Painful memories, and effortful actions

How does the brain evaluate a painful episode?  When you look back at an unpleasant episode of your life, how does your impression of it now relate to the actual experience that you had during the episode?

Surprisingly, when we recall a painful experience we seem not to evaluate it based on its duration, or its temporal integral, or its mean pain.  That is, it does not matter very much if one experience was on average more painful than another, nor does it matter that one experience was longer than another.  Rather, we seem to evaluate the totality of a painful experience using two factors: magnitude of the peak of the pain, and the magnitude of the pain as the episode ended.  Here, I will describe the basic experiments that led to these ideas, and then suggest a new interpretation of rather puzzling results regarding how the brain evaluates effort in simple motor control tasks.

Cold water bath

In 1993, Kahneman and colleagues asked 32 volunteers at University of California Berkeley to put both their hands in a cold water bath for 5 seconds.  Next, one hand was chosen at random and placed in cold water for 60 seconds (or 90).  After a brief rest period, the other hand was placed in cold water for 90 seconds (or 60).  In these two episodes the temperature of the water was the same for the first 60 seconds (21 degrees Centigrade).  However, in the last 30 seconds of the 90 second episode, the temperature was increased by 1.1 deg.  So in the 90 second episode one hand always experienced a longer period of discomfort, but the episode for that hand ended with slightly warmer water. 

During the time that their hand was in water the subjects used their other hand to adjust a knob to continuously indicate their discomfort.  As you would expect, the discomfort increased immediately as the hand was placed in the cold water, reached a peak at around 60 seconds, and then declined for the next 30 seconds. 

After the two episodes were completed, the subjects were told that they would need to put their hand in cold water one more time but that they could choose which episode they wanted.  The main dependent variable was the subject’s choice for this third episode.  Logically, no one should pick the episode that lasted 90 seconds.  But remarkably, most subjects (22 of 32, 69%) preferred to repeat the longer episode.  Indeed, most subjects indicated that the longer episode had caused less overall discomfort!

This suggested that when people evaluate painful episodes, what matters is not the duration, but rather the magnitude of the pain as the episode ended.  However, a potential confound with the cold water experiment is that we know that memory fades with time, and so perhaps evaluating the pain of an episode relies more on the ending because the memory of the early parts have faded.  Perhaps if the subjects were asked to remember the episode a few days later, they would not recall it the same way as a few minutes after the end of the episode.  Was this temporal decay the reason for the seemingly illogical choice?  To test for this, Kahneman and colleagues performed a new experiment.

The perceived pain of a medical procedure

Redelmeier and Kahneman (1996) asked patients that were undergoing colonoscopy (n=154) or lithotripsy (a procedure to destroy hardened masses, n=133) to give assessment of their pain by pointing to a scale at one minute intervals.  The colonoscopy lasted from 4-67 minutes, and the lithotripsy lasted from 18-51 min.  One hour after the procedure the patients were asked to judge the total amount of pain experienced using the same scale. 

To check for reliability of the evaluations, some of the patients were asked to recall the experience 6 months (colonoscopy) or 1 year (lithotripsy) later and again evaluate the total pain.  The retrospective ratings at 6 months and 1 year were correlated at r=0.77 and r=0.54 for the two groups.  For the colonoscopy group the ratings at 6 months had the same mean as at 1 hour, for the lithotripsy group the average ratings at 1 year were 15% higher than at 1 hour. 

In the colonoscopy procedure the pain intensity was higher at start than at end, whereas in the lithotripsy procedure pain intensity was low in the first few minutes and ended higher. 

Having collected these data, the investigators asked what aspect of the painful experience was a predictor of the immediate ratings at 1 hour, or the follow-up ratings at 6 months or 1 year.  Duration of the procedure was not a predictor of the immediate or follow-up ratings.  Rather, peak pain was the most powerful predictor of both ratings (r=0.6 for each), and end pain was the second most powerful predictor (r=0.4 for each).  These correlations held for both of the procedures.  The combination of the two factors increased the correlations to about 0.67 and 0.65 for immediate and follow-up ratings.

