Finding the missing piece

Summer is time for love, and I offer you an analysis of the probability of meeting your soul mate. In his Symposium, Plato writes that people were originally both male and female. To prevent them from acquiring the power of the Gods, Zeus cut them in half. Life then became for humans a search for the other half that was lost, in order for them to once again attempt to ascend Mount Olympus.

It is a pretty story, and one that resonates with many a New Age follower’s conception of love. Even if it doesn’t quite jive with reality. But why not?

The reason once again has to do with probability. There is a well known problem in the statistics literature called the Birthday Paradox. Basically, the paradox questions, “How many people do you need to put into a room to get a 50% chance that two of the people have the same birthday?” The answer to this is 23. Therein lies the paradox – this seems like a very small number. Most people intuitively think that one needs to have 365/2 or 183 people in the room. But that intuition is wrong. The true formula is as follows:

N = .5 + SQRT((.25 + 2 * 365 * ln(2))

I would like to generalize this problem to the question of finding one’s soul mate. Specifically, the question I address is how many people would you have to include in a room for there to be a 50% chance that any two people in the room were once joined at the hip before Zeus took his shears and sliced them apart? Now, this assumes that the people in the room were randomly selected from the entire world population, which is approximately six billion people. The answer to this is simple, and follows the formula above:

N = .5 + SQRT((.25 + 2 * 6,000,000,000 * ln(2)) = 91,202

Wow! It would take a room of 91,202 people for there to be a 50% chance that any two people in that room were actually soul mates. One would have to have a pretty big room, perhaps as large as this room, which fits over 100,000 people.

Imagine a speed dating service in which you have five minutes to talk with every other person in this room. For those two lucky halves to actually have a chance to meet, the speed dating round would have to last for 91,202*5 minutes, which comes out to 316.67 days. All for only two of those 91,202 people to meet. This says nothing of the 91,200 people who leave Michigan Stadium brokenhearted or satisficing with someone who is not their other half.

But that doesn’t help you, dear reader, who doesn’t care about any two people encountering their soul mate, but rather about the probability that YOU will meet your soul mate. Well, the problem is that to calculate this, one would require a supercomputer that can handle a hell of a lot more decimal places than my humble Dell laptop. Needless to say, you would need a room about as big as this place to have a 50% chance of meeting your other half.

What does this tell you? Well, quite simply, you have about as much of a chance of meeting your other half as you do winning the powerball lottery. Either that, or the search for love isn’t a search for that one soul mate that Zeus cut from your side, but that any of a number of possible other halves fit approximately well enough that they can serve as soul mates. I tend to believe this is the case, because I know many a person who has claimed to have met their soul mate, and I know the probability of this actually occurring has about a snowball’s chance in hell. And whether or not I believe in soul mates matters very little. I do believe in probability!

But I tend to be hopeful. And I am a romantic who enjoys Greek mythology. I know my other half is wandering around out there. Of this I am certain beyond any statistical doubt. Whoever she is, I know she would appreciate my calculation of the infinitesimally small likelihood that we would ever meet.

Experimentaholic discovers a new force in the universe!

Leg day. There is nothing worse than leg day.

So ever since my semester ended, I have been spending more time at my gym. I generally don’t have much time for working out during the semester, but summer means time to try and avoid the ravages of time by exercise. Once you turn 25 apparently you lose a pound of muscle and gain a pound of fat per year. Lord knows I’m fat enough already to know that I don’t need another pound of fat come January, so there I go. But the other day I was really annoyed about going, since it was leg day.

Leg day is the day everyone hates, the day when you throw several hundred pounds on the barbell and do squats, or hold dumb bells and do lunges. Arm day is easy. Leg day just blows. But one thing I have noticed recently is that most men skip the leg exercises. They have skinny legs but massive chests and arms, which is obviously because they only do chest and arm exercises. But women don’t seem to skip those leg exercises – there are generally many women doing the ass and thigh machines. With one exception.

Over a month ago, when I started to go to the gym more regularly, I ran into this woman named Kelly. Kelly is stunningly beautiful. Tall, dark hair, gorgeous eyes, she could be mistaken for an actress. (She is actually a fashion model and aspiring actress…I know this only because we once got into a conversation because we were both wearing the same university tee shirt.) Kelly is one of those women who does her leg exercises quite regularly. And suddenly one day I noticed something rather perplexing about the nature of the universe. First, I noticed Kelly was doing her leg exercises. But then I noticed that there were several men, also doing leg exercises. I thought, “Wait a minute – that section is usually empty!” The next day…same thing. The following day, yet again.

