Quotable

"If I can be any help at all, you're in worse trouble than I thought."
- Blind jazz saxophonist to Steve Martin, All of Me

I sometimes feel this way reading fellow applicants' posts to the Livejournal applying to grad community.

More on the Linda the bank teller:
"As Stephen Jay Gould noted, knowledge of the truth does not dislodge the feeling that Linda is a feminist bank teller: 'I know [the right answer], yet a little homonculus in my head continues to jump up and down, shouting at me - "but she can't just be a bank teller; read the description."'"
- Daniel Kahneman & Shane Frederick, Representativeness Revisited

(Those nested quotation marks are making me crazy here.)

You know, sometimes you just gotta tell that little homonculus to shut up and sit his ass down.

MIT Open Course Ware

For those readers who may be jonesing for more math instruction or are just interested in checking out some college coursework, the MIT Open Course Ware program looks pretty cool. I have not used it, but it is "a free publication of MIT course materials that reflects almost all the undergraduate and graduate subjects taught at MIT." You don't get any kind of college credit with it, but you can take advantage of lecture notes, assignments, and classroom lecture videos to learn something new or review something you used to know. They have over 1800 undergraduate and graduate courses available.

Bunnmunk

Robert was looking at this article about a bunch of new species of animals and plants found in Southeast Asia. Though there is something to be said for a spider with a foot-long leg span, a rat thought to be extinct for centuries until being spotted in an outdoor restaurant, and a bright pink milipede, I only have eyes for the bunnmunk (okay, a rabbit called nesolagus timminsi).


"We're the bunnmunks! B-U-N-N-MUNK!"

I mean, really, he's got serious chipmunk coloring:


Much cuteness.

I Hope So Too

Although I do not share the pink-haired girl's overall attitude toward life, I heartily agree with her statement in the last panel. I hope this much of the time.

Defending the Family (Mathematical) Honor

I have now done my part to uphold the family honor: I have finished the diff equations class and barring some bizarre problem like this has all been a dream, I should have an A. Hopefully this effort, combined with my sister's previous ones, will help counter the blemish of my dad's differential equations F.

I am now well-prepared to begin forgetting more about differential equations than most people will ever know.

...which, by the way, has to be one of the least compelling arguments for credibility ever. "I have forgotten more about macroeconomics than you will ever know!" or "She has forgotten more about state purchasing guidelines than he ever knew!" This is particularly strange when used as a reason that the speaker should be trusted to make a decision, etc., over the other person mentioned. Wait, we're supposed to put all this confidence in you because you used to know something about the topic? I'm going to put my trust in someone who has learned a lot about something and not, you know, forgotten it. I used to think that this phrase was merely a joke, but it seems that people do use it seriously as a testament to an individual's knowledge and expertise (and not, as it may sound to one upon first hearing it, their cognitive decline).

Do the math. Hey, we can do this in the form of a GRE quantitative comparison question.

"Ann has forgotten more about math than Brenda ever knew.

Column A: the amount Ann currently knows about math
Column B: the amount Brenda currently knows about math

A - the quantity in Column A is larger
B - the quantity in Column B is larger
C - the two quantities are equal
D - the relationship cannot be determined from the information given"

Ann forgot X amount, and once knew Y amount, and currently knows Y - X amount about math.

Brenda forgot S amount, and once knew T amount, and currently knows T - S amount about math.

X > T

Is Y - X larger, smaller, or equal to T - S?

It's easy to see if you try different numbers. Say X = 10 and T = 5. How does Y - 10 compare to 5 - S? That depends on Y (how much Ann once knew) and S (how much Brenda forgot).

If Y = 100 and S = 1, then 100 -10 = 90 > 5 - 1 = 4.
If Y = 11 and S = 3, then 11 - 10 = 1 < 5 - 3 = 2.
If Y = 14 and S = 2, then 13 - 10 = 3 = 5 - 2 = 3.

So without additional information, the statement means squat in terms of who knows more about math right now.

Movie Anachronisms

I finally watched No Country for Old Men, which many reviewers believe to be the Coen brothers' best movie since Fargo. I have to disagree. It's better than Fargo; it's their best movie, full-stop. Don't get me wrong - I liked Fargo a lot, but the pacing, the suspense, and most of all, the overall context for the violence was far superior in No Country. Also, Tommy Lee Jones rocked a part that could easily have been too full of small-town old-timer wisdom and gets special recognition for that uber-rarity: making you interested in hearing about a dream he had, a dream that has a frickin' point even.

But one thing that surprised me was the reference to an ATM in a movie set in West Texas in 1980. I have found out that the first ATM in Texas was opened in 1978, but it's hard to imagine that they were very common in some small town in the Del Rio area. (Various sources online suggest they did not come into common usage until the mid-1980's. This matches up with my experience.) Of course, it's possible that the non-local who refers to the ATM could have been lying about its existence. So it's not certain to me that it's an anachronism, but it was kind of jarring.

Last week, I also enjoyed the silly fish-out-of-water-coming-of-age-story-with-quiz-bowl movie Starter For 10 (which also featured two actors from the TV show Rome in further evidence of my "there are only 50 British actors" hypothesis) that was set in 1985. The soundtrack was full of mid-80's favorites, but also two songs from the 1989 Disintegration album by the Cure. I know, "Pictures of You" is a fantastic song, almost impossible to resist putting in a movie like this, but come on, guys, it's a full 4 years too early.

Of course, the most egregious recent use of that song is in this HP commercial. What part of lyrics like "I've been looking so long at these pictures of you that I almost believe that they're real / I've been living so long with these pictures of you that I almost believe that the pictures are all I can feel" did the ad agency not understand? This is a totally inappropriate song for that ad.

It's funny that from watching modern movies set in the 1980's, you would assume that bands like the Smiths, the Psychedelic Furs, the Cure, the Replacements, New Order, and the Pixies were the dominant bands of the era. And OK, these groups were pretty popular, and they definitely have held up well with time, and I basically love them, but they were totally eclipsed by the vastly different, pre-alternative pop rock of people like Madonna, Prince, Michael Jackson, the Police, U2, et al., who owned the 1980s. I don't mean to seriously complain - I would much, much rather listen to a Kate Bush song than a Whitney Houston song in a movie soundtrack. I never need to hear that song "Every Breath You Take" ever again. No question this selective memory fits my own tastes. But the 1980's soundtrack of most people's lives did not feature Camper van Beethoven.

"Inside Business" Column: December 10, 2008

by Dominique Argente

Insiders report that there's trouble in paradise over at Salligent this week! Recently promoted Chief Morale Officer Leopold Rex is not so happy with his job or his boss lately, which can't bode well for the organization as a whole. If your CMO ain't happy, can anyone be happy?

It appears that the "carrot, not stick" strategy Rex recommends for motivating employees and increasing satisfaction hasn't caught on with company bigwigs. Sources say that Salligent CEO Sally Porter and CFO Robert Eggman have been ganging up on Rex and undermining his position: "Porter holds him down and Eggman stabs him in the back, literally, every day! You should hear the thumping!"

The only hope is that both Porter and Eggman have been "feeling sick" this week. After all this mistreatment, perhaps their consciences are catching up with them, or perhaps they simply recognize that they risk alienating their CMO for good with their aggressive, back-stabbing ways.

CORRECTION to "Inside Business" Column

On December 10, we reported that the Salligent company has been demoralizing their Chief Morale Officer Leopold Rex by "literally" stabbing him in the back on a daily basis. Unfortunately, this paper assumed that the source describing these events was using the word "literally" to mean "figuratively" or "metaphorically" rather than "literally."

Further discussions with CEO Sally Porter, CFO Robert Eggman, and Dr. Tina Bunnyluv of the local House Rabbit society revealed that Mr. Rex is suffering from a potentially deadly infection that Salligent's executive management staff have been treating with daily shots of antibiotic. Porter says, "Leopold hasn't liked this whole 'grab and stab' approach to treatment, but it has been necessary. We've all been pleased with how much he grumbles and fights it, since this grumpiness demonstrates how much he has regained his strength. He's now well on the road to recovery and is taking his medication orally. I was concerned about him refusing to take pills, but since the medication is a liquid, it has gone well so far. Leopold continues to delight and motivate all members of this organization in sickness and in health. We couldn't be happier with him. And all things considered, he seems pretty happy with us, too." Mr. Eggman could not be reached for comment since he is at home, sick and asleep.

-ed.

Extensional Versus Intuitive Reasoning

Let's revisit a famous psychology experiment from 1974. In fact, you should play along yourself by reading the following description of a person and then ranking the 8 statements that follow according to their probability, with 1 being the most probable and 8 being the least probable.

"Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Linda is a teacher in elementary school.
Linda works in a bookstore and takes Yoga classes.
Linda is active in the feminist movement.
Linda is a psychiatric social worker.
Linda is a member of the League of Women Voters.
Linda is a bank teller.
Linda is an insurance agent.
Linda is a bank teller and is active in the feminist movement."

OK, all done?

Notice anything interesting about this list?

What the experimenters are really interested in is seeing how you rank the items "active in the feminist movement" (F), "bank teller" (B), and "bank teller and active in the feminist movement" (B+F).