So people’s impression of the relative pain they endured during an episode remained fairly consistent at 1 hour and at many months after the episode.  Their impressions were predicted by two aspects of their actual experience: magnitude of the peak of the pain, and magnitude of the end pain.  Duration of the episode played little or no role.  

When we remember a painful episode, the most salient aspects of that episode seem to be the peak of the pain, and how it ended.  To improve our perception of a difficult episode, it may be more beneficial to prolong it and gradually reduce the pain, rather than shorten it and abruptly end the pain. 

Perception of effort

This idea of peak-end perception of pain may help us understand a rather puzzling result in the field of motor control.  One of the fundamental questions in motor control is how the brain evaluates effort.  The variables of interest are force and time, and the question is with regard to our perception of effort as a function of these variables.

In 2004, +Konrad Kording, +Daniel Wolpert and colleagues performed an experiment in which volunteers held a robotic arm and experienced a sinusoidal-like force profile of peak F and duration T.   Next, they experienced another force pattern of peak F’ and duration T’.  They then asked their volunteers which force they would like to experience again.  They were told that they should choose the force that required the least effort.  In this way, the investigators estimated indifference curves, i.e., curves along which the subjects were indifferent to changes in peak force and duration.

The rather unexpected result was that as the duration of a force pattern increased (beyond about 200ms), the indifference curve also increased.  This means that given a choice between some peak force and short duration, vs. the same peak force and longer duration, the subjects picked the longer duration!  

How could a longer duration of an effortful task be preferable to a shorter duration?

A close look at how the force patterns were produced provides a possible answer.  The forces were sinusoidal with a period that depended on T.  So as the duration increased, the rate at which the force changed decreased.  This means that for a longer duration force, the forces gradually came to an end, whereas for a short duration force, the forces rapidly came to an end.  People preferred the gradually ending force, despite the fact that they would be producing the forces for a longer amount of time.

The peak-end hypothesis of pain perception may have relevance to how the brain measures effort.

Acknowledgements: I am grateful to +Alaa Ahmed of University of Colorado for discussions regarding these ideas.

References

Kahneman D, Fredrickson BL, Schreiber CA, and Redelmeier DA (1993) When more pain is preferred to less: adding a better end. Psychological Science 4:401-405.

Kording KP, Fukinaga I, Howard IS, Ingram JN, and Wolpert DM (2004) A neuroeconomic approach to inferring utility functions in sensorimotor control.  PLoS Biology 2:e330.

Redelmeier DA, and Kahneman D (1996) Patients’ memories of painful medical treatments: real-time and retrospective evaluations of two minimally invasive procedures.  Pain 66:3-8.

Why are gun rights proponents more politically active?

In January of 2013, about a month after the horrific shootings of children in Newtown, Connecticut, the Pew Research Center released a survey of gun-related political leanings of people in America.  They first asked the respondents to identify themselves as either gun rights proponents, or gun control proponents.  They then asked the respondents questions about their political activity: did they contribute money to organizations that took a position on gun policy?  Had they contacted a public official to express an opinion on gun policy?  Had they signed a petition on gun policy?  Etc.  The results indicated that those who prioritized gun rights were 1.7 times more likely to have been politically active (i.e., participated in one or more of these activities) than those who prioritized gun control.  Why should gun rights advocates be almost twice as likely to be politically active than gun control advocates?

To understand this behavior, it is useful to consider how the human brain makes choices when faced with gains and losses. 

In 1990, Kahneman and colleagues performed an experiment in which they selected some participants and gave them a coffee mug as a gift.  They then asked them to assign a minimum price on the mug that they were willing to sell it.  These participants asked for about $7.  They then took another group of participants and showed them the same mug and asked how much they would be willing to pay to own it.  They responded around $3.  Knetsch (1989) found that people who are given a chocolate bar want $1.83 to sell it, but will pay only $0.90 to buy it.  The difference in the two prices is explained by loss aversion: the sellers evaluate the choice of giving up something that they already own by viewing it as a psychological loss.  In order to compensate for that loss, they request a lot of money.  Buyers, on the other hand, evaluate the choice as a psychological gain.  They are willing to pay much less for the pleasure that they perceive in owning it. 

