intellectual vanities… about close to everything

Some argue that happiness is not having what you want, but wanting what you have. This maxim sounds reasonable enough, but can it be tested, and if so, is it true?

It turns out it can be tested. Texas Tech University psychologist Jeff Larsen and Amie McKibban of Wichita State University asked undergraduates to indicate whether they possessed 52 different material items, such as a car, a stereo or a bed.

Their results, which appear in the April issue of the Association for Psychological Science’s journal, Psychological Science, suggest that people can grow accustomed to their possessions and thereby derive less happiness from them.

They also suggest, however, that people can continue to want the things they have and that those who do so can achieve greater happiness.

“Simply having a bunch of things is not the key to happiness,” Larsen said. “Our data show that you also need to appreciate those things you have. It’s also important to keep your desire for things you don’t own in check.”

If the students owned a car, the researchers asked them to rate how much they wanted the car they had. If they didn’t have a car, they were asked to rate how much they wanted one.

Larsen and McKibban then calculated the extent to which people want what they have and have what they want. Their findings show that wanting what you have is not the same as having what you want. While people who have what they want tend to desire those items, the correlation between the two was far from perfect.

The researchers found that people who want more of what they have tend to be happier than those who want less of what they have. However, people who have more of what they want tend to be happier than those who have less of what they want.

Psychol Sci. 2008 Apr;19(4):371-7.
Is happiness having what you want, wanting what you have, or both?
Larsen JT, McKibban AR.

Rabbi Hyman Schachtel (1954) proposed that “happiness is not having what you want, but wanting what you have” (p. 37). In two studies, we tested Schachtel’s maxim by asking participants whether or not they had and the extent to which they wanted each of 52 material items. To quantify how much people wanted what they had, we identified what they had and the extent to which they wanted those things. To quantify how much people had what they wanted, we identified how much they wanted and whether or not they had each item. Both variables accounted for unique variance in happiness. Moreover, the extent to which people wanted what they had partially mediated effects of gratitude and maximization on happiness, and the extent to which they had what they wanted partially mediated the effect of maximization. Results indicate that happiness is both wanting what you have and having what you want.

Most people agree that emotions can be caused by a specific event and that the person experiencing it is aware of the cause, such as a child’s excitement at the sound of an ice cream truck. But recent research suggests emotions also can be unconsciously evoked and manipulated.

Psychologists Kirsten Ruys and Diedrick Stapel of the Tilburg Institute for Behavioral Economics Research at Tillburg University in The Netherlands have uncovered the first empirical evidence to suggest humans do not need to be aware of the event that caused their mood or feelings in order to be affected by it. The scientists hypothesized that, since humans have evolved to respond quickly and unconsciously to stimuli, they should be able to react to an emotional event without full awareness: “You are likely to live longer if you immediately stop moving at the sight of a growling grizzly bear and do not need full awareness for such a response to be instigated,” explained Ruys and Stapel.

The researchers measured people’s thoughts, feelings and behavior to determine whether specific emotions were induced without awareness of their cause—a study based on the theory implying that, due to natural selection, humans should be able to detect specific emotion-evoking information automatically. Participants were separated into three groups and were told that very short flashes would appear on a computer screen. They were then instructed to press the ‘R’ key if it appeared on the right side of the screen or the ‘L’ key if it appeared on the left.

In actuality, the ‘flashes’ were subliminal images selected to elicit fear, disgust or no emotion at all. The images flashed at varying speeds making it impossible for the participants to be fully conscious of their presence. In other words, the participants were unaware that they were viewing images of growling dogs and dirty toilets or even neutral images, such as horses or chairs.

The participants then underwent three tests to measure the effect of the images on their cognition, feelings and behavior. For the cognitive measure, they completed word fragments with a variety of words including those that expressed disgust, fear, anger, generally negative, generally positive and neutral feelings. Next, participants rated the overall positivity or negativity of their mood and the extent to which they felt fearful, disgusted, satisfied, relieved, proud, angry, shameful and joyful on 7-point scales.

During the behavioral measure, participants were asked to take part in either a ‘strange food test’ or a ‘scary movie test,’ assuming that, for example, those who were exposed to the disgusting images would want to avoid the possibility of eating something unpleasant. At the end of the study, the researchers asked gradually more specific questions about the subliminal images to gauge the participants’ awareness of the study’s purpose and intent.

