Post Hoc Conclusions

Post Hoc Conclusions

Our minds see a lot of patterns that don’t exist. We make observations of randomness and find patterns that we assume to be based on a causal link when in reality no causal structure exists between our observations. This can happen in 3 point shooting in basketball, in observations of bomb locations in WWII London, and in music streaming services. We are primed to see patterns and causes, and we can construct them even when we shouldn’t. One contributing factor for incorrect pattern observation is that we tend to make post hoc conclusions, making observations after the fact without predicting what we might expect to see before hand.


Using the WWII example, Cass Sunstein and Richard Thaler in the book Nudge show how people developed misconstructions of German bombing patterns in London during the war. The German bombing wasn’t precise, and there was no real pattern to the bombing raids and where bombs actually exploded across the city. Nevertheless, people mistakenly viewed a pattern in the random distribution of bombs. The authors describe the mistaken pattern identification by writing, “We often see patterns because we construct our informational tests only after looking at the evidence.”


People could map where bombs fell, and then create explanations for what targets the Germans were aiming at, for why the Germans would target a certain part of the city, and what strategic purpose the bombing was trying to accomplish. But these reasons are all post hoc constructions meant to satisfy a non-existent pattern that someone expected to find. We also see this in basketball, when a shooter makes a few baskets and is believed to have the hot hand or be on fire. In music streaming services, algorithms are actually tweaked to be less random, because listeners who hear two consecutive songs or more by the same band will assume the streaming isn’t randomizing the music, even though random chance will sometimes pick a string of songs from the same band or even from the same album.


The examples I mentioned in the previous paragraph are harmless cognitive errors stemming from poorly constructed post hoc explanations of phenomena.  However, post hoc conclusions based on non-existent patterns are important to consider because they can have real consequences in our lives and societies. If we are in a position to make important decisions for our families, our companies, or our communities, we should recognize that we possess the ability to be wildly wrong about observed patterns. It is important that we use better statistical techniques or listen to the experts who can honestly employ them to help us make decisions. We should not panic about meaningless stock market fluctuations and we should not incarcerate people based on poor crime statistic understandings. We should instead remember that our brains will look for patterns and find them even if they don’t actually exist. We should state assumptions before we make observations, rather than making post hoc conclusions on poor justifications for the patterns we want to see.
Imaginary Reference Points

Imaginary Reference Points

My last post was about reference points and how they can create subjective experiences that differ from person to person. If my refence point is dramatically different than another person’s, then our experience of the same objective fact or reality can be quite different. If I suddenly won $1 million dollars my life might change dramatically, but if an incredibly wealthy person suddenly won $1 million, they might not care at all.


Reference points can get even more complicated than the example I just shared which was borrowed from yesterday’s post. Sometimes reference points don’t need to be real in order to shape our subjective experiences of the world. In his book Thinking Fast and Slow, Daniel Kahneman uses the example of an expected raise. If someone knows that their colleagues have received a raise, and expects to get a similar raise but does not, then they can feel as though they have really lost. Their financial situation has not changed, but they created an imaginary reference point in their mind which has shaped the way they think about their current situation.


We all have certain expectations about the world that we adopt as reference points. These reference points don’t have to reflect anything real about the world, but they can still greatly impact our subjective opinions and considerations of the world. They can be vain, such as how attractive we expect our spouse to be, or more positively aspirational, such as how much we expect everyone in society to participate in social causes to help those who are the most needy.  There is no real reference point that we are using, just hazy ideas of the way we think things should be, but nevertheless, these imaginary reference points can guide a lot of our thinking and behavior.


