How a Math Algorithm Could Educate the Whole World – for Free
Mathematics professor Po-Shen Loh has created Expii, a free education tool that democratizes learning by turning your smartphone into a tutor.
Po-Shen Loh, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant professor in the Department of Mathematical Sciences. As a Hertz Fellow, Professor Loh received his PhD in combinatorics of the Pure Math Department at Princeton University. His thesis discussed several original results that he discovered during his graduate study in joint projects with his advisor and other collaborators. Professor Loh studies questions that lie at the intersection of two branches of mathematics: combinatorics (the study of discrete systems) and probability theory.
Prior to his work at Princeton, Loh received the equivalent of a master's degree in mathematics from the University of Cambridge (United Kingdom) in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.
In his spare time, Loh has maintained his involvement with the United States Mathematical Olympiad program. He is now the head coach of the national delegation, as well as a lead fundraiser for the organization. As a high school student, he won a silver medal at the 1999 International Mathematical Olympiad (IMO), and following his win continued to be active in the training of high school students at the U.S. national Math Olympiad Summer Program. In 2004, he served as the deputy leader for the U.S. team at the IMO in Athens, Greece, where our national team placed second. After completing his PhD, Loh again, served as deputy team leader for the United States at the International Mathematical Olympiad from 2010 to 2013. Afterwards Professor Loh was promoted to national head coach of the U.S.A. IMO team, and on his second attempt, Team U.S.A. won first place, in a competition with teams from over 100 countries represented.
Earlier this year, Loh received an NSF CAREER award, the most prestigious NSF award for junior faculty, which honors outstanding research combined with a commitment to teaching. Professor Loh is the founder of the educational technology startup expii.com, a crowd-sourced platform for the world to share interactive lessons in math and science.
Po-Shen Loh: About three years ago I became the national coach of the United States International Math Olympian Team. I was very happy for a day thinking this is very interesting. But the next day I started to think that maybe I should do something with this. And I decided that I wanted to focus not only on training an elite group of students but trying to do as much as I could to boost the baseline mathematics capability in this entire country.
Unfortunately I had no money, no connections and only one person. So the only thing I knew was mathematics, algorithms and this probability and network theory. So after thinking for some time I actually came to an idea which was based on using these core mathematical areas that I'd been working with to actually build a solution for education that could be delivered for free on every smart phone. This is actually the project I'm working on right now called Expii.
Our principle is that actually you could turn that smart phone into a virtual tutor which automates what a person would get if they hired a tutor. It wouldn't be as good as a tutor, but it could get very close. And if you could deliver a free almost tutor on every smart phone in the United States you might solve equity problems, you might be able to allow everyone, even if they live in a different ZIP Code, to be able to access this tutor, which previously had only been accessible to people who are quite wealthy. Because today the cost of a tutor is in the $30 an hour, $20 an hour, $50 an hour depending on how you look at it. If you can reduce that to zero dollars an hour you would actually open up this accessibility to everyone.
If we realize that what we're trying to build is this virtual tutor then you actually, again, can start to conceptualize well knowledge happens to be all of these concepts linked together in this network. Then the problem becomes if you have this network how do you mathematically analyze where a person should go next? That can be done by using probability and statistics to find new ways to measure how much each person understands about each concept. Statistics, because the way that one would measure this is by asking them questions.
The experience someone has is they indicate what they want to learn and then the system starts to pitch questions at them, questions that they would need to know how to answer in order to understand what they claim they want to understand. As the questions come, based on people's responses to the questions, the system adjusts the difficulty of the questions and where the next questions come from in the same way that a human tutor adjusts their line of questioning based on whether a person is successful or not successful at the previous question. If the student reaches a point where they are hopelessly confused, meaning they don't know how to do this question at all, then the system suggests that maybe they could read some explanations.