The intriguing results strongly support the psychologists’ theory. Those participants who viewed only the disgust-inducing subliminal images were more likely to use disgust words in the word-completion task, to describe their feelings with the disgust words and to choose to take the ‘scary movie test.’ The same held true for those who viewed only the fear-inducing images—they also were more likely to use words related to fear and to take the ‘strange food test.’

The psychologists also found that after quick (120ms) speed exposures to emotional stimuli, a general, negative mood developed accompanied by a specific emotion, such as fear after seeing fearful pictures. After the super-quick (40ms) speed exposure, only a general negative mood was induced without a specific emotion involved. These empirical findings are the first to demonstrate that specific emotions can be evoked without awareness of the cause and that a person’s global mood can develop into a specific emotion.

And while the study did not investigate how an individual eventually becomes conscious of their emotions, the scientists did pose an additional hypothesis: “When emotions are full-blown, people become aware of their emotions by perceiving their own actions and bodily reactions; likewise, when emotions are weak, people fail to notice their weakly-related actions and bodily reactions.”

Psychol Sci. 2008 Apr;19(4):385-91.
The secret life of emotions.
Ruys KI, Stapel DA.

The possibility of unconsciously evoked emotions is often denied because awareness of an emotion’s cause is considered to be precisely what produces the emotion. However, we argue that because emotional responding is important for successful living, both global and specific emotional responses can be induced without awareness. The present research used quick and super-quick subliminal priming techniques, and cognitive, feelings, and behavioral measures, to test this hypothesis. Our results show that both global moods and specific emotions can be evoked without conscious awareness of their cause.

Most people agree that emotions can be caused by a specific event and that the person experiencing it is aware of the cause, such as a child’s excitement at the sound of an ice cream truck. But recent research suggests emotions also can be unconsciously evoked and manipulated.

Psychologists Kirsten Ruys and Diedrick Stapel of the Tilburg Institute for Behavioral Economics Research at Tillburg University in The Netherlands have uncovered the first empirical evidence to suggest humans do not need to be aware of the event that caused their mood or feelings in order to be affected by it. The scientists hypothesized that, since humans have evolved to respond quickly and unconsciously to stimuli, they should be able to react to an emotional event without full awareness: “You are likely to live longer if you immediately stop moving at the sight of a growling grizzly bear and do not need full awareness for such a response to be instigated,” explained Ruys and Stapel.

The researchers measured people’s thoughts, feelings and behavior to determine whether specific emotions were induced without awareness of their cause—a study based on the theory implying that, due to natural selection, humans should be able to detect specific emotion-evoking information automatically. Participants were separated into three groups and were told that very short flashes would appear on a computer screen. They were then instructed to press the ‘R’ key if it appeared on the right side of the screen or the ‘L’ key if it appeared on the left.

In actuality, the ‘flashes’ were subliminal images selected to elicit fear, disgust or no emotion at all. The images flashed at varying speeds making it impossible for the participants to be fully conscious of their presence. In other words, the participants were unaware that they were viewing images of growling dogs and dirty toilets or even neutral images, such as horses or chairs.

The participants then underwent three tests to measure the effect of the images on their cognition, feelings and behavior. For the cognitive measure, they completed word fragments with a variety of words including those that expressed disgust, fear, anger, generally negative, generally positive and neutral feelings. Next, participants rated the overall positivity or negativity of their mood and the extent to which they felt fearful, disgusted, satisfied, relieved, proud, angry, shameful and joyful on 7-point scales.

During the behavioral measure, participants were asked to take part in either a ‘strange food test’ or a ‘scary movie test,’ assuming that, for example, those who were exposed to the disgusting images would want to avoid the possibility of eating something unpleasant. At the end of the study, the researchers asked gradually more specific questions about the subliminal images to gauge the participants’ awareness of the study’s purpose and intent.

The intriguing results strongly support the psychologists’ theory. Those participants who viewed only the disgust-inducing subliminal images were more likely to use disgust words in the word-completion task, to describe their feelings with the disgust words and to choose to take the ‘scary movie test.’ The same held true for those who viewed only the fear-inducing images—they also were more likely to use words related to fear and to take the ‘strange food test.’