In my own life, examining these imaginary reference points has been incredibly helpful for making me a more happy and confident person. It is easy to let imaginary reference points fall to the background, where they run our lives without being considered in a critical way. By thinking deeply about our reference points we can better consider what we should and should not strive for, how much effort or money we need to put toward certain endeavors, and whether our behaviors are really reasonable and worthwhile. Through self-reflection and self-awareness we can recognize goals that serve as reference points which are unreasonable, desires which are vain and should be discarded, and ideas about who we are supposed to be that don’t truly align with our lives and what would help us live in a meaningful and fulfilling manner. Imaginary reference points matter, and they can greatly influence how we live our lives. We should make sure we think about them and let go of those which drive us in the wrong direction.
Take the Outside View

Take the Outside View

Taking the outside view is a shorthand and colloquial way to say, think of the base rate of the reference class to which something belongs, and make judgements and predictions from that starting point. Take the outside view is advice from Daniel Kahneman in his book Thinking Fast and Slow for anyone working on a group project, launching a start-up, or considering an investment with a particular company. It is easy to take the inside view, where everything seems predictable and success feels certain. However, it is often better for long-term success to take the outside view.


In his book, Kahneman writes, “people who have information about an individual case rarely feel the need to know the statistics of the class to which the case belongs.” He writes this after discussing a group project he worked on where he and others made an attempt to estimate the time necessary to complete the project and the obstacles and hurdles they should expect along the way. For everyone involved, the barriers and likelihood of being derailed and slowed down seemed minimal, but Kahneman asked the group what to expect based on the typical experience of similar projects. The outlook was much more grim when viewed from the outside perspective, and helped the group better anticipate challenges they could face and set more reasonable timelines and work processes.


Kahneman continues, “when forecasting the outcomes of risky projects, executives too easily fall victim to the planning fallacy. In its grip, they make decisions based on delusional optimism rather than on a rational weighting of gains, losses, and probabilities. They overestimate benefits and underestimate costs.”


Taking the outside view helps us get beyond delusional optimism. It helps us make better expectations about how long a project will take, what rate of return we should expect, and what the risks really look like. It is like getting a medical second opinion, to ensure that your doctor isn’t missing anything and to ensure they are following the most up-to-date practices. Taking the outside view shifts our base rate, anchors us to a reality that is more reflective of the world we live in, and helps us prepare for challenges that we would otherwise overlook.
Regression to the Mean Versus Causal Thinking

Regression to the Mean Versus Causal Thinking

Regression to the mean, the idea that there is an average outcome that can be expected and that overtime individual outliers from the average will revert back toward that average, is a boring phenomenon on its own. If you think about it in the context of driving to work and counting your red lights, you can see why it is a rather boring idea. If you normally hit 5 red lights, and one day you manage to get to work with just a single red light, you probably expect that the following day you won’t have as much luck with the lights, and will probably have more red lights than than your lucky one red light commute. Conversely, if you have a day where you manage to hit every possible red light, you would probably expect to have better traffic luck the next day and be somewhere closer to your average. This is regression to the mean. Simply because you had only one red or managed to hit every red one day doesn’t cause the next day’s traffic light stoppage to be any different, but you know you will probably have a more average count of reds versus greens – no causal explanation involved, just random traffic light luck.


But for some reason this idea is both fascinating and hard to grasp in other areas, especially if we think that we have some control of the outcome. In Thinking Fast and Slow, Daniel Kahneman helps explain why it is so difficult in some settings for us to accept regression to the mean, what is otherwise a rather boring concept. He writes,


“Our mind is strongly biased toward causal explanations and does not deal well with mere statistics. When our attention is called to an event, associative memory will look for its cause – more precisely, activation will automatically spread to any cause that is already stored in memory. Causal explanations will be evoked when regression is detected, but they will be wrong because the truth is that regression to the mean has an explanation but does not have a cause.”


Unless you truly believe that there is a god of traffic lights who rules over your morning commute, you probably don’t assign any causal mechanism to your luck with red lights. But when you are considering how well a professional golfer played on the second day of a tournament compared to the first day, or when you are considering whether intelligent women marry equally intelligent men, you are likely to have some causal idea that comes to mind. The golfer was more or less complacent on the second day – the highly intelligent women have to settle for less intelligent men because the highly intelligent men don’t want an intellectual equal. These are examples that Kahneman uses in the book and present plausible causal mechanisms, but as Kahneman shows, the more simple though boring answer is simply regression to the mean. A golfer who performs spectacularly on day one is likely to be less lucky on day two. A highly intelligent woman is likely to marry a man with intelligence closer to average just by statistical chance.


