Hello! My name is Rebecca Williamson, and I am a freshman here at Duke University. Coming into college, I plan to major in economics, but that could very well change. As for my interests outside of the classroom, I enjoy singing and theater and am a member of Out of the Blue, one of the all-female a cappella groups here at Duke!
Rebecca Williamson, Duke 2022
I fell in love with Duke the second I stepped on campus. I am excited to see what Duke has to offer me, but more importantly, what I can offer to Duke.
My interest in science, specifically astronomy, was piqued at a very young age. By age six, I had not one, but three, Moon in my Room light up toys (remote controlled models of the Moon that scrolled through the waxing and waning phases of the Moon at the touch of a button) mounted in my bedroom. By nine, I had the entire planetary system (yes, including Pluto) hanging from my ceiling. Though I cannot say that my interests remain with astronomy, it is what first got me invested in science. I have since gained interest in the natural sciences and animal sciences, though every so often I do press some of the buttons on my Moon in my Room remote.
Some random boy imagines he’s as cool as six-year-old Rebecca.
My love of writing, however, was spawned by my love of theater. As an active member of my high school’s theater community, I was roped into being a part of, and eventually became the president, of my school’s Cappies Critics team. As a Cappie, I was expected to watch local high school plays and musicals and write critical, holistic reviews of them. This program jump-started my love for writing and helped me to develop my own unique journalistic voice.
I hope to combine my interest in the natural and animal sciences with my love for writing and chronicle some of the amazing research going on in these fields both on campus and around Durham! I also hope to incorporate my interests in music and theater into my inquiries and document scientific research surrounding music and the arts in the Duke community.
Duke University Research Blog, look out, because here I come!
Duke biologist Alejandro Berrio creates larger-than-life insect sculptures. This wooden mantis was exhibited at the Art Science Gallery in Austin, Texas in 2013.
On a recent spring morning, biologist Alejandro Berrio took a break from running genetic analyses on a supercomputer to talk about an unusual passion: creating larger-than-life insect sculptures.
Berrio is a postdoctoral associate in professor Greg Wray’s lab at Duke. He’s also a woodcarver, having exhibited his shoebox-sized models of praying mantises, wasps, crickets and other creatures in museums and galleries in his hometown and in Austin, Texas, where his earned his Ph.D.
The Colombia-born scientist started carving wood in his early teens, when he got interested in model airplanes. He built them out of pieces of lightweight balsa wood that he bought in craft shops.
When he got to college at the University of Antioquia in Medellín, Colombia’s second-largest city, he joined an entomology lab. “One of my first introductions to science was watching insects in the lab and drawing them,” Berrio said. “One day I had an ‘aha’ moment and thought: I can make this. I can make an insect with wings the same way I used to make airplanes.”
Beetle carved by Duke biologist Alejandro Berrio.
His first carvings were of mosquitoes — the main insect in his lab — hand carved from soft balsa wood with an X-Acto knife.
Using photographs for reference, he would sketch the insects from different positions before he started carving.
He worked at his kitchen table, shaping the body from balsa wood or basswood. “I might start with a power saw to make the general form, and then with sandpaper until I started getting the shape I wanted,” Berrio said.
He used metal to join and position the segments in the legs and antennae, then set the joints in place with glue.
“People loved them,” Berrio said. “Scientists were like: Oh, I want a fly. I want a beetle. My professors were giving them to their friends. So I started making them for people and selling them.”
Soon Berrio was carving wooden fungi, dragons, turtles, a snail. “Whatever people wanted me to make,” Berrio said.
He earned just enough money to pay for his lunch, or the bus ride to school.
Duke biologist Alejandro Berrio carved this butterfly using balsa wood for the body and legs, and paper for the wings.
His pieces can take anywhere from a week to two months to complete. “This butterfly was the most time-consuming,” he said, pointing to a model with translucent veined wings.