Those of us who took probability and statistics will remember something called the conjunction rule: P(A+B)<=P(B). This means simply that the probability of two things together being true must be less than or equal to the probability of one of the two things being true by itself. For example, the probability that "my pet is a rabbit named Leo" (R+L) cannot be greater than the probability that "my pet is a rabbit" (R). This is because the pet has to be a rabbit (R) in order for it to be a rabbit named Leo (R+L) and it is possible for R to be true while L is not true: I could have a rabbit, but his name is Blackberry or Hazel or Bigwig or ....

Although looking at the formula can be confusing, I think the central idea is pretty easy to grasp. The probability that "Joe has a computer that is a Mac" can't be higher than the probability that "Joe has a computer." The probability that "Kevin had a burger and fries at lunch" cannot be higher than the probability that "Kevin had a burger at lunch." And so we see, the probability that "Linda is a bank teller and is active in the feminist movement" cannot be higher than the probability that "Linda is a bank teller."

So how did you do? Did you rank "bank teller + feminist" higher than "bank teller" alone? If so, you have plenty of company. In the experiments, 88% of students thought it was more likely that Linda was a feminist bank teller than a bank teller, thus violating the conjunction rule. When they tested students with higher levels of "statistical sophistication" (i.e. had taken more statistics classes), 85% of them violated the conjunction rule.

They did another experiment in which students looked at the same list, but instead of ranking the probability of the events, they ranked how well Linda resembles the typical member of the class. In this case, 85% ordered the descriptions Feminist > Feminist Bank Teller > Bank Teller, which matched up very well with the rankings in the probability experiment.

So it appeared that when people were asked to think about the probabilities of various things being true, they thought about how well the description matched up with what they knew about Linda. Since Linda had many characteristics associated with the stereotypical feminist, and few traits associated with the stereotypical bank teller, it seemed natural to assume that she was more likely a feminist than a bank teller, even to the point of finding "feminist bank teller" more plausible, and hence probable, than just "bank teller," despite the mathematical incoherence of such a thing.

The experimenters were a bit dismayed by these results and hence proceeded to create "increasingly desperate manipulations designed to induce subjects to obey the conjunction rule." One of these desperate manipulations was to see if people could at least recognize that they should be using the conjunction rule in determining these probabilities. Subjects were shown two arguments and asked to indicate which they found more convincing:

"Argument 1: Linda is more likely to be a bank teller than she is to be a feminist bank teller, because every feminist bank teller is a bank teller, but some women bank tellers are not feminists, and Linda could be one of them.

Argument 2: Linda is more likely to be a feminist bank teller than she is to be a bank teller, because she resembles an active feminist more than she resembles a bank teller."

65% of subjects found Argument 2 more convincing.

Then the experimenters changed the experiment, giving the same description of Linda's personality and background, but then saying: "If you couuld win $10 by betting on an event, which of the following would you bet on? (Check one.)" and listing the bank teller and feminist bank teller descriptions. 56% of subjects selected feminist bank teller.

I thought this was particularly interesting:

"Why do intelligent and reasonably well-educated people fail to recognize the applicability of the conjunction rule in transparent problems? Postexperimental interviews and class discussions with many subjects shed some light on this question. Naive as well as sophisticated subjects generally noticed the nesting of the target events [i.e. that "bank teller" includes "feminist bank teller"] in the direct-transparent test, but the naive, unlike the sophisticated, did not appreciate its significance for probability assessment. However, most naive subjects did not attempt to defend their responses. As one subject said after acknowledging the validity of the conjunction rule, 'I thought you only asked for my opinion.' "

The experimenters then liken the naive subjects to children in the preconservative stage of cognitive development who recognize the validity of concepts such as conservation of volume but do not see that the conservation argument is "decisive" and should over-rule their impression that when you pour a given quantity of liquid from a short, wide glass into a tall, skinny glass, there is a greater amount of liquid because it looks like more.

I find it rather endlessly fascinating and depressing that even when the error is pointed out to them, so many adults could believe, "Well, yes, technically she is more likely to be a bank teller, but it's my opinion that she's probably a feminist bank teller." While this may seem like a trivial example, the implications are disturbing. Even in situations in which the person's belief is not even possible, they stick to it as a matter of "opinion." So imagine the situations in which the belief is possible - like, Barack Obama has the middle name Hussein so he is probably a Muslim. How much evidence would be required to make the person change their "opinion" about that? And while in experiments with other types of things (like a gambling scenario with a sequence of die rolls given) subjects were able to be more logical with their reasoning, person perception scenarios seem to be particularly prone to triggering this intuitive (and faulty) reasoning based on stereotypes. What's more, the thinking process doesn't have to be motivated by bad intentions to come up with these impossible beliefs.

The researchers conclude their article by observing, "A system of judgments that does not obey the conjunction rule cannot be expected to obey more complicated principles that presuppose this rule, such as Bayesian updating, external calibration, and the maximation of expected utility. The presence of bias and incoherence does not diminish the normative force of these principles [i.e. that people should follow them], but it reduces their usefulness as descriptions of behavior and hinders their prescriptive applications." Economists, they are looking at you.

The researchers, psychologists Amos Tverksy and Daniel Kahneman, pioneered the hugely influential area of "heuristics and biases" in judgment (of which these experiments give a taste of the impact of the "representativeness heuristic") and also collaborated on "prospect theory" (another theory that showed deficiencies in the expected utility model in decision-making under uncertainty), for which Kahneman was awarded the Nobel Prize in Economics in 2002. (Tversky died in 1996 and was not eligible for the award.) Apparently, Kahneman has never taken a course in economics.

Source: Tversky, A. & Kahneman, D. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment (originally published 1984), in Heuristics and Biases, eds. Thomas Gilovich, Dale Griffin, Daniel Kahneman, 2002.

Grad School & Leo Update

I have completed and sent in the 6 applications that I had scheduled myself to have done prior to Christmas break. I now only have one left, with a late deadline, that I hope I will not have to finish. So now, we wait.

On Saturday night, Leo developed a head tilt - he was sitting up, trying to sleep, but his head kept tilting over to the side until he'd jerk it back into position, over and over. Head tilt is a very serious symptom in rabbits and generally indicates that the bunny should get immediate care. We are fortunate that the House Rabbit group in Austin, from whom we adopted Leo, provides such excellent support for their bunnies. Robert got on the phone with one of the women from the group I will call T and half an hour later, we were in her living room, with Leo getting shots of steroids (to remove pressure from the nerve in his ear) and antibiotics. She sent us home with three days of medication. Leo has already improved drastically (no more tilting! and he is behaving/eating mostly normally) so on Wed. night, we will go to her house again to pick up some oral antibiotic that she is compounding for us.

A weekend emergency visit to an animal hospital would have been several hundred dollars. When Robert asked about how much we owed her, she said, "Let's call it a $10 donation to cover the costs. You can give it to me when you pick up the oral meds." $10?! Needless to say, the organization will be getting a substantially larger donation from us than that.

Keeping You Up All Night

I post this as a warning to my readers who spend a lot of time looking at animal videos on YouTube, surfing cuteoverload.com, and searching for the best lolcats/lolbuns/etc. -- you know who you are. (I know who three of you are.)

http://questionablecontent.net/view.php?comic=1290

(Note: this makes me want to post another photo of Leo just to mess with this cartoon girl's mind.)

Liz's Candied Sweet Potatoes

This is a slight variant on the recipe Robert's aunt made at Thanksgiving, with a somewhat lower butter and sugar to potato ratio, but still yummy. The ratios definitely don't need to be precise; you can work with the amount of potato you have and decide how sweet a glaze you want for them. You will want to make sure you increase the water in proportion to the potato, however.

Liz's Candied Sweet Potatoes

1 1/2 lb. peeled and cubed sweet potato*
2 T butter
1/4 c. packed light brown sugar
1/3 t. salt
1/4 t. black pepper
1/2 c. water

* This was the post-peeled and cubed weight according to my scale.

Melt the butter in a large saucepan over medium-high heat.

Add remaining ingredients and bring to a simmer.

Reduce heat to medium-low and cover. Cook until the sweet potatoes are tender, 30 minutes to 55 minutes (varies greatly based on the size of your "cubes"), stirring every 5 minutes or so (I did it more like every 10 minutes).

When the sweet potatoes are tender, remove the lid and bring the sauce to a rapid simmer over medium-high heat. Simmer until the sauce has reduced to a glaze (this happened for me almost immediately).

Makes 4 servings, about 250 calories each.

I had it for dinner tonight with oven baked chicken strips. I made the potatoes this afternoon, and I think they tasted better after setting in the fridge for a few hours than they did right off the stovetop.

The Opportunity to Resist Temptation

Another interest of mine is research that aids in developing strategies that people can use to improve their ability to reach long-term goals in the face of temptations to satisfy short-term goals instead: studying and working instead of playing, exercising instead of watching TV, eating an apple intead of a doughnut, etc. Since I'm pretty good about getting work done and exercising daily and saving money, but have difficulty not eating too much, especially of sweets, I have a particular interest in how people can better meet their healthy eating goals.

This is the topic of another article in the December issue of the Journal of Consumer Research.

Specifically, they are addressing two rather contradictory theories / streams of research on the influence of food temptations on later eating opportunities.

The first, I think we're all familiar with: exposure to food cues (such as the sight and smell of food) activates our desire to eat, thus making it difficult for us to control ourselves. Research on self-regulation as a limited resource (which I've talked about before) suggests that when you have to control yourself in one situation, you deplete your self-regulation ability, setting yourself up for self-control failure in the future. These ideas would indicate that the best way to overcome temptation is to avoid it - keeping yummy snacks (e.g. Oat Crack cereal) out of the house, not exposing yourself to ads for food, etc.