When regression to the mean violates our causal expectation it becomes an interesting and important concept. It reveals that our minds don’t simply observe an objective reality, they observe causal structures that fit with preexisting narratives. Our causal conclusions can be quite inaccurate, especially if they are influenced by biases and prejudices that are unwarranted. If we keep regression to the mean in mind, we might lose some of our exciting narratives, but our thinking will be more sound, and our judgments more clear.
Estimating Our Schedule

Estimating Our Schedule

How much time do you need for some of the mundane tasks in your life? You probably have a good sense for how long it takes you to get yourself together for work in the morning, how long it takes to prep your easy Thursday dinner, and how long it takes you to brush your teeth and get into bed at night. What you probably don’t have a great sense of, however, is how long it will take you to complete something new in your routine. If you are looking to introduce something new into your routine you will probably misjudge just how much time you will need.


This is an idea that Cal Newport presents in his book Deep Work. Newport specifically writes about new habits for work and leisure that help us improve our focus and spend more time with important things that truly matter. He encourages us to create schedules not just for our workdays, but four our entire days, and warns us that it is going to be hard to plan our days when we first start. Newport writes,


“Almost definitely you’re going to underestimate at first how much time you require for most things. When people are new to this habit [scheduling their full day], they tend to use their schedule as an incarnation of wishful thinking – a best-case scenario for their day.”


I started this post reflecting on common activities that we do daily, and our sense of how long those activities really take us. The reality for even these simple things is that we don’t have a great sense of how long they actually take, especially if we are not focused while working through those tasks. Deliberately getting ready for bed is a lot quicker than distractedly getting ready for bed while simultaneously watching YouTube videos. If we likely get these daily things wrong, then we will surely have a poor estimate for just how long new habits, routines, and tasks will take us.


For work, scheduling just how long a spreadsheet or report will take us can be challenging, especially if we have varying demands and levels of interest from our supervisor. But the more we practice, the more we can focus and engage with deep work, the better we will eventually be at getting a sense for how long something will take. This will carry over into other areas of our life as well. We will eventually get a good sense for how long the new physical therapy routine will take us, how much time we need to set aside for exercising, or how long a board-game with our family will take. Along the way, we will develop muscles for flexibility in our time and scheduling, helping us make better predictions and adjustments as we schedule out our days.

Lets Consider Our Standards for Life

In Letters From a Stoic Seneca writes, “Let us try to maintain a higher standard of life than that of the multitude, but not a contrary standard; otherwise, we shall frighten away and repel the very persons whom we are trying to improve.”


On an initial quick read, this quote seems to be saying, live better than the masses but don’t act like you are better than everyone else. That’s good advice that has been said so many times that it is basically useless. We already all believe that we are morally superior to other people and we are especially likely, according to Robin Hanson in an interview he gave on Conversations with Tyler, to say that our group or tribe is morally  superior to others. If you give the quote a second thought however, you see that there is a deeper meaning within the idea being conveyed.


The first thing we should consider is what it would look like to maintain a high standard of life. In his same letter, Seneca advises that a high standard of life does not mean that one wears the nicest possible toga or that one has silver dishes laced with pure gold. A high standard of life is not about maintaining exorbitant material possessions. Advertising in the United States would make you think differently. A high standard of life is advertised to us as driving the finest sports car, demanding the best possible wrist watch, and having exquisitely crafted faucets. Seneca would argue that these things don’t create a high standard of living, but just show off our wealth. I would agree.