Then, I had an epiphany. Maybe there is a new physical force in the universe, akin to gravity, that emanates solely from Kelly. Let’s call it the Kelly Field. It is a physical force that somehow attracts men to go to the leg section of the gym and work away those chicken-legs. I felt like Newton, but instead of an apple that struck me, it was a dumb bell.

I began to wonder how I could test whether Kelly was the source of a new force field that should be further investigated by more empirical studies, or whether this effect was merely due to chance or coincidence. So I designed a little experiment to test the hypothetical existence of the Kelly Field. Whenever I saw Kelly doing leg exercises, I counted the number of men and the number of women who would also be doing leg exercises. But after about two seconds of thinking, I realized this is not a very good experimental design: One needs a control condition. Maybe it is the case that when anyone – not just Kelly - goes into the leg section, that it attracts men to that section of the gym. So I had to have an alternative hypothesis…the existence of a Experimentaholic Field. If it were the case that anyone going to the leg section would attract men, then when I go to the leg section I would find just as many men working their legs as when Kelly was working out in that section. So I simply began to count the number of men in the leg section when Kelly was working out there, and the number of men when I was working out there. I eliminated a possible confound by never doing leg exercises when Kelly was doing leg exercises. Unlike other men, I was somehow unaffected by this force field, or at least could resist it at times.

At the end of three weeks, I had tallied the following totals over the course of 10 observations of Kelly and Experimentaholic. Below is a chart with the actual counts

Kelly: Men = 20, Women = 14

Experimentaholic: Men = 3, Women = 18

As can be seen in the contingency table above, there were far more men doing leg exercises in the presence of Kelly than in the presence of Sean. But this could be due to chance, right? How can one tell?

Well, the British statistician Karl Pearson saved the day when he came up with the formula for the Chi-Square test. Chi square allows you to determine whether there are associations among binary variables are likely to be due to chance. I ran the test, and found that the Chi Square test showed that the probability of such a large discrepancy in the number of men versus women working on their legs in the presence of Kelly versus Sean being due to chance is extremely low…like one in ten thousand. So the effect is real: there actually is a Kelly Field.

I wonder about the mechanism behind the Kelly Field. Does it work like gravity, and that its effect is a function of the squared distance between Kelly and men? Or is it something more like magnetism? Will we someday be able to throw out the theory of the Kelly Field and replace it with a Quantum Kelly Relativity Theory? Or a String Theory of Kelly? Only further investigations into the Kelly Field will provide us with these answers.

Currently I am working on my manuscript for the journal Science about this.

Actually, I’ll get to it once I get back from the gym.

What 3600 feels like

The number of American soldiers who have been killed in Iraq is rapidly approaching 3600. I knew none of them, but I know that none of them deserve to be included in a number as massive as 3600. But what do such massive numbers mean? I think we are used to the physical reality of small numbers. We can think about 5 or 10 or 100 in real terms, because these are sets of objects that are common in our daily life experiences.

Sure, you may be thinking, I paid $300,000 for my house...but I am sure you didn't pay it in ones you've been stuffing in your mattress from the tip jar at the coffee shop where you may work, counting it out one by one. Money was electronically transferred between financial institutions in less than a second. Every once in a while, we find a box of 500 nails, or 1000 plastic bags, but even then, we don’t often really have an experience with all 500 or 1000 at once. Over the years you use the nails one or two at a time, or accumulate the bags in your drawer, in batches of 5 or 10 every time you go to the store. You don't really have a sudden understanding of 1000 bags until the sleepless night you take them from your drawer and put them in a pile, or 500 nails until you accidentally knock them on the floor and have to pick each and every one up.

Perhaps an understanding through analogy, temporality, spatiality?

Sit still for one hour and count, one number a second. At the end of that long and boring hour, you will hit 3600.

See the sea of periods below? That is 3600 periods.

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3600 is the number of days in 9.86 years.

Want to drive from New York to Los Angeles? Drive 3600 miles west and you'll end up in the Pacific Ocean, because L.A. is only 2800 miles from New York.

Want to build a time Machine and go back and have a long chat with Socrates (I would like to give him a piece of my mind about that whole thing about physical reality not mattering)…go back 3600 years and you’ll have overshot him by about 800 years. In fact, you would have also missed Ancient Greece and have ended up in one of Homer’s stories.

