 exposures but as soon as a 51st exposure occurred the individual developed a cancer? Long-term exposure to chemicals and an increased cancer risk seems pretty obvious to us, but the actual causal mechanism in this situation is a bit hazy.
The same can apply in the other direction within the field of medicine. Some cancer drugs or immune therapy treatments work for a long time, stop working, or require changes in combinations based on how disease has progressed or how other side effects have manifested. Additionally, as we have all learned over the past year with vaccines, some medical combinations work better with boosters or time delayed components. Thinking about causality in these kinds of situations is difficult because the differing time scopes and combinations make it hard to understand exactly what is affecting what and when. I don’t have any deep answers or insights into these questions, but simply highlight them to again demonstrate complex causation and how much work our minds must do to fully understand a causal chain.
Complex Causation

Complex Causation

In linear causal models the total effect of an action is equal to the direct effect of that action and its indirect effect. We can think of an oversimplified anti-tobacco public health campaign to conceptualize this equation. A campaign could be developed to use famous celebrities in advertisements against smoking. This approach may have a direct effect on teen smoking rates if teens see the advertisements and decide not to smoke as a result of the influential messaging from their favorite celebrity. This approach may also have indirect effects. Imagine a teen who didn’t see the advertising, but their best friend did see it. If their best friend was influenced, then they may adopt their friend’s anti-smoking stance. This would be an indirect effect of the advertising campaign in the positive direction. The total effect of the campaign would then be the kids who were directly deterred from smoking combined with those who didn’t smoke because their friends were deterred.
However, linear causal models don’t capture all of the complexity that can exist within causal models. As Judea Pearl explains in The book of Why, there can be complex causal models where the equation that I started this post with doesn’t hold. Pearl uses a drug used to treat a disease as an example of a situation where the direct effect and indirect effect of a drug don’t equal the total effect. He says that in situations where a drug causes the body to release an enzyme that then combines with the drug to treat a disease, we have to think beyond the equation above. In this case he writes, “the total effect is positive but the direct and indirect effects are zero.”
The drug itself doesn’t do anything to combat the disease. It stimulates the release of an enzyme and without that enzyme the drug is ineffective against the disease. The enzyme also doesn’t have a direct effect on the disease. The enzyme is only useful when combined with the drug, so there is no indirect effect that can be measured as a result of the original drug being introduced. The effect is mediated between the interaction of both the drug and enzyme together. In the model Pearl shows us, there is only the mediating effect, not a direct or indirect effect.
This model helps us see just how complicated ideas and conceptions of causation are. Most of the time we think about direct effects, and we don’t always get to thinking about indirect effects combined with direct effects. Good scientific studies are able to capture the direct and indirect effects, but to truly understand causation today, we have to be able to include mediating effects in complex causation models like the one Pearl describes.
Counterfactuals

Counterfactuals

I have written a lot lately about the incredible human ability to imagine worlds that don’t exist. An important way that we understand the world is by imagining what would happen if we did something that we have not yet done or if we imagine what would have happened had we done something different in the past. We are able to use our experiences about the world and our intuition on causality to imagine a different state of affairs from what currently exists. Innovation, scientific advancements, and social cooperation all depend on our ability to imagine different worlds and intuit causal chains between our current world and the imagined reality we desire.
In The Book of Why Jude Pearl writes, “counterfactuals are an essential part of how humans learn about the world and how our actions affect it. While we can never walk down both the paths that diverge in a wood, in a great many cases we can know, with some degree of confidence, what lies down each.”
A criticism of modern science and statistics is the reliance on randomized controlled trials and the fact that we cannot run an RCT on many of the things we study. We cannot run RCTs on our planet to determine the role of meteor impacts or lightning strikes on the emergence of life. We cannot run RCTs on the toxicity of snake venoms in human subjects. We cannot run RCTs on giving stimulus checks  to Americans during the COVID-19 Pandemic. Due to physical limitations and ethical considerations, RCTs are not always possible. Nevertheless, we can still study the world and use counterfactuals to think about the role of specific interventions.
If we forced ourselves to only accept knowledge based on RCTs then we would not be able to study the areas I mentioned above. We cannot go down both paths in randomized experiments with those choices. We either ethically cannot administer an RCT or we are stuck with the way history played out. We can, however, employ counterfactuals, imagining different worlds in our heads to think about what would have happened had we gone down another path. In this process we might make errors, but we can continually learn and improve our mental models. We can study what did happen, think about what we can observe based on causal structures, and better understand what would have happened had we done something different. This is how much of human progress has moved forward, without RCTs and with counterfactuals, imagining how the world could be different, how people, places, societies, and molecules could have reacted differently with different actions and conditions.
Alternative, Nonexistent Worlds - Judea Pearl - The Book of Why - Joe Abittan