A high standard of life, Seneca suggests and I would argue, is a well ordered life in which we can live comfortably but don’t embrace the mindset that it is our possessions that define our success and value. A high standard for life means that we cultivate habits which help us be more kind and considerate. We pursue activities and possessions that help us be more effective, less impulsive, and allow us to better use our resources and intelligence.


Maintaining this version of a high standard of life can have the same pitfalls we may associate with the Real Housewives of LA if we don’t give thought to the second part of Seneca’s advice. Maintaining high living standards can lead us to selfishness and self-serving decisions if we don’t think about other people and how we operate as a society. Seneca’s advice is about becoming a model for other people and helping become a force that improves lives by encouraging and inspiring others. This idea was echoed in Peter Singer’s book about effective altruism, The Most Good You Can Do. Effective altruists want to direct their efforts, donations, and resources in the direction where they can have the greatest possible positive impact on the world to help the most people possible. One of the ways to do that is to inspire others to also strive to do the most good they can do. No one would follow an effective altruist who gave away all their money and lived a miserable life. But someone would follow an effective altruist who gave a substantial amount of their money to an effective and meaningful charity and still lived an enjoyable and happy life.


Our high standard of living in the end should be one that drives us toward continual improvement. A life that makes us more considerate, more thoughtful, less judgmental, and less impulsive. It should encourage others to live in a way that helps them be happier and healthier, rather than living in a way that suggests that having expensive things and showing off is what life is all about.

Writing, Physics, Inspiration, and Life

One of Amanda Gefter’s favorite physicists was John Wheeler, and in her book Trespassing on Einstein’s Lawn, Gefter quotes him numerous times and describes the impact that Wheeler had on her life. What made Wheeler different from other physicists, what entranced Gefter with his work, was his often poetic way of describing the universe and interpreting what the mathematics of the universe told us. In a world of complex physics, daunting mathematics, and mind bending conclusions, Wheeler’s voice cut through with simplicity and his poetic style was elegant yet clear and inviting.


One part of Gefter’s book describes a trip she took with her father to Philadelphia to look over Wheeler’s old notebooks after he passed away in 2008. At the American Philosophical Society, Gefter and her father poured over his old notebooks, studying his thoughts, the progression of his studies, and analyzing the conclusions he reached along the way. One of his annotations in a notebook was included in Gefter’s book, and I think it does an excellent job illuminating Wheeler’s poetic style and what it was that drew Gefter to his writing, speaking, and way of describing science.


“Still,” Gefter writes, “Wheeler was lost. ‘Not seeing a dramatic clear path ahead,’ he wrote. ‘Now have concluded just have to push in through the undergrowth. ‘Traveler, there are no paths. Paths are made by walking.’”


In his personal notebook, describing what appeared to be a dead end in his research, Wheeler turned to a phrase we have probably heard before, but probably not in our science classes. Wheeler was pushing the edge of scientific thought, and he had come to a point where he could no longer rely on the research of others to show him the path forward. The quote was used to describe propositions, yes/no or true/false statements about some reality. Wheeler, like Gefter years later, was searching for some truth to the universe that was not observer dependent, that did not need to change or adjust based on a observer’s position, speed, or quantum composition. Propositions seemed to be a place to start, but even there, the dreaded sentence, “this sentence is false” seemed to break even propositions and seemed to pull apart any basic form of reality.


Altogether this short section from Gefter, the lessons she shared about Wheeler, and the scientific challenge which served as the genesis for Wheeler’s note teach us a few things. Often times we want a dramatically clear choice in our life, but for each of us, the path has not been made. We must push through the undergrowth of life, creating our own  path as we go. We must abandon expectations of how things should be and how things ought to turn out for us, because there is no solid truth that we march toward. We are not pushing forward in the universe and in our lives to an inherently perfect and true destiny. The reality we find as we cut through the undergrowth is as observer dependent as gravity and time. How we choose to see it depends on our reference frame, and our reference frame is something we have some choice in. And while we are using that choice, we can be boring, stuffy, and self pitying, or we can be inventive, flourishing, and excited for the new discoveries that know will lie ahead of us.