The psychologists also found that after quick (120ms) speed exposures to emotional stimuli, a general, negative mood developed accompanied by a specific emotion, such as fear after seeing fearful pictures. After the super-quick (40ms) speed exposure, only a general negative mood was induced without a specific emotion involved. These empirical findings are the first to demonstrate that specific emotions can be evoked without awareness of the cause and that a person’s global mood can develop into a specific emotion.

And while the study did not investigate how an individual eventually becomes conscious of their emotions, the scientists did pose an additional hypothesis: “When emotions are full-blown, people become aware of their emotions by perceiving their own actions and bodily reactions; likewise, when emotions are weak, people fail to notice their weakly-related actions and bodily reactions.”

Psychol Sci. 2008 Apr;19(4):385-91.
The secret life of emotions.
Ruys KI, Stapel DA.

The possibility of unconsciously evoked emotions is often denied because awareness of an emotion’s cause is considered to be precisely what produces the emotion. However, we argue that because emotional responding is important for successful living, both global and specific emotional responses can be induced without awareness. The present research used quick and super-quick subliminal priming techniques, and cognitive, feelings, and behavioral measures, to test this hypothesis. Our results show that both global moods and specific emotions can be evoked without conscious awareness of their cause.

A research group supported by the National Institutes of Health (NIH) has uncovered a new route for attacking the human immunodeficiency virus (HIV) that may offer a way to circumvent problems with drug resistance. In findings published April 28 in the online edition of the Proceedings of the National Academy of Sciences, the researchers report that they have blocked HIV infection in the test tube by inactivating a human protein expressed in key immune cells.

Most of the drugs now used to fight HIV, which is the retrovirus that causes acquired immune deficiency syndrome (AIDS), target the virus’s own proteins. However, because HIV has a high rate of genetic mutation, those viral targets change quickly and lead to the emergence of drug-resistant viral strains. Doctors have tried to outmaneuver the rapidly mutating virus by prescribing multi-drug regimens or switching drugs. But such strategies can increase the risk of toxic side effects, be difficult for patients to follow and are not always successful. Recently, interest has grown in attacking HIV on a new front by developing drugs that target proteins of human cells, which are far less prone to mutations than are viral proteins.

In the new study, Pamela Schwartzberg, M.D., Ph.D., a senior investigator at the National Human Genome Research Institute (NHGRI), part of NIH; Andrew J. Henderson, Ph.D., of Boston University; and their colleagues found that when they interfered with a human protein called interleukin-2-inducible T cell kinase (ITK) they inhibited HIV infection of key human immune cells, called T cells. ITK is a signaling protein that activates T cells as part of the body’s healthy immune response.

“This new insight represents an important contribution to HIV research,” said NHGRI Scientific Director Eric D. Green, M.D., Ph.D. “Finding a cellular target that can be inhibited so as to block HIV validates a novel concept and is an exciting model for deriving potential new HIV therapies.”

When HIV enters the body, it infects T cells and takes over the activities of these white blood cells so that the virus can replicate. Eventually, HIV infection compromises the entire immune system and causes AIDS. The new work shows that without active ITK protein, HIV cannot effectively take advantage of many signaling pathways within T cells, which in turn slows or blocks the spread of the virus.

“We were pleased and excited to realize the outcome of our approach,” Dr. Schwartzberg said. “Suppression of the ITK protein caused many of the pathways that HIV uses to be less active, thereby inhibiting or slowing HIV replication.”

In their laboratory experiments, the researchers used a chemical inhibitor and a type of genetic inhibitor, called RNA interference, to inactivate ITK in human T cells. Then, the T cells were exposed to HIV, and the researchers studied the effects of ITK inactivation upon various stages of HIV’s infection and replication cycle. Suppression of ITK reduced HIV’s ability to enter T cells and have its genetic material transcribed into new virus particles. However, ITK suppression did not interfere significantly with T cells’ normal ability to survive, and mice deficient in ITK were able to ward off other types of viral infection, although antiviral responses were delayed.

“ITK turns out to be a great target to examine,” said Dr. Schwartzberg, noting that researchers had been concerned that blocking other human proteins involved in HIV replication might kill or otherwise impair the normal functions of T cells.

