Turning a circle into a square is possible with this kirigami-inspired formula

Kirigami takes pop-up books to a whole new level. The Japanese paper craft involves cutting patterns in paper to transform a two-dimensional sheet into an intricate, three-dimensional structure when partially folded. In the hands of an artist, kirigami can yield remarkably detailed and delicate replicas of structures in nature, architecture, and more.

Scientists and engineers have also taken inspiration from kirigami, applying principles from paper-cutting to design robotic grippers, stretchable electronics, water-harvesting sheets, and other shape-shifting materials and devices. For the most part, such inventions are products of from-scratch design. There’s been no blueprint for engineers to determine the pattern of cuts that will transform a material from one desired shape to another — that is, until now.

A new study in Nature Computational Science presents a general computational strategy that can solve any two-dimensional, kirigami-inspired transformation. The method can be used to determine the angle and length of cuts to make, such that a sheet can transform from one desired shape to another when pulled open and pushed back together, like an intricate, expandable lattice.

With their new method, researchers designed and fabricated a number of transformable, 2D kirigami structures, including a circle that turns into a square, and a triangle that morphs into a heart.

“People have talked of the square and circle as one of the impossible problems in mathematics: You cannot turn one into the other,” says Gary Choi, a postdoc and instructor in applied mathematics at MIT. “But with kirigami, we can actually turn a square shape into a circle shape.”

For engineers, the new method could be used to solve various design problems, such as how a robot can be engineered to transform from one shape to another to carry out a particular task or navigate certain spaces. There’s also potential to design active materials, for instance as smart coverings for buildings and homes.

“One of the first applications we thought of was building façades,” says Kaitlyn Becker, an assistant professor of mechanical engineering at MIT. “This could help us to make large, kirigami-like façades that can transform their shape to control sunlight, ultraviolet radiation, and be adaptive to their environment.”

Becker and Choi are co-authors of the new study, along with Levi Dudte, a quantitative researcher at Optiver, and L. Mahadevan, a professor at Harvard University.

The space between

The study grew out of the team’s previous work in both kirigami and origami — the Japanese art of paper folding.

“We found there are a lot of mathematical connections in kirigami and origami,” Choi says. “So we wanted to come up with a mathematical formulation that can help people design a large variety of patterns.”

In 2019, the team devised an optimization approach for kirigami to find the pattern of cuts that would be required to turn one shape into another. But Choi says the approach was too computationally intensive, and it took a large amount of time to derive an optimal pattern to achieve a particular transformation.

In 2021, the researchers took on a similar problem in origami and found that through a slightly different perspective, they were able to derive a more efficient strategy. Rather than planning out a pattern of individual folds (similar to kirigami’s individual cuts), the team focused on growing a pattern from a simple folded seed. By working panel by panel, and establishing relationships between panels, such as how one panel would move if an adjacent panel were folded, they were able to derive a relatively efficient algorithm for planning out the design of any origami structure.

The team wondered if a similar approach be applied to kirigami. In traditional kirigami, once cuts have been made in a sheet of paper, the sheet can be partially folded such that the resulting empty spaces create a three-dimensional structure. Like the panels between origami folds, could the empty spaces between cuts, and their relation to each other, yield a more efficient formula for kirigami design? This question motivated the team’s new study.

Math links

The study focuses on two-dimensional kirigami transformations. The researchers considered a general kirigami design comprising a mosaic of interconnected quadrilateral tiles, each cut to various angles and sizes. The conceptual mosaic begins as one shape and can be pulled apart and pushed back together to form an entirely new shape. The challenge was to describe how one shape can transform into another, based on the empty spaces between tiles and how the spaces change as the tiles are pulled apart and pushed back together.

“If the tiles themselves are solid and unchangeable, then it’s the empty spaces between that are an opportunity for motion,” Becker says. 

The team first considered the simplest representation of empty space, in the form of a rhombus, or what they term a “four-bar linkage.” Each side of the rhombus represents a bar, or the edge of a solid tile. Each corner of the rhombus represents a linkage, or hinge that connects tiles. By changing the length and angle of the rhombus’ edges, the team could study how the empty space in between changes.

By studying progressively larger assemblages of four-bar linkages, the team identified relationships between the angle and length of bars, the shape of individual empty spaces, and the shape of the overall assemblage. They worked these relationships into a general formula, and found that it could efficiently identify the pattern of cuts — including their angle and length — that would be required to transform a two-dimensional sheet from one desired shape to another.

“Without a tool like this, I might brute force this problem in Matlab, or guess and check, but it would take me a very long time to get something that can transform from a circle to a square,” Becker says.

In simulations, the team found that the formula could indeed find a pattern of tiles that would turn a circle-shaped mosaic into a square, as well as virtually any shape into any other desired shape.

Going a step further, the team developed two fabrication methods to physically realize the formula’s designs. They quickly realized that a key challenge in making the transformable mosaics was in finding the right material to serve as the tile-connecting hinges. The connections needed to be strong, yet easily bendable.

“I thought, what is very strong in tension, and tear-resistant, but can have a zero bending radius, almost like a pinpoint hinge?” Becker says. “And the answer, it turns out, is fabric.”

The team used two methods — 3D printing, and mold casting — to embed small strips of fabric into quadrilateral plastic tiles, in a way that closely connected the tiles while allowing them to bend against each other. Using these two methods, the team fabricated circle-shaped mosaics that transformed into squares, as well as simple triangle mosaics that morphed into more complex heart shapes.

“We can basically go to any two-dimensional shape,” Choi says. “That’s guaranteed, using our mathematical formulation. Now we’re looking to extend this to 3D kirigami.”

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Driven to driverless

When Cindy Heredia was choosing an MBA program, she knew she wanted to be at the forefront of the autonomous driving industry. While doing research, she discovered that MIT had a unique offering: a student-run driverless team. Heredia applied to MIT to join the team, hoping to get hands-on experience.

“My hope is that we’re able to find ways to leverage tools and technologies, such as ride-sharing and autonomous vehicles, and harness the variety of modes available to serve vulnerable populations that have traditionally been underserved by existing options,” Heredia shares.

At age 8, Heredia was immersed with cars, repairing car radios to help support her family. Growing up in the low-income neighborhood of Laredo, Texas, Heredia understood mobility as a necessary resource for greater access to employment, education, and opportunity early on in life. Her family's sole car was constantly in use for work, making it difficult for them to meet essential needs such as going to the doctor. As she grew older, she saw her friends unable to take job opportunities due to the long bus rides that would take hours.

Getting accepted into MIT and joining the Driverless team was her first step toward repairing disparities in transportation. Under the auspices of the MIT Edgerton Center, MIT Driverless develops their own artificial intelligence software to race in autonomous driving competitions. Leveraging talent and resources, Driverless teamed up with the University of Pittsburgh, Rochester Institute of Technology (RIT), and the University of Waterloo, Canada, to form MIT-PITT-RW and compete in the Indy Autonomous Challenge.

In winter 2021, Heredia became co-captain of the team. This hasn’t always been easy. At the Indy Autonomous Challenge in November, MIT-PITT-RW was the only entirely student-run team out of nine teams. “There have been many ‘no’s’ our team has received,” Heredia shares. “We've been told that a student-led team shouldn’t even be on the grid. We've been through a devastating crash two days before a race (that we thankfully came back from!). We've seen teammates go. We’ve had personal life events happen. But we’ve always been able to push through it all and come out strong. Nothing has ever brought us down.”

Developing reliable decision-making algorithms is a challenge due to the potential for misinterpretation of sensor data, which could result in collisions. Furthermore, when traveling at speeds exceeding 150 mph, the demand for rapid decision-making intensifies, prompting teams to continually enhance their technology stack. Teams like MIT-PITT-RW are pushing boundaries by testing novel algorithms at speeds deemed too hazardous for conventional roads, driving advancements across the field.

Despite these challenges, in January MIT-PITT-RW hit a new speed record of 152 mph during time trials (competing for the fastest lap time) at the Indy Autonomous Challenge and placed fourth in the overall competition for the first time. They also hit another team record of 154 mph while passing another car.

Now, as she prepares to graduate with her MBA, Heredia reflects on leading the team and stresses the importance of building trust between team members: “This is largely a people role. You have to be able to work with all different types of personalities. Understanding how to manage your team is very important, and I think that starts by first building trust with them. I’ve learned that the best way to do that is to not ask anything of anyone that you wouldn’t ask of yourself. It’s one thing to tell your team, ‘You’re important to me, and I’m here for you.’ It’s another thing entirely to prove that repeatedly with your actions.”

Heredia encourages other women of color to take leadership positions in the self-driving industry. “You will have to put yourself out there, made to be seen, and never hide away. If you’re invited into a room, you have to remind yourself that you deserve to be in that room.” She believes there is more support available than you might think. “There is a surprising number of women of color in leadership roles at self-driving companies, and I’m grateful to call some of them my mentors.” 

Heredia says that anyone going into this field should be prepared for a lot of failure. “There are moments where you can try to listen as much as you can and make a decision, but it might not be the right one. A project like this comes with a lot of risk, and having comfort knowing that it will come with failures at times is critical. And that is OK. You will learn the most when you go through some of your most difficult moments. So you reflect, pivot, and keep going. So, my advice would be to come in with the mindset that this is a learning experience. And use that to help people believe in what’s possible by sharing what you’ve learned along the way.”