Cutting Through

The truly great thing about physics is that it is universal. Literally. What we discover about physics here in the United States is true in South Africa, and what is discovered in South Africa can be learned just as well in Vietnam, and it all holds true on Jupiter or in the Andromeda Galexy. Physics is based in mathematics and repeatable experiments and it can be understood anywhere. It takes our perceptions and it boils them down into their most simplistic forms, tests them, repeats the test, and then determines what is real and what is unsupported. This means that physics has the ability to help us understand things in incredible new ways. We can better understand the universe and how it is held together, but only if we can study the physics and step beyond ourselves to understand what the tests, experiments, and math are trying to explain to us.

For Amanda Gefter, this is one of the best parts of physics. It takes our expectations, our assumptions, and what we want to be true, and completely ignores it. A good scientist, during their search for what is real and what is not, is able to cut through the noise of our expectations, beliefs, and desires to see the science underneath, holding things together.

Gefter writes, “That was what I loved about physics—that moment of pure surprise when you suddenly realize that what you had thought was one thing is really something else, or that two things that seemed so different are really two ways of looking at the very same thing. It was the perennial comfort that comes from discovering that the world is not remotely what it seems.”

By cutting through the noise of humanity, physics helps us to see the world more thoroughly. The world and the universe are not the way they simply appears to us from our perspective on Earth. Much of how we interpret and understand the universe is through what we see, but so much of the universe does not emit electromagnetic radiation or react with light in any way. How we perceive the universe depends on our point of view, and of our experience as human beings living on our planet. What physics does, is move beyond our experience of the universe to tell us how things are at any point in the universe, not just on planet Earth today. If we accept the world as it appears to us, then we somehow cease to move forward, and we begin to live in a story that never completely captures the reality we experience around us. We begin to live in ways that don’t add up, that put us at the center and don’t allow for the types of evolution and adaptation that we need to live in this universe responsibly. Physics takes the stories that we tell and re-writes them, adjusting the language to be the language of mathematics, giving us a new perspective from which to tell our story.

What Reality Ought To Be

The universe is filled with paradoxes, but often times those paradoxes seem to be the result of how our brains and thinking work. Amanda Gefter addresses this in her book, Trespassing on Einstein’s Lawn. In the book Gefter describes how she found her way to a career as a science journalist, something she never set out to do directly, and at many points never believed would be possible for her. Her descriptions of science and physics are as much a description about the progression of human life that we all share, and it is a perfect opportunity to reflect on paradoxes within our personal lives and within areas like science.


Gefter describes the challenges of quantum mechanics and the reality that we can measure some parts of the universe one way, but get a different result if we measure them a different way or at a different time. Also, with quantum particles, we seem to be a able to measure with incredible precision a particle’s position or its momentum, but not both. We can accurately look at where a particle is, but in doing so we can’t describe where it is going. Alternatively, we can look at where a particle is going and how it is moving through space, but we can’t actually then pinpoint where in space it is. This measurement paradox is challenging and creates a lot of problems and further questions for scientists. Describing the way we are challenged by measurements and observations and our inability to separate ourselves from the measurements and observations we make, Gefter writes the following:


“There’s no normal reality lurking behind the quantum scene, no objective Einsteinian world that sits idly by regardless of who’s looking. There’s just the stuff we measure. The whole thing reeked of paradox, but as Feynman said, ‘The ‘paradox’ is only a conflict between reality and your feeling of what reality ‘ought to be.’”


I think this idea extends well beyond physics throughout our lives. A paradox is something that sounds like it would be correct and obvious, but leads to a conclusion or reality that could not possibly exist. Paradoxes are contradictions that break our expectations and are outcomes that run counter to our intentions. With this framework, we can begin to see that Feynman’s description of paradoxes extends beyond the world of science into any aspect of our lives today.