Since moving to Durham in 2016, he has devoted less time to his hobby than he once did. “Last year I made a crab for a friend who studies crustaceans,” Berrio said. “She got married and that was my wedding gift.”
Still no apes, or finches, or prairie voles — all subjects of his current research. “But I’m planning to restart,” Berrio said. “Every time I go home to Colombia I bring back some wood, or my favorite glue, or one of my carving tools.”
Insect sculptures by Duke biologist Alejandro Berrio.
Encountering and creating art may be some of mankind’s most complex experiences. Art, not just visual but also dancing and singing, requires the brain to understand an object or performance presented to it and then to associate it with memories, facts, and emotions.
A piece in Dario Robleto’s exhibit titled “The Heart’s Knowledge Will Decay” (2014)
In an ongoing experiment, Jose “Pepe” Contreras-Vidal and his team set up in artist Dario Robleto’s exhibit “The Boundary of Life Is Quietly Crossed” at the Menil Collection near downtown Houston. They then asked visitors if they were willing to have their trips through the museum and their brain activities recorded. Robleto’s work was displayed from August 16, 2014 to January 4, 2015. By engaging museum visitors, Contreras-Vidal and Robleto gathered brain activity data while also educating the public, combining research and outreach.
“We need to collect data in a more natural way, beyond the lab” explained Contreras-Vidal, an engineering professor at the University of Houston, during a talk with Robleto sponsored by the Nasher Museum.
More than 3,000 people have participated in this experiment, and the number is growing.
To measure brain activity, the volunteers wear EEG caps which record the electrical impulses that the brain uses for communication. EEG caps are noninvasive because they are just pulled onto the head like swim caps. The caps allow the museum goers to move around freely so Contreras-Vidal can record their natural movements and interactions.
By watching individuals interact with art, Contreras-Vidal and his team can find patterns between their experiences and their brain activity. They also asked the volunteers to reflect on their visit, adding a first person perspective to the experiment. These three sources of data showed them what a young girl’s favorite painting was, how she moved and expressed her reaction to this painting, and how her brain activity reflected this opinion and reaction.
The volunteers can also watch the recordings of their brain signals, giving them an opportunity to ask questions and engage with the science community. For most participants, this is the first time they’ve seen recordings of their brain’s electrical signals. In one trip, these individuals learned about art, science, and how the two can interact. Throughout this entire process, every member of the audience forms a unique opinion and learns something about both the world and themselves as they interact with and make art.
Children with EEG caps explore art.
Contreras-Vidal is especially interested in the gestures people make when exposed to the various stimuli in a museum and hopes to apply this information to robotics. In the future, he wants someone with a robotic arm to not only be able to grab a cup but also to be able to caress it, grip it, or snatch it. For example, you probably can tell if your mom or your best friend is approaching you by their footsteps. Contreras-Vidal wants to restore this level of individuality to people who have prosthetics.
Contreras-Vidal thinks science can benefit art just as much as art can benefit science. Both he and Robleto hope that their research can reduce many artists’ distrust of science and help advance both fields through collaboration.
When you think of the word “model,” what do you think?
As an Economics major,
the first thing that comes to my mind is a statistical model, modeling phenomena such as the effect of class size on student test scores. A
car connoisseur’s mind might go straight to a model of their favorite vintage Aston
Martin. Someone else studying fashion even might imagine a runway model. The point is, the term “model” is used in popular discourse incredibly frequently, but are we even sure what it implies?
Annabel Wharton, a professor of Art, Art History, and Visual Studies at Duke, gave a talk entitled “Defining Models” at the Visualization Friday Forum. The forum is a place “for faculty, staff and students from across the university (and beyond Duke) to share their research involving the development and/or application of visualization methodologies.” Wharton’s goal was to answer the complex question, “what is a model?”
Wharton began the talk by defining the term “model,” knowing that it can often times be rather ambiguous. She stated the observation that models are “a prolific class of things,” from architectural models, to video game models, to runway models. Some of these types of things seem unrelated, but Wharton, throughout her talk, pointed out the similarities between them and ultimately tied them together as all being models.