While many people predict the end of personal vehicle ownership with the advent of autonomous vehicles, Heredia believes it will be a slow and gradual process. She plans to pursue a career in the self-driving industry, recognizing the significant challenges it presents. In the future, she hopes that we can also use these technologies for social good and bring them to communities such as the one she grew up in. "It's an incredibly interesting problem that, I think, still has a long road ahead (pun intended).”

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He made linear algebra fun

The following series of numbers might help to summarize the MIT career of MathWorks Professor of Mathematics Gilbert “Gil” Strang ’55, who taught his last class on May 15.

3+2+61=66, or 75% of his life

Strang has spent 66 of his 88 years at MIT — as a student, an instructor, and a faculty member.

“There were about eight math majors then,” says Strang, a William Barton Rogers Scholar who took just three years to graduate from MIT with a BS, in 1955. “And now there are hundreds.”

Strang received a BA and MA in 1957 as a Rhodes Scholar at Balliol College in Oxford, England, and a PhD in 1959 from the University of California at Los Angeles, where he was advised by Peter Henrici. His dissertation was "Difference Methods for Mixed Boundary Value Problems.”

A CLE Moore instructor from 1959 to 1961, he joined the MIT faculty in 1962. A full professor in 1970, Strang focuses his research on mathematical analysis, linear algebra, and partial differential equations.

“He has had a tremendous impact on the teaching of mathematics to tens of thousands of students at MIT through his lectures, to countless students at other academic institutions through his textbooks, and to millions of people all over the globe through his online lectures and digital media,” says Professor Michel Goemans, head of the Department of Mathematics.

1934

Year in which Strang was born, in Chicago.

His parents William and Mary Catherine Strang emigrated to the United States from Scotland. Strang and his sister Vivian grew up in Washington and Cincinnati, Ohio, and attended the Principia School in St. Louis, Missouri. He and his wife Jillian have three sons, David, John, and Robert, and 10 grandchildren.

15,000

Number of students he has taught at MIT since he was a CLE Moore instructor.

Strang has taught calculus, analysis, and computational science and engineering (18.085). But it’s his linear algebra class that evolved into a course eventually taken by a third of the MIT student body.

Strang began teaching linear algebra in the 1970s, during a time when engineers and scientists wrote large software packages using the finite element method to solve structural problems in mechanics. But he saw the need to restructure the class so he could teach linear algebra in a constructive way, to show that it was related to everything from pure math to the internet. “We needed to explain the ideas in concrete language that students could follow and understand and use,” he explains.

17

Number of awards and recognitions he has received for his research, service, and teaching.

These include the 1976 Chauvenet Prize; the Society for Industrial and Applied Mathematics’ (SIAM’s) 2003 Award for Distinguished Service; and the 2020 Irwin Sizer Award for the Most Significant Improvement to MIT Education.

Strang also won the Graduate School Teaching Award in 2003; the Von Neumann Prize Medal of the U.S. Association for Computational Mechanics in 2005; the Mathematical Association of America’s Lester Ford Prize in 2005 and the Haimo Prize in 2006; and the Henrici and Su Buchin Prizes of the International Congress of Industrial & Applied Mathematics in 2007.

He is a member of the National Academy of Sciences, a fellow of the American Academy of Arts and Sciences, and an honorary fellow of Balliol College, Oxford. In 2019, he was elected as a foreign member of the Russian Academy of Sciences, in the section of Applied Mathematics and Computer Science. His service to the academic community includes serving as president of SIAM, chair of the Joint Policy Board for Mathematics, chair of the U.S. National Committee on Mathematics, member of the Abel Prize Committee, and chair of the math department’s Pure Mathematics Committee.

20

Number of books Strang has written so far.

Strang recently released “Introduction to Linear Algebra,” the sixth edition of the book he first published over 40 years ago. In 2019 he released "Linear Algebra and Learning from Data."

In his retirement he will continue running Wellesley-Cambridge Press, which has published his books since 1986. Its newest outlet is Wellesley Publishers in India; “Introduction to Linear Algebra” has been translated into French, German, Greek, Japanese, Portuguese, and Chinese.

His textbooks are celebrated for their simple methods to teach complex subjects.

“The good abstractions from the deeper classes are in Gil’s texts — but yet they are made accessible the Gil Strang way,” says MIT Professor Alan Edelman. “You can still find vector spaces, subspaces, dimensions … and linear transformations. All those ideas from pure linear algebra are not lost, just made more relevant. I love watching how he weaves these deeper ideas into the flow of the class. Gil sneaks in the real spirit of this beautiful mathematical subject, and it’s for everybody.”

“Undergraduate mathematics textbooks are not what they used to be, and Gilbert Strang's superb new edition of ‘Introduction to Linear Algebra’ is an example of everything that a modern textbook could possibly be, and more,” says book reviewer Douglas Farenick of the University of Regina. The book “keeps one eye on the theory, the other on applications, and has the stated goal of ‘opening linear algebra to the world.’” He called the writing “engaging and personal … rarely does an undergraduate mathematics text feel so alive as this one.”

2001

Year in which Strang first uploaded his classes to MIT OpenCourseWare, the same year of its launch. 

“OCW transformed my life,” he says. “It was my good fortune to be teaching when President [Charles] Vest approved the creation of OpenCourseWare, opening the way for lectures to reach far beyond MIT.”

20 million — and counting

Number of views for Strang's OCW courses, making him one of the most recognized mathematicians in the world.

Strang was one of the first faculty members at MIT to share his course materials on OCW, for class 18.06 (Linear Algebra), and he continued until his last lecture, on May 15. Strang was “a YouTube star even before there was such a thing,” says Edelman.

“The OCW team and learners around the world will continue to be grateful for and benefit from his generosity and wisdom for years to come,” says OCW Senior Publication Manager Elizabeth DeRienzo.

Strang’s classes became a valuable and free resource to help educators and students around the world. 

Strang’s lessons are “clear, interesting, and nonthreatening,” commented one high school teacher. “I watch his linear algebra lessons and wish I could tell him how terrific he is.”

Other educators admit to watching him just for entertainment. “This teacher would be fun to sit down with and have a cup of coffee and conversation,” said one commenter.

460

Record number of students who took his last class, 18.06 (Linear Algebra), this spring.

This doesn’t count the standing-room-only gathering of family members, friends, and colleagues in the back of 26-100. Math instructor Andrew Horning assisted him “in a beautiful way,” says Strang.

6,000 and 352,000 — and counting

Audience for Strang's final lecture, held at MIT on May 15.

The lecture, which had a full house of students on hand in person at MIT, is posted on MIT OCW’s YouTube channel. Online attendees surpassed 6,000, and more than 352,000 have viewed the video over the week that followed.

Incalculable

Over the years, this friendly math professor learned to deftly, clearly, and humanely explain linear algebra, computational science, finite elements, wavelets, GPS, and calculus to countless students, first in the classroom, and then online.

In one of his newer classes, 18.065 (Matrix Methods in Data Analysis, Signal Processing, and Machine Learning), he expanded his linear algebra teachings into the area of deep learning.

“Professor Strang structures the class so that ideas seem to flow from the students into proofs,” says a former student of the class, Jesse Michel. “Every class includes a cool math trick or joke that keeps the class laughing. Professor Strang’s energy and emphasis on the exciting points keeps the class on the edge of their seats.”

Strang’s easy smile, energetic lessons, and unflagging encouragement make for interactive classes. What’s his secret to effective teaching?

“I like students, and I want to help,” he said in a 2019 interview. “Maybe the key point is to think with them, not to just say, ‘OK, here it is, listen up.’ I think through the question all over again as they do. And you have to give it time. You can’t zip through a proof.”

His former students and colleagues recall how easy it was to work with him.

“When you’re in Gil’s presence, you’re just in a better, more beautiful world,” said his doctoral student Pavel Grinfeld PhD ’03, at Strang’s last lecture. “I think that’s why I chose to pursue the same line of studies as Gil … My life especially has been touched by you.”

Former teaching assistant D. Andrew Brown, now a Clemson University statistics professor, recalls him as “kind, elegant, and engaging.”

Edelman says that Strang teaches with “dignity and humility” and recognizes “in everyone the thirst for knowledge.”

“Whether a student was struggling or at the top of the class, Gil knew just what to say. Whether you are a colleague right next door or a stranger that landed in the hallways, one feels that Gil is your old or new best friend.”

“So, what makes Gil’s lectures so very special? I love his words, his tone, his pace, and the very way that the answer seems like a surprise when we all know, he understood it from the beginning.”

Chat comments from around the world

Edelman and Grinfeld led a team intent on publicizing Gil’s last lecture, including creating a web page with an online countdown to the May 15 event. In response, countless Strang fans posted their well-wishes and thanks via online comments on social media and in the video’s chat stream.

“Gil, Best wishes for a great final lecture, from your #1 fan in Ithaca!” posted Cornell University math professor and former MIT math instructor Steven Strogatz, in the final lecture chat stream. When a fellow chat member called him “a fan boi,” Strogatz responded, “You bet I'm fan-boying! I had the honor of teaching Gil's 18.085 course many times at MIT and loved learning from Gil and working with him. He's as wonderful as he seems online.”