One of the folks who visits my site has a project on plastic bags with a counter of the number of plastic bags used so far this year. Last I checked it was up to 231,253,112,013. Which is far more than the number of seconds I have lived this far in my life (I am 30): 480,924,000.

How do we think about such large numbers? How can we make large numbers more accessible to our reasoning so that we can think better about quantities Because I want a subjective experience of a large number that carries representational heft. I want to know what 200,000 feels like when someone tells you that over 200,000 people died in the atomic bombings in Hiroshima and Nagasaki, or what 800,000 feels like when I am told that the Rwandan genocide killed up to 800,000 people, or what 6 million feels like when I am told that 6 million people died in the holocaust?

And I want to feel what 3600 feels like when I discover that 3600 Americans have sacrificed their lives in the Iraq war.

What's the meaning of your life?

Last year I was asked to give a speech at a dinner for my school's psychology honor society. I just stumbled across it today and figured I would put it out there.

Thank you for inviting me today. It truly is an honor to speak to you on this special day when you join the prestigious group of psychologists who comprise this honor society. I know I speak for the faculty in saying that we are proud of your accomplishments and enjoy having you all in our classes and laboratories.

As psychologists, we often ask ourselves questions. And at some point, as human beings, most of us have asked ourselves the biggest question out there: what is the meaning of life. If you attempt to find an answer to this question, I’m sure you will become frustrated fairly quickly, because you may find there are so many smaller questions that have yet to be answered. And without answers to the smaller questions, you can’t even begin to approach the most massive question of all.

So today I want to tell you about a question so seemingly insignificant that you probably have never thought about it before. However, trivial as it might seem, it has taken up a majority of the past 5 years of my life, and I still believe that I might understand perhaps less than 5 percent of the answer. So the question is this: how do we come to understand that objects have size. To answer this question one must first consider the history of how we have conceptualized the process of cognitive development.

A long standing belief in the history of philosophy and psychology is that infants come into the world with few cognitive abilities or skills. This is best captured by the British Empiricist philosopher John Locke’s proposal that the infant mind is a tabula raza, a blank slate. Locke claimed that experience writes all knowledge upon this slate. This perspective led William James to claim that the infant experiences the world as a blooming, buzzing confusion of sensory information. Jean Piaget, the father of developmental psychology, argued that knowledge emerges through interactive processes of assimilation and accommodation between innate reflexes and the physical world. Yet innate reflexes are relatively primitive, and many have found his theory thus far lacking. But recently, developmental psychologists have come to understand that infants are not so clueless as they might appear, and have a remarkable set of innate skills that, along with experience, gradually develop into the mature abilities that all of us Psi Chi members share – and perhaps some of their parents and loved ones as well.

The skill I have examined extensively in my attempt to answer the question of how we understand size is a curious finding that young infants seem to have a primitive ability to automatically encode the size of an object. This finding was a surprise to a lot of people, because the traditional view was that children do not understand the concept of size until about eight years of age when they are able to use rulers to measure things. But what I found was that infants do notice a change in the size of an object, but only when that object is next to another object that serves the functional role of a ruler. They encode the size of the object as a proportion of that second object. When such objects are not available (such as when you have a glowing ball in a dark room) they can not encode size. Yet when you consider the ecological world of infants, there are plenty of objects in their perceptual world that can serve the role of perceptually-available rulers. A parent, for instance, always walks through the door, and the door itself remains the same size over time, so the infant simply encodes the size of the adult relative to the size of the door. So long as these objects do not change size, infants are able to remember and recall how big or small an object happens to be. Only later, when a teacher or parent shows the child how to use a ruler, do they begin to understand the functional role of conventional standard objects such as rulers, and decontextualize the size of objects from their immediately surrounding contexts. Thus, this primitive ability becomes obsolete and replaced with a new understanding of the concept of size.

But these primitive strategies for encoding size never become obsolete enough. Have any of you ever bought a piece of furniture that looked small in the enormous warehouse where you bought it but once in your home it ended up taking up half the living room? This happened because instead of using your mature adult brain and digging out a ruler or tape measure, you used the primitive strategy from your infant brain and encoded the size of the piece of furniture relative to an available context, namely the size of he warehouse itself. The problem is that the warehouse is much larger than your living room, and thus the piece of furniture appeared a heck of a lot smaller. Only when you bring it home and find it is far too large do you begin to regret the fact that you bought it at a going-out of business sale where there is no hope of a refund! But the point is that as adults we can sometimes see this primitive ability to encode size contextually echoes through our lives and affects us as adults.