The word “model” itself has become a heavily loaded term. According to Wharton, the dictionary definition of “model” is 9 columns of text in length. Wharton then stressed that a model “is an autonomous agent.” This implies that models must be independent of the world and from theory, as well as being independent of their makers and consumers. For example, architecture, after it is built, becomes independent of its architect.
Next, Wharton outlined different ways to model. They include modeling iconically, in which the model resembles the actual thing, such as how the video game Assassins Creed models historical architecture. Another way to model is indexically, in which parts of the model are always ordered the same, such as the order of utensils at a traditional place setting. The final way to model is symbolically, in which a model symbolizes the mechanism of what it is modeling, such as in a mathematical equation.
Wharton then discussed the difference between a “strong model” and a “weak model.” A strong model is defined as a model that determines its weak object, such as an architect’s model or a runway model. On the other hand, a “weak model” is a copy that is always less than its archetype, such as a toy car. These different classifications include examples we are all likely aware of, but weren’t able to explicitly classify or differentiate until now.
Wharton finally transitioned to discussing one of her favorite models of all time, a model of the Istanbul Hagia Sophia, a former Greek Orthodox Christian Church and later imperial mosque. She detailed how the model that provides the best sense of the building without being there is found in a surprising place, an Assassin’s Creed video game. This model is not only very much resembles the actual Hagia Sophia, but is also an experiential and immersive model. Wharton joked that even better, the model allows explorers to avoid tourists, unlike in the actual Hagia Sophia.
Wharton described why the Assassin’s Creed model is a highly effective agent. Not only does the model closely resemble the actual architecture, but it also engages history by being surrounded by a historical fiction plot. Further, Wharton mentioned how the perceived freedom of the game is illusory, because the course of the game actually limits players’ autonomy with code and algorithms.
After Wharton’s talk, it’s clear that models are definitely “a prolific class of things.” My big takeaway is that so many thing in our everyday lives are models, even if we don’t classify them as such. Duke’s East Campus is a model of the University of Virginia’s campus, subtraction is a model of the loss of an entity, and an academic class is a model of an actual phenomenon in the world. Leaving my first Friday Visualization Forum, I am even more positive that models are powerful, and stretch so far beyond the statistical models in my Economics classes.
When William Dawson took over the Performing Arts program at Duke Hospital, he became the first full-time staff Musician in Residence and Semans/Byrd Performing Arts Coordinator. As a teacher, band director and international performer, Dawson understood the effect music could have on one’s mood and emotions. Still, he had a challenging task ahead of him – Dawson had to prove that music could make an impact in a hospital setting.
In the spring of 2014, as part of the larger Arts & Health program at Duke Hospital, the department administered a survey. Staff had the opportunity to reflect on what programs had improved their hospital experience. As it turned out, live music was one of the top patient satisfiers. Armed with the information, Arts & Health chose to expand the Performing Arts program.
The Performing Arts program differs from music therapy, where board certified professionals work one-on-one or in small groups to achieve a personalized goal. Instead, it is composed of Artists in Residence, Performing Arts Volunteers and Hospital Concerts. Throughout the week, professional musicians are assigned to hospital units to visit patients at the bedside. The professional musicians play for relaxation, company, religious services, and special events including birthdays, weddings, anniversaries and the final moments of life.
Performing Arts Volunteers are students and community members who perform in hospital lobbies and concourses. To assess the musicians’ audience, Dawson used a handheld tally counter and noted that on average, 600-800 people pass through the hospital’s heavily trafficked areas per hour. The instrumental music provides an opportunity for a shared connection, he said.
“It’s like a magic trick,” Dawson said. “I can’t tell you how many times I’ve been playing there piano and a person has cried. It’s beautiful – it’s a reminder that there’s life.”
Hospital Concerts are offered periodically by the Artists in Residence and professional organizations. Recognizing the diversity of the hospital staff and patients, Dawson ensures that performers reflect a variety of backgrounds and can cater to a wide audience.