According to Dr. Schwartzberg, ITK already is being investigated as a therapeutic target for asthma and other diseases that affect immune response. In people with asthma, ITK is required to activate T cells, triggering lung inflammation and production of excess mucus.

“There are several companies who have published research about ITK inhibitors as part of their target program,” Schwartzberg said. “We hope that others will extend our findings and that ITK inhibitors will be pursued as HIV therapies.”

Published online on April 28, 2008
Proc. Natl. Acad. Sci. USA, 10.1073/pnas.0709659105
OPEN ACCESS ARTICLE

T cell signaling | transcription | tyrosine kinase | viral entry | kinase inhibitors

Everyone probably has experienced one way or the other: Émile Coué meant well with his positive thinking, but created, unintentionally, a trap that leaves many a life in disaster. Looking on the bright side can lead to irresponsible financial behavior as well, reveals an article in the Journal of Consumer Research. In a series of studies, Elizabeth Cowley (University of Sydney) examines repeat gambling in the face of loss. She finds that people often engage in too much positive thinking, selectively focusing on one win among hundreds of losses when they think back on the overall experience.

“When we want to justify engaging in an activity which could potentially be irresponsible — like gambling — we may need to distort our memory of the past to rationalize the decision,” Cowley explains. “People who have frequently spent more money than planned on gambling edit their memories of the past in order to justify gambling again.”

For example, Cowley had participants in one study play a computer game in which they could win credits with the financial equivalent of one cent per credit. Each participant played the game 300 times. Everyone experienced one big win and one big loss. But for the other 298 games, one half of the group experienced all small losses, while the other experienced all small wins.

Cowley also manipulated the distance between the big win and the big loss.

A week later, participants were surveyed for their memories of the experience. Surprisingly, Cowley found that even some losers remembered having a positive experience. If the big win and the big loss occurred far apart, losers had fond memories and indicated a willingness to spend their own money on the game.

As Cowley explains, the further apart the big win and the big loss, the easier it was for losers to isolate their memories and focus only on the positive, a “silver lining” effect.

“The tendency to segregate positive and negative events in a mixed-loss experience is based on the logic that remembering a large gain allows people to feel good even when the objective outcome was negative,” Cowley says.

Conversely, Cowley found that winners — those who experienced 298 small wins — were happier when the big win and the big loss were closer together, allowing them to lump all the games together and ignore the big loss. She termed this the “cancellation effect.”

“When the outcome of an experience including both positive and negative events results in a net gain, people look for ways to integrate positive and negative events to reduce, if not cancel, the pain associated with the negative events,” Cowley explains.

The research is the first to consider a motivated memory explanation for justifying irresponsible behavior. Apparently, positive thinking can sometimes be negative.

JOURNAL OF CONSUMER RESEARCH, Inc. • Vol. 0 •
All rights reserved. 0093-5301/2008/3501-0006$10.00
DOI: 10.1086/527267

The Perils of Hedonic Editing

Elizabeth Cowley*

How good are we at guessing other people’s likes and dislikes? Ever bring a favorite dish to a potluck — only to watch it go uneaten? Or receive an unwelcome shock when a cherished product is discontinued for lack of sales? People have the tendency to assume the whole world likes what we like, reveals new research from the June 2008 issue of the Journal of Consumer Research. However, we don’t generalize the same way when it comes to things we hate.

Ambiguity - Look twice, as in Magic-Eye-Images, so in buying decisions…

“The degree of false consensus depends on whether a person likes or dislikes an item,” explain Andrew D. Gershoff (University of Michigan), Ashesh Mukherjee (McGill University), and Anirban Mukhopadhyay (University of Michigan).

Participants in one study were asked to choose a movie they like. They were then asked to guess what percentage of their peers liked the movie as well. On average, people estimated that 51.2 percent of other people also liked the movie, a significant overestimate. They also estimated that only 18.2 percent of people, on average, disliked it — a reflection of the belief that more people agree with us than disagree.

In contrast, when asked to choose a movie they dislike and make the same estimate, participants were less self-centered: they thought people would agree and disagree with their opinion in roughly the same numbers.