But I would like to tell you the story of how I came to this knowledge about infant sensitivity to size. Like many of you, I started working in a psychology lab as an undergraduate probably. I designed an infant study in which I presented babies with sticks of various lengths either inside glass containers or alone on a small stage in a visual habituation task. I predicted that the glass containers provided the role of a perceptually available standard. I spent weeks collecting data that consisted of the amount of time infants stared at the different sticks. Finally, in the lab one night at 2:00 AM, I opened SPSS and conducted an ANOVA on the data. I clicked analyze, and the output showed the following, which, if you took my methods and theory class, you will know exactly what this means F(1, 47) = 5.6, p < .01. For those of you who missed class those days, this means that the experiment worked – I found a real result. I sat there, alone, with my coffee, and just stared at the screen in wonder, because I realized that I was the first person on earth to know this fact about the world. I was addicted.

But not every night has been so lucky. In another study, I spent several months collecting data from infants. I was interested in whether infants could rotate an object in working memory to encode its size. It's not important. I entered the data, hit analyze, and out spat a ANOVA with a p value of .78, meaning I had nothing, nada, ziltch. Three months of waiting for parents to bring in their babies on Saturday afternoons, with many of them not showing up, and those that did often crying in the middle of the experiment and thus rendering their data useless. A lot of sweat and elbow grease for nothing.

The next day I went to my advisor, Janellen Huttenlocher, in frustration. I told her that these goddamn babies were not behaving as they were supposed to. I told her that these infants were ruining my theory. I truly believed that I just had a batch of stupid babies.

She looked at me, in consternation and bemusement, and said, “Sean, the world has spoken to you: Listen to it.” And I realized at that moment that this statement is the essence of what we as psychologists do: we listen to what the world has to say. Many times, it had nothing to say. Many times we asked the world the wrong question. Many times the world speaks a language that we can’t even begin to comprehend.

But when the world does speak to us, and we have the knowledge and wisdom to listen, it usually is says something so fascinating that it is worth all the times that you have to throw up your hands and admit that your presumptions were wrong. Psychological science allows us to understand that we often view the world through myopic lenses; that we might think we understand the way things work and have a theory to explain it, but end up, in the end, being totally wrong. And as disappointing as this may be, this fact speaks to the very complexity of both the questions that we as psychologists wrestle with and the answers we come up with. Even questions so simple as how we understand the concept of size have not so simple answers.

So far, we have waded only ankle deep in this sea of psychological knowledge, and the waters seem warm and inviting. But I also know that we will never really swim far enough out there to answer enough of the unanswered smaller questions so that we can finally answer the question of the meaning of life. But I DO believe that I have come to a better understanding of what the meaning of my life is about, and perhaps a bit of what your lives are about, as well. And it is this: To use the tools of psychological science to come to a better understanding of the world around us, the people within it, and the processes that govern our thoughts and actions. And through this understanding, change the world, inspire the people within it, and help each other maximize all the potential in all of our thoughts and actions.

So I applaud all of you for pursuing an education and career in psychology. I applaud your friends and family for putting up with late night studying sessions and for being guinea pigs in your psychological experiments. I applaud you for doing so well in your coursework and research that you are able to join this elite group of psychologists who are members of Psi Chi. And most importantly, I hope all of you continue to enjoy listening to the world throughout the rest of your lives.

Thank you.

Reviews Blues

So, I seriously got a case of the reviews blues, and I got a tell you, it hurts so bad. I could sing a song about it, to a blues rift. I received a set of reviews from a journal asking me to basically go back to conceptual square one and redesign this entire piece of work. And run more Experiments. Normally, running experiments makes me warm and fuzzy inside, but it is summer, and there are no students around to serve as subjects. So the paper will have to lay dormant until the start of subject pool time.

I recently presented some data at the Association for Psychological Science conference in Washington, D.C. I like the conference because it is filled mainly with people of an experimental sort – not those clinical folks. Not that I have a problem with clinical psych – some of my best friends are clinicians! (I love that excuse) But if another person says, “Are you analyzing me?” when they find out I’m a psychologist…there will be hell to pay. But the highlight for me was meeting my doppelganger – a professor from the Midwest who falls asleep reading statistics books, and not just to read something so boring that she falls asleep, but because she loves statistics. Mmmm. My kind of person! She actually did something really cool – she taught a statistics course that had a service learning component in which the students created this large project to eliminate plastic bag waste. You can read about it here. I’m sold on the idea because I am sick of all the plastic bags crammed in my closet.