And from others:

“A legend! Helped me get into robotics in my mid-30s.”

“Teaching math in a way that instills a love for the subject is a challenging task, much harder than solving complex equations. But your teaching style effortlessly achieves this.”

“The best teacher I never had. But thanks to MIT for sharing his linear algebra lectures. He has been a blessing for thousands of his students.”

“I can’t believe this legend is retiring. At least his former lectures will be available for future students.”

“Your 18.06 course was my first-ever experience with a superb quality math professor who taught me a new subject in an intuitive way & made me appreciate the abstract beauty!”

“Your teaching was my only source of quality education growing up in India.”

“That was a very emotional hour for so many people around the world! Prof. Strang made the world a better place in his own personal way!”

“Gil Strang made linear algebra accessible to the masses. I often ask myself when teaching, ‘Am I being as clear and approachable as Strang?’ I'm still working on it.”

“Gil’s lecture was probably the first time I realized the difference between MIT and other universities.”

“Your amazing lectures on OCW helped me not only snag an A+ for linear algebra but also lend a hand to a bunch of other students who were struggling.”

“Prof. Strang's 18.06 MIT OCW series was the first lecture series I watched while waiting to study university math. … To this day, I still remember and use his column picture and row picture of matrix multiplication (each column of AB is a linear combination of columns of A) — this is seldom taught elsewhere but it really helped.”

Linear moments

Strang hopes that, among other parts of his legacy, he has left behind a good road map to keep stoking a love of linear algebra.

“Teaching has been a wonderful life,” says Strang. “And I am so grateful to everyone who likes linear algebra and sees its importance. So many universities (and even high schools) now appreciate how beautiful it is and how valuable it is. That movement will continue because it is right.”

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Professor Emeritus Arnoldo Hax, who reprioritized corporate strategy, dies at 87

Arnoldo Hax, the Alfred P. Sloan Professor of Management Emeritus at the MIT Sloan School of Management and an operations management expert who introduced a customer-centered approach to competitive strategy with his Delta Model, died April 20. He was 87.

Hax joined MIT Sloan in 1973 as a member of the Operations Management group. An industrial engineer who believed that management could be improved through rationalization, Hax was an early member of the strategy group at MIT Sloan, and strengthened ties with the School of Engineering.

“He was a big proselytizer for the idea that management can be made more effective,” says Professor Emeritus Michael Scott Morton of MIT Sloan. “The Delta Model was the synthesis of the factors that he saw as most important in setting a strategy.”

Inside the Delta Model

Customer bonding is at the heart of strategy; it is “fundamental” for a company to get to know the customer and provide a unique value proposition from its competitors, Hax said in a 2010 interview with Emerald Publishing.

His customer-centric view challenged the notion of putting the competition at the center of a strategy and prioritizing domination over competitors.

“The danger here is that you tend to view strategy as rivalry and the way to win is to beat someone,” he said. “That anchors us in the past, and most dangerously, it creates an obsession about the competitor’s behavior.”

To illustrate this idea, Hax and MIT Sloan’s Dean Wilde created the Delta Model. In a 1999 MIT Sloan Management Review article, they wrote that under the Delta Model, strategy and execution are connected through adaptative processes. This is achieved by:

• defining the three strategic positionings (best product, total customer solution, and system lock-in);
• aligning a firm’s competencies with the desired strategic position;
• seeking a coherent integration across business processes to produce unifying action; and
• incorporating supplier and complementor companies to ensure fulfillment of the customer value proposition.

The Delta Model was an alternative to Michael Porter’s Five Forces, the strategy field’s dominant framework.

“Porter's view was quite simple: You were either a low-cost producer or you were differentiated in some shape or form. But Arnoldo's point was that there are different ways to compete,” says MIT Sloan Deputy Dean Michael Cusumano.

“The Delta Model was more from a customer perspective. You can either compete with the best product — and ‘best’ could be related to lower cost or differentiated through quality — or you can compete as a total solutions provider, or you could have what Arnoldo called a system lock-in. Today, we would call that platform competition.”

Nicolás Majluf PhD ’79, a systems and industrial engineering professor at the Catholic University of Chile, completed his PhD in management at MIT Sloan. He and Hax co-authored several books and papers on the content and process of corporate strategy.

“He told me many times when we were writing, ‘I want to be helpful, I want to tell people how to do strategic management,’” Majluf says. “He was trying to help companies, and he was refining the Delta Model at every step of his consulting work.”

Hax’s mathematical background led him to create 10 “Haxioms” for his Delta Model and “a distillation of his knowledge in strategy.”

The 10 Haxioms are:

1. The center of strategy is the customer.
2. You don’t win by beating the competition, you win by achieving customer bonding.
3. Strategy is not war, it is love.
4. A product-centric mentality is constraining. Open your mindset to include the customers, the suppliers, and the complementors as your key constituencies.
5. Try to understand your customer deeply. Strategy is done one customer at a time.
6. Commodities only exist in the minds of the inept.
7. The two foundations of strategy are: Customer segmentation and customer value proposition, and the firm as a bundle of competencies.
8. Reject these two clichés: “The customer is always right,” and “I know the customer needs and how to satisfy them.”
9. The strategic planning process is a dialogue among the key executives of the firm.
10. Metrics are essential; experimentation is crucial.

The Delta Model isn’t the only work Hax produced at MIT Sloan with real-world applications.

In 1973 he authored a paper on hierarchical production planning, which outlined four levels of decision-making, each with its own characteristics such as the type of manager in charge of execution, the scope of the planning activity, the level of collected information, and timeline. 

“The lower one gets in the hierarchy, the narrower is the scope of the plan, the lower is the management level involved, the more detailed is the information needed, and the shorter the planning time horizon,” Hax wrote. “Each level of planning has its own objectives and constraints in which decisions have to be made.”

Connecting with the business community

Born in Santiago, Chile, Hax helped launch what is now the Leadership in Global Operations program, a dual-degree engineering and MBA track, and he led the MIT-Chile program — in 2013 he received the Medal of the Order of Commander from the president of Chile.

Hax’s integrative approach to strategy spurred him to explore new partnerships within MIT and made him notably successful with his consulting clients.

“Even though he came from operations research, having consulted with lots of companies and worked with them on planning and execution, he realized that you need people trained in organizations and strategy and management processes,” Cusumano says.

Gerhard Schulmeyer SM ’74 tapped Hax for help while Schulmeyer was navigating leadership positions including president and CEO of Siemens in the United States and as a senior vice president at Motorola.

“He helped me sort out where the strategy stood and what the changes were for the companies I took over,” says Schulmeyer, who eventually became a professor of the practice at MIT Sloan.

Executives loved him because “he could speak their language and he was teaching strategy,” says Thomas Magnanti, professor of operations research at MIT Sloan. “He was teaching how corporations can improve themselves, and these senior people who were coming to industry loved that.”

A version of this article was first published by MIT Sloan.

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Fueled by problem-solving

“Every time I try to solve a problem — whether it be physics or computer science — I always try to find an elegant solution,” says MIT senior Thomas Bergamaschi, who spent four years learning how to solve problems while an Undergraduate Research Opportunities Program (UROP) student in the Engineering Quantum Systems (EQUS) laboratory at MIT.

“Of course,” he adds, “there are many times where a problem doesn't have an elegant solution, or finding an elegant solution is much harder than a normal solution, but it is something I always try to do, as it helps me understand at most something. Another compelling reason is that these solutions are usually the simplest to teach other people, which is always appealing to me.”

Now, as the physics and electrical engineering and computer science (EECS) major ponders post-graduation life, he believes he’s ready to tackle challenges in his career as a software engineer at Five Rings, where he had an internship. “There are a lot of hard and interesting problems to be solved there,” he says. “Challenges are something that fuels me.”

STEM family

Born in Brazil, Bergamaschi lived in the United States until he was 6, when his family moved back to a small town in rural Sao Paulo called Vinhedo. His Brazilian father is a software engineer, and his mother, who is from England, studied biology in college and now teaches English. He followed in the footsteps of his older brother, Thiago, who was the first in the family to be drawn to physics. And when his brother entered physics competitions in high school, Thomas did too.

He had high school teachers who encouraged him to study physics beyond the usual curriculum. “One teacher accompanied me on many bus and plane rides to physics competitions and classes,” he recalls. “She was a huge motivator for me to continue studying physics and helped find me new books and problems throughout high school.”  

The younger Bergamaschi went on to win silver medals at the International Physics Olympiad and at the International Young Physicists’ Tournament, and more than a dozen other medals in national and regional Brazilian science competitions in physics, math, and astronomy.

MIT Time

Thiago Bergamaschi '21 joined MIT as a physics and EECS major in 2017, and his brother wasn’t far behind him, entering MIT in 2019.

Bergamaschi ended up spending nearly all four years at MIT as a UROP student in the Engineering Quantum Systems (EQUS) laboratory, under the supervision of PhD student Tim Menke and Professor William Oliver. That’s when he was introduced to quantum computing — his supervisors were constructing a device that had a phenomenon where many qubits could interact simultaneously.