In general, the pleasure that you feel if someone was to give you an item tends to be much less than the pain you feel if you were to own that item and were to lose it.  This is called an endowment effect. 

Carmon and Ariely (2000) explain this behavior by suggesting that when faced with loss of something (e.g., selling), people focus on their sentiment toward surrendering the item (and not the money that they are gaining), whereas when faced with gain of something (e.g., buying), people focus on their sentiment toward what they forgo (typically money, and not the item they are gaining).

Now let us consider the question of why gun rights proponents are more politically active than gun control proponents.  The current political climate is one in which the President and the Congress are considering laws that would limit gun rights.  This is viewed as a loss to gun rights proponents.  In contrast, the same laws are viewed as a gain for gun control advocates. 

The gun rights proponents (but not the gun control proponents) are under the influence of the endowment effect because if the proposed laws are enacted, it would result in a loss of what they already ‘own’.  For them, the proposed laws carry a negative psychological value.  If we could generalize from behavioral economics literature, we would speculate that this negative value is about twice as large as the positive psychological value that would be gained from the perspective of gun control proponents.  This may be the reason why the gun rights proponents are about twice as likely to be politically active as the gun control proponents. 

The deeper idea is that any change from the status quo will meet with much stronger resistance by those who view the change as a loss, as compared to the enthusiasm that it fosters in those who view the change as a gain.

References

Carmon, Z. and Ariely, D. (2000) Focusing on the forgone: How value can appear so different to buyers and sellers.  Journal of Consumer Research 30:15-29.

Kahneman D., Knetsch J., and Thaler R. (1990) Experimental tests of the endowment effect and the coase theorem.  Journal of Political Economy 98:1325-1348.

Knetsch J. (1989) The endowment effect and evidence for nonreversible indifference curves. American Economic Review 79:1277-1284.

How to find an outlier

How do we know when a data point is an outlier?  Take a look at the figure below.  It represents 15 data points that were gathered in some experiment.  Would you say that the left-most point is an outlier? 

Maybe the instrument that collected this data point had a malfunction, or maybe the subject that produced that data did not follow the instructions.  If we have no other information than the data, how would we decide?

When we say a data point is an outlier, we are saying that it is unlikely that it was generated by the same process that generated the rest of our data.  For example, if we assume that our data was generated by a random process with a Gaussian distribution, then there is only a 0.13% chance that we would collect a data point that is 3 standard deviations from the mean.  So what we need to do is try to estimate the standard deviation of the underlying process that generated the data.  Here I will review two approaches, and then show how successful they are in labeling outliers.

Median Absolute Deviation (MAD)                                          

Hampel (1974) suggested that we begin with finding the median of the data set.  

Next, we make a new data set consisting of the distance (this is a positive number) between each data point and the median.  Finally, we find the median of the new data set.  That is, we compute the following:

MAD = b median( abs(x – median(x) ) )

If we set b=1.4826, then MAD is an estimate of the standard deviation of our data set, assuming that the true underlying data came from a Gaussian distribution.  For our data set above, here is the estimate of the standard deviation, centered on the median:

Based on MAD estimate of the standard deviation, we would say that the left-most data point is indeed more than 3 estimated standard deviations (MADs) from our estimate of the mean (the median). 

So a typical approach is to label as ‘outlier’ a data point that is farther than 3 times the MAD (standard deviation) than the median of the data.  That is, compute the following for each data point:

abs(x – median(x) ) / MAD

Label as ‘outlier’ the data points for which this measure gives you a number greater than 3.   But how good is this method?  To check it, I did the following experiment.  I generated data sets drawn from a normal distribution with a constant mean and standard deviation, and then computed the probability of a false positive, that is, I computed how likely it was that a point would be labeled as outlier by MAD, when in fact it was less than 3 standard deviations from the mean.  Here is the resulting probability, plotted as a function of the data size:

The above plot shows that when the data set is small (say 10 data points), about 20% of the data points that the algorithm picks as outliers are in fact within 3 standard deviations of the mean.  As the data set grows larger, the probability of false positives declines and the algorithm does better.  But even for a data set of size 20, there is better than 15% chance that the bad data point is in fact not bad.