As the researchers explain, “This finding arises from a deeper truth about the human mind, namely that things we like are seen to contain primarily good characteristics, while things we dislike are seen to contain a mix of bad, neutral, or good characteristics.”

We might even like everything about an item — except for one unforgivable, deal-breaking trait.

“This difference leads us to make more exaggerated predictions that people like the same things we do, compared to predictions that people will dislike the same things that we dislike,” the researchers add.

Another study of ice cream sundaes found that those who liked a certain flavor combination — say, mint ice cream with walnuts and hot fudge — overestimated that people would share their fondness for the sundae by 9.9 percent. Those who disliked it only overestimated that people would share their repulsion by 0.8 percent.

They conclude: “Our research indicates that decision-makers in such situations need to be highly sensitive to the danger of over-projecting their own likes, more so than their own dislikes.”

JOURNAL OF CONSUMER RESEARCH, Inc. • Vol. 33 • March 2007
All rights reserved. 0093-5301/2007/3304-0009$10.00
DOI: 10.1086/510223

Few Ways to Love, but Many Ways to Hate: Attribute Ambiguity and the Positivity Effect in Agent Evaluation

Andrew D. Gershoff

Ashesh Mukherjee

Anirban Mukhopadhyay

A can of Coke next to the word “awesome”; a can of Pepsi next to a picture of a happy couple. Seem too basic to be effective advertising? Prior research has shown that reported attitudes towards brands are not affected by such simple juxtapositions. However, a new paper in the June 2008 issue of the Journal of Consumer Research examines our implicit opinions — and finds that we may actually be more susceptible than we think.

Bryan Gibson (Central Michigan University) showed undergraduate psychology students pairings of well-known cola brands with words and images. Some had positive associations: a field of flowers, the word “awesome,” or a mother holding a child. Others had negative associations: people at a gravesite, the word “terrifying,” or a person in a contamination suit.

Participants were then distracted by an unrelated cognitive task — memorizing an eight-digit number — and offered a can of Coke or Pepsi to take home with them.

When distracted, those who were initially neutral towards both brands strongly tended to choose the brand that had been paired with positive images or words in the earlier task. Importantly, this happened even when the participant couldn’t remember which brand had been paired with positive information, Gibson reports.

Those who had an established preference for one brand before the experiment, as established by a pre-test, were not affected by the inclusion of a distracting task while making their choices.

“These results have implications regarding how consumer attitudes are formed, and how they are then applied in brand choice situations,” Gibson explains. “This suggests that implicit product attitudes may play a greater role in product choice when the consumer is distracted or making an impulse purchase.”

JOURNAL OF CONSUMER RESEARCH, Inc. • Vol. 0 •
All rights reserved. 0093-5301/2008/3501-0011$10.00
DOI: 10.1086/527341
Can Evaluative Conditioning Change Attitudes toward Mature Brands? New Evidence from the Implicit Association Test

Electronically published January 18, 2008

Stereotypes can boost as well as hinder our chances of success, according to psychologists from the University of Exeter and St Andrews University. They argue that the power of stereotypes to affect our performance should not be underestimated.

Drawing on a large body of research, the authors* argue that success or failure at work, at school or in sport cannot always be attributed solely to ability or incompetence. Studies suggesting that gender or race can play a part in performance have proved controversial.

The researchers argue that the roots of such handicaps lie partly in the preconceptions that other people hold about these groups. For example, a woman who has been led to believe that women generally do worse than men at mathematics, will perform less well in a maths test as a result. Following a similar logic, in the sporting domain, one reason why the England football team performs badly in penalty shoot-outs (winning only 1 of 7 in major tournaments) is that performance is impeded by knowledge of stereotypes associated with a history of failure.

However, the researchers also point out that stereotypes can have positive dimensions that are able to boost individual or group’s performance. For example, research has shown that Asian women do better on maths tests if they identify themselves as Asian rather than as women. Another study has shown that white golfers tend to perform better against black opponents if they are told that they are being judged on their “sport strategic intelligence” than if they are told they are being tested on their “natural athletic ability.”