“This type of interaction is very useful for quantum computers, as it gives us a possible way that we can map problems we are interested in onto a quantum computer,” he says. “My project was to try to answer the question of how we can actually measure things, and prove that the constructed device actually had this coupling term we were interested in.”

He proposed and analyzed methods to experimentally detect many-body quantum systems. “These systems are extremely important and interesting as they have many cool applications, and in particular can be used to map computationally hard problems — such as route optimization, Boolean satisfiability, and more — to quantum computers in an easy way.”

This project was supposed to be a warmup project for his UROP. “However, we soon noticed that the problem of accurately measuring these effects was a pretty tricky problem. I ended up working on this problem for around six months — my summer, the fall semester, and the beginning of IAP [Independent Activities Period] — trying to figure out how we can measure these effects.”

He presented his research at the 2021 and 2022 American Physical Society March meetings, and published “Distinguishing multi-spin interactions from lower-order effects” in Physical Review Applied.   

“The experience of presenting my work in a conference and publishing a paper is a huge highlight from my time at MIT and gave me a taste of scientific communication and research, which was invaluable for me,” Bergamaschi says. “Being able to do research with the help of Tim Menke and Professor Oliver was inspiring, and is one of the largest highlights from my time at MIT.”

He also worked with William Isaac Jay, a postdoc at the MIT Center for Theoretical Physics, on lattice quantum field theory. He studies quantum theories at the microscopic level, where strong nuclear interactions are relevant. “This is particularly appealing as we can simulate these theories on a computer — albeit usually a huge supercomputer — and try to make predictions about phenomena involving atoms at a minuscule scale. I UROP'd in this lab over both my junior and senior year, and my project involved implementing techniques from one of these computer simulations, how can we go back to the real world and obtain something that an experiment would measure.”

Brazil blues

Bergamaschi missed Brazil but found community playing soccer with intramural teams Ousadia and Alegria Futebol Clube, and eating churrasco with his friends at Oliveira’s Brazilian-style steakhouse in Somerville, Massachusetts. He also loved going to college with his brother, who graduated in 2021 and is now pursuing his PhD in physics at the University of California at Berkeley.

“One of my favorite memories of MIT is from my sophomore spring, when I managed to take two classes with him just before he graduated,” he recalls. “It was a lot of fun discussing physics problem sets and projects with him.”

What also keeps him in touch with his homeland is working with Brazilian high school students competing in physics tournaments. He is part of an academic committee that creates and grades the physics problems taken by the top 100 Brazilian high school students. Those with top scores go on to the International Physics Olympiad. He says he sees this as a way to pay forward what his high school teacher did for him: to encourage others to study physics.

“These olympiads were one of the main reasons for my interest in physics and me coming to MIT, and I hope that other Brazilian students can have these same opportunities as I had,” he says. “These students are all incredibly talented. A large amount of them end up coming to MIT after they graduate high school, so it’s a very gratifying and incredible experience for me to be able to participate and help in their physics education.”

Post-graduation thoughts

What will he miss most at MIT? “Late-night problem set sessions immediately before a deadline, trying to find a free food event across campus, and getting banana lounge bananas and coffee.”

And what were his biggest lessons? He says that MIT taught him how to work with other people, “handle imposter syndrome,” and most importantly, unravel complicated challenges.

“I think one of my major motivators is my desire to learn new things, whether it be physics or computer science. So, I am a big fan of very difficult problems or projects which require continual work but have large payoffs at the end. I think there are many instances during my time at MIT in which I worked all night for a project, just to get up and hop back on because of the excitement of obtaining a result or solution.”

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Facing up to democratic distrust

In October 2020, two rival candidates for office in Utah made an unusual television ad together. Incumbent Republican Gov. Spencer Cox and his Democratic challenger, Chris Peterson, appeared in the same spot to note they were both “dedicated to the American values of liberty, democracy, and justice for all people,” as Cox said, and that “our common values transcend our political differences,” as Peterson put it.

Such reassurances are unusual, however, and can be overwhelmed by other messages. Indeed, a new study co-authored by an MIT scholar finds that U.S. citizens likely overestimate how much their political opponents seek to undermine democracy — a finding presenting both bad news and good news.

One ominous implication of the research is that by believing their political opponents wish to curtail democracy, some partisans will then justify the erosion of democratic norms by their own side.

“This can result in a death spiral for democracy,” says Alex “Sandy” Pentland, an MIT professor and co-author of a new paper detailing the results, which are based on surveys and experiments involving thousands of Americans.

As the paper notes, false claims about the 2020 election by former president Donald Trump and others, as well as false news reports about purported election malfeasance, have made such beliefs common among Republicans; at the same time, Democratic Party leaders publicly emphasize that many Republican-backed measures imperil democracy.

Yet the more positive implication of the findings is that partisans on both sides largely avow that they support democracy, to a greater degree than their rivals think, and seem receptive to hearing that their political opponents do as well — perhaps through approaches like the joint Utah ad.

Pentland adds: “We find that making people aware of how much voters on each side support democracy has the effect of rather dramatically lowering the temperature on toxic polarization, and even changing which candidates people say they will vote for. Knowing that opposing groups also support democracy may be a core requirement for maintaining a strong democracy.” For this reason, he notes, “There is also hope in these findings, and that is that by reducing fear between partisans, we can strengthen democratic institutions.”

The paper, “Why voters who value democracy participate in democratic backsliding,” appears in Nature Human Behavior. The authors are Alia Braley, a doctoral candidate in political science at the University of California at Berkeley; Gabriel Lenz, a professor of political science at UC Berkeley; Dhaval Adjodah ’11, SM ’13, PhD ’19, a fellow at the philanthropic research initiative Schmidt Futures and a former research scientist at MIT; Hossein Rahnama, an associate professor at Toronto Metropolitan University and a former visiting professor at the MIT Media Lab; and Pentland, professor of media arts and sciences and the Toshiba Professor at the Media Lab.

To conduct the study, the researchers conducted an online survey and then a pair of experiments, using the Lucid and Mechanical Turk platforms. The survey asked a representative sample of 1,973 U.S. citizens to estimate their political opponents’ willingness to subvert democratic norms, and to state their own willingness to do so, when presented with seven types of nondemocratic actions, such as limiting polling stations, banning rallies, and more.

Overall, the results were similar between members of the two main U.S. parties; Democrats estimated that Republicans would be willing to subvert 5.0 democratic norms on average, while being willing to subvert 1.5 themselves; Republicans estimated Democrats would be willing to subvert 5.2 democratic norms on average, while being willing to subvert 1.2 themselves.

Individuals who estimated their opponents were relatively more ready to stop democratic practices were, themselves, more willing to abandon those norms. The scholars believe this tendency is exacerbated by the debunked claims of leaders like Trump.

In general, people “have overlooked the significance of would-be authoritarians’ frequent claims that their opponents are breaking democratic rules,” Lenz says, alluding to similar claims by leaders such as former president Jair Bolsonaro in Brazil. He adds: “It causes their supporters, in this case Republicans, to tolerate the erosion of democratic norms by politicians like Trump. Instead of perceiving Trump as undermining democracy, they view him as leveling a playing field they believe has already been heavily tilted against them.”

However, the research also shows that people are receptive to valid information showing that their opponents are intent on upholding democratic practices. In an experiment involving 2,545 U.S. citizens, the researchers queried respondents about their perceptions of norm-breaking, then divided them into treatment and control groups, and gave the first group feedback about how their perceptions aligned with the facts.

On a scale from 0 to 1, using the same seven cases from the initial survey, participants who had received fact-based feedback only rated their political opponents’ willingness to subvert democratic norms at 0.40, whereas those given no factual feedback rated their opponents’ intent to subvert democratic norms at 0.64. People in the treatment group were less willing to break democratic norms themselves, and, in hypothetical election scenarios, were less willing to vote for candidates who support the subversion of norms.

In still another online experiment, this time again involving 1,973 U.S. citizens, the researchers then changed the format of the previous experiment to reduce the chances that respondents could anticipate follow-up questions. The results were broadly similar, although, in an additional observation, the scholars found that both Republican and Democratic participants reporting higher levels of ethnic antagonism were more likely to support subverting democratic norms.

Overall, the results of the two follow-on experiments suggest that better information about political opponents helps raise confidence and trust levels; when Democrats see that many Republicans value democracy, and when Republicans see that many Democrats value democracy, there is at least an opening for people to avoid the downward spiral the U.S. may be facing. 

“This work has important implications in a time when many people are looking for solutions to toxic polarization,” Braley says. “People will become more willing to uphold democracy when they are less afraid of the other side."

She adds: “One possibility when facing a politician like Trump is to launch a counter-narrative aimed at Republicans, showing that Democrats actually will uphold democracy. According to our research, this should make Republicans more willing to hold their representatives accountable."

Exactly how to do that at a large scale is unclear. While the ad by the Utah candidates in 2020 was probably effective, it can be hard to reach large numbers of citizens. The researchers — like their colleagues elsewhere in the U.S. — say they will have to continue studying which approaches seem to help bolster bipartisan support for democracy.

“Our next step is to take these findings and test the best mechanisms for reducing these mutual fears between partisans in real-world contexts,” Braley says.