The second one is new to me: the "critical level model" states that only once a problem reaches some threshhold level of seriousness or difficulty do people engage their problem-solving abilities. It is theorized that this occurs because people expect intense states to last longer than milder states and thus find the serious problem worth trying hard to solve. In the context of achieving long-term eating goals, I can see how this might play out. People frequently put effort into thinking of strategies for dealing with major Diet Threat situations like holidays, parties, vacations, all-you-can-eat buffets, and so forth, while we are rather blase about the small-time temptations we encounter on a daily basis. This model would suggest that encountering a large enough problem / threat to our eating goals in the form of a food temptation might trigger self-control strategies that would benefit you in a later self-control situation.

In this paper, they look at two kinds of temptations: Actionable temptations, in which the food is physically present and available for you to "act" on the temptation by eating, and Nonactionable temptations, like advertisements that make you think about food but do not provide an immediate opportunity to act on your desire to eat. They hypothesized that Actionable temptations (in their experiment, real candy that participants were looking at to do a survey but were not allowed to eat) would lead to greater self-control in a later eating situation compared to Nonactionable temptations (participants seeing drawings of candy).

This research is difficult to describe because of the complexity of the experiments, so I will cut to the overall results:

* Previous exposure to the real candy made something happen to block thoughts about eating when they later encounter a chance to eat.

* When given the chance to eat some M&M's, the drawings of candy group and control group ate a lot more when the experiment included the eating "cues" of the smell of chocolate and the availability of the chocolate in easy-to-grab trays, compared to when they were just presented with the M&M's with no smell and in less convenient containers. Those in the real candy group did not increase their intake of M&M's when those cues were present compared to when they were absent. Again, the idea is that something about their previous exposure to the real candy protected them from cues that typically make people eat like crazy.

* They rejected the idea that previous exposure to real candy (Actionable temptation) made people more likely to think about dieting than those who had only seen drawings (Nonactionable temptation); both groups had elevated thoughts about dieting compared to the control group. Their position is that something made the real candy group think less about eating and actually eat less compared to those who only saw pictures of food and the control group, but it wasn't increased thinking about dieting. The question remains: What is that "something"?

It's clearly unwise to interpret this single study as a reason to go to Sam's Club and buy the biggest damn bag of candy you can find. For one, the "future" eating opportunities they provided were not very distant in time from the original exposure to the candy at the beginning of the experiment. It's unknown how long this "something" that protects you against future eating temptations lasts. Your own big bag of candy may function as both exposure to temptation and later eating opportunity in the same afternoon.

Also, critically, the sorts of social inhibitions that allowed people to be tempted by the original real candy, but not actually eat any of it in the lab, are unlikely to exist in your own kitchen; if you've just eaten a pound of chocolate, you're probably not going to feel very tempted by candy for a while anyway and you've already hosed your diet.

In any event, it'll be interesting to see where future research on this topic goes.

Source: Geyskens, K., Dewitte, S., Pandelaere, M., & Warlop, L. (2008). Tempt me just a little bit more: the effect of prior food temptation actionability on goal activation and consumption, Journal of Consumer Research, 35, 600-610.

Mysteriously Disappearing Comments

There appears to be some weird interaction between the comment function and posts with YouTube videos. Last night, I had to try posting the "Science" video several times before the comments line showed up. The "Peaches" post originally allowed comments, and now even though there is a comment, the ability to see that comment or make new comments has disappeared. Weird. I am not doing any of this on purpose.

Looking Cheap

As those of you who have read some version of my statement of purpose know, one research area of great interest to me is social cognition (how people process social information, think about other people, etc.) in the context of consumer psychology. This is a broad field that could look at things like:

* Stereotypes about people who buy certain things or shop at certain stores. Take a moment to consider "Whole Foods shopper" and "Wal-Mart shopper" - for most of us, images of these two categories of people come readily to mind, even if we also understand that individual people in these groups will not match up with the stereotype very well. Humans rely a great deal on these kind of simplifying generalizations in dealing with the social world.

* The influence of self-identities on consumer behavior. For a trivial example, imagine that I am in the grocery store to pick up something for dinner. Depending on what aspect of my identity is ascendant at the time, I may make a different choice. If I'm aware of myself as a "healthy eater," I will be more likely to choose something natural, with a lot of vegetables, good fats, etc. If I'm aware of myself as a "dieter," I may pick up something lower in fat and calories, but that has more chemical additives and less nutritional value. If I'm aware of myself as "college student on Operation Cheap Ass," I might gravitate toward the least expensive alternatives.

* The use of consumer goods in bolstering impression management efforts. The objects in our lives serve a lot of purposes, and communicating something about ourselves to others, in order to make a favorable impression on people whose opinions we care about, is a big one.

A paper in the December issue of the Journal of Consumer Research ties together several things close to my heart - grocery shopping, impression management, and saving money.

They start with the psychological concept of "stigma by associaton" (SBA) - when a negative trait a person has or is believed to have (a stigma) is also attributed to someone associated with (or similar to) that individual. In this case, they are examining the stigma of "cheapness" that comes with using coupons, especially those of low value. Other research has demonstrated that people believe that using low value coupons is something cheap people do (and is thus stigmatized), while using higher value coupons is an action of a "smart" shopper and does not produce the same negative perception.

In a series of experiments and field studies, they test whether other people will view another, "normal" shopper as cheap if a "coupon-using" shopper uses low or high value coupons in a variety of situations.

They found:

* A bystander will view a "normal" shopper following a "coupon-using" shopper in the grocery store line as more cheap when the coupon-user uses a low value (50 c) coupon than a high value ($2) coupon or no coupon. Even though the two shoppers had no actual relationship, the proximity of the normal to the "low value coupon-using" shopper made the former shopper look cheap too.

* However, when the normal shopper is in a different line from the coupon-user, the perception of cheapness does not rub off on the normal shopper regardless of coupon value. (This appears to be more about the different line than mere physical distance based on further tests.)

* When the normal shopper is very physically attractive and the coupon-user is of average appearance, some interesting stuff happens. Not only is there no SBA for the "normal/attractive" shopper regardless of coupon value or proximity to the coupon-user (he is protected by his dissimilarity to the coupon user and the fact that he has a socially desirable trait), the coupon-user himself looks less cheap. Something of the social desirability of the attractiveness of the normal shopper appears to be transferred back to the coupon-user, protecting him against a negative evaluation in the form of perceived cheapness.

* When a second person accompanies a coupon-user in the store, the second person himself feels a sense of cheapness by association. When the second person is a stranger to the coupon-user, the felt SBA is fairly low and does not depend on the coupon value, but when he is the coupon-user's friend, the felt SBA is higher, especially when a low value coupon is used.

I found the "contrast effect" produced by the highly attractive normal shopper and the typical-looking coupon-user interesting, but it seems to me that they were testing two things at once. From their experiment, it's hard to separate out how much of the effect is caused by the normal shopper being dissimilar to the coupon-user, and thus less likely to be affected by SBA, and how much is due to his having a positive trait that is known to produce a halo effect (makes the person seem good on other dimensions that have nothing to do with their attractiveness). I wonder what would happen if the normal shopper was especially ugly instead of especially good-looking, but equally dissimilar in appearance? Would this make the coupon-user appear even cheaper?

Source: Argo, J.J., & Main, K.J. (2008). Stigma by association in coupon redemption: looking cheap because of others, Journal of Consumer Research, 35, 559-572.

The Limits of Science

Forget Popper and Kuhn. You may think you understand the scientific process, but I guarantee you will find much to learn from this educational video, brought to us by Mr. Show:



It's a bit eerie how much my wizard hat (that I constructed for a Halloween party when I was about 16) resembles the one in this video. I didn't realize how historically accurate my costume was.

Peaches

I was realizing tonight that I suck. I have two KSAL disks sitting on my desk that I have not even made a copy of for myself yet, let alone anyone else. (Wait, I think Tam has a copy of the first one; it's been sitting around since before my last visit to Denver. At least they both say "2008" on them.)

This weekend, I need to get these copies made and sent out while I still have some hope of identifying what the songs are. I know one of them has a couple of songs by The Presidents of the United States of America. The song "Peaches" is not one of them, but I like the video, so to tide over KSAL listeners, I present this for your amusement, and for evocations of a warmer time. Enjoy.



Note: the line "Peaches come from a can" reminds me of how it twangs my brain whenever I see a recipe that starts with a can of sweet potatoes. It's like seeing...I don't know...what's weirder than canned sweet potatoes? Canned lettuce?

Fun & Games

I just finished watching the movie "Who's Afraid of Virginia Woolf?" (based on the Edward Albee play). Although its caustic, cruel, witty dark humor is not for everyone, I was pretty much blown away by it. Elizabeth Taylor and Richard Burton are extremely good in their roles of drunk, middle-aged harridan and her smart, ineffectual, yet increasingly boisterous semi-failed academic husband as they go after each other all night long in the company of a handsome young new assistant professor in the math or biology (controversy exists here) department and his "mousy" wife.

The dialogue was intelligent and surprisingly raw at times, with quite a bit of swearing. I particularly enjoyed Richard Burton's lines - e.g. "You bet your historical inevitability" and "Will you show her where we keep the ... euphemism?" and "You disgust me on principle and you're a smug son of a bitch personally but I'm trying to give you a survival kit."