Since becoming coordinator, Dawson has been statistically analyzing the growth of the program, because potential donors and current financial backers would like to see measurable impact. Dawson has the figures: In the 2016-2017 fiscal year, the number of bedside requests increased by 282 percent, from 109 to 416. To match demand, the number of Performing Arts Volunteers increased by 120 percent and 1,156 hours of live music were performed.
In the future, Dawson looks forward to continued program expansion. Additional funding would also enable the Uke in Duke program, a hospital in-patient instructional ukulele program, to expand and serve more patients. With Dawson’s leadership and a dedicated team of professional musicians and volunteers, the Performing Arts program has an undeniable impact.
For their recent retreat, Regeneration Next tried something a little different for the time-honored poster session.
Rather than simply un-tubing that poster they took to the American Association of Whatever a few months ago, presenters were asked to DRAW their poster fresh and hot on a plain sheet of white paper in 15 minutes, using nothing more than an idea and a couple of markers.
“People are always nervous about something they haven’t tried before,” said Regeneration Next Executive Director Sharlini Sankaran. “There was a lot of anxiety about the new format and how they would explain their research without charts and graphs.”
There was palpable poster panic as the retreat moved to the wide open fifth floor of the Trent Semans Center in the late afternoon. Administrative coordinator Tiffany Casey had spread out a rainbow of brand-new sharpies and the moveable bulletin boards stood in neat, numbered ranks with plain white sheets of giant post-it paper.
After some nervous laughter and a few attempts at color-swapping, the trainees and junior faculty got down to drawing their science on the wobbly tackboards.
And then, it worked! It totally worked. “I think I saw a lot more interactivity and conversation,” Sankaran said.
A fist-full of colorful sharpies gave Valentina Cigliola a colorful launching point for some good conversations about spinal cord repair, rather than just standing there mutely while visitors read and read and read.
Louis-Jan Pilaz used the entire height of the giant post-it notes to draw a beautifully detailed neuron, with labeled parts explaining how the RNA-binding protein FMRP does some neat tricks during development of the cortex.
Delisa Clay’s schematics of fruitfly cells having too many chromosomes made it easier to explain. Well, that and maybe a glass of wine.
Jamie Garcia used her cell-by-cell familiarity with the zebrafish to make a bold, clear illustration of notochord development and the fish’s amazing powers of self-repair.
Don’t you think Lihua Wang’s schematic of experimental results is so much more clear than a bunch of panels of tiny text and bar charts?
In the post-retreat survey, Sankaran said people either absolutely loved the draw-your-poster or hated it, but the Love group was much larger.
“Those who hated it felt they couldn’t represent data accurately with hand-drawn charts and graphs,” Sankaran said. “Or that their artistic skills were ‘being judged’.”
A few folks also pointed out that the drawing approach might work against people with a disability of some sort – a concern Sankaran said they will try to address next time.
There WILL be a next time, she added. “I had a few trainees come up to me to say they weren’t sure how it was going to go, but then they said they had fun!”
Post and pix by Karl Leif Bates, whose hand-drawn poster on working with the news office contained no data and was largely ignored.
Screamfest V combed through centuries of Rubenstein materials to find the very spookiest of artifacts
At least, that’s what Rubenstein Library seemed to be saying this Halloween with the fifth installment of its sometimes freaky, always fascinating “Screamfest” exhibition. With everything from centuries-old demonology textbooks, to tarot cards, to Duke-based parapsychology studies, Screamfest V took a dive into the deep end of the research Duke has gathered throughout its long history.
There’s a lot to unpack about this exhibit, but one of the most unsettling parts has to be the 1949 written exchange between Duke parapsychologist Joseph Rhine and Lutheran Reverend Duther Schulze, speaking about a boy they thought could be demonically possessed.
“Now he has visions of the devil and goes into a trance and speaks a strange language,” Duther wrote.