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A telescope’s last view

More than 5,000 planets are confirmed to exist beyond our solar system. Over half were discovered by NASA’s Kepler Space Telescope, a resilient observatory that far outlasted its original planned mission. Over nine and a half years, the spacecraft trailed the Earth, scanning the skies for periodic dips in starlight that could signal the presence of a planet crossing in front of its star.

In its last days, the telescope kept recording the brightness of stars as it was running out of fuel. On Oct. 30, 2018, its fuel tanks depleted, the spacecraft was officially retired.

Now, astronomers at MIT and the University of Wisconsin at Madison, with the help of citizen scientists, have discovered what may be the last planets that Kepler gazed upon before going dark.

The team combed through the telescope’s last week of high-quality data and spotted three stars, in the same part of the sky, that appeared to dim briefly. The scientists determined that two of the stars each host a planet, while the third hosts a planet “candidate” that has yet to be verified.

The two validated planets are K2-416 b, a planet that is about 2.6 times the size of the Earth and that orbits its star about every 13 days, and K2-417 b, a slightly larger planet that is just over three times Earth’s size and that circles its star every 6.5 days. For their size and proximity to their stars, both planets are considered “hot mini-Neptunes.” They are located about 400 light years from Earth.

The planet candidate is EPIC 246251988 b — the largest of the three worlds at almost four times the size of the Earth. This Neptune-sized candidate orbits its star in around 10 days, and is slightly farther away, 1,200 light years from Earth.

“We have found what are probably the last planets ever discovered by Kepler, in data taken while the spacecraft was literally running on fumes,” says Andrew Vanderburg, assistant professor of physics in MIT’s Kavli Institute for Astrophysics and Space Research. “The planets themselves are not particularly unusual, but their atypical discovery and historical importance makes them interesting.”

The team has published their discovery today in the journal Monthly Notices of the Royal Astronomical Society. Vanderburg’s co-authors are lead author Elyse Incha, at the University of Wisconsin at Madison, and amateur astronomers Tom Jacobs and Daryll LaCourse, along with scientists at NASA, the Center for Astrophysics of Harvard and the Smithsonian, and the University of North Carolina at Chapel Hill.

Data squeeze

In 2009, NASA launched the Kepler telescope into space, where it followed the Earth’s orbit and continuously monitored millions of stars in a patch of the northern sky. Over four years, the telescope recorded the brightness of over 150,000 stars, which astronomers used to discover thousands of possible planets beyond our solar system.

Kepler kept observing beyond its original three-and-a-half-year mission, until May 2013, when the second of four reaction wheels failed. The wheels served as the spacecraft’s gyroscopes, helping to keep the telescope pointed at a particular point in the sky. Kepler’s observations were put on pause while scientists searched for a fix.

One year later, Kepler restarted as “K2,” a reworked mission that used the sun’s wind to balance the unsteady spacecraft in a way that kept the telescope relatively stable for a few months at a time — a period called a campaign. K2 went on for another four years, observing over half a million more stars before the spacecraft finally ran out of fuel during its 19th campaign. The data from this last campaign comprised only a week of high-quality observations and another 10 days of noisier measurements as the spacecraft rapidly lost fuel.

“We were curious to see whether we could get anything useful out of this short dataset,” Vanderburg says. “We tried to see what last information we could squeeze out of it.”

By eye

Vanderburg and Incha presented the challenge to the Visual Survey Group, a team of amateur and professional astronomers who hunt for exoplanets in satellite data. They search by eye through thousands of recorded light curves of each star, looking for characteristic dips in brightness that signal a “transit,” or the possible crossing of a planet in front of its star.

The citizen scientists are especially suited to combing through short datasets such as K2’s very last campaign.

“They can distinguish transits from other wacky things like a glitch in the instrument,” Vanderburg says. “That’s helpful especially when your data quality begins to suffer, like it did in K2’s last bit of data.”

The astronomers spent a few days efficiently looking through the light curves that Kepler recorded from about 33,000 stars. The team worked with only a week’s worth of high-quality data from the telescope before it began to lose fuel and focus. Even in this short window of data, the team was able to spot a single transit in three different stars.

Incha and Vanderburg then looked at the telescope’s very last, lower-quality observations, taken in its last 11 days of operation, to see if they could spot any additional transits in the same three stars — evidence that a planet was periodically circling its star.

During this 11-day period, as the spacecraft was losing fuel, its thrusters fired more erratically, causing the telescope’s view to drift. In their analysis, the team focused on the region of each star’s light curves between thruster activity, to see if they could spot any additional transits in these less data-noisy moments.

This search revealed a second transit for K2-416 b and K2-417 b, validating that they each host a planet. The team also detected a similar dip in brightness for K2-417 b in data taken of the same star by NASA’s Transiting Exoplanet Survey Satellite (TESS), a mission that is led and operated by MIT. Data from TESS helped to confirm the planet candidate around this star.      

“Those two are pretty much, without a doubt, planets,” Incha says. “We also followed up with ground-based observations to rule out all kinds of false positive scenarios for them, including background star interference, and close-in stellar binaries.”

“These are the last chronologically observed planets by Kepler, but every bit of the telescope’s data is incredibly useful,” Incha says. “We want to make sure none of that data goes to waste, because there are still a lot of discoveries to be made.”

This research was supported, in part, by MIT, NASA, and the University of Wisconsin Undergraduate Academic Awards.

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Pamela Z: Singing the body electric

In the mid-1980s, artist Pamela Z was working at Tower Records on Columbus Street in San Francisco, where one of her jobs was replacing pages in the store’s Phonolog, an enormous alphabetized directory of all the music available at the time, which formed a kind of bible of pop. When she ripped one loose-leafed sheet from the book, she noticed that all the titles on that sheet began with “you.” You stayed on my mind. You stole my heart. You stepped out of a dream. When spoken, the repetition of the words had an undulating, musical quality. It soon found its way into one of her electronic compositions, the found poetry processed with four-track cassette recorder, the simple list of phrases made incantatory through the looped rhythms of the human voice. 

Pamela Z, the recipient of this year’s Eugene McDermott Award in the Arts at MIT, has become renowned for her pioneering work in live digital looping and interactive audio/video performance. Her voice is the centerpiece of these performances, manipulating and layering recordings in real time to produce complex sonic textures. Through the use of experimental extended vocal techniques, operatic bel canto, multimedia and sampled sounds, digital processing, and wireless MIDI controllers that use physical gestures to manipulate sound, Z creates immersive and magical aural collages.  

While her first tool was a hollow-body guitar, which Z would use to accompany herself in clubs at night as she sang opera arias by day, her art changed once she discovered a digital delay in the '80s. “I came home from the music store, hooked everything up and started singing through it,” she remembers. “I never went to sleep that night because I was just looping my voice over and over again, and discovering beautiful properties of repetition, of layering, of being able to harmonize with myself, of being able to make complicated things by feeding back into the delay as I added more and more layers. I really think that I was never the same after that.” Having new technological tools, she said, allowed her to listen in new ways, discovering all the polyphonic dimensions within a single sound. 

In the decades since, Z has sought possibility in the objects of everyday life — Slinkies, plastic water jugs, hair clippers, and power tools — working these found materials into densely layered compositions, woven through with her classically trained soprano. The sound of the freight elevator in her loft, a glass falling on the floor, or a fragment of conversation can all become defamiliarized and creatively repurposed in the work. What begins as a simple act of noticing, then, in the process of composition, evolves into much larger meditations on the human condition. 

In the 2010 work “Baggage Allowance,” for example, the experience of hauling suitcases through airport security expanded into a philosophical investigation of memory, belonging, and what it means to carry things with you. “Her process is ‘Let's explore a subject area, or take these objects and put them together. Let's take this language and cut it up, letting its meaning evolve through examining it in what seems to be an objective way,'” says Evan Ziporyn, Kenan Sahin Distinguished Professor of Music and faculty director of the Center for Art, Science and Technology, “and then ending up with something very subjective, personal, and moving.”

At MIT, Z worked with students on their own compositions incorporating found sounds. The students, says Ziporyn, submitted their sounds two hours before the start of class. By the time the group met with Z, she had not only listened to each one but found in each something unique. What she modeled for the students, says Ziporyn, was a form of deep attention to a world swelling with sonic potential. “It was a good lesson in the idea of recontextualizing a sound that you find out in the world somewhere,” says Z, “And just by the act of recording it and listening to it on its own, you've already begun making a piece.” By the last session, she says, each student “had made really beautifully sculpted sound pieces.” 

Z often performs her compositions with sensor-based, gesture-controlled MIDI instruments, wearing pieces of hardware as jewelry. Her gloved hands, like a conductor’s, summon sound from empty air. As part of her residency, Z performed a suite of her compositions for solo voice and electronics, ranging from early groundbreaking works to recently premiered ensemble pieces. Joining her, among musicians from the Boston area, were pianist Sarah Cahill, violinist Kate Stenberg, and flutist and MIT student Sara Simpson. Ziporyn conducted one of the pieces. For Z, the creation of the performance — its movements, feeling, and visuals — is deeply integrated into the process of composing itself. “It seems like magic — one voice becoming many, bird calls emerging and dispersing with the wave of a palm — but it’s really a multilayered virtuosity,” writes Ziporyn, “imbuing every aspect of Pamela’s work, smoothly masked by her grace as a performer. Pamela works with interactive music systems designer Donald Swearingen to develop the instruments and designs her own hardware, then learns how to use both as second nature.”