“The power of stereotypes should not be underestimated. What we think about ourselves - and also, what we believe others think about us - determines both how we perform and what we are able to become,” said Professor Alex Haslam of the University of Exeter. “As well as holding people back, stereotypes and preconceptions can boost both individual and group performance. For example, if you belong to a group that is always exposed to the message ‘we are the best’, this can promote personal achievement. While we’re often told “believe in yourself”, it can actually be more beneficial to focus on beliefs about your group, as group identity is a powerful vehicle for both personal and social change.”

The authors argue that minorities can overcome their disadvantages by changing external perceptions of their group. The article highlights the flexibility of stereotypes and argues that rather than being fixed, they are very sensitive to change. Professor Stephen Reicher of St Andrews University commented: “In many ways our stereotype of the stereotype is wrong. Stereotypes are neither fixed, nor necessarily harmful. Indeed, in our own hands, they can be tools of progress”. As the authors note, it was precisely by challenging stereotypes that activists like Steve Biko and Emmeline Pankhurst were able to achieve emancipation for black South Africans and British women.
Scientific American Mind April 2008

By S. Alexander Haslam, Jessica Salvatore, Thomas Kessler and Stephen D. Reicher

People who score high on intelligence tests are also good at keeping time, new Swedish research shows. The team that carried out the study also suspect that accuracy in timing is important to the brain processes responsible for problem solving and reasoning.

Researchers at the medical university Karolinska Institutet and Umeå University have now demonstrated a correlation between general intelligence and the ability to tap out a simple regular rhythm. They stress that the task subjects performed had nothing to do with any musical rhythmic sense but simply measured the capacity for rhythmic accuracy. Those who scored highest on intelligence tests also had least variation in the regular rhythm they tapped out in the experiment.

“It’s interesting as the task didn’t involve any kind of problem solving,” says Fredrik Ullén at Karolinska Institutet, who led the study with Guy Madison at Umeå University. “Irregularity of timing probably arises at a more fundamental biological level owing to a kind of noise in brain activity.”

According to Fredrik Ullén, the results suggest that the rhythmic accuracy in brain activity observable when the person just maintains a steady beat is also important to the problem-solving capacity that is measured with intelligence tests.

“We know that accuracy at millisecond level in neuronal activity is critical to information processing and learning processes,” he says.

They also demonstrated a correlation between high intelligence, a good ability to keep time, and a high volume of white matter in the parts of the brain’s frontal lobes involved in problem solving, planning and managing time.

“All in all, this suggests that a factor of what we call intelligence has a biological basis in the number of nerve fibres in the prefrontal lobe and the stability of neuronal activity that this provides,” says Fredrik Ullén.

J Neurosci. 2008 Apr 16;28(16):4238-43.

Intelligence and variability in a simple timing task share neural substrates in the prefrontal white matter.

Ullén F, Forsman L, Blom O, Karabanov A, Madison G.

Neuropediatric Research Unit Q2:07, Department of Woman and Child Health, Karolinska Institutet, SE-171 77 Stockholm, Sweden. fredrik.ullen@ki.se

General intelligence is correlated with the mean and variability of reaction time in elementary cognitive tasks, as well as with performance on temporal judgment and discrimination tasks. This suggests a link between the temporal accuracy of neural activity and intelligence. However, it has remained unclear whether this link reflects top-down mechanisms such as attentional control and cognitive strategies or basic neural properties that influence both abilities. Here, we investigated whether millisecond variability in a simple, automatic timing task, isochronous tapping, correlates with intellectual performance and, using voxel-based morphometry, whether these two tasks share neuroanatomical substrates. Stability of tapping and intelligence were correlated and related to regional volume in overlapping right prefrontal white matter regions. These results suggest a bottom-up explanation of the link between temporal stability and intellectual performance, in which more extensive prefrontal connectivity underlies individual differences in both variables.

The connection between music and mathematics has fascinated scholars for centuries. More than 2000 years ago Pythagoras reportedly discovered that pleasing musical intervals could be described using simple ratios.

And the so-called musica universalis or “music of the spheres” emerged in the Middle Ages as the philosophical idea that the proportions in the movements of the celestial bodies — the sun, moon and planets — could be viewed as a form of music, inaudible but perfectly harmonious.

Now, three music professors — Clifton Callender at Florida State University, Ian Quinn at Yale University and Dmitri Tymoczko at Princeton University — have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric.