Anything about that sound familiar? If so, that might be because this case was the basis for the 1973 horror classic The Exorcist. (And people say research isn’t cool!)
The Rubenstein also exhibited a pack of cards used by Rhine’s parapsychology lab to test for extrasensory perception. Inscribed with vaguely arcane symbols, one of these “Zener cards” would be flipped over by a researcher behind a screen, and a test subject on the other side would attempt to “sense” what card the researcher displayed.
A pack of “Zener cards” Duke researchers once used to test for ESP
Although the results of this test were never replicated outside of Duke and are today widely considered debunked, Rhine’s research did create a stir in some circles at the time. One of the most interesting things about this exhibit, in fact, was the way it showed how much methods and topics in science have changed over time.
A 1726 publication of the book Sadducismus triumphatus: or, A full and plain evidence concerning witches and apparitions, for example, was loaded with supernatural “research” and “findings” every bit as dense and serious as the title would suggest. The section this tome was opened to bore this subheading: “Proving partly by Holy Scripture, partly by a choice Collection of Modern Relations, the Real EXISTENCE of Apparitions, Spirits, & Witches.”
A similar book titled The Discoverie of Witchcraft, was also on display—only this one was printed over two centuries later, in 1930.
A Depression-era miniature of the Duke mascot, somewhat worse for wear.
Other historical gems the exhibit offered included an a threadbare ‘blue devil’ doll from the ‘30s; a book made up of a lengthy collection of newspaper clippings following the case of Lizzie Borden, a reported axe murderer from the 1890s; and an ad for the 1844 “Life Preserving Coffin … for use in doubtful cases of death.”
It’s not every day research will leave the casual viewer quaking in their boots, but Screamfest V was quick to live up to its name. Covering a broad swath of Duke materials from several centuries, this exhibit successfully pulled off vibes of education, spookiness, and Halloween fun, all at the same time.
DURHAM, N.C. — A mere seven-plus decades after she first appeared in comic books in the early 1940s, Wonder Woman finally has her own movie.
In the two months since it premiered, the film has brought in more than $785 million worldwide, making it the highest grossing movie of the summer.
But if Hollywood has seen a number of recent hits with strong female leads, from “Wonder Woman” and “Atomic Blonde” to “Hidden Figures,” it doesn’t signal a change in how women are depicted on screen — at least not yet.
Those are the conclusions of three students who spent ten weeks this summer compiling and analyzing data on women’s roles in American film, through the Data+ summer research program.
The team relied on a measure called the Bechdel test, first depicted by the cartoonist Alison Bechdel in 1985.
The “Bechdel test” asks whether a movie features at least two women who talk to each other about anything besides a man. Surprisingly, a lot of films fail. Art by Srravya [CC0], via Wikimedia Commons.
To pass the Bechdel test, a movie must satisfy three basic requirements: it must have at least two named women in it, they must talk to each other, and their conversation must be about something other than a man.
It’s a low bar. The female characters don’t have to have power, or purpose, or buck gender stereotypes.
Even a movie in which two women only speak to each other briefly in one scene, about nail polish — as was the case with “American Hustle” — gets a passing grade.
And yet more than 40 percent of all U.S. films fail.
The team used data from the bechdeltest.com website, a user-compiled database of over 7,000 movies where volunteers rate films based on the Bechdel criteria. The number of criteria a film passes adds up to its Bechdel score.
“Spider Man,” “The Jungle Book,” “Star Trek Beyond” and “The Hobbit” all fail by at least one of the criteria.
Films are more likely to pass today than they were in the 1970s, according to a 2014 study by FiveThirtyEight, the data journalism site created by Nate Silver.
The authors of that study analyzed 1,794 movies released between 1970 and 2013. They found that the number of passing films rose steadily from 1970 to 1995 but then began to stall.
In the past two decades, the proportion of passing films hasn’t budged.
Since the mid-1990s, the proportion of films that pass the Bechdel test has flatlined at about 50 percent.