Definitely worth seeing, if you can stomach this level of intensity.

Not Entirely Dazzled

One of the most disconcerting aspects of the Freakonomics book is how weirdly gushing it is about how much of a genius economist Steven Levitt is. What makes it nauseating is that Steven Levitt is himself co-author of the book.

Perhaps it was not completely inappropriate for journalist Stephen Dubner to be so laudatory and hagiographical when he was writing about Levitt in his series of articles in the NY Times. He wanted people to know, Hey, this guy's research may look frivolous, but he's totally smart and stuff! (Although I think he went too far even in that context.) But when you then co-write a book with the target of all this overwrought verbiage, you should really have the sense to not go on at such length about what a brainiac maverick he is.

And if you're the rogue economist in question, you really shouldn't let him. This shit is going out under your own name. Doesn't that seem bizarrely self-aggrandizing? You really should make the point of establishing your own credibility as an expert in the book you write other ways. A classic approach is to let your bio point out that you won the Clark Medal, etc. But perhaps they were afraid we wouldn't read it and may come away with anything less than complete conviction that Steven Levitt is an utterly brilliant, visionary thinker. Or whatever.

Perhaps they had to call the book "Freakonomics" because the phrase "Staggering Genius" was already used in that Dave Eggers memoir. And "Iamanecongodonomics" is too long.

I found it hard to judge the value of this book, which is basically a discussion of the different research projects Levitt and his collaborators have done. It is definitely intended for the layman audience. Perhaps too much of the important stuff seemed obvious to me and the rest, well, it really is pretty insignificant-seeming at times.

It was also kind of unusual to read a book that is so strongly (it seems to me) in the spirit of traditional economic thinking, for all that Levitt is positioned as a rebel. At the same time (the book came out in 2005) that other economists are writing about how research in the other social sciences can enrich economic theory by complicating naive assumptions about rationality and so forth (i.e. behavioral economics), Levitt seems to be trying to use the rather stunted tools of homo-economicus-based economic analysis to understand everything in the world. It's a rather grandiose vision. Or it could be, if it weren't so clear that Levitt sees it mostly as a fun game to play.

One of the big stories told in the book was about the link between legalized abortion and the crime rate. Levitt and another economist had done research (regression analysis of available data) suggesting that the crime rate in the 1990's went down because a lot of the people who would have grown up to be criminals during that time had instead been aborted after the legalization of abortion in the 1970's. This was a very controversial finding. In fact, controversial enough that other people analyzed the data and believed the results to be flawed. I have not followed the back-and-forth on this issue, which is very technical, so I really have no strong sense of whether Levitt has been vindicated or his findings are questionable.

I didn't write down much that I read from the book, but I did make note of the following "fundamental ideas" that motivated the book:
1. Incentives are the cornerstone of modern life.
2. Conventional wisdom is often wrong.
3. Dramatic effects often have distant, even subtle, causes.
4. Experts use their information advantage to serve their own agenda.
5. Knowing what to measure and how to measure it makes a complicated world less so.

I also thought the findings of an analysis of real-estate ad terms and sales price were kind of interesting. Terms associated with a higher price: granite, state of the art, Corian, maple, gourmet. Terms associated with a lower price: fantastic, spacious, !, charming, great neighborhood. The authors suggest that realtors use a coded language to talk to each other and can communicate negative qualities while using phrases that appear positive to their customers.

In a good example of the more frivolous research, they found that voting on the TV show "Weakest Link" discriminates against Hispanics and the elderly: Hispanics because other team members believe they have poor skills and the elderly because other team members just prefer not to interact with them.

The best part about the book was that it inspired me to have a long argument with Robert, which I spent standing in the kitchen, about something involving incentives and the utility function and a bunch of other things that I can't even remember now. Good times, good times.

The Anticlimactic Application Process

After a series of minor adventures (and some grumbling disagreement with Robert over aspects of a need-based aid form, in which I capitulated from realizing my boredom with the whole thing was probably making me dumb), this evening I submitted 3 of the 7 online applications. 3 of the others I am either waiting on emails to be answered by university staff members or need an online recommendation finished. The 7th one I am not going to submit for a couple of months, since it's my back-up school.

I started getting the various supplemental documentation that has to be mailed in to the schools together, but kept running into stupid problems (screwy jump drives, pens running out of ink, printer cartridges running out of ink, photocopies I need to make) and gave up on it for the weekend just now. Tomorrow I have already dedicated to other projects (my weekly major tread, differential equations, housework), so I will get back on this stuff Monday or Tuesday. I still have a lot of time, objectively speaking, but just want to be done.

Have I mentioned that I am on Day 6 of a tension headache that has me walking around feeling like I've been hit on the back of the head with a club? Fortunately, the intensity is varying from minor to nausea-inducing with an average around painful enough to feel pouty and grumpy and generally pissed that I can't take any headache medication that would do any good but still mostly functional.

This entire grad school application process is feeling ultimately unsatisfying. I had thought that finishing things up would make me feel relieved and happy, but mostly, it's like "I have been working on it for an eon and all I have to show for it is this?" Every little aspect of the process has been ungodly time-consuming and the final product seems unimpressive. I am hoping that this is because I am, by this point, so utterly familiar with my CV, statements of purpose, assistantship essays, GRE scores, coursework record, publications, selection of programs that have an excellent research match, etc., that I can no longer see that I have assembled an awesome package of credentials that will make the adcoms say "Daaaaamn."

Hmmm....working on a long, tedious academic project with a thousand little bureaucratic requirements that in the end, you have difficulty bringing yourself to care about anymore, even to celebrate its completion - this does sound like good preparation for graduate school. Doesn't every grad student feel this way about their thesis / dissertation?

Perhaps I will start feeling more excited about this whole thing after: (1) my headache recedes, (2) there is no longer part of my brain sending out excitement-dampening waves due to the need to retain exceedingly boring information about mass-spring systems and series circuits, (3) I have all these applications truly, totally completed, and (4) Ed McMahon's minion shows up at the door with the (Relatively) Big Check.

At least I am not like some people posting on the LiveJournal grad application forum who are freaking out over the fact that they have Dec 1 deadlines but don't have their statement of purpose, letters of recommendation, writing sample, etc., ready to go yet. I definitely prefer dull and bored to vibrating-into-other-dimensions from anxiety and fear.

I will wait for the anxiety to kick in as I wait to hear from the programs.

Science Meets Dance

Tam sends this link featuring videos put together by scientists attempting to interpret their PhD research in dance form.

I have to admit, the dances were much more accessible than anything else with a title like "Resolving Pathways of Functional Coupling in Human Hemoglobin Using Quantitative Low Temperature Isoelectric Focusing of Asymmetric Mutant Hybrids" could possibly be.

Sock Puppet Bailout

It's one thing to bail out the organizations that our entire economic system depends on to function. But GM? This company has been failing for a long time. They've been talking about the potential for bankruptcy for years. GM's not just caught up in the liquidity crisis. It's an "our products suck, we are not responsive to consumer demand, and we have been overpaying labor for way too long" sort of problem.

I liked this video on a bailout that has received somewhat less media attention:



Of course, if he were a bunny puppet, I simply couldn't deny him the $25 billion.

(via Megan McArdle)

Looking Ahead

UPDATE: I have all of my recommendation letters now. I am really relieved to have that part done with! (Actually, one prof still needs to complete an online one, but I feel confident she'll get it done this week.)

Yesterday I picked up the recommendation letters from Professor #2, and I will pick up the last batch from Professor #3 this afternoon. She should also have comments on my statement of purpose (SOP). Somehow, I have almost reached the end of this grad school application process. The hard part is over. I hope this weekend to finish the online applications, finalize the SOPs for the various programs, get my other supporting materials (C.V., etc.) together, and mail off my packets to 6 programs. (I have one additional program with a late application deadline that I will put together later if I haven't heard from one of the more-preferred programs already.)

Last "weekend" (Thurs - Sun), because I was at a standstill with these masters program applications, I turned my attention again to PhD programs and a little bit beyond. I have a list of 40-odd marketing programs I am working with. I had already put together information on research fit with professors in these programs.

Another piece of the puzzle is program quality. Unlike MBA programs (or psychology PhD programs) there is no standard ranking list of marketing PhD programs. However, there are several sources of rankings based on faculty publications, with programs having a greater number of publications, and publications in more prestigious journals, given a higher rank. These rankings cover different time periods (e.g. based on consumer psychology publications from the 1990s, based on general marketing publications from 2001) and give a sort of mixed result. For instance, UT-Austin is a top 10 program by some of these lists, but comes in at #66 using another one. So it's not entirely clear to me how to weight these rankings, though I suspect I will be able to generally place them in tiers such as Top 10, Top 30, Top 50, etc. Other programs have strengths in niche areas. For instance, I know (from reading it in a thousand places) that the University of Florida is a very top program in consumer behavior, though their overall marketing or business school rank is lower.

A very important aspect of a program's quality is its placement record: where do graduates of the program get their first academic job? Depending on whether you are interested in getting a position with the highest-ranked program you can, a job at a research-oriented university, a teaching college, or heaven-forfend industry, you need to be more or less selective about the PhD program you attend. Programs often mention placement on their web sites, but this is usually a selective list, in which they cherry-pick the best placements and say things like "In recent years, our graduates have found positions in excellent universities such as X College, Y University" etc., with the emphasis on "such as."