Median Deviation of the Medians (MDM)

Rousseeuw and Croux (1993) suggested a method that, as we will see, is better.  For each data point xi, we find the distance to all other data points and find the resulting median.  We do this for all data points and we get n medians.  Now we find the median of this new data set:

MDM = c median( median( abs(xi –xj) ) )

If we set c=1.1926, then MDM is a robust estimate of the standard deviation of the data set, assuming that the true underlying data came from a Gaussian distribution.  For our data set above, here is the estimate of the standard deviation:

To check how this method compares with MAD, I generated data sets drawn from a normal distribution with a constant mean and standard deviation, and then computed the probability of a false positive, that is, I computed how likely it was that a point would be labeled as outlier by MDM, when in fact it was less than 3 standard deviations from the mean.  Here is the resulting probability, plotted as a function of the data size:

The above plot shows that regardless of the size of the data (here ranging from 6 data points to 20), a data point that MDM labels as an outlier has about 9% chance of being a false positive, i.e., not an outlier.  For small data sets, MDM is two to three times better than MAD.

References

Hampel FR (1974) The influence curve and its role in robust estimation. Journal of American Statistical Association 69:383-393.

Rousseeuw PJ, Croux C (1993) Alternatives to the median absolute deviation. Journal of American Statistical Association 88:1273-1283.

Tehran cemetary

The transition from west to the Middle East begins at a European airport.  In the waiting area for the flight to Tehran, a young woman stands up and holds her hands close to her face, appearing to be reading a small, imaginary book.  She bows her head slightly, and then kneels to the ground, bringing her head down to the cold stone floor.   The ritual lasts no more than a couple of minutes, and after she finishes, she simply sits down and carries on a conversation with her fellow traveler.  But then someone else, over at the corner of the room, stands up and starts the ritual, facing exactly the same direction, holding up the same imaginary book.  

It’s time for afternoon prayers, and the devout do not need anything other than their faith to perform it.

Tehran is a densely populated, sprawling city that sits on the edge of a mountain range.  In the winter, when the westerly wind blows away the brown smog, the city is spectacular: a pearl necklace of snow covered jagged granite rise up toward the clouds, seemingly a few feet away from the tall apartments in the northern edge of the city.

The only reasonable method of transportation is the metro: a clean, modern system that is slowly growing.  At the last stop on the southernmost point of Line 1, something delightful awaits the traveler.  As you near the exit turn styles, a few people are standing with baskets or boxes full of cookies or sweets, giving them away for free.  They wait until all their food is gone before they go in to catch the train.  This is the stop for Beheshte-Zahra, the city’s main cemetery for its millions of inhabitants.  In the Iranian tradition, visiting your loved ones at the cemetery is a ritual, filled with compassion and giving to strangers; you offer food to a stranger, and silently ask for a prayer for your departed. 

The cemetery itself is a checkerboard of graves, marked only with black rectangular granite or white marble tombstones, lying flat on the ground, with the face of the departed chiseled in the stone.  The tombstones are works of art commissioned by ordinary people, each piece using calligraphy to describe a departed, often including a few tearful lines of poetry to measure the loss.

Many of the tombstones have only the top half marked, leaving one half unfinished.  Here is a wife or a husband, awaiting their mate.

People are grieving, of course, but there is a sense of shared pain, as all have brought something to give, making a friend for a moment, receiving a smile, a nod of the head, a few words of comfort.  Some even bring small stoves and make traditional soups (in winter) near the grave that they have come to visit.  You see the elderly woman making the soup, and the young boy walking with small bowls and spoons, offering it to strangers.