Alternative, Nonexistent Worlds

Judea Pearl’s The Book of Why hinges on a unique ability that human animals have. Our ability to imagine alternative, nonexistent worlds is what has set us on new pathways and allowed us to dominate the planet. We can think of what would happen if we acted in a certain manner, used a tool in a new way, or if two objects collided together. We can visualize future outcomes of our actions and of the actions of other bodies and predict what can be done to create desired future outcomes.
In the book he writes, “our ability to conceive of alternative, nonexistent worlds separated us from our protohuman ancestors and indeed from any other creature on the planet. Every other creature can see what is. Our gift, which may sometimes be a curse, is that we can see what might have been.”
Pearl argues that our ability to see different possibilities, to imagine new worlds, and to be able to predict actions and behaviors that would realize that imagined world is not something we should ignore. He argues that this ability allows us to move beyond correlations, beyond statistical regressions, and into a world where our causal thinking helps drive our advancement toward the worlds we want.
It is important to note that he is not advocating for holding a belief and setting out to prove it with data and science, but rather than we use data and science combined with our ability to think causally to better understand the world. We do not have to be stuck in a state where we understand statistical techniques but deny plausible causal pathways. We can identify and define causal pathways, even if we cannot fully define causal mechanisms. Our ability to reason through alternative, nonexistent worlds is what allows us to think causally and apply this causal reasoning to statistical relationships. Doing so, Pearl argues, will save lives, help propel technological innovation, and will push science to new frontiers to improve life on our planet.
Laboratory Proof

Laboratory Proof

“If the standard of laboratory proof had been applied to scurvy,” writes Judea Pearl in The Book of Why, “then sailors would have continued dying right up until the 1930’s, because until the discovery of vitamin C, there was no laboratory proof that citrus fruits prevented scurvy.” Pearl’s quote shows that high scientific standards for definitive and exact causality are not always for the greater good. Sometimes modern science will spurn clear statistical relationships and evidence because statistical relationships alone cannot be counted on as concrete causal evidence. A clear answer will not be given because some marginal unknowns may still exist, and this can have its own costs.
Sailors did not know why or how citrus fruits prevented scurvy, but observations demonstrated that citrus fruits managed to prevent scurvy. There was no clear understanding of what scurvy was or why citrus fruits were helpful, but it was commonly understood that a causal relationship existed. People acted on these observations and lives were saved.
On two episodes, the Don’t Panic Geocast has talked about journal articles in the British Medical Journal that make the same point as Pearl. As a critique of the need for randomized controlled trials, the two journal articles highlight the troubling reality that there have not been any randomized controlled trials on the effectiveness of parachute usage when jumping from airplanes. The articles are hilarious and clearly satirical, but ultimately come to the same point that Pearl does with the quote above – laboratory proof is not always necessary, practical, or reasonable when lives are on the line.
Pearl argues that we can rely on our abilities to identify causality even without laboratory proof when we have sufficient statistical analysis and understanding of relationships. Statisticians always tell us that correlation is not causation and that observational studies are not sufficient to determine causality, yet the citrus fruit and parachute examples highlight that this mindset is not always appropriate. Sometimes more realistic and common sense understanding of causation – even if supported with just correlational relationships and statistics – are more important than laboratory proof.
The Screening-Off Effect

The Screening-Off Effect

Sometimes to our great benefit, and sometimes to our detriment, humans like to put things into categories – at least Western, Educated, Industrialized, Rich, Democratic (WEIRD) people do. We break things into component parts and categorize each part as belonging to a category of thing. We do this with things like planets, animals, and players within sports. We like established categories and dislike when our categorization changes. This ability has greatly helped us in science and strategic planning, allowing our species to do incredible things and learn crucial lessons about the world. What is remarkable about this ability is how natural and easy it is for us, but how hard it is to explain or program into a machine.
One component of this remarkable ability is referred to as the screening-off effect by Judea Pearl in The Book of Why. Pearl writes, “how do we decide which information to disregard, when every new piece of information changes the boundary between the relevant and the irrelevant? For humans, this understanding comes naturally. Even three-year-old toddlers understand the screening-off effect, though they don’t have a name for it. … But machines do not have this instinct, which is one reason that we equip them with causal diagrams.”
From a young age we know what information is the most important and what information we can ignore. We intuitively have a good sense for when we should seek out more information and when we have enough to make a decision (although sometimes we don’t follow this intuitive sense). We know there is always more information out there, but don’t have time to seek out every piece of information possible. Luckily, the screening-off effect helps us know when to stop and makes decision-making possible for us.
Beyond knowing when to stop, the screening-off effect helps us know when to ignore irrelevant information. The price of tea in China isn’t a relevant factor for us when deciding what time to wake up the next morning. We recognize that there are no meaningful causal pathways between the price of tea and the best time for us to wake up. This causal insight, however, doesn’t exist for machines that are only programmed with the specific statistics we build into them. We specifically have to code a causal pathway that doesn’t include the price of tea in China for a machine to know that it can ignore that information. The screening-off effect, Pearl explains, is part of what allows humans to think causally. In cutting edge science there are many factors we wouldn’t think to screen out that may impact the results of scientific experiments, but for the most part, we know what can be ignored and can look at the world around us through a causal lens because we know what is and is not important.
Slope is Agnostic to Cause and Effect