I happened across a thread on the Business Week forums from 2004-2007 that included over 6500 posts (!) from various business PhD applicants, students, and a handful of professors, that took forever to read but did have some interesting information and perspectives that got me thinking about several things:

1. The Great Age Debate

Most of the applicants on the forum were trying to get into top tier (top 10 or perhaps top 20) business PhD programs. There was a lot of furious debate over to what extent top programs prefer younger over older students. There was a consensus that for top programs, being as ancient as 30 is a serious disadvantage and being over 35 will hugely reduce your chances at getting in (and your chances are pretty bad to begin with, given the strong competition for a very few slots). While this was felt to be more significant the more math-oriented the field (e.g. finance being very mathy and strategy being less so), it's a concern for all fields.

Of course, I am already very familiar with the age discrimination of other academic (vs. professional) programs, but had thought that this was less of a factor in business schools. But it would make sense that the top business programs would function a lot like their counterparts in economics, psychology, etc., since they tend to prefer students with undergrad credentials in one of the foundational academic subjects from the elite universities.

It's a bit hard, though, to say whether fewer older applicants are admitted to these programs due to age discrimination (or a preference for younger students among faculty) or at least in part because older applicants tend to be less competitive on dimensions that matter.

Since my age is the aspect of my application that I have the least control over, there is a limit to how useful this information is, but I do think it's helpful in targetting programs to realize that I may have an even tougher time getting admitted to certain places, especially the Stanford, Cornell, Northwestern type programs. Whether ultimately this will influence me to avoid certain programs, or only impact my expectations of success, I don't know. It does suggest that looking at the ages of current students might help identify programs that indicate a willingness to admit (exceptionally qualified) older applicants vs. a tendency to prefer fresh 22-year-old Ivy League undergrads. It also means that I should probably be especially careful to apply to a wide range of schools, since the age issue is less problematic the farther down the rankings you go.

2. The MBA Question

This brings up another controversial question they discussed - whether applicants with MBAs are seen as less desirable. I had noted before that students with MBAs were a lot more common among the mid-tier and lower programs than the very top ones. The commenters mostly felt that masters degrees in academic disciplines (math, stat, econ, psych, engineering, etc.) were more valuable than an MBA, which is a professional degree and not a "rigorous" program. This is in line with what I had already decided for myself.

3. The Placement Issue

As I've discussed before, the outlook for academic jobs amongst business PhDs is very good compared to most other disciplines. But this doesn't mean that graduating from a top 20 program guarantees you a job at another top 20 institution. There is the same "downward movement" in placement that you see elsewhere, only not as severe. Plenty of graduates of Wharton (the very best business school in the world) end up at less-than-elite universities. And apparently, some top schools are utterly notorious for making tenure nearly impossible to get. One school (Harvard?) was mentioned as granting tenure to only 1 of 7 people, so a lot of people work their asses off on research for the first 6 years and still end up moving down to a much lower school. Current professors talked about people they knew who were placed in a less highly-ranked program to begin with getting tenure easier and with less stress. People talked about how surprised they were to find that the status game, as played out by comparing who is at a better school than someone else, who is at what rank in the program, etc., is so much more important in academia than in industry. (This makes sense, though; in industry, people can feel superior through really high earning power, but the difference between the top paid and lowest paid professors is not very large, leaving prestige as the main way to differentiate yourself from others.)

The comments on this subject really got me thinking about what level of placement I would consider "good enough" or even preferable to getting a job at a top 20 program. I am fortunate that I actually just want to be a college professor, unlike some of the applicants who are only interested in doing it if they can get an elite academic job. I am not thinking about giving up the possibility of becoming a powerful, insanely-well-paid businessman or whatever by taking the academic route because I have no interest in the kind of career that getting a Harvard MBA instead of a PhD could make possible for me. I am not motivated by the desire to be a professor at Wharton so I can feel like a major hot-shot and be well-connected for lucrative consulting opportunities that arise. I just like the idea of getting paid to do something I really like doing.

Although I am sort of an academic snob, I basically view getting a PhD and then an academic job at any kind of decent university as pretty elite. And I'm not at all motivated to do something so that my grandmother can impress her friends at church by saying that I'm at Harvard or whatever.

And it does sound like life at the top of this academic food chain is really hard. You may not be teaching a lot of classes at Northwestern, but the expectations in terms of publication productivity is kind of insane. I might be happier at a more middle-of-the-road institution that puts a little bit less overwhelming publication pressure. (The publication pressure at any research-oriented university is going to be hard enough.)

While this doesn't necessarily mean I'd turn down the chance to attend a top program or get a job at a great university, it is sort of reassuring to realize that there is a pretty good range of outcomes that I would find satisfying - especially given that the probabilities are a lot higher for getting a job at the University of Georgia than the University of Chicago.

A Solid Foundation, Revisited

As an example of what is implied when people get nostalgic over the way math "used" to be taught, before all this crazy New Math and so forth, when kids learned the "basics" and didn't futz around with silly theory that nobody understands, etc., and got a "solid foundation" in facts, and walked up hill to school both ways in the snow with no shoes -- both of my parents learned to multiply using the multiplication table without being told that multiplication represented a short cut for repeated addition. I have no idea how common this was, but I thought it interesting that it was true for both of them, who attended school in different states.

You know, I agree that it's a useful skill to quickly and accurately come up with the fact that 8 x 9 = 72. Less useful than it was in the pre-calculator/pre-Excel/pre-etc. era, but still useful. Of course, it seems to me awfully useful to know why 8 x 9 = 72 also. I mean, isn't memorizing the multiplication table a lot easier when you realize that 8 x 9 = 2 x 4 x 9 and that 8 x 9 = 8 x 8 plus another 8? When I was learning my table, there were times I couldn't quite remember this particular number (I knew it was something in the range of 71 - 74) but I was able to figure it out again on the fly because I did know that 4 x 9 = 36 and I knew how to double that number. I also knew that 8 x 8 = 64 and could add 8 to that if I forgot 4 x 9 during the same brain freeze. I had a lot of different ways to approach the problem.

I don't see how it's to any kid's advantage to learn that 8 x 9 = 72 in the same way that they learn that "in 1492, Columbus sailed the ocean blue." It gives the impression that all these numbers are what they are through some mysterious process or accident of history while in reality, there's a lot of sense to it. And in my opinion, it is (I hesitate to use this word, but I think it fits) empowering to realize that you are dealing with a sensible system in which things can be figured out using rational thinking. Once you learn why 8 x 9 = 72, you can figure out what is 16 x 9 pretty easily, and 16 x 27, and well, a whole lot of numbers, without ever having to be told by someone else or memorizing a bunch of things.

I don't mean to imply that every person who talks about "solid foundation" really wants to return to an era when children did not know what multiplication means. But I wonder how many people (and here I mean normal people in the general population who are reactant against all stripes of innovative "New Math"-esque curriculum, not math educators who are arguing about these issues at a much higher level and with a lot more knowledge than the rest of us have and who would rightly view my comments as knocking down a strawman in terms of where the informed debate is occuring) who yearn for that supposedly wonderful pre-New Math time realize/remember quite how fact (and not theory) focused the instruction really was. Perhaps some of them would not even recognize the idea of multiplication as repeated addition to even be "theory" now that it's so commonly taught.

I was lucky to learn this stuff during the post-New Math era and to have a dad who thought it was fun to teach me algebra when I was quite young. (He also bought me and worked with me on geology sets, chemistry sets, and electricity sets. The fact that I did not grow up to be a scientist or engineer is not through any lack of exposure, sexist or otherwise. I joke to my younger sister the applied math and computer science major that where math, science, and computers are concerned, I peaked early.)

Modern Technology

RB and I were going to a restaurant tonight that I thought I knew where was, but wasn't quite sure (always a dangerous situation with his and my poor sense of direction).

I said, "Oh, do I have my cell phone? ... No."

RB said, "Do you have a web browser on your phone?" (This would be genuinely surprising, given my ancient, frills-free cell phone ways.)

I said, "Of course not. I was going to call Robert and have him look it up."

So I used RB's phone, though the first time, it didn't work because I could not remember my own telephone number. Neither could he, but at least he had it in memory. Robert told us where the restaurant was (and I had two pancakes roughly the size of the tabletop. At least they were full of blueberries, high in antioxidants. Ahem. They also had good regular iced tea and the great decaf herbal "crocodile" tea.)

Robert is my web browser sort of the way that back before the machines existed/were common, "calculators" referred to people who performed mathematical calculations. It's nice the way he responds to semi-incoherent questions in plain English and so forth. I don't know that the artificial intelligence exists that could come even close to matching his performance.

In only semi-related news, I have determined that RB is my "magical technology friend." He has many other content areas in which he is a magical friend, but he is especially strong in all things tech-related. He is the magical computer geek friend for a lot of people, it seems.

Quote of the Day: Game Theory Edition

"One of the most difficult challenges of all is rooted in the very origins of game theory: it was developed by men of nearly superhuman intellect like Nash and von Neumann. That is both its great strength and its great weakness, because for game theory to be successful, it must provide insight into what mere mortals will do. Game theory expresses the way people would act as the solution to a mathematical equation. It presumes hyperrational players who are instantly able to solve very tough problems, and this description starts to look unrealistic if game theory is to be a practical tool for explaining how real people actually behave. Nash and von Neumann really could solve such problems instantly. The rest of us cannot."
-Tim Hartford, The Undercover Economist, 2006

You'll remember John Nash from the movie "A Beautiful Mind."