Choosing sides

On thanksgiving, after the turkey, homemade fruit salad, mango salsa, cheesecake, and blackberry pie, about fourteen of us, two families, head to an indoor volleyball court.  The young ones, from 12 to 20 something, take off early to buy a volley ball, which turns out to be a little difficult.  The older ones, the two dads (me and my friend), join them a little later. 

On the court, after a couple of hours of fun where teams are randomly put together, we come to the final game, where the two dads pick their teams.  Your competitive nature takes over your brain, and you pick the best player among the ones waiting to be called, not thinking that these are your kids, and you are choosing sides.  

On game point, my friend’s daughter, who is on my team, serves a good ball, but they return it strong, and our back center puts it in the net.  We all think that the point is over, but my son digs it out of the net, and another of my friend’s daughters puts it over for a win. 

Explosion of laughter and cheering.                                                                                  

My friend’s daughter yells out to him: "you should have picked me dad!"

Book of friendship

On the plane ride home, in the seat pocket in front of me, I pick up a magazine.  On the front cover it says “3 perfect days in Istanbul”.  Inside, there is a nice house, overlooking a wooded area.  The house has a beautiful swimming pool, and a lovely lady diving in the water.  But she is all alone.  I think they missed the point.

My three perfect days in Spokane were spent in the exact opposite of alone, with my childhood friend and his family.  What made it perfect?

Watching, together,
the sun change the hues on a mountain range miles away as it warmed our bare toes;
the breeze caressing the golden wheat on a hill that leaned against a deep blue sky;
the moon rising slowly between two tall pines on a cloudless night;
nature, absolutely silent, awaiting sunrise;

our white long-haired dog, sleeping in the shade, on green, green grass;
tomatoes from the garden, just picked, sliced thick on white china;
homemade scones late at night, with hot tea, under Orion’s Belt;
four games of  two-on-two volley ball with ‘commercial breaks’, laughing while someone looks for the stray ball in the tall grass;

hawks circling slowly;
our lives unhurriedly shared;
adding a page of memories to our 35 year old book of friendship. 

A question of identity

During the summer, scientists like to organize short courses that are a couple of weeks long and are held at small research institutions near a beach or a mountain.  The classes are small, acceptance is tough, and the students come from diverse places around the world.  One morning this week after I gave a lecture at one of these courses, I hung around to chat with some of them over a cup of tea.  I was astonished to hear that about four or five of the students could speak Persian!  Curious to learn more, I inquired about their paths in life.  All were kids of parents who were displaced or otherwise negatively affected by the Iranian revolution in 1978.  The parents had been young intellectuals who had immigrated to the west, and these were their kids, raised with Persian language at home, a different language at school, and two cultures entangled.  What exactly are you when you are born and raised in London, the most important holiday for you is Norooz, and your favorite food is basmati rice with Khorshe Gheymeh?  Your passport says something about your nationality, but where is home?

A few years back, Yo Yo Ma, the famous cellist, talked about this question of identity in an interview with National Public Radio.  Here is what he said:  “I was born in Paris, my parents were from China, and I was brought up mostly in America. When I was young, this was very confusing: everyone said that their culture was best, but I knew they couldn't all be right. I felt that there was an expectation that I would choose to be Chinese or French or American. For many years I bounced among the three, trying on each but never being wholly comfortable. I hoped I wouldn't have to choose, but I didn't know what that meant and how exactly to "not choose." However, the process of trying on each culture taught me something. As I struggled to belong, I came to understand what made each one unique. At that point, I realized that I didn't need to choose one culture to the exclusion of another, but instead I could choose from all three.  The values I selected would become part of who I was, but no one culture needed to win. I could honor the cultural depth and longevity of my Chinese heritage, while feeling just as passionate about the deep artistic traditions of the French, and the American commitment to opportunity and the future.”

Thinking about Yo Yo Ma’s view, I realized that the diversity in the students’ experiences had provided them with options, samples of what different cultures could provide.  But in addition to cultures rooted in geographical locations, they had been exposed to the culture of science.  Science provided a few of the things that countries tend to provide: deep history, myths, inspirational heroes, and sensational legends.  For some students, science was a comfortable community, the closest thing to what they might call home.