As you can see it turns the lesson flow upside down. It's not that the class comes first and then the homework and then the exam, the first thing that comes is the exam essentially followed by these practice problems, which adapt to you, followed by the class for anything that you don't know. The idea is that this should cure boredom at the high end and also cure confusion at the struggling end.
I actually started this with a brilliant Carnegie Mellon undergraduate student and then the two of us built this system together. But when you start with no resources you need to think of ways to actually generate all of this content in a way which doesn't cost enormous amount of resources. And we took inspiration from Wikipedia. Our system aggregates all of the questions and explanations that anyone in the world might want to contribute, uses voting like a website called Quora in order to find out which content is strong, and uses statistics, the algorithms, to figure out what questions are easy and difficult. So actually in the end it turns out that it sucks in all of this content, it licenses it all with the creative commons license like Wikipedia and then puts it all across on a platform that anyone with a smart phone can use.
So as we keep developing these mathematics and algorithms our goal is actually to deliver free education to all of the world using a system that self-organizes in the same way that mathematics self-organizes from its basic assumptions.
Po-Shen Loh is a Hertz Foundation Fellow, Princeton-educated mathematician, Carnegie Mellon professor, the head coach of the U.S. International Math Olympiad team, and now he’s adding start-up entrepreneur to his knock-out resume. Loh has created Expii, a math and science education tool that aims to turn every smartphone into a tutor. With the support of the Fannie and John Hertz Foundation, he pursued a PhD in combinatorics at the Pure Math Department at Princeton University.
The Hertz Foundationmission is to provide unique financial and fellowship support to the nation's most remarkable PhD students in the hard sciences. Hertz Fellowships are among the most prestigious in the world, and the foundation has invested over $200 million in Hertz Fellows since 1963 (present value) and supported over 1,100 brilliant and creative young scientists, who have gone on to become Nobel laureates, high-ranking military personnel, astronauts, inventors, Silicon Valley leaders, and tenured university professors. For more information, visit hertzfoundation.org.
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Eating veggies is good for you. Now we can stop debating how much we should eat.
- A massive new study confirms that five servings of fruit and veggies a day can lower the risk of death.
- The maximum benefit is found at two servings of fruit and three of veggies—anything more offers no extra benefit according to the researchers.
- Not all fruits and veggies are equal. Leafy greens are better for you than starchy corn and potatoes.
An open letter predicts that a massive wall of rock is about to plunge into Barry Arm Fjord in Alaska.
- A remote area visited by tourists and cruises, and home to fishing villages, is about to be visited by a devastating tsunami.
- A wall of rock exposed by a receding glacier is about crash into the waters below.
- Glaciers hold such areas together — and when they're gone, bad stuff can be left behind.
The Barry Glacier gives its name to Alaska's Barry Arm Fjord, and a new open letter forecasts trouble ahead.
Thanks to global warming, the glacier has been retreating, so far removing two-thirds of its support for a steep mile-long slope, or scarp, containing perhaps 500 million cubic meters of material. (Think the Hoover Dam times several hundred.) The slope has been moving slowly since 1957, but scientists say it's become an avalanche waiting to happen, maybe within the next year, and likely within 20. When it does come crashing down into the fjord, it could set in motion a frightening tsunami overwhelming the fjord's normally peaceful waters .
The Barry Arm Fjord
Camping on the fjord's Black Sand Beach
Image source: Matt Zimmerman
The Barry Arm Fjord is a stretch of water between the Harriman Fjord and the Port Wills Fjord, located at the northwest corner of the well-known Prince William Sound. It's a beautiful area, home to a few hundred people supporting the local fishing industry, and it's also a popular destination for tourists — its Black Sand Beach is one of Alaska's most scenic — and cruise ships.