The physical universe and the ever confusing and challenging world of particle physics is under no obligation to act in ways that our limited brains and current extent of mathematical and scientific understanding would expect. We make predictions based on observations, but we are never playing with all the data and never have a complete set of all possible observations when we make our predictions. Our ideas of what should and should not be possible are shaped by our experiences and by all the information we can hold in our head, and that information is astoundingly limited compared to the vastness of possibilities within the universe.


Looking at our actual day-to-day lives, we can see that this concept translates into the expectations, generalizations, and predictions we make about our futures and desires. I live in Reno, Nevada, and at the moment housing prices in Reno have increased dramatically as the number of homes and quality apartments has remained level while economic development and population growth have occurred. One result of a stronger economy and a lagging housing infrastructure is increased home costs, and fewer living accommodations for those who want to live on their own. I was recently running with a friend of mine who stated that an individual graduating from college should be able to afford a starter home if they are in an introductory position and have a solid and stable job. My friend is not wrong to say this, but his statement is simply a value judgement based on the experiences of his family and expectations that have been shaped by where he has lived and what he has been told he should do to be successful. Whenever we begin talking in terms of how things should be, we need to recognize that we are making value judgements, and that we are expressing only our ideas of what reality ought to be. The conflicts this creates and the paradoxes it leads us to are not paradoxes that actually exist in the universe, they are just situations where the real world does not align with the way that our brains comprehend our experiences.


The set of possibilities within the universe is virtually infinite as far as the human mind is concerned, and thinking that we know how things should be is to some extent arrogant and irrational. The world and universe in physical terms and in terms of our social ordering can have many forms, and if we try to force the universe to be the way that makes sense from our perspective, we will simply be frustrated and confused in a spiral of paradox. When we take away our opinion and think through our expectations, we can begin to see the world more clearly and better react to and adjust to the actual realities of our world. When we take away the expectations of how the world ought to be, we can live in the world we actually have and learn and adapt with greater skill.


One of the things we often do in life is take shortcuts to understand the world, our place in the world, and how everything relates. These heuristics allow us to develop mental models of how we think things should interact, helping us build narratives of meaning, moral frameworks, and pathways toward success. The problem thought, if we let these heuristics run amuck without constraining them through self-awareness, is that we begin to cast people, situations, and reality into buckets defined by things we have experienced in the past or seen on TV. In his book, Some Thoughts About Relationships, author Colin Wright encourages us to go beyond archetypes in our relationships to understand others as full people and not as character types from TV shows or stories.


In his book he writes, “Don’t try to force a person to be someone they’re not. … Let’s start with self-archetyping. We’re given examples of people to emulate from a young age, an this generally means being presented with role models who represent a certain ideal to our parents, educators, older siblings, or someone else with influence over our growth. The result is that we grow up with a notion about the “correct” way to act, and this carries over into how we behave in the context of a relationship.”


In this passage, Wright is encouraging us to understand our selves and not force ourselves to be a character that we believe others want us to be. He is also encouraging us to allow other people to be original versions of themselves, rather than trying to force people into boxes that describe them based on other people that we know. This means that you don’t try to assign roles to yourself and your friends to see who matches who from shows like Friends or the Big Bang Theory, and it means you approach each person as if they are themselves, and not as if they are like a character from a movie or even a person from your past.


What we can do when we avoid archetypes is avoid conflicts that arise from hidden expectations of what we want ourselves or another person to be. We can be honest and open about our roles in our relationship, and build a constructive partnership or friendship based on who we truly are as people. Archetypes and shortcuts help us learn lessons about the world and build models, but they are necessarily constrained versions of reality that limit our lives when we enact them in the real world. Avoiding archetypes means that you can be the person that makes you happy, that lives life in your regular resonance, not in the image of someone else. You can allow your spouse to be the spouse that fits with their lifestyle, and makes you happy, rather than the idealized spouse from story or fiction. Driving beyond these narratives of people and roles allows us to interact with people in the world in a much more authentic manner, thought it requires that we take more time to understand those around us.