The Duke team was also able to obtain data from a 2016 study of the gender breakdown of movie dialogue in roughly 2,000 screenplays.
Men played two out of three top speaking roles in more than 80 percent of films, according to that study.
Using data from the screenplay study, the students plotted the relationship between a movie’s Bechdel score and the number of words spoken by female characters. Perhaps not surprisingly, films with higher Bechdel scores were also more likely to achieve gender parity in terms of speaking roles.
“The Bechdel test doesn’t really tell you if a film is feminist,” but it’s a good indicator of how much women speak, said team member Sammy Garland, a Duke sophomore majoring in statistics and Chinese.
Previous studies suggest that men do twice as much talking in most films — a proportion that has remained largely unchanged since 1995. The reason, researchers say, is not because male characters are more talkative individually, but because there are simply more male roles.
“To close the gap of speaking time, we just need more female characters,” said team member Selen Berkman, a sophomore majoring in math and computer science.
Achieving that, they say, ultimately comes down to who writes the script and chooses the cast.
The team did a network analysis of patterns of collaboration among 10,000 directors, writers and producers. Two people are joined whenever they worked together on the same movie. The 13 most influential and well-connected people in the American film industry were all men, whose films had average Bechdel scores ranging from 1.5 to 2.6 — meaning no top producer is regularly making films that pass the Bechdel test.
“What this tells us is there is no one big influential producer who is moving the needle. We have no champion,” Garland said.
Men and women were equally represented in fewer than 10 percent of production crews.
But assembling a more gender-balanced production team in the early stages of a film can make a difference, research shows. Films with more women in top production roles have female characters who speak more too.
“To better represent women on screen you need more women behind the scenes,” Garland said.
Dollar for dollar, making an effort to close the Hollywood gender gap can mean better returns at the box office too. Films that pass the Bechdel test earn $2.68 for every dollar spent, compared with $2.45 for films that fail — a 23-cent better return on investment, according to FiveThirtyEight.
Other versions of the Bechdel test have been proposed to measure race and gender in film more broadly. The advantage of analyzing the Bechdel data is that thousands of films have already been scored, said English major and Data+ team member Aaron VanSteinberg.
“We tried to watch a movie a week, but we just didn’t have time to watch thousands of movies,” VanSteinberg said.
A new report on diversity in Hollywood from the University of Southern California suggests the same lack of progress is true for other groups as well. In nearly 900 top-grossing films from 2007 to 2016, disabled, Latino and LGBTQ characters were consistently underrepresented relative to their makeup in the U.S. population.
Berkman, Garland and VanSteinberg were among more than 70 students selected for the 2017 Data+ program, which included data-driven projects on photojournalism, art restoration, public policy and more.
They presented their work at the Data+ Final Symposium on July 28 in Gross Hall.
From the highlands of north central Peru to high schools in North Carolina, student researchers in Duke’s Bass Connections program are gathering data in all sorts of unique places.
As the school year winds down, they packed into Duke’s Scharf Hall last week to hear one another’s stories.
Students and faculty gathered in Scharf Hall to learn about each other’s research at this year’s Bass Connections showcase. Photo by Jared Lazarus/Duke Photography.
The Bass Connections program brings together interdisciplinary teams of undergraduates, graduate students and professors to tackle big questions in research. This year’s showcase, which featured poster presentations and five “lightning talks,” was the first to include teams spanning all five of the program’s diverse themes: Brain and Society; Information, Society and Culture; Global Health; Education and Human Development; and Energy.
“The students wanted an opportunity to learn from one another about what they had been working on across all the different themes over the course of the year,” said Lori Bennear, associate professor of environmental economics and policy at the Nicholas School, during the opening remarks.
Students seized the chance, eagerly perusing peers’ posters and gathering for standing-room-only viewings of other team’s talks.