Not Alaska’s first watery rodeo, but likely the biggest
Image source: whrc.org
There have been at least two similar events in the state's recent history, though not on such a massive scale. On July 9, 1958, an earthquake nearby caused 40 million cubic yards of rock to suddenly slide 2,000 feet down into Lituya Bay, producing a tsunami whose peak waves reportedly reached 1,720 feet in height. By the time the wall of water reached the mouth of the bay, it was still 75 feet high. At Taan Fjord in 2015, a landslide caused a tsunami that crested at 600 feet. Both of these events thankfully occurred in sparsely populated areas, so few fatalities occurred.
The Barry Arm event will be larger than either of these by far.
"This is an enormous slope — the mass that could fail weighs over a billion tonnes," said geologist Dave Petley, speaking to Earther. "The internal structure of that rock mass, which will determine whether it collapses, is very complex. At the moment we don't know enough about it to be able to forecast its future behavior."
Outside of Alaska, on the west coast of Greenland, a landslide-produced tsunami towered 300 feet high, obliterating a fishing village in its path.
What the letter predicts for Barry Arm Fjord
Moving slowly at first...
Image source: whrc.org
"The effects would be especially severe near where the landslide enters the water at the head of Barry Arm. Additionally, areas of shallow water, or low-lying land near the shore, would be in danger even further from the source. A minor failure may not produce significant impacts beyond the inner parts of the fiord, while a complete failure could be destructive throughout Barry Arm, Harriman Fiord, and parts of Port Wells. Our initial results show complex impacts further from the landslide than Barry Arm, with over 30 foot waves in some distant bays, including Whittier."
The discovery of the impeding landslide began with an observation by the sister of geologist Hig Higman of Ground Truth, an organization in Seldovia, Alaska. Artist Valisa Higman was vacationing in the area and sent her brother some photos of worrying fractures she noticed in the slope, taken while she was on a boat cruising the fjord.
Higman confirmed his sister's hunch via available satellite imagery and, digging deeper, found that between 2009 and 2015 the slope had moved 600 feet downhill, leaving a prominent scar.
Ohio State's Chunli Dai unearthed a connection between the movement and the receding of the Barry Glacier. Comparison of the Barry Arm slope with other similar areas, combined with computer modeling of the possible resulting tsunamis, led to the publication of the group's letter.
While the full group of signatories from 14 organizations and institutions has only been working on the situation for a month, the implications were immediately clear. The signers include experts from Ohio State University, the University of Southern California, and the Anchorage and Fairbanks campuses of the University of Alaska.
Once informed of the open letter's contents, the Alaska's Department of Natural Resources immediately released a warning that "an increasingly likely landslide could generate a wave with devastating effects on fishermen and recreationalists."
How do you prepare for something like this?
Image source: whrc.org
The obvious question is what can be done to prepare for the landslide and tsunami? For one thing, there's more to understand about the upcoming event, and the researchers lay out their plan in the letter:
"To inform and refine hazard mitigation efforts, we would like to pursue several lines of investigation: Detect changes in the slope that might forewarn of a landslide, better understand what could trigger a landslide, and refine tsunami model projections. By mapping the landslide and nearby terrain, both above and below sea level, we can more accurately determine the basic physical dimensions of the landslide. This can be paired with GPS and seismic measurements made over time to see how the slope responds to changes in the glacier and to events like rainstorms and earthquakes. Field and satellite data can support near-real time hazard monitoring, while computer models of landslide and tsunami scenarios can help identify specific places that are most at risk."
In the letter, the authors reached out to those living in and visiting the area, asking, "What specific questions are most important to you?" and "What could be done to reduce the danger to people who want to visit or work in Barry Arm?" They also invited locals to let them know about any changes, including even small rock-falls and landslides.
The famous cognition test was reworked for cuttlefish. They did better than expected.
- Scientists recently ran the Stanford marshmallow experiment on cuttlefish and found they were pretty good at it.
- The test subjects could wait up to two minutes for a better tasting treat.
- The study suggests cuttlefish are smarter than you think but isn't the final word on how bright they are.