If some artworks fetishize the novelty of new technology, while others might dismiss it as somehow removed from what we perceive as human, Z has found a way to seamlessly combine digital tools with the ancient arts of performance, the manipulated sounds of the machine coalescing with the music of her own body. 

Z’s expressive form of electronic music, Ziporyn says, reflects how we live today. It reflects the condition of living in a world mediated by technology, a world of bits and atoms, where the digital and analog are continually overlapping zones of experience. Her work, he says, defies any artificial separation between the so-called natural and the synthetic. And, as Z reminds us, we ourselves are electric: Everything we do, think, and feel is powered by the electrical currents coursing throughout the body. Her performances, says Ziporyn, are arguments for accepting that both the material and digital are part of what it means to think, feel, sense, and express — part of what it means to be human.

Presented by the Council for the Arts at MIT, the Eugene McDermott Award in the Arts at MIT was first established by Margaret McDermott in honor of her husband, a legacy that is now carried on by their daughter Mary McDermott Cook. The Eugene McDermott Award plays a unique role at the Institute by bringing the MIT community together to support MIT’s principal arts organizations: the Department of Architecture; the Art, Culture and Technology program; the Center for Art, Science and Technology; the List Visual Arts Center; the MIT Museum; and the Music and Theater Arts Section.

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Even lawyers don’t like legalese

It’s no secret that legal documents are notoriously difficult to understand, causing headaches for anyone who has had to apply for a mortgage or review any other kind of contract. A new MIT study reveals that the lawyers who produce these documents don’t like them very much either.

The researchers found that while lawyers can interpret and recall information from legal documents better than nonlawyers, it’s still easier for them to understand the same documents when translated into “plain English.” Lawyers also rated plain English contracts as higher-quality overall, more likely to be signed by a client, and equally enforceable as those written in “legalese.”

The findings suggest that while impenetrable styles of legal writing are well-entrenched, lawyers may be amenable to changing the way such documents are written.

“No matter how we asked the questions, the lawyers overwhelmingly always wanted plain English,” says Edward Gibson, an MIT professor of brain and cognitive sciences and the senior author of the study. “People blame lawyers, but I don’t think it’s their fault. They would like to change it, too.”

Eric Martínez, an MIT graduate student and licensed attorney, is the lead author of the new study, which appears this week in the Proceedings of the National Academy of Sciences. Frank Mollica, a former visiting researcher at MIT who is now a lecturer in computational cognitive science at the University of Edinburgh, is also an author of the paper.

Parsing legal language

Since at least the 1970s, when President Richard Nixon declared that federal regulations should be written in “layman’s terms,” efforts have been made to try to simplify legal documents. However, another study by Martínez, Mollica, and Gibson, not yet published, suggests that legal language has changed very little since that time.

The MIT team began studying the structure and comprehensibility of legal language several years ago, when Martínez, who became interested in the topic as a student at Harvard Law School, joined Gibson’s lab as a research assistant and then a PhD student.

In a study published last year, Gibson, Martínez, and Mollica used a text analysis tool to compare legal documents to many other types of texts, including newspapers, movie scripts, and academic papers. Among the features identified as more common in legal documents, one stood out as making the texts harder to read: long definitions inserted in the middle of sentences.

Linguists have previously shown that this type of structure, known as center-embedding, makes text much more difficult to understand. When the MIT team tested people on their ability to understand and recall the meaning of a legal text, their performance improved significantly when center-embedded structures were replaced with more straightforward sentences, with terms defined separately.

“For some reason, legal texts are filled with these center-embedded structures,” Gibson says. “In normal language production, it’s not natural to either write like that or to speak like that.”

Those findings raised a question that Gibson and his colleagues set out to explore in their new study: Why do lawyers write documents with such an impenetrable style? To get at that question, the researchers decided to perform a similar study using lawyers as their test subjects.

Before beginning the study, the researchers came up with five possible explanations for why lawyers produce this kind of legal text. The most likely possibility, Gibson believed, was one he calls “the curse of knowledge.” This means that lawyers are so skilled at writing and reading legal documents, they don’t realize how difficult they are for everyone else.

Other possible explanations included that lawyers simply copy and paste from existing templates; that they write in legalese to make themselves sound more “lawyerly” to their colleagues; that they wish to preserve a monopoly on legal services and justify their fees; or that legal information is so complex that it can only be conveyed in very prescribed ways.

To explore these hypotheses, the researchers recruited a group of more than 100 lawyers, from a diverse range of law schools and law firms, and asked them to carry out the same comprehension tasks that they had nonlawyers perform in their 2022 study.

They found that lawyers, not surprisingly, were much better at parsing and recalling information from legal documents. As shown in the 2022 study, nonlawyers could typically recall about 38 percent of what they read in a legal document, and their success rate went up to between 45 and 50 percent with plain English versions of those texts. When faced with legal documents, lawyers could remember about 45 percent of what they read, and that number jumped to more than 50 percent when they were asked to read the simplified versions of the documents.

This suggests that legal language represents a stumbling block for lawyers as well as nonlawyers. The finding also refutes the curse of knowledge hypothesis, because if that hypothesis were correct, then lawyers would be equally good at recalling both styles of information.

“Lawyers are much better, it turns out, at reading these contracts either in plain English or in legalese and understanding them and answering questions about them. However, they have a much harder time with the legalese, just like regular people,” Gibson says.

“Using plain language would be beneficial for everybody, given that legalese is harder for both lawyers and nonlawyers to understand,” Martínez adds.

Simpler is better

In a second set of experiments, the researchers evaluated lawyers’ attitudes toward legal documents and simplified versions of those documents. After recruiting another group of more than 100 lawyers, the researchers asked them to rate the documents on a variety of criteria, including enforceability, willingness to sign such a document, overall quality, and the likelihood that a client would agree to the terms. The lawyers were also asked if they would hire the person who wrote each of the documents.

Surprisingly, the lawyers rated the plain English documents as being higher quality than the original documents, and more likely to be agreed to by themselves and their clients. They also rated them to be equally enforceable as the original legal documents, and said they would be more likely to hire the person who wrote the plain English version.

These findings essentially ruled out all of explanations that the researchers had considered, except for the copy and paste hypothesis: the idea that lawyers are copying old contracts and editing them for each new use. One possible reason why that has become a common practice is that lawyers want to keep using contracts that have been previously demonstrated to be enforceable.

Over time, these contracts may have become increasingly complex as lawyers amended them for specific situations by adding center-embedded clauses.

“Maybe an original contract was written for one set of people, and if you want it to be more restricted, you add a whole new definition of that restriction. You can add it within a sentence, and that ends up being center-embedded,” Gibson says. “That’s our guess. We don’t know the details of how, and that’s what we’re working on right now.”

The research was funded by MIT’s Department of Brain and Cognitive Sciences.

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MIT students Rupert Li and Audrey Xie named 2023-24 Goldwater Scholars

MIT undergraduates Rupert Li and Audrey Xie have been selected to receive Barry Goldwater Scholarships for the 2023-24 academic year. From an estimated pool of more than 5,000 college sophomores and juniors, nearly 1,300 students were nominated by 427 academic institutions to compete for the scholarship, with Li and Xie representing two of only 413 recipients selected based on academic merit.

Since 1989, the Barry Goldwater Scholarship and Excellence in Education Foundation has awarded more than 10,000 Goldwater scholarships. The program was designed to foster and encourage outstanding students to pursue research careers in the fields of the natural sciences, engineering, and mathematics. Past Goldwater Scholars have gone on to win an impressive array of prestigious postgraduate fellowships, and most of the 2023-24 scholars, including the two recipients from MIT, plan to obtain a doctoral degree in their area of research.

Rupert Li

Rupert Li is a third-year student majoring in mathematical sciences. His research interests center on the field of discrete mathematics, and his current work utilizes a variety of mathematical tools to explore high-dimensional versions of the famous “sphere-packing problem,” as well as coding theory.

Since spring 2021, Li has been supervised by Henry Cohn, an adjunct professor in the Department of Mathematics. In a letter recommending Li for the Barry Goldwater Scholarship, Cohn speaks at length about his insight and creativity. “What I find particularly impressive about Rupert’s work is how fresh and innovative it is,” Cohn writes. “He isn’t just making incremental progress on other people’s ideas, but rather exploring old topics from a new and different perspective.”

Li, for his part, is deeply thankful for the guidance and support Cohn has provided. “He has opened my eyes to incredible areas of math,” Li says.

Li is also grateful to his advisor, Professor Julee Kim, for her mentorship and guidance over the past few years. He also extends his thanks to Joe Gallian at the University of Minnesota Duluth, Jim Propp at the University of Massachusetts Lowell, and Nike Sun, an associate professor in MIT’s Department of Mathematics. Finally, he acknowledges the organizers of the MIT PRIMES-USA program, specifically head mentor Tanya Khovanova, lecturer Slava Gerovitch, Professor Pavel Etingof, and RSA Professor of Mathematics and Department Head Michel Goemans.

Li plans to pursue a PhD in mathematics and hopes to one day conduct research in mathematics and teach at the university level.