The different investigations took students from rural areas of Peru, where teams interviewed local residents to better understand the transmission of deadly diseases like malaria and leishmaniasis, to the North Carolina Museum of Art, where mathematicians and engineers worked side-by-side with artists to restore paintings.
Machine learning algorithms created by the Energy Data Analytics Lab can pick out buildings from a satellite image and estimate their energy consumption. Image courtesy Hoël Wiesner.
Students in the Energy Data Analytics Lab didn’t have to look much farther than their smart phones for the data they needed to better understand energy use.
“Here you can see a satellite image, very similar to one you can find on Google maps,” said Eric Peshkin, a junior mathematics major, as he showed an aerial photo of an urban area featuring buildings and a highway. “The question is how can this be useful to us as researchers?”
With the help of new machine-learning algorithms, images like these could soon give researchers oodles of valuable information about energy consumption, Peshkin said.
“For example, what if we could pick out buildings and estimate their energy usage on a per-building level?” said Hoël Wiesner, a second year master’s student at the Nicholas School. “There is not really a good data set for this out there because utilities that do have this information tend to keep it private for commercial reasons.”
The lab has had success developing algorithms that can estimate the size and location of solar panels from aerial photos. Peshkin and Wiesner described how they are now creating new algorithms that can first identify the size and locations of buildings in satellite imagery, and then estimate their energy usage. These tools could provide a quick and easy way to evaluate the total energy needs in any neighborhood, town or city in the U.S. or around the world.
“It’s not just that we can take one city, say Norfolk, Virginia, and estimate the buildings there. If you give us Reno, Tuscaloosa, Las Vegas, Pheonix — my hometown — you can absolutely get the per-building energy estimations,” Peshkin said. “And what that means is that policy makers will be more informed, NGOs will have the ability to best service their community, and more efficient, more accurate energy policy can be implemented.”
Some students’ research took them to the sidelines of local sports fields. Joost Op’t Eynde, a master’s student in biomedical engineering, described how he and his colleagues on a Brain and Society team are working with high school and youth football leagues to sort out what exactly happens to the brain during a high-impact sports game.
While a particularly nasty hit to the head might cause clear symptoms that can be diagnosed as a concussion, the accumulation of lesser impacts over the course of a game or season may also affect the brain. Eynde and his team are developing a set of tools to monitor both these impacts and their effects.
A standing-room only crowd listened to a team present on their work “Tackling Concussions.” Photo by Jared Lazarus/Duke Photography.
“We talk about inputs and outputs — what happens, and what are the results,” Eynde said. “For the inputs, we want to actually see when somebody gets hit, how they get hit, what kinds of things they experience, and what is going on in the head. And the output is we want to look at a way to assess objectively.”
The tools include surveys to estimate how often a player is impacted, an in-ear accelerometer called the DASHR that measures the intensity of jostles to the head, and tests of players’ performance on eye-tracking tasks.
“Right now we are looking on the scale of a season, maybe two seasons,” Eynde said. “What we would like to do in the future is actually follow some of these students throughout their career and get the full data for four years or however long they are involved in the program, and find out more of the long-term effects of what they experience.”
Living in a 3-dimensional world, we can easily visualize objects in 2 and 3 dimensions. But as a mathematician, playing with only 3 dimensions is limiting, Dr. Henry Segerman laments. An Assistant Professor in Mathematics at Oklahoma State University, Segerman spoke to Duke students and faculty on visualizing 4-dimensional space as part of the PLUM lecture series on April 18.
What exactly is the 4th dimension?
Let’s break down spatial dimensions into what we know. We can describe a point in 2-dimensional space with two numbers x and y, visualizing an object in the xy plane, and a point in 3D space with 3 numbers in the xyz coordinate system.
Plotting three dimensions in the xyz coordinate system.
While the green right-angle markers are not actually 90 degrees, we are able to infer the 3-dimensional geometry as shown on a 2-dimensional screen.
Likewise, we can describe a point in 4-dimensional space with four numbers – x, y, z, and w – where the purple w-axis is at a right angle to the other regions; in other words, we can visualize 4 dimensions by squishing it down to three.
