# Magnet blocks, connect the dots, and the world of modern mathematics

At the Mathematical Sciences Research Institute in Berkely, CA with the Klein quartic sculpture. Photo by Charles Camacho

Charles Camacho, a sixth-year PhD student in the Department of Mathematics at Oregon State University, spends a lot of time thinking about shapes. He describes his research as such: “I study the symmetries of abstract mathematical surfaces made from gluing triangles together.”

Charles explaining his thesis research at the Latinx in the Mathematical Sciences conference at UCLA. Photo by Farida Saleh from the Daily Bruin.

Charles works in a branch of mathematics called topology. Topologists think about shapes and surfaces. There’s a joke among mathematicians that a topologist is someone who can’t tell the difference between a coffee cup and a donut, and there’s some truth to that. It’s not that they can’t see a difference, but that they look past the difference to see the core similarity: both are solid objects punctured with a single hole. Topology as a formal area of mathematics is fairly recent (early 20th century). Topology’s roots go much further back, though, through the streets of Königsberg in the 1700s and to the geometry of the ancient Greeks.

Königsberg bridge problem
There’s a famous puzzle that originated in  Königsberg, Prussia in the 1700s (Königsberg is now Kaliningrad, Russia). The puzzle didn’t originate among mathematicians—but my understanding is that it’s mainly mathematicians that think about the puzzle now. Back then, there were seven bridges crossing the river Preger.

The Bridges of Königsberg (illustration by Leonard Euler, 1736).

The puzzle is this: Is it possible to cross each one of the seven bridges exactly once? (Go on, try it!) In his description of the problem and its solution, Euler said “it neither required the determination of quantities, nor did calculation with quantities help towards its solution.” He was interested in solving this superficially trivial problem because he couldn’t see a way for algebra, counting, or geometry to solve it. This goes against most people’s conception of mathematics—can it really be a math problem if you don’t fill a chalkboard with calculations?

The fact that no one yet had found a way to cross all the bridges without a repeat did not prove that it could not be done. To do that, and thus solve the problem for good, Euler had the insight to try and reduce the problem to its core. Reframing the Königsberg Bridges problem (elements of image from Wikimedia Commons, composited graphic by Daniel Watkins)
Knowing the layout of the city and all of its streets is irrelevant, so we can simplify to a map of just bridges. But even knowing that there is a river and land doesn’t really matter. All we really need is to know is represented in the network on the right (what mathematicians today call a graph). Euler’s solution was this: “If there are more than two regions with an odd number of bridges leading into them, then it can safely be stated that there is no such crossing.” It didn’t matter where the bridges were, it just mattered how many of the possible paths led to each landmass.

With collaborators at a summer research workshop on graph theory. Photo copyright American Mathematical Society

Being a mathematician, Euler wasn’t satisfied just stating a solution to the Königsberg problem. He went further, and generalized: he came up with rules and a solution that would work for any city with any number of bridges. All you have to do is look at the crossings, and note whether there’s an odd number of ways to get there, or an even number of ways. Euler’s method was developed by later mathematicians into graph theory, a branch of mathematics focusing on sets of points and the paths connecting them. Graph theory has a reputation for having many problems that are simple to state, but incredibly difficult to solve conclusively. In this sense, graph theory has a lot in common with geometric toy blocks.

Platonic solids
Charles has a set of magnetic toys in familiar shapes: triangles, squares, pentagons. These shapes are known as regular polygons, which just means that they are shapes composed of straight lines, each of which has the same length. Playing with these, one can hardly help but to arrange them into three-dimensional shapes. Playing with the triangles, you can quickly form a triangular pyramid: a tetrahedron. With six squares, a cube. With eight triangles, an octahedron. And with twelve pentagons, a dodecahedron. Surprisingly, there are only five shapes that can be made this way! Why is this the case? And must this always be the case?

The Platonic Solids: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron. Image copyright Daniel Watkins.

You might notice some other interesting things about these shapes. If you turn a cube while holding the middle of a side, you will see that it looks the same after each turn. It has rotational symmetry. Each of these shapes has multiple axis of symmetry. They can be rotated holding them in different ways and still show symmetry.