Hartford points out that a great many people thought John von Neumann the most brilliant person alive, and since he worked at Princeton with Albert Einstein, that's saying something.

Why are People Resistant to Math Ed Changes

Reading this article about the exploration-oriented math program I worked on this summer made me think again about how many people have a negative, knee-jerk reaction to the idea of changes in middle school math education. It's sort of weird because at the same time, a lot of people (often the same people) believe that the current system is a failure and that kids are not learning math.

The following observations on the topic are informed simply by my own experiences and opinions. I am going to be thinking of an exploration-based approach as discussed in the article as the alternative to the current approach that privileges memorization and repeated drills.

(1) Miscategorization

I think when people hear about any kind of innovative math teaching approach, they immediately think of "New Math" and assume that since it was a failure, this other approach will also be a failure, even though the correspondence between the two programs may be limited. In my experience, they often don't even wait to hear any details about what the innovative approach entails before shuddering with horror at "New Math" memories.

(2) Face Validity

In a lot of contexts, I've noticed that people put more emphasis on face validity (does it look on the surface as though it will work) than they should when deciding whether something is likely to be effective. For example, people untrained in survey research may look at a questionnaire and say "But we want to find out X; why are you asking Q, Y, and Z?" not realizing that asking X directly may not be the best way to get the information. There are all kinds of things that look like they shouldn't work, but do when you actually test them, and vice versa. For instance, many people would say that the DARE anti-drug program has high face validity because it addresses the major aspects of keeping kids off drugs, but in reality, it doesn't work.

I believe that most people, if asked whether it would be possible to teach children how to speak a language fluently without explicit instruction in grammar, vocabulary, usage, etc., but rather through exposure to repeated examples of (or complete immersion in) the language with no attempt at explanation of what was going on, would say it doesn't seem plausible. Yet basically every child does this when they learn their mother tongue, and immersion programs are considered very effective for teaching children additional languages.

People's mental models of how the brain works are generally not informed by any actual knowledge of cognitive science, so "obvious" or "commonsensical" ideas about learning are not grounded in theory and don't necessarily mean squat.

Just today, watching an episode of Sherlock Holmes, I watched a horse trotting down the street, with a view from the back. A horse's legs are unbelievably skinny! It is not plausible that a horse should be able to walk any distance on such scrawny-looking little legs, let alone be an excellent runner that can carry human weight at great speed and/or for long distances. And yet...

This doesn't mean that we should all accept that anything can be true and draw no distinctions. It's reasonable to attempt to judge the plausibility of assertions that we hear. But it seems important to recognize whether we actually have any basis for those judgments and what those underlying assumptions or facts consist of. And it's always a good idea to ask whether there is actual evidence on the issue. Sometimes there's not, and we have to decide whether to tentatively favor one take on the situation or withhold judgment.

(3) The "Solid Foundation" Myth

Many people maintain that novel math approaches that downplay the priority of e.g. memorization of the multiplication tables do not allow children to get a "solid foundation" in the basics of arithmetic before moving on to other material, and without this foundation, it is impossible to ever learn higher math. I don't know whether this is true or not. But I don't think that it's necessarily true, despite the possible face validity of it.

One driver of the exploration-based approach discussed in the article is kids often have trouble with math starting in Algebra I. They have difficulty moving from the arithmetic of the earlier years to understanding math with all these variables. This approach introduces the fundamentals of algebra during 6th and 7th grade (without ever calling attention to that), with the idea that kids will not have to go through such a stark transition phase if they've been already doing it as they go on.

Robert put this pretty well: If you imagine that higher math is at the top of the mountain, and teachers are helping kids build a rock solid foundation from which to make their way up the mountain, it doesn't help much if the platform is only a few feet tall and the mountain itself is hundreds of feet tall. How do they get the rest of the way up? (This is assuming that the foundation really is solid and that all kids start from this point, some big ifs.)

I think of it like this: The traditional arithmetic approach really gives kids the idea that math is all about numbers and manipulating them in various specified ways. Ideally, kids develop fluency and speed in performing these manipulations which are, when you come down to it, pretty easy and straightforward. About the time they feel comfortable with that (or, in reality, often before), we pull out the algebra book and basically tell them that everything they think they know about math is wrong. They know that 6 * 9 = 54 because of the multiplication table, but not what's underlying it, so how do they make sense of 6 * X = 54?

(4) The Self-Confidence Paradox

I think many people also find it crazy that an exploration-based approach attempts to both challenge students to do harder problems starting at a younger age and simultaneously improve kids' self-confidence toward math. I mean, it's obvious that mathematical self-esteem comes from feeling like you have complete mastery of the material and can answer all the problems, so isn't this attempt to ensure that even the smartest kids will encounter problems that are at the edge of or even beyond their abilities going to cripple them?

And I can attest that some of the problems are quite difficult.

However, there is, to my mind, a certain logic in the idea of having kids encounter hard problems from early days because everyone reaches a point where math gets hard for them. (If this is not the case for you, it's because you quit too early. There's tons of math that nobody has figured out yet, I am sure.) If you have found math pretty easy up to this point, being unable to immediately grasp some concept or get the right answer to some problem in algebra, geometry, calculus, differential equations, topology, whatever is going to be kind of disconcerting. You may start to question whether you are "good" at math or not. You may start to lose your confidence in your ability to do math. (As I believe I've mentioned, Taylor series did this to me in Calculus 2 the first time, though I did encounter a question on my high school calculus final exam that prompted me to write "Only God knows the answer," a fact my teacher remembers to this day.)

You may not understand that working at a problem is just part of the normal process of doing math and that being unable to answer a given problem does not mean that you are stupid. Math ability is not a Superpower. It's something you can develop through effort. And getting comfortable with the idea that some problems are harder than others, and sometimes you'll encounter problems that you can't get the answers to, but that often after working on a problem, you can actually solve things that looked impossibly crazy hard at first glance...that's how you develop the confidence in your own ability to tackle hard problems. And how you learn to not get totally freaked out when something is beyond you.

(5) And What's the Ultimate Goal Anyway?

It is my opinion that, with the increasing amount of technology available for gathering and crunching numbers, knowing how to do math is more important than ever. But we need people who can figure out that given the data S, T, U, V, X, Y, and Z that X = S * T * U/(Y - Z) more than we need people who can calculate 0.283 * 73146 * 9.4 / (2.4 - 0.005) without using a calculator. Oh, and V? That variable wasn't relevant in answering the question at hand.

In summary:

- People may automatically think any new math is going to be "New Math" all over again.

- "Looking right" isn't much of a criterion for validity. Horses can run even with those wimpy-looking legs.

- It may be ultimately more effective to teach kids to climb the mathematical mountain than help them build a "solid foundation" that doesn't get them very close to the top. Mountain climbing isn't easy, but has its rewards, including "the ... exertion it requires, the satisfaction of overcoming difficulties by working with others, the thrill of reaching a summit, and the unobstructed view from a mountaintop."

- I am no longer afraid of Taylor series.

- A great many adults probably still believe that math is about numbers.

As for the exploration-based program in the article - does it work? This is, to coin a phrase, an empirical question. I would say there are reasons to be hopeful that it could work better than the current system (needs a thorough evaluation), but whether it would work better in practice...that would be an implementation challenge, no question, even with substantial evidence in its favor.

Incorrect Assumptions: College Major Edition

Tam mentioned that she and her boyfriend were talking about their perceptions of various college majors. (She also said she might blog on this, but she hasn't yet, so I am anticipating her by talking about my experience first.)

People tend to have incorrect assumptions about both of my college majors:

"Economics...that's about money."

"Psychology...why people are depressed or crazy or whatever."

In both cases, WRONG. Not that there aren't people who do study those particular topics, but they are not the central, or even most important, aspects of the fields. Both subjects would exist without money or insanity. All you need is scarcity and want for economics; psychology just requires people (or arguably, just some kind of animal that does things).

I have almost zero interest in money (mine, yours, the federal government's, anybody's; I'm a totally lazy investor who gets by through a combination of mooching, cheapness, and various good habits) and only a passing interest in craziness per se (though I did enjoy my job in psychiatric research, that was mostly about the research - I got to look at construct validity of DSM categories and evaluate programs and that sort of thing). Yet I enjoyed majoring in psychology and economics. Perhaps it comes as no surprise that I did not take a single class on money or abnormal psychology in the process.

What do people assume the field(s) you studied was about? Were they right? Were you right or did you find out later that the subject was something other than what you expected?

Organic Food Paper - Check

My professor and I sent in the organic paper this morning to the conference organizers - yay! I now get to basically not think about it for another two months until we find out whether it has been accepted or not. Given its limitations, I think it turned out quite well. It is not any kind of ground-breaking research, but it seems interesting enough (even to me having been working on it all this time) and does fit a kind of niche for qualitative research on the topic.