So in the meantime, I sit and peruse the internet, when I stumbled upon this great website called edge.com that is a community of people who are much smarter than I am. Every year the host of the website posts a question for people smarter than I to answer, questions of a metaphysical nature. In 2005 the question was the following:

“What do you believe is true even though you cannot prove it?”

The answers to this question are intriguing – and worth reading. (You can find the answers at the Edge Foundation website above). But this got me into thinking how I would answer the question.

My first response is that basically everything I believe to be true I can not prove. I don't even know if there really is anything I can prove to be true, but rather, I can only tell you how likely something I found to be true will replicate if you try to figure it out for yourself. But I believe I am composed of 70 percent water, I believe water consists of two hydrogen atoms and one oxygen atoms, I believe that atoms consist of protons, neutrons, and electrons, and that protons are composed of quarks, and so on. But I can prove none of it. I accept it as truth because I have no real reason to doubt these beliefs, and I don’t see how anyone has anything to gain by foolishly making me believe these falsehoods (perhaps the corporate entity that makes the VitaminWater I drink religiously?) But this is a somewhat unsatisfying answer – a cop out, if you will. The following is a list of some of the things I truly believe but can not prove, but wish I could.

1. Destiny is for the most part a series of random accidents one can not predict

Who are you? I am a cognitive-developmental-cultural psychologist who studies memory, spatial reasoning, and culture’s effects on the mind. I am also a pianist, a painter, a photographer, and on some rare days a writer. But how did it come to pass that these things came to identify me?

That I am now a professor of psychology is a total accident. Once, while an undergraduate at the University of Chicago, I was walking through a building. I could have taken a shortcut through a quad, but I decided to take the longer route for no real reason. In walking down the hallway, I noticed a help wanted sign for a lab technician in a psychology laboratory. Needing a bit of cash, I took the number down, called, and was interviewed and hired. The job was boring - transcribing hundreds of hours of videos of children interacting with parents – but the professor noticed that I worked hard and encouraged me with posing that I work on an idea that eventually became my M.A. thesis.

I often wonder about the person I didn’t become – that moment the universe divided and in this alternative world that person who once was me took the shorter route. I wonder what his destiny would have been. Maybe I would be here (here is a coffee shop in the Bella Vista neighborhood in Philadelphia) or maybe I would be somewhere completely different. Either way, my feeling tends to be that we would like to believe in destiny because it makes the universe seem purposeful. I’d rather simply accept the world I happened to stumble into.

2. People do not differ in intelligence, they only differ in their intrinsic motivation to come up with correct answers

People do not differ in intelligence. This is the great error with our national fetish for testing and ranking, quantifying without truly understanding what the numbers mean. One’s I.Q. score may say something about a person, but it is not any intrinsic and innate level of cognitive abilities. It is rather a habitual and chronic level of motivation for trying hard enough to answer questions correctly.

Now, this claim is in a way is a notational variant of intelligence – you could say that if they both have the same predictive power, why chose motivation over intelligence? However, it is very different from an ontological perspective, and the implications for pedagogy is enormous. You can not change one’s innate level of cognitive ability, but you certainly can change their level of motivation.

3. Babies are far stupider than many developmental psychologists claim, but they have enormous potential

I recently attended a conference in which one fellow was claiming that babies have an innate sense of helping and hurting behaviors, another was claiming that they could solve complex statistical and mathematical problems, and another was saying that infants can judge the intentions of others. Some of these guys I consider my friends. However, I can’t help but wonder why it is the case that a 6 month old infant can solve probability problems, but my 20 year old undergraduates struggle like it is solving Fermat’s Theorem. And as I see it: either the developmental folks are simply wrong, or we get stupider as we get older.

I truly believe that babies start out just like John Locke stated – a blank slate. But not any old blank slate…a slate with lines already carved onto it. These lines are the hardwiring of what will eventually be a rich and complicated system of interacting systems and mechanisms. But there is nothing there are the beginning. There is nothing there in the genes that we can consider to be representational knowledge. And what gets written onto those lines of this blank slate are some kind of universal language that has to do with the universal experience of being a baby – learning to see and perceive the world, act upon and within it, and ultimately, come to understand that the probability of getting heads or tails with the flip of a fair coin are 50-50. We come prepared to learn a great deal about the world, but I can not buy the claim that we come hardwired with a rich set of conceptual schemes.