As a mathematician, Charles thinks about ways to generalize these ideas. We know that the five Platonic shapes are the only solids that can be formed from regular polygons, but what shapes could be formed if you used slightly different definitions? What if, for example, you used arcs of a circle to form the lines? What can we say about different kinds of surfaces? These shapes are defined on flat planes, like a piece of paper, but we know of lots of other surfaces, like the world we live on, that aren’t perfectly flat.  What kind of symmetry do polygons in these geometries show? Specifically, I wanted to know all the ways that such surfaces can be rotated a given number of times. I generalized previous research on counting symmetries and discovered a formula describing the number of these rotational symmetries,” Charles said.

A topological representation of a four-holed surface with a twelve-fold rotational symmetry (blue arrows indicate which edges are to be glued to make the surface. Graphic copyright Charles Camacho

Tune in to KBVR Corvallis 88.7 FM on Sunday March, 10 at 7 PM to hear more about Charles’s research, his inspirations, and his path to research in mathematics. Stream the show live or catch this episode as a podcast.

# Being the Multilingual, Racialized “Other” in an English Dominated Linguistic Landscape

Jason at the whiteboard

Consider the language and messages you process each day. As you navigate your daily routine, what language do you hear and see most frequently? For folks living in the Corvallis, Oregon, the answer is probably English. In the last month, how many times, when, and where have you been exposed to spoken words or even signs in another language? For those of us on the Oregon State University campus, you could easily overhear or may participate in a conversation in Spanish, Chinese, or Arabic in the Memorial Union or Valley Library. How does the “linguistic landscape” (written or spoken words you encounter in life) affect you? What do you feel and how do you react to hearing a language you don’t understand? Have you been told that you don’t speak English well enough?

Shenanigans in Portland with Pat

Jason Sarkozi-Forfinski, a PhD student in Anthropology, wants to gain insight into the linguistic landscape students at Oregon State University are exposed to and their actions and feelings about about it, especially for students from non-English speaking countries. Jason’s research involves interviewing students and community members about their experiences in the US such as:

• How do Thai-speaking folks fair when practicing English with a non-American accent?
• How does a (white) American- English speaker from Roseburg regard different accents?
• How do Mandarin speakers from Malaysia react to others speaking English with different accents?
• How does an Arabic speaker from the Gulf region perceive their own accent?
• How comfortable do Japanese speakers feel speaking a language other than English in the US?
• How is all of this connected to the institutionalized tool of racism?

Jason has found that folks have preferences or biases about their linguistic landscape. Oregon State recruits both students from around the world and a large multilingual community of more local students. His respondents have reported being discouraged from speaking in a non-English language or facing negative social and professional consequences for speaking other languages or English with a non-(white)American accent. Could a preference for English with a (white) American accent perpetuate division? Or even bigoted practices?

Jason’s current research developed from years of conversations with friends and colleagues about being multilingual in the US. He began exploring language in his undergraduate education where he majored in Spanish and also studied Portuguese. He also studied English in Miami,

Grilled cheese on a school bus in Portland with Veronica (left) and husband, Nick.

Florida, and worked to understand how non-English languages influences local English. Before coming to OSU for his PhD, Jason has worked as a Spanish and English instructor in the US, Spain, Japan, and China.

Tune in to KBVR Corvallis 88.7 FM on Sunday March, 10 at 7 PM to hear more about Jason’s research and his path to graduate school. Stream the show live or catch this episode as a podcast.

Clarification [See Podcast at 25:45]: Asking someone to change their accent, according to Lippi-Green a linguistic who wrote “Speaking with an Accent,” is like asking someone to change their height. It’s doable (with lots of surgery) but would require a lot of intervention. The point here is that it’s not realistic to ask someone to work on their accent. It’s also rather demeaning.

Summary: Graduate student researchers Brian Erickson and Chelsea Behymer talk about their transition from natural sciences to social sciences and the process of finding their place within their disciplines.

As graduate students, many of our academic conversations focus around our research. But graduate school is about more than just designing and carrying out a project; it also involves finding your place within a larger community.

Chelsea Behymer and Brian Erickson met through a science communication course in the Integrative Biology department (IB599), and they quickly found common ground. Although their research interests are very different, both have had experiences that sparked interest and conviction to explore the human dynamic of the ecological systems with which they are more familiar. While neither is new to academia, they find themselves navigating new identities as they explore what it means to be a social scientist working on human components of environmental issues.

Chelsea takes guests onboard a coastal Alaskan expedition on an intertidal walk.