One of my interviewees had mentioned that Jason's Deli is highlighting their use of organic products, and last week when Robert and I ate there, I took especial notice of the prominent signage regarding "natural" and "organic" products, as well as a new sign saying they don't use high fructose corn syrup (except in soft drinks). (I ate the blue corn chips with my turkey wrap; they must be healthy because they are organic, right? I also like how the color makes them both pretty and obviously different from regular tortilla chips in a way that can be suggestive of superiority along various axes.) Still unknown is how they managed to make the gingerbread muffin have more combined grams of fat, carb, and protein than is possible given the muffin's mass. I think they must have figured out a way to make them unhealthily delicious into another dimension. Probably links up to the dark matter problem in some fashion, although I will leave the details to some poor doctoral student looking for a dissertation topic in their interdisciplinary nutrition science/physics program.

A Geeky Halloween Costume

Remember how on the TV show "Laverne & Shirley" Laverne always wore sweaters and shirts with a big script L on the front?



I was thinking that if you added a small, raised "-1" to the script L, you could be an inverse Laplace transform.



And if you had a friend who wanted to wear the original shirt, you could go to a party together as "Laverne & The Inverse Laplace Transform." This was, of course, the original premise of the TV show, but it did not go over as well with test audiences as originally expected. The shifts from the t domain to the s domain and back again were just too hard to follow.

An Observation

It would take a really long time to complete a dissertation on judgment and decision-making in Ents. The experimentation phase alone would last an eon.

Diff E Update

After Exam #2, I now have a 98.5 going into the last few quizzes and final exam. Sitting pretty, I think; it's quite a relief.

Quote of the Day: Dismal Science Edition

"We can appreciate [Thomas] Carlyle's idealization of hierarchy best when we find his industrious disciple Charles Dickens offering plans to 'reform' American racial slavery. In contrast, those who idealized exchange had no plan to reform slavery. Five letters, appropriately arranged around a space, would exhaust their insight as to how to bring existing slavery into correspondence with the ideal. These letters are END IT."

- How the Dismal Science Got Its Name, David M. Levy, Professor of Economics, George Mason University, 2001

Many people believe that the "dismal science" referred to Thomas Malthus's prediction that population growth would outstrip agricultural growth, leading to widespread famine. Rather, Thomas Carlyle opposed the view of the (now called "classical") economists, such as John Stuart Mill, who strongly argued for the end of slavery on the basis that under the skin, all people are equal and share the same human nature:

"Truly, my philanthropic friends, Exeter Hall Philanthropy is wonderful; and the Social Science—not a 'gay science,' but a rueful—which finds the secret of this universe in 'supply-and-demand,' and reduces the duty of human governors to that of letting men alone, is also wonderful. Not a 'gay science,' I should say, like some we have heard of; no, a dreary, desolate, and indeed quite abject and distressing one; what we might call, by way of eminence, the dismal science. These two, Exeter Hall Philanthropy and the Dismal Science, led by any sacred cause of Black Emancipation, or the like, to fall in love and make a wedding of it,—will give birth to progenies and prodigies; dark extensive moon-calves, unnameable abortions, wide-coiled monstrosities, such as the world has not seen hitherto!"

- An Occasional discourse on the Negro Question, Thomas Carlyle, 1849

What's Exeter Hall Philanthropy? British evangelicalism. Christian evangelicals also opposed slavery because they believed that all men and women were brothers and sisters under God.

It's interesting that market egalitarianism is now viewed as "right wing" or "conservative," given its radical history. As Levy points out in his book, this fact speaks to the huge success of those who pushed for emancipation. We now see the spectrum as those who do not believe in property in things (far left) to those who do believe in property of things (right), with the previous far right end point of those who believe in property in people having fallen completely off the scale.

For more information, see this interesting and informative web site. It includes some pretty crazy political cartoons, like this one, showing one of Carlyle's compatriots killing a black man/classical economist hybrid figure (who to me looks like a grotesquely racial Nosferatu in the clothing of a business man) as though he is St. George slaying the dragon.


The slain man is holding a bag of money with the words "The Wealth of Nations" (the title of Adam Smith's seminal text on the superiority of the free market economy) written on it. It also says "L.S.D." - apparently an abbreviation for "pounds, shillings, and pence," among other things.

Overestimating Ants

Robert points out this inadvertently hilarious article on the topic of what drivers can learn from ants.

Now collective intelligence expert Dr Dirk Helbing says understanding more about ants could help solve one of the banes of modern life - road congestion.

His team set up an "ant motorway" with two routes of different widths from the nest to some sugar syrup. Soon the narrower route soon became congested.

But when an ant returning along the congested route to the nest collided with another ant just starting out, the returning ant pushed the newcomer onto the other path.

However, if the returning ant had enjoyed a trouble-free journey it did not redirect the newcomer.

The result was that just before the shortest route became clogged the ants were diverted to another route and traffic jams never formed.

He notes: "The reason the ants were able to inform each other about congestion, and use that information to reroute traffic, is not because the oncoming ants ‘told’ the others about it, it is because, in their experiment, the network already had enough spare capacity to handle the traffic. Humans are perfectly capable of reaching this same equilibrium. In fact, we have – that is what “Loop” highways and bypasses are for. The problem humans have is that spare road capacity is rather expensive, and is an explicit, and socialized, cost, while traffic jams have an only the implicit cost which falls on the private commuter, and so our roads have insufficient capacity. “Knowing” the traffic is bad going into downtown Austin on I-35 doesn’t provide me with a useful alternative route."

I would like to point out that human beings do not have any problem avoiding obstacles and finding alternative routes either... on foot. We simply go around. This is not something that can do in cars, traveling at high speed, on dedicated lanes where there is noplace else to go. If another road is not there, knowing that the route is backed up, once you are already on it, isn't very helpful. Another major source of traffic problems, aside from general congestion caused by overall insufficient road capacity, are accidents, and those are sudden events that screw up everyone who is already committed to driving on that road. I do not know of any way of "bumping" somebody who is between two exits on I-35 all the way over to MoPac.

I mean, shit, why screw around? I advise that we learn from the crows. When the road is backed up, just fly, okay? Actually, "as the crow flies" is basically always the shorter driving route anyway. Just shows how stupid we are. And ants, when you come down to it.

You know, this research about ants was pretty interesting; why the need to make it "relevant" to humanity's problems?

One Reason That My Goal is Not Totally Crazy

I've been reading up on the humanities PhD market recently, primarily motivated by the endless discussions on the getting into grad school forum on LiveJournal, which appears to attract a rather large number of people who want to get a PhD in medieval literature or French poetry or women's studies or whatever sort of a thing. Also, my psychology professor told me that I could get into a psychology PhD program right now and advised me to consider applying to a couple to see if I could get in, and this had me rethinking the job market for psychology PhDs.

A couple of stats from a 1999 article:

- After 10 years, the majority of humanities PhD students have not finished their degrees.

- While 80 percent of the English PhDs [who graduated between 1982 and 1985] surveyed wanted to become professors at the end of their doctoral education, only 53 percent were tenured by 1995 [10-12 years after graduation], the study found.

Elsewhere, average salaries for those fortunate enough to secure new assistant professor positions (i.e. first tenure-track job out of the PhD program) in 2006 - and remember that those in the humanities typically take twice as long to hit the job market as other PhDs, having spent 10 years or more languishing as a very poorly paid teaching assistant, and have limited job prospects outside academia, so there is not a significant portion of the PhDs in those fields that have been attracted to super-lucrative jobs in industry:
- English $47,000
- History $47,000
- Performing arts $47,000
- Foreign languges $48,000
- Philosophy and religion $48,000
- And for comparison: Psychology $50,000; Math $52,000; Engineering $70,000; Law $81,000; Business $82,000

I found some information on the American Marketing Association's website from a survey of 2008 marketing PhD graduates. Some stats on these new assistant professors:

- The average 9 month salary was $115,000; median $118,000; range $65,000 - $151,000

- The average for a consumer behavior hire was $126,500

- Only 3% had already defended their dissertation before they were hired; there were more who had not even defended their dissertation proposal

- Most students had been in their PhD program for 3 or 4 years before they were on the job market; <3% had been in the program for 5 or more years (compare to the poor humanities students still trying to eke it out after 10)

- The median graduate put out 70 applications, did 19 interviews and got 2 assistant professor job offers; the average number of job offers was 2.7

- A 3 course academic year teaching load was the most common - yes, that means teaching 3 classes over 3 semesters (including the summer)

- The typical person had 4 conference presentations and zero peer-reviewed publications at the time of hire (but it takes a long time, often a couple of years, to get a submitted paper into print)

Frankly, based on the strength of placement for marketing PhDs - they seem to basically all get jobs that pay a lot of money and do not have stringent teaching requirements, though there are obviously high expectations for publishing before you can get tenure - compared to psychology PhDs, I would be poorly served by getting a psychology PhD instead. Even if it takes me an extra 2 years, because I do a masters degree first, it quickly pays for itself when you look at the difference in salary. And while it is not impossible to get a marketing placement from a psychology department, it is much less common and often requires doing a 2-year post doc in a marketing department to make that transition.

Basically, this examination re-iterates the conclusions I have already drawn, and has convinced me to keep the marketing PhD -> marketing department job as my number one play.

Further, I have decided that both theory and my own gut imagining of my future self's decision-making process would suggest that were I to actually be accepted to a psychology PhD program, I would find it overwhelmingly attractive to take it, even if it's not in my long run interests. When thinking about a decision in the more distant future, I can consider it from a "big picture" viewpoint and recognize the value of making a decision that most helps me toward my long-term goals; when thinking about a decision close in time, I will place too much weight on concrete details like "never having to apply to graduate school again" and "being able to get started on a PhD right away" and "only having to move once before my first job."