Audrey Xie

Audrey Xie is a third-year undergrad majoring in mathematics and computer science. Her research focuses on using gradient-based optimizers to train neural networks.

In January 2020, Xie began doing work in the lab of Jonathan Ragan-Kelly, the Esther and Harold E. Edgerton Assistant Professor of Electrical Engineering and Computer Science. “It has been obvious almost from the start that Audrey is destined for a highly successful research career,” Ragan-Kelly writes in his recommendation letter. “She is intelligent, driven, creative, and analytically and empirically rigorous.”

During her first semester working with Ragan-Kelly, Xie designed and ran numerous novel experiments to assess a more efficient method for tuning hyperparameters, which are needed to optimize neural networks. Xie then compiled her results and co-authored a paper that was accepted to ​​the Conference and Workshop on Neural Information Processing Systems, the most prestigious conference in the field of machine learning.

Xie plans to pursue a PhD in computer science and hopes to one day conduct research in machine learning and teach at the university level.

The Barry Goldwater Scholarship and Excellence in Education Program was established by the U.S. Congress in 1986 to honor Senator Barry Goldwater, a soldier and national leader who served the country for 56 years. Awardees receive scholarships of up to $7,500 a year to cover costs related to tuition, room and board, fees, and books.

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Celebrating the impact of IDSS

The “interdisciplinary approach” is something that has been lauded for decades for its ability to break down silos and create new integrated approaches to research.

For Munther Dahleh, founding director of the MIT Institute for Data, Systems, and Society (IDSS), showing the community that data science and statistics can transcend individual disciplines and form a new holistic approach to addressing complex societal challenges has been crucial to the institute's success.

“From the very beginning, it was critical that we recognized the areas of data science, statistics, AI, and, in a way, computing, as transdisciplinary,” says Dahleh, who is the William A. Coolidge Professor in Electrical Engineering and Computer Science. “We made that point over and over — these are areas that embed in your field. It is not ours; this organization is here for everyone.”

On April 14-15, researchers from across and beyond MIT joined together to celebrate the accomplishments and impact IDSS has had on research and education since its inception in 2015. Taking the place of IDSS’s annual statistics and data science conference SDSCon, the celebration also doubled as a way to recognize Dahleh for his work creating and executing the vision of IDSS as he prepares to step down from his director position this summer.

In addition to talks and panels on statistics and computation, smart systems, automation and artificial intelligence, conference participants discussed issues ranging from climate change, health care, and misinformation. Nobel Prize winner and IDSS affiliate Professor Esther Duflo spoke on large scale immunization efforts, former MLK Visiting Professor Craig Watkins joined a panel on equity and justice in AI, and IDSS Associate Director Alberto Abadie discussed synthetic controls for policy evaluation. Other policy questions were explored through lightning talks, including those by students from the Technology and Policy Program (TPP) within IDSS.

A place to call home

The list of IDSS accomplishments over the last eight years is long and growing. From creating a home for 21^st century statistics at MIT after other unsuccessful attempts, to creating a new PhD preparing the trilingual student who is an expert in data science and social science in the context of a domain, to playing a key role in determining an effective process for Covid testing in the early days of the pandemic, IDSS has left its mark on MIT. More recently, IDSS launched an initiative using big data to help effect structural and normative change toward racial equity, and will continue to explore societal challenges through the lenses of statistics, social science, and science and engineering.

“I'm very proud of what we've done and of all the people who have contributed to this. The leadership team has been phenomenal in their commitment and their creativity,” Dahleh says. “I always say it doesn't take one person, it takes the village to do what we have done, and I am very proud of that.”

Prior to the institute’s formation, Dahleh and others at MIT were brought together to answer one key question: How would MIT prepare for the future of systems and data?

“Data science is a complex area because in some ways it's everywhere and it belongs to everyone, similar to statistics and AI,” Dahleh says “The most important part of creating an organization to support it was making it clear that it was an organization for everyone.” The response the team came back with was to build an Institute: a department that could cross all other departments and schools.

While Dahleh and others on the committee were creating this blueprint for the future, the events that would lead early IDSS hires like Caroline Uhler to join the team were also beginning to take shape. Uhler, now an MIT professor of computer science and co-director of the Eric and Wendy Schmidt Center at the Broad Institute, was a panelist at the celebration discussing statistics and human health.

In 2015, Uhler was a faculty member at the Institute of Science and Technology in Austria looking to move back to the U.S. “I was looking for positions in all different types of departments related to statistics, including electrical engineering and computer science, which were areas not related to my degree,” Uhler says. “What really got me to MIT was Munther’s vision for building a modern type of statistics, and the unique opportunity to be part of building what statistics should be moving forward.”

The breadth of the Statistics and Data Science Center has given it a unique and a robust character that makes for an attractive collaborative environment at MIT. “A lot of IDSS’s impact has been in giving people like me a home,” Uhler adds. “By building an institute for statistics that is across all schools instead of housed within a single department, it has created a home for everyone who is interested in the field.”

Filling the gap

For Ali Jadbabaie, former IDSS associate director and another early IDSS hire, being in the right place at the right time landed him in the center of it all. A control theory expert and network scientist by training, Jadbabaie first came to MIT during a sabbatical from his position as a professor at the University of Pennsylvania.

“My time at MIT coincided with the early discussions around forming IDSS and given my experience they asked me to stay and help with its creation,” Jadbabaie says. He is now head of the Department of Civil and Environmental Engineering at MIT, and he spoke at the celebration about a new MIT major in climate system science and engineering.

A critical early accomplishment of IDSS was the creation of a doctoral program in social and engineering systems (SES), which has the goal of educating and fostering the success of a new type of PhD student, says Jadbabaie.

“We realized we had this opportunity to educate a new type of PhD student who was conversant in the math of information sciences and statistics in addition to an understanding of a domain — infrastructures, climate, political polarization — in which problems arise,” he says. “This program would provide training in statistics and data science, the math of information sciences and a branch of social science that is relevant to their domain.”

“SES has been filling a gap,” adds Jadbabaie. “We wanted to bring quantitative reasoning to areas in social sciences, particularly as they interact with complex engineering systems.”

“My first year at MIT really broadened my horizon in terms of what was available and exciting,” says Manxi Wu, a member of the first cohort of students in the SES program after starting out in the Master of Science in Transportation (MST) program. “My advisor introduced me to a number of interesting topics at the intersection of game theory, economics, and engineering systems, and in my second year I realized my interest was really about the societal scale systems, with transportation as my go-to application area when I think about how to make an impact in the real world.”

Wu, now an assistant professor in the School of Operations Research and Information Engineering at Cornell, was a panelist at the Celebration’s session on smart infrastructure systems. She says that the beauty of the SES program lies in its ability to create a common ground between groups of students and researchers who all have different applications interests but share an eagerness to sharpen their technical skills.

“While we may be working on very different application areas, the core methodologies, such as mathematical tools for data science and probability optimization, create a common language,” Wu says. “We are all capable of speaking the technical language, and our diversified interests give us even more to talk about.”

In addition to the PhD program, IDSS has helped bring quality MIT programming to people around the globe with its MicroMasters Program in Statistics and Data Science (SDS), which recently celebrated the certification of over 1,000 learners. The MicroMasters is just one offering in the newly-minted IDSSx, a collection of online learning opportunities for learners at different skill levels and interests.

“The impact of branding what MIT-IDSS does across the globe has been great,” Dahleh says. “In addition, we’ve created smaller online programs for continued education in data science and machine learning, which I think is also critical in educating the community at large.”

Hopes for the future

Through all of its accomplishments, the core mission of IDSS has never changed.

“The belief was always to create an institute focused on how data science can be used to solve pressing societal problems,” Dahleh says. “The organizational structure of IDSS as an MIT Institute has enabled it to promote data and systems as a transdiciplinary area that embeds in every domain to support its mission. This reverse ownership structure will continue to strengthen the presence of IDSS in MIT and will make it an essential unit within the Schwarzman College of Computing.”

As Dahleh prepares to step down from his role, and Professor Martin Wainwright gets ready to fill his (very big) shoes as director, Dahleh’s colleagues say the real key to the success of IDSS all started with his passion and vision.

“Creating a new academic unit within MIT is actually next to impossible,” Jadbabaie says. “It requires structural changes, as well as someone who has a strong understanding of multiple areas, who knows how to get people to work together collectively, and who has a mission."

“The most important thing is that he was inclusive,” he adds. “He didn't try to create a gate around it and say these people are in and these people are not. I don't think this would have ever happened without Munther at the helm.”

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River erosion can shape fish evolution, study suggests

If we could rewind the tape of species evolution around the world and play it forward over hundreds of millions of years to the present day, we would see biodiversity clustering around regions of tectonic turmoil. Tectonically active regions such as the Himalayan and Andean mountains are especially rich in flora and fauna due to their shifting landscapes, which act to divide and diversify species over time.

But biodiversity can also flourish in some geologically quieter regions, where tectonics hasn’t shaken up the land for millennia. The Appalachian Mountains are a prime example: The range has not seen much tectonic activity in hundreds of millions of years, and yet the region is a notable hotspot of freshwater biodiversity.

Now, an MIT study identifies a geological process that may shape the diversity of species in tectonically inactive regions. In a paper appearing today in Science, the researchers report that river erosion can be a driver of biodiversity in these older, quieter environments.