4. White Capri pants are an evolutionary mistake

White Capri pants universally make anyone wearing them look terrible. I don’t know why this is, but I have never seen someone wearing white Capri pants and said, “Wow, that person looks great!” Perhaps it is something local, having to do with my own fashion preferences, but I think there is more to it than that because I’ve had many a discussion with many a man and have not yet once met someone who hasn’t held the same opinion.

5. You are almost there

This is a fortune from a fortune cookie that I keep in my wallet. I opened this one in Chicago, in China Town, shortly before I left the chains and shackles of graduate school. I believed then that I was almost there. I believe now that I am almost there. And I believe you, too, are almost there. I don’t where there is for me, nor do I know where there is for you, but it is comforting for both of us to know that it is approaching. I hope it is beautiful for me. I hope it is beautiful for you.

Bayesian bar hopping, Einsteinian insanity, and the seduction of soft science

A few months ago I was having dinner with a friend, a professor of physics. We'll call him professor base-rate-neglect. He's one of those hard science jerks who always reminds me that the social sciences are soft sciences. I'm used to claims like these from idiots like him. But, still, I love the guy. So professor BRN was complaining about his love life, or lack thereof. "I don't get it. I'm smart. I'm fairly attractive. I have a good job. But I can't seem to meet women."

Experimentaholic replies, "Well, how are you trying to meet them? Or rather, how have you met the women you've dated most recently?"

Dr. BRN says, "I met Kelly at a bar. That ended horribly. I met Jen at the park. Ended terribly. I met Susan at the bookstore. Ended because she moved to Oregon."

Experimentaholic: "Well, have you ever heard of a guy names Thomas Bayes?"

BRN: Sure. He did Bayes Theorem. I forget about what it says, though. I hated statistics. It's soft math.

Experimentaholic: I hate it when you people say that. Especially since I will use soft math to solve your problems. Bayes dealt with a statistical problem having to do with where billiard balls would end up resting on a table. I think this directly relates to your problem.

BRN: This is why I don't trust you soft scientists. Soft thinking. Billiard balls. What do billiard balls have to do with my love life?

Experimentaholic: More than you'd think. I won't go into the gory details of marginal and conditional probability, because you probably slept through stats. But let me ask you another question. How many times per week do you do any of these activities?

BRN: Well, I might seem a bit like an alcoholic, but I probably go out to bars three times per week. I go running on the weekend, and probably go to the bookstore once a month or so.

Experimentaholic: Okay. Think for a minute. So you go to bars 12 times a month, and you got one hit and 11 misses. You go running four times a month, and you get one hit and three misses. You go to the bookstore once a month, and you get one hit, no misses. Do you get where I am going with this?

BRN: Not really.

Experimentaholic: Dude, for every time you go to the bar each year, say, there is a less than one percent chance you are going to meet someone. Why? Because you head to the bar 144 times per year, and only have one relationship to show for it. You go running 36 times per year, and you have one relationship to show for it. That means the probability of you meeting someone while running is around 2 percent. Now, you go to the bookstore 12 times a year, and you have one relationship to show for it. That's an 8 percent chance that every time you go to the bookstore, you'll meet someone.

It seems as if you're doing everything backwards. What would Thomas Bayes do, if he either were alive today or not a Presbyterian minister, or not a [explicative deleded] lush like you? He would be going to the bookstore 3 times a week, going running twice a week, and avoiding bars altogether. Man, you got your strategies mixed up. All because you are ignoring the base rates - or the hits and misses - of your strategies of meeting people.

BRN: I never thought of it that way.

Experimentaholic: I know you think that my kind of science is soft, and that psychology is bullshit. I think a lot of psychology is bullshit too. But I am forcing you to do a little experiment. I don't care if you keep going to bars three times a week, you're a lush after all, and the tenure track thing is stressful. Drown yourself in beer. But I am forcing you to go to the bookstore three times a week. An hour at the bookstore, perusing the shelves, and let's see how your love life changes.

BRN: We'll see. I'll have to think about it.

Experimentaholic: Think all you want. It's the fact that you're not thinking about base rates that makes you miserably unhappy and sitting here complaining to me, and going home alone to your miserable apartment and crying your lonely self to sleep.

BRN: Whatever, you [explicative deleted] soft scientist.