Basically, sitting with a psychology PhD acceptance in hand will resemble too closely standing next to the doughnut box in a meeting at work.

Clearly, the outcome of going to a psychology PhD program will not be self-defeating in the same fashion as eating a high-fat, high-sugar treat -- because getting your PhD is forever. I can eat a doughnut today and then eat salads for the rest of the month and be fine. But you usually only get one shot at a PhD. Going into a psych PhD program will result in either failing or dropping out (which is bad) or getting a psych PhD, which means not getting a marketing PhD (okay, but not optimal).

It's like right now, I'm standing in the train station, and there's a slow train to Marketingland, with a long stop in Mastersville, and an express train to Psychworld, both leaving the station at the same time but reaching their destinations years apart. And there's a ferry from Psychworld to Marketingland, but that takes quite a while too and is not that reliable. I have to resist that desire to get to an okay place sooner rather than a better place later, even though I know that the journey itself will be uncomfortable, even hellish, at times.

I recently read an interesting piece of advice that I had not seen before and that I do not necessarily privilege as being desirable but that brings up something I hadn't thought about before, though I should have. My plan has been to do a masters thesis, both as a "proof of concept" to PhD programs that I can do the kind of research that a PhD student is expected to do and to myself get in a practice run. But this person pointed out that doing a masters thesis can be a time-consuming and emotionally-draining experience that frequently delays one's graduation and leaves the student less interest in doing a PhD from thesis fatigue. From this perspective, you would be better served by getting through your masters degree more quickly and not 'wasting' your fortitude to do a big research project on a thesis when you will have to do more research later.

I really do see the logic of not extending your masters program for an extra semester or year to finish a thesis, but sort of feel that if I don't have it in me to finish a thesis, then turn around and do a solid first-year research project in my PhD program, and possibly another masters thesis (depending on whether the program will accept my previous one in lieu), then perhaps I'm really not cut out to be a professor at a research institution. And I don't want to be an instructor at a teaching-oriented college enough to put this much of my life into it - I would rather go back to the private or government sector than do a full teaching courseload. I mean, almost everybody hates finishing their PhD dissertation, even those who go on to very successful research careers and enjoy it a lot, but having a masters thesis tax a person that much seems like a bad sign. Of course, this person's advice may be much more justified for the future doctoral student who wants primarily to teach rather than do research.

In summary:
- People in the humanities spend forever in school and have trouble getting tenure-track jobs afterwards and may be completely nuts.
- Preferring the superior job placement prospects and salary of a marketing job over that of a psychology job is not crazy. The extra time invested now more than pays for itself very soon.
- I will not be applying this year to any psychology PhD programs that may be too attractive, a la a doughnut, to resist. The psych PhD will remain a backup to marketing PhD programs two years from now.
- I don't want to get a job teaching 4 classes per semester to undergraduates at Directional State University and finding it difficult to find time to do research.
- I am still hoping that Ed McMahon will show up this spring on my doorstep with a giant check from Wake Forest University that says "$8,500 per year plus full tuition waiver" on it.

Death by Chocolate

I just discovered that the chocolate cake I had at Macaroni Grill tonight has 1180 calories and 68 g of fat. Holy. Shit.

I knew it was huge, but ... man, I wouldn't have guessed that it was possible to make something so saturated with useless calories. I'm not having that again. I ate most of it, too - my chocolate allotment for the next 6 months or so.

Obviously, I did not think chocolate cake would be healthy or diet food, but this is yet another example of how everything in a restaurant turns out to be even more scary and evil nutrition-wise than it seems.

Pursuit and Assessment of Happiness Can Be Self-Defeating

One of the great ironies to come out of happiness research is the finding that attempting to be happy, and thinking about whether one is happy, actually undermines one's success in being happy.

Some notes on a chapter by Jonathon Schooler (a psychologist at UC-Santa Barbara), Dan Ariely (behavioral economist from Duke), and George Loewenstein (a decision scientist at Carnegie Mellon):

There are three main problems that interfere with people's ability to optimize their own levels of utility (happiness):

1. "People may have limited explicit access to the utility they get from experience." In other words, people have trouble figuring out how happy something they are doing or have done makes them. (This is separate from the issue of predicting how happy something will make them, at which people also suck, as we will see.)

There is a distinction between the happiness that you experience and how you will evaluate that experience later. Research on flow states has shown that people who are busy on engaging, challenging tasks may be very happy while not noticing it at the time.

Determining whether something makes you happy is an inferential process. People will look to "self-observation, situational context, and theories about how they 'should' be feeling...in order to translate visceral states into an explicit hedonic appraisal." Two prominent social psychological theories are relevant here: Bem's Self Perception Theory says that people make inferences about their own attitudes the same way they infer those of others. Festinger's Cognitive Dissonance Theory posits that people alter their attitudes to reduce the inner conflict that comes from having discrepancies between their attitudes and behavior. "Both processes can come into play depending on circumstances": large discrepancies are likely influenced by cognitive dissonance while smaller discrepancies may be more tied to self perception theory.

People are also sensitive to "anchoring effects" in determining how much something is worth to them: the value that they place on something is affected by the initial reference value (e.g. would you pay $X? Would you pay $Y?). For example, in an experiment, they had students who were offered to listen to part of a recording of The Leaves of Grass; initially, some students were asked "Would you pay $10?" to listen to the recording, while others were asked "Would you do it if you were paid $10?" Later, they were asked how much they would pay/be paid to listen to an even longer recording, and both groups increased the amount. So those who were initially asked a question that implied that listening should have a value to them that they would be willing to pay were willing to pay more to listen to more, while those who were set up with the idea that they should be paid to listen wanted even more money to listen to a longer recording. This is despite the fact that both groups were reacting to the same offer (and presumably did not differ systematically in how much they like Walt Whitman poetry).

2. "Efforts to assess one's utility level can adversely affect the utility" (sort of like the Heisenberg uncertainty principle). This is similar to findings in decision-making research, in which people who are asked to verbally reflect upon their decision processes increase the weight they attach to things that could be verbalized relative to their gut feelings. For example, in a jam-tasting experiment, participants who were asked to verbalize their evaluations achieved a correlation with Consumer Reports experts of a lowly 0.16, while those who just tasted them and rated them achieved a correlation of 0.56 with expert opinion.

"Hedonic introspection may increase the focus on the self, so attention devoted to the experience is reduced, causing the individual to overlook subtle aspects of the experience or think about what could or should have been rather than what was," leading to disappointment. They note that chronically unhappy people show higher levels of self-consciousness, self-focused attention, and ruminative thinking (though they are also more realistic about their situations). However, it's not clear to me that research has been done to demonstrate whether self-focused attention leads to unhappiness or unhappiness leads to self-focused attention or what.

3. Despite being enshrined in the Declaration of Independence as an inalienable right (though there is a very interesting backstory on how the right to property became the right to the pursuit of happiness that is not within the purview of this post), the conscious pursuit of happiness - "treating activities as a means toward something else, rather than as ends in themselves" - can backfire. Activities undertaken for "extrinsic rewards lose their intrinsic appeal" and pursuing happiness can lead to increased introspection, which we've already seen can undermine one's happiness.

People have faulty theories about what will make them happy. They "tend to underestimate the tendency to adapt hedonically to positive and negative continuing experiences...and over-select goals that produce lasting material changes, such as an increase in income or status." In an experiment, participants played the Dictator Game - the person was given an amount of money and told to decide how much to keep for himself and how much to give to the other player. Those who gave a higher amount away to the other player reported overall higher levels of happiness and life satisfaction. But again, it's not clear to me how the causality there works; I could just as easily see a happy person being willing to give away more money than an unhappy person. (Note: the fact that people do not just keep the entire amount for themselves poses difficulties for the economic rational-man hypothesis.)

The authors did try to get a more clear sense of the causality in a pair of experiments; they had people monitor their experience (or not) while listening to music or celebrating New Year's Eve. (They also had some manipulation of the "pursuit" variable that I did not take note of, but that I recall had to do with making a special effort to enjoy their New Year's Eve celebrations.) They found that those who pursued happiness and monitored the experience reported lower levels of happiness with the experience; they theorize that this is because high expectations lead to disappointment.

Implications for Economics:
- Economic models that emphasize the deliberate pursuit of self-interest may not be the optimal approach once the costs of the "effortful focus of utility maximization is entered into the equation." Decreasing the emphasis on self-interest may increase net utilities even if the overall material output is reduced. (Or, my take: we could be happier with less stuff if we weren't losing utility in pursuing all that stuff that we think will make us happy, but probably won't. Or, maybe someone else's take: maybe those Europeans with less money and less of a frenzy to obtain it aren't so wrong after all.)

Implications for Psychology:
- These studies "add to the growing body of evidence that thinking and reflection are not always productive activities."
- "Unhappiness may be more likely to induce an explicit meta-awareness of one's hedonic state." I would say that this is true to my own experience; I generally can tell these days when things have been going well because I find that I haven't been thinking about it much at all.

They recommend that the optimal approach is to periodically engage in monitoring of your hedonic state (happiness level) and pursuit of happiness.

Reference: The psychology of economic decisions / edited by Isabelle Brocas and Juan D. Carrillo. New York: Oxford University Press, 2003.