They make their case in the southern Appalachians, and specifically the Tennessee River Basin, a region known for its huge diversity of freshwater fishes. The team found that as rivers eroded through different rock types in the region, the changing landscape pushed a species of fish known as the greenfin darter into different tributaries of the river network. Over time, these separated populations developed into their own distinct lineages.

The team speculates that erosion likely drove the greenfin darter to diversify. Although the separated populations appear outwardly similar, with the greenfin darter’s characteristic green-tinged fins, they differ substantially in their genetic makeup. For now, the separated populations are classified as one single species. 

“Give this process of erosion more time, and I think these separate lineages will become different species,” says Maya Stokes PhD ’21, who carried out part of the work as a graduate student in MIT’s Department of Earth, Atmospheric and Planetary Sciences (EAPS).

The greenfin darter may not be the only species to diversify as a consequence of river erosion. The researchers suspect that erosion may have driven many other species to diversify throughout the basin, and possibly other tectonically inactive regions around the world.

“If we can understand the geologic factors that contribute to biodiversity, we can do a better job of conserving it,” says Taylor Perron, the Cecil and Ida Green Professor of Earth, Atmospheric, and Planetary Sciences at MIT.

The study’s co-authors include collaborators at Yale University, Colorado State University, the University of Tennessee, the University of Massachusetts at Amherst, and the Tennessee Valley Authority (TVA). Stokes is currently an assistant professor at Florida State University.

Fish in trees

The new study grew out of Stokes’ PhD work at MIT, where she and Perron were exploring connections between geomorphology (the study of how landscapes evolve) and biology. They came across work at Yale by Thomas Near, who studies lineages of North American freshwater fishes. Near uses DNA sequence data collected from freshwater fishes across various regions of North America to show how and when certain species evolved and diverged in relation to each other.

Near brought a curious observation to the team: a habitat distribution map of the greenfin darter showing that the fish was found in the Tennessee River Basin — but only in the southern half. What’s more, Near had mitochondrial DNA sequence data showing that the fish’s populations appeared to be different in their genetic makeup depending on the tributary in which they were found.

To investigate the reasons for this pattern, Stokes gathered greenfin darter tissue samples from Near’s extensive collection at Yale, as well as from the field with help from TVA colleagues. She then analyzed DNA sequences from across the entire genome, and compared the genes of each individual fish to every other fish in the dataset. The team then created a phylogenetic tree of the greenfin darter, based on the genetic similarity between fish.

From this tree, they observed that fish within a tributary were more related to each other than to fish in other tributaries. What’s more, fish within neighboring tributaries were more similar to each other than fish from more distant tributaries.

“Our question was, could there have been a geological mechanism that, over time, took this single species, and splintered it into different, genetically distinct groups?” Perron says.

A changing landscape

Stokes and Perron started to observe a “tight correlation” between greenfin darter habitats and the type of rock where they are found. In particular, much of the southern half of the Tennessee River Basin, where the species abounds, is made of metamorphic rock, whereas the northern half consists of sedimentary rock, where the fish are not found.

They also observed that the rivers running through metamorphic rock are steeper and more narrow, which generally creates more turbulence, a characteristic greenfin darters seem to prefer. The team wondered: Could the distribution of greenfin darter habitat have been shaped by a changing landscape of rock type, as rivers eroded into the land over time?

To check this idea, the researchers developed a model to simulate how a landscape evolves as rivers erode through various rock types. They fed the model information about the rock types in the Tennessee River Basin today, then ran the simulation back to see how the same region may have looked millions of years ago, when more metamorphic rock was exposed.

They then ran the model forward and observed how the exposure of metamorphic rock shrank over time. They took special note of where and when connections between tributaries crossed into non-metamorphic rock, blocking fish from passing between those tributaries. They drew up a simple timeline of these blocking events and compared this to the phylogenetic tree of diverging greenfin darters. The two were remarkably similar: The fish seemed to form separate lineages in the same order as when their respective tributaries became separated from the others.

“It means it’s plausible that erosion through different rock layers caused isolation between different populations of the greenfin darter and caused lineages to diversify,” Stokes says.

“This study is highly compelling because it reveals a much more subtle but powerful mechanism for speciation in passive margins,” says Josh Roering, professor of Earth sciences at the University of Oregon, who was not involved in the study. “Stokes and Perron have revealed some of the intimate connections between aquatic species and geology that may be much more common than we realize.”

This research was supported, in part, by the Terra Catalyst Fund and the U.S. National Science Foundation through the AGeS Geochronology Program and the Graduate Research Fellowship Program. While at MIT, Stokes received support through the Martin Fellowship for Sustainability and the Hugh Hampton Young Fellowship.

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Gravitational-wave detectors start next observing run to explore the secrets of the universe

The following article is adapted from a press release issued by the Laser Interferometer Gravitational-wave Observatory (LIGO) Laboratory, in collaboration with the LIGO Scientific Collaboration and Virgo Collaboration. LIGO is funded by the National Science Foundation (NSF) and operated by Caltech and MIT, which conceived and built the project.

On Wednesday, the LIGO-Virgo-KAGRA (LVK) collaboration began a new observing run with upgraded instruments, new and even more accurate signal models, and more advanced data analysis methods. The LVK collaboration consists of scientists across the globe who use a network of observatories — LIGO in the United States, Virgo in Europe, and KAGRA in Japan — to search for gravitational waves, or ripples in space-time, generated by colliding black holes and other extreme cosmic events.

This observing run, known as O4, promises to take gravitational-wave astronomy to the next level. Beginning on May 24 and lasting 20 months, including up to two months of commissioning breaks, O4 will be the most sensitive search yet for gravitational waves. LIGO will resume operations May 24, while Virgo will join later in the year. KAGRA will join for one month, beginning May 24, rejoining later in the run after some upgrades. 

“Thanks to the work of more than a thousand people around the world over the last few years, we’ll get our deepest glimpse of the gravitational-wave universe yet,” says Jess McIver, the deputy spokesperson for the LIGO Scientific Collaboration (LSC). “A greater reach means we will learn more about black holes and neutron stars and increases the chances we find something new. We’re very excited to see what’s out there.”

The Virgo detector will continue commissioning activities in order to increase its sensitivity before joining O4 later this year. "Over the past few months we have identified various noise sources and have made good progress in sensitivity, but it is not yet at its design goal," says recently elected Virgo spokesperson Gianluca Gemme. "We are convinced that achieving the best detector sensitivity is the best way to maximize its discovery potential.”

KAGRA is now running with the sensitivity planned for the beginning of O4. Jun'ichi Yokoyama, the chair of KAGRA Scientific Congress, says, "KAGRA is the first 2.5th generation detector in the world which started 20 years after LIGO. We will join O4 for one month and resume commissioning to further improve the sensitivity toward our first detection."

With the detectors’ increased sensitivity, O4 will observe a larger fraction of the universe than previous observing runs. 

This increased sensitivity will result in a higher rate of observed gravitational-wave signals and in the ability to extract more physical information from the data. This increased signal fidelity will improve scientists’ ability to test Einstein’s theory of general relativity and infer the true population of dead stars in the local universe.

"Data from the previous runs have answered some questions but also created new puzzles. We have discovered that the masses of black holes in our binaries seem to include a cluster at roughly 35 solar masses, but we don't quite yet know what astrophysical processes are creating that feature, nor whether there are other ‘bumps’ in the mass distribution. More sources will help," says Salvatore Vitale, an associate professor at MIT, describing the importance of increasing the sensitivity of the gravitational-wave detectors.

The first gravitational-wave signals were detected in 2015. Two years later, LIGO and Virgo detected a merger of two neutron stars, which caused an explosion called a kilonova, subsequently observed by dozens of telescopes around the world. So far, the global network has detected more than 80 black hole mergers, two probable neutron star mergers, and a few events that were most likely black holes merging with neutron stars. During O4, researchers expect to observe even more energetic cosmic events and gain new insights into the nature of the universe.

As in previous observing runs, alerts about gravitational-wave detection candidates will be distributed publicly during O4.

LIGO is funded by the NSF, and operated by Caltech and MIT, which conceived and built the project. Financial support for the Advanced LIGO project was led by NSF with Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council) and Australia (Australian Research Council) making significant commitments and contributions to the project. More than 1,500 scientists from around the world participate in the effort through the LIGO Scientific Collaboration, which includes the GEO Collaboration.

The Virgo Collaboration is currently composed of approximately 850 members from 143 institutions in 15 different (mainly European) countries. The European Gravitational Observatory (EGO) hosts the Virgo detector near Pisa in Italy, and is funded by Centre National de la Recherche Scientifique (CNRS) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, and the National Institute for Subatomic Physics (Nikhef) in the Netherlands.

KAGRA is the laser interferometer with 3-kilometer-arm-length in Kamioka, Gifu, Japan. The host institute is the Institute for Cosmic Ray Research (ICRR), the University of Tokyo, and the project is co-hosted by the National Astronomical Observatory of Japan (NAOJ) and High Energy Accelerator Research Organization (KEK). The KAGRA collaboration is composed of over 480 members from 115 institutes in 17 countries/regions. Resources for researchers are accessible from http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/KAGRA.

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