Chelsea is a first-year Ph.D student in the Environmental Sciences graduate program, with a focus on informal science education. For the past six years, Chelsea has engaged diverse groups of people in marine biology and natural history as a Naturalist onboard both large and smaller, expedition style cruise ships. Interacting with a diversity of people in shared travel and learning experiences across the world’s oceans has been one of the most rewarding roles of her career. At the same time, being immersed in nature-based tourism has opened her eyes to the nature-based tourism industry as not only a place where human connections to the natural world are fostered, but provides wonderful opportunities for science communication.

With the growing nature-based tourism industry, perhaps the opportunities to connect have never been more abundant. Chelsea’s research interests aim to understand the potential for citizen science in nature-based tourism to act as both an effective means of engaging people with local scientists, while at the same time providing opportunities for the kind of collaborative environment where meaningful conversations between scientists and the public can occur.

Brian presents work on ocean acidification education during the State of the Coast conference.

Brian is also a first-year Ph.D student studying fisheries social science in the Department of Fisheries and Wildlife. Growing up in the midwest, he first fell in love with the ocean while working as a field technician in the US Virgin Islands, Panama, and the Northwest Hawaiian islands. Partially because he defined himself as a biologist, it took him almost a decade to realize that he was interested in answering social science questions. Brian is generally interested in applying what we know about human behavior to improve marine conservation outcomes for people and the planet. His master’s work at OSU focused on exploring a commonly held assumption – that knowledge of environmental problems leads to action to fix those problems – through the lens of a high school ocean acidification curriculum. For his PhD work, Brian will be collaborating with the SMART Seas Africa Programme to examine social aspects of marine conservation in East Africa.

In this special segment, Chelsea and Brian will talk with ID host Kristen Finch about the challenge of finding their way as social scientists in a field that is working towards interdisciplinary collaboration. Don’t miss this conversation; tune in to KBVR Corvallis 88.7FM at 6 pm PST on Sunday March, 10. Stream the show live or catch the podcast.

Written by Chelsea Behymer and Brian Erickson. Edited by Kristen Finch.

# Who Runs the World? Exploring Gender Diversity in the Forest Sector

The following article was written by Pipiet Larasatie and edited by Kristen Finch.

Pipiet Larasatie is a third year PhD student in Wood Science and Engineering Department, College of Forestry, at Oregon State University. Her friends and close colleagues describe her as “Ms. Social” and “Ms. Doing-All.”

And she is! Pipiet is currently involved with four research projects and has standing on four committees at the Department and College level (e.g. College of Forestry’s Diversity Equity Inclusion Committee). Additionally, she is a digital communications coordinator for the International Society of Wood Science and Technology. One of her initiatives is #WomenInWoodScience or a network for women who are associated with wood science.

Pipiet working in the Forest Sciences Dept. University of Helsinki in 2017.

As a woman and a first generation student in her male dominated family, Pipiet has a high passion on empowering young females. For this reason, Pipiet switched her research focus from wood centric to gender diversity in the forest sector.

So far, Pipiet’s research involved collaboration with folks at OSU (her advisor and a Master’s student), but also international collaboration with a professor and a Master’s student in University of Helsinki, Finland. During this part of the project, the team interviewed female executives in the global forest sector companies about gender aspects in the North American and Nordic industries. Some trends became apparent across interview responses. Their respondents agreed that the North American and Nordic forest sector is a historically male-oriented and male-dominated industry, which can lend itself to characteristics of a chauvinistic and masculine culture. This also was clear: to be successful in the male-dominated work setting, young females need a support on multiple levels e.g. good bosses/leaders, mentors, and networks. The interviewees also voiced that education is important when finding a niche in the workplace and for making young females more competitive in the job market.

Pipiet with one of her mentees joining a faculty led summer course, “The Forest Sector in Alpine Europe.” Photo shows group at University of Primorska, Slovenia.

Tune in to KBVR Corvallis 88.7FM to hear our special segment with Pipiet at 7 pm on March 3, 2019. Pipiet present her research findings alongside pop songs from Beyoncé and Alicia Keys. Later, Pipiet will be accompanied by one of her mentees, Taylor Barnett, a third year undergraduate student studying Natural Resources at College of Forestry. Taylor will share her experience with mentorship programs at OSU and how these mentorship has aided her professional development.

Not a local listener? No sweat! Stream the show live or check out the podcast version of this special episode.