Writing in the April 18 issue of Science, the trio has outlined a method called “geometrical music theory” that translates the language of musical theory into that of contemporary geometry. They take sequences of notes, like chords, rhythms and scales, and categorize them so they can be grouped into “families.” They have found a way to assign mathematical structure to these families, so they can then be represented by points in complex geometrical spaces, much the way “x” and “y” coordinates, in the simpler system of high school algebra, correspond to points on a two-dimensional plane.

Different types of categorization produce different geometrical spaces, and reflect the different ways in which musicians over the centuries have understood music. This achievement, they expect, will allow researchers to analyze and understand music in much deeper and more satisfying ways.

The work represents a significant departure from other attempts to quantify music, according to Rachel Wells Hall of the Department of Mathematics and Computer Science at St. Joseph’s University in Philadelphia. In an accompanying essay, she writes that their effort, “stands out both for the breadth of its musical implications and the depth of its mathematical content.”

The method, according to its authors, allows them to analyze and compare many kinds of Western (and perhaps some non-Western) music. (The method focuses on Western-style music because concepts like “chord” are not universal in all styles.) It also incorporates many past schemes by music theorists to render music into mathematical form.

“The music of the spheres isn’t really a metaphor — some musical spaces really are spheres,” said Tymoczko, an assistant professor of music at Princeton. “The whole point of making these geometric spaces is that, at the end of the day, it helps you understand music better. Having a powerful set of tools for conceptualizing music allows you to do all sorts of things you hadn’t done before.”

Like what?

“You could create new kinds of musical instruments or new kinds of toys,” he said. “You could create new kinds of visualization tools — imagine going to a classical music concert where the music was being translated visually. We could change the way we educate musicians. There are lots of practical consequences that could follow from these ideas.”

“But to me,” Tymoczko added, “the most satisfying aspect of this research is that we can now see that there is a logical structure linking many, many different musical concepts. To some extent, we can represent the history of music as a long process of exploring different symmetries and different geometries.”

Understanding music, the authors write, is a process of discarding information. For instance, suppose a musician plays middle “C” on a piano, followed by the note “E” above that and the note “G” above that. Musicians have many different terms to describe this sequence of events, such as “an ascending C major arpeggio,” “a C major chord,” or “a major chord.” The authors provide a unified mathematical framework for relating these different descriptions of the same musical event.

The trio describes five different ways of categorizing collections of notes that are similar, but not identical. They refer to these musical resemblances as the “OPTIC symmetries,” with each letter of the word “OPTIC” representing a different way of ignoring musical information — for instance, what octave the notes are in, their order, or how many times each note is repeated. The authors show that five symmetries can be combined with each other to produce a cornucopia of different musical concepts, some of which are familiar and some of which are novel.

In this way, the musicians are able to reduce musical works to their mathematical essence.

Once notes are translated into numbers and then translated again into the language of geometry the result is a rich menagerie of geometrical spaces, each inhabited by a different species of geometrical object. After all the mathematics is done, three-note chords end up on a triangular donut while chord types perch on the surface of a cone.

The broad effort follows upon earlier work by Tymoczko in which he developed geometric models for selected musical objects.

The method could help answer whether there are new scales and chords that exist but have yet to be discovered.

“Have Western composers already discovered the essential and most important musical objects?” Tymoczko asked. “If so, then Western music is more than just an arbitrary set of conventions. It may be that the basic objects of Western music are fantastically special, in which case it would be quite difficult to find alternatives to broadly traditional methods of musical organization.”

The tools for analysis also offer the exciting possibility of investigating the differences between musical styles.

“Our methods are not so great at distinguishing Aerosmith from the Rolling Stones,” Tymoczko said. “But they might allow you to visualize some of the differences between John Lennon and Paul McCartney. And they certainly help you understand more deeply how classical music relates to rock or is different from atonal music.”
Science 18 April 2008: Vol. 320. no. 5874, pp. 346 - 348
DOI: 10.1126/science.1153021

1 College of Music, Florida State University, Tallahassee, FL 32306, USA.
2 Music Department, Yale University, New Haven, CT 06520, USA.
3 Music Department, Princeton University, Princeton, NJ 08544, USA.