Plotting four dimensions in the xyzw coordinate system.
One commonly explored 4D object we can attempt to visualize is known as a hypercube. A hypercube is analogous to a cube in 3 dimensions, just as a cube is to a square.
How do we make a hypercube?
To create a 1D line, we take a point, make a copy, move the copied point parallely to some distance away, and then connect the two points with a line.
Similarly, a square can be formed by making a copy of a line and connecting them to add the second dimension.
So, to create a hypercube, we move identical 3D cubes parallel to each other, and then connect them with four lines, as depicted in the image below.
To create an n–dimensional cube, we take 2 copies of the (n−1)–dimensional cube and connecting corresponding corners.
Even with a 3D-printed model, trying to visualize the hypercube can get confusing.
How can we make a better picture of a hypercube? “You sort of cheat,” Dr. Segerman explained. One way to cheat is by casting shadows.
Parallel projection shadows, depicted in the figure below, are caused by rays of light falling at a right angle to the plane of the table. We can see that some of the edges of the shadow are parallel, which is also true of the physical object. However, some of the edges that collide in the 2D cast don’t actually collide in the 3D object, making the projection more complicated to map back to the 3D object.
The stereographic projection is a mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except the point at the top of the sphere.
For the object below, the curves on the sphere cast shadows, mapping them to a straight line grid on the plane. With stereographic projection, each side of the 3D object maps to a different point on the plane so that we can view all sides of the original object.
Stereographic projection of a grid pattern onto the plane. 3D print the model at Duke’s Co-Lab!
Just as shadows of 3D objects are images formed on a 2D surface, our retina has only a 2D surface area to detect light entering the eye, so we actually see a 2D projection of our 3D world. Our minds are computationally able to reconstruct the 3D world around us by using previous experience and information from the 2D images such as light, shade, and parallax.
Projection of a 3D object on a 2D surface.
Projection of a 4D object on a 3D world
How can we visualize the 4-dimensional hypercube?
To use stereographic projection, we radially project the edges of a 3D cube (left of the image below) to the surface of a sphere to form a “beach ball cube” (right).
The faces of the cube radially projected onto the sphere.
Placing a point light source at the north pole of the bloated cube, we can obtain the projection onto a 2D plane as shown below.
Stereographic projection of the “beach ball cube” pattern to the plane. View the 3D model here.
Applied to one dimension higher, we can theoretically blow a 4-dimensional shape up into a ball, and then place a light at the top of the object, and project the image down into 3 dimensions.
Left: 3D print of the stereographic projection of a “beach ball hypercube” to 3-dimensional space. Right: computer render of the same, including the 2-dimensional square faces.
Forming n–dimensional cubes from (n−1)–dimensional renderings.
Thus, the constructed 3D model of the “beach ball cube” shadow is the projection of the hypercube into 3-dimensional space. Here the 4-dimensional edges of the hypercube become distorted cubes instead of strips.
Just as the edges of the top object in the figure can be connected together by folding the squares through the 3rd dimension to form a cube, the edges of the bottom object can be connected through the 4th dimension
Why are we trying to understand things in 4 dimensions?
As far as we know, the space around us consists of only 3 dimensions. Mathematically, however, there is no reason to limit our understanding of higher-dimensional geometry and space to only 3, since there is nothing special about the number 3 that makes it the only possible number of dimensions space can have.
From a physics perspective, Einstein’s theory of Special Relativity suggests a connection between space and time, so the space-time continuum consists of 3 spatial dimensions and 1 temporal dimension. For example, consider a blooming flower. The flower’s position it not changing: it is not moving up or sideways. Yet, we can observe the transformation, which is proof that an additional dimension exists. Equating time with the 4th dimension is one example, but the 4th dimension can also be positional like the first 3. While it is possible to visualize space-time by examining snapshots of the flower with time as a constant, it is also useful to understand how space and time interrelate geometrically.