Slope is Agnostic to Cause and Effect

I like statistics. I like to think statistically, to recognize that there is a percent chance of one outcome that can be influenced by other factors. I enjoy looking at best fit lines, seeing that there are correlations between different variables, and seeing how trend-lines change if you control for different variables. However, statistics and trend lines don’t actually tell us anything about causality.
In The Book of Why Judea Pearl writes, “the slope (after scaling) is the same no matter whether you plot X against Y or Y against X. In other words, the slope is completely agnostic as to cause and effect. One variable could cause the other, or they could both be effects of a third cause; for the purpose of prediction, it does not matter.”
In statistics we all know that correlation is not causation, but this quote helps us remember important information when we see a statistical analysis and a plot with linear regression line running through it. The regression line is like the owl that Pearl had described earlier in the book. The owl is able to predict where a mouse is likely to be and able to predict which direction it will run, but the owl does not seem to know why a mouse is likely to be in a given location or why it is likely to run in one direction over another. It simply knows from experience and observation what a mouse is likely to do.
The regression line is a best fit for numerous observations, but it doesn’t tell us whether one variable causes another or whether both are influenced in a similar manner by another variable. The regression line knows where the mouse might be and where it might run, but it doesn’t know why.
In statistics courses we end at this point of correlation. We might look for other variables that are correlated or try to control for third variables to see if the relationship remains, but we never answer the question of causality, we never get to the why. Pearl thinks this is a limitation we do not need to put on ourselves. Humans, unlike owls, can understand causality, we can recognize the various reasons why a mouse might be hiding under a bush, and why it may chose to run in one direction rather than another. Correlations can help us start to see where relationships exist, but it is the ability of our mind to understand causal pathways that helps us determine causation.
Pearl argues that statisticians avoid these causal arguments out of caution, but that it only ends up creating more problems down the line. Important statistical research in areas of high interest or concern to law-makers, business people, or the general public are carried beyond the cautious bounds that causality-averse statisticians place on their work. Showing correlations without making an effort to understand the causality behind it makes scientific work vulnerable to the epistemically malevolent who would like to use correlations to their own ends. While statisticians rigorously train themselves to understand that correlation is not causation, the general public and those struck with motivated reasoning don’t hold themselves to the same standard. Leaving statistical analysis at the level of correlation means that others can attribute the cause and effect of their choice to the data, and the proposed causal pathways can be wildly inaccurate and even dangerous. Pearl suggests that statisticians and researchers are thus obligated to do more with causal structures, to round off  their work and better develop ideas of causation that can be defended once their work is beyond the world of academic journals.
The Fundamental Nature of Cause and Effect

The Fundamental Nature of Cause and Effect

In my undergraduate and graduate studies I had a few statistics classes and I remember the challenge of learning probability. Probability, odds, and statistics are not always easy to understand and interpret. There are some concepts that are pretty straightforward, and others that seem to contradict what we would expect if we had not gone through the math and if we had not studied the concepts in depth. To contrast the difficult and sometimes counter-intuitive nature of statistics, we can think about causality, which is a challenging concept, but unlike statistics, is something we are able to intuit from very young age.
In The Book of Why Judea Pearl writes, “In both a cognitive and a philosophical sense, the idea of cause and effect is much more fundamental than probability. We begin learning causes and effects before we understand language and before we understand mathematics.”
As Pearl explains, we see causality naturally and experience causality as we move through our lives. From a young child who learns that if they cry they receive attention to a nuclear physicist who learns what happens when two atoms collide at high energy levels, our minds are constantly looking at the world and looking for causes. It begins by making observations of phenomena around us and continues as we predict what outcomes would happen based on certain system inputs. Eventually, our minds reach a point where we can understand why our predictions are accurate or inaccurate, and we can imagine new ways to bring about certain outcomes. Even if we cannot explain all of this, we can still understand causation at a fundamental and intuitive level.
However, many of us deny that we can see and understand the world in a causal way. I am personally guilty of thinking in a purely statistical way and ignoring the causal. The classes I took in college helped me understand statistics and probability, but also told me not to trust my intuitive causal thinking. Books like Kahneman’s Thinking Fast and Slow cemented this mindset for me. Rationality, we believe, requires that we think statistically and discount our intuitions for fear of bias. Modern science says we can only trust evidence when it is backed by randomized controlled trials and directs us to think of the world through correlations and statistical relationships, not through a lens of causality.
Pearl pushes back against this notion. By arguing that causality is fundamental to the human mind, he implies that our causal reasoning can and should be trusted. Throughout the book he demonstrates that a purely statistical way of thinking leaves us falling short of the knowledge we really need to improve the world. He demonstrates that complex tactics to remove variables from equations in statistical methods are often unnecessary, and that we can accept the results of experiments and interventions even when they are not fully randomized controlled trials.  For much of human history our causal thinking nature has lead us astray, but I think that Pearl argues that we have overcorrected in modern statistics and science, and that we need to return to our causal roots to move forward and solve problems that statistics tells us are impossible to solve.