Now, I haven't seen BRN for a little while, and I just received the following email from him.

Experimentaholic:

Yo, man. Sorry I've been out of touch, but the most amazing thing happened. So at first, I basically ignored your little "experiment" and kept doing what I always do. I thought, "You're dumb, and what do you know?" Then, a few weeks later, after a pretty bad hangover, I decided to try your little experiment. For two weeks, I went to the bookstore three times a week. During the third week, I'm sitting there, reading a copy of Dawkins's The God Delusion, when this totally gorgeous woman walks up and says that she loved that book. We started chatting, and she is a biology grad student at [redacted] university. We totally hit it off, and she gives me her number. I call a few days later, we go out on a date, and you know where this is heading. Long story short, I'm seeing this girl. It's been five weeks now, and I am totally falling for her. Man, I can not believe that a psychologist of all people could [increase the frequency of his sexual encounters]. I thought you soft scientists were idiots. Next time we get together, dinner's on me.

My response?

I guess it takes a psychology professor to remind a physics professor that Einstein defined insanity as "doing the same thing over and over again and expecting different results." Perhaps there is something to soft science after all? Either way, I will relish the dinner. And I look forward to meeting the new lady.

Experimentaholic saves the day.

Prediction and postdiction

I share in the horror over the massacre at Virginia Tech. Part of the shock for all of us in academia is that we tend to think of school as the diving board of life: a place where lives begin, not end. I see my own students and colleagues in the images of both the victims as well as the perpetrator. And that both saddens and terrifies me.

However, I find it upsetting that people are criticizing Virginia Tech for ignoring warning signs. I find that response represents a severe and all-too-common error in thinking about direct versus inverse probability.

The basic premise rests in the fact that the following statements are not identical:

1. Given person A wears a trenchcoat, is quiet, and writes plays involving murder, there is a high probability that he will go on a shooting spree.
2. Given person A went on a shooting spree, there is a high probability that he wore a trenchcoat, was quiet, and wrote plays involving murder.

The first statement is one that is a matter of direct probability. You multiply the proportion of people who wear trenchcoats, who are quiet, and who write plays about murder, and you get a number which represents the proportion of the population that are going to go on shooting sprees. However, there is a little problem: a lot of people wear trenchcoats, are quiet, and write plays about murder. Round them up, and you might find a group that includes a significant proportion of the undergraduate population. However, a significant proportion of the undergraduate population will not end up going on a shooting spree. That concerns the error inherent in mistaking direct and inverse probability.

A 17th century minister named Thomas Bayes noted that probability of event A conditional on B is generally different than the probability of B conditional on A. Bayes came up with a solution that links them mathematically by a simple equation called Bayes Theorem. In short, the theorem explains that the relationship between direct and inverse probability is a function of the base rate, or frequency, of the two events. Psychologists have long known that people ignore base rates, resulting in serious errors in reasoning that can be fatal.

For example, there are many cases of heterosexual, non-IV drug users who killed themselves because they received news of a positive HIV test. Their doctors probably informed them that the HIV test has an accuracy of 99.99 percent. However, that does not mean that they can be 99.99% sure that they have HIV. Why? Because of the base rate: tens of thousands of people take the HIV test, and HIV prevalence is extremely low (about 1 in 10,0000) among that particular population (heterosexual non-IV drug users). Every once in a while, given the fact that tens of thousands of tests are run, a negative sample will test positive (the 0.01 percent inaccuracy part). So the actual probability of being HIV positive given a positive HIV test (again, if you are a heterosexual non-IV drug user) is actually about 50% (I calculated this using Bayes Theorem). But most doctors I've interviewed never even heard of Thomas Bayes or his theorem, and make the same mistake their patients do in assuming that direct and inverse probability are the same.

In a similar way, it is easy to say, after the fact, the postdiction that someone should have known, that someone should have done something, that the university was irresponsible for not having seen the warning signs. But the problem with these statements is that they ignore the base rate of the frequency of these warning signs. A lot of college students show warning signs, and many students show warning signs that are considerably worse than those exhibited by Mr. Cho. And unless one were to come up with a better diagnostic tool than trenchcoats or murderous plays - like a crystal ball - I don't believe it is possible to predict who is just an awkward student (of which there are many) and who is going to be a serial killer. I hope we someday can tell them apart, but knowing a bit about human nature - and the way we make errors in our reasoning about probability - makes me doubt it.