Proof that some people are less patient than invertebrates<iframe width="730" height="430" src="https://www.youtube.com/embed/H1yhGClUJ0U" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe><p> The common cuttlefish is a small cephalopod notable for producing sepia ink and relative intelligence for an invertebrate. Studies have shown them to be capable of remembering important details from previous foraging experiences, and to adjust their foraging strategies in response to changing circumstances. </p><p>In a new study, published in <a href="https://royalsocietypublishing.org/doi/10.1098/rspb.2020.3161" target="_blank" rel="noopener noreferrer">The Proceedings of the Royal Society B</a>, researchers demonstrated that the critters have mental capacities previously thought limited to vertebrates.</p><p>After determining that cuttlefish are willing to eat raw king prawns but prefer a live grass shrimp, the researchers trained them to associate certain symbols on see-through containers with a different level of accessibility. One symbol meant the cuttlefish could get into the box and eat the food inside right away, another meant there would be a delay before it opened, and the last indicated the container could not be opened.</p><p>The cephalopods were then trained to understand that upon entering one container, the food in the other would be removed. This training also introduced them to the idea of varying delay times for the boxes with the second <a href="https://www.sciencealert.com/cuttlefish-can-pass-a-cognitive-test-designed-for-children" target="_blank" rel="noopener noreferrer">symbol</a>. </p><p>Two of the cuttlefish recruited for the study "dropped out," at this point, but the remaining six—named Mica, Pinto, Demi, Franklin, Jebidiah, and Rogelio—all caught on to how things worked pretty quickly.</p><p>It was then that the actual experiment could begin. The cuttlefish were presented with two containers: one that could be opened immediately with a raw king prawn, and one that held a live grass shrimp that would only open after a delay. The subjects could always see both containers and had the ability to go to the immediate access option if they grew tired of waiting for the other. The poor control group was faced with a box that never opened and one they could get into right away.</p><p>In the end, the cuttlefish demonstrated that they would wait anywhere between 50 and 130 seconds for the better treat. This is the same length of time that some primates and birds have shown themselves to be able to wait for.</p><p>Further tests of the subject's cognitive abilities—they were tested to see how long it took them to associate a symbol with a prize and then on how long it took them to catch on when the symbols were switched—showed a relationship between how long a cuttlefish was willing to wait and how quickly it learned the associations. </p>
All of this is interesting, but what use could it possibly have?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNTcxNzY2MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MTM0MzYyMH0.lKFLPfutlflkzr_NM6WmnosKM1rU6UEIHWlyzWhYQNM/img.jpg?width=1245&coordinates=0%2C10%2C0%2C88&height=700" id="77c04" class="rm-shortcode" data-rm-shortcode-id="7eb9d5b2d890496756a69fb45ceac87c" data-rm-shortcode-name="rebelmouse-image" data-width="1245" data-height="700" />
A diagram showing the experimental set up. On the left is the control condition, on the right is the experimental condition.
Credit: Alexandra K. Schnell et al., 2021<p> As you can probably guess, the ability to delay gratification as part of a plan is not the most common thing in the animal kingdom. While humans, apes, some birds, and dogs can do it, less intelligent animals can't. </p><p>While it is reasonably simple to devise a hypothesis for why social humans, tool-making chimps, or hunting birds are able to delay gratification, the cuttlefish is neither social, a toolmaker, or is it hunting anything particularly <a href="https://gizmodo.com/cuttlefish-are-able-to-wait-for-a-reward-1846392756" target="_blank" rel="noopener noreferrer">intelligent</a>. Why they evolved this capacity is up for debate. </p><p>Lead author Alexandra Schnell of the University of Cambridge discussed their speculations on the evolutionary advantage cuttlefish might get out of this skill with <a href="https://www.eurekalert.org/pub_releases/2021-03/mbl-qc022621.php" target="_blank" rel="noopener noreferrer">Eurekalert:</a> </p><p style="margin-left: 20px;"> "Cuttlefish spend most of their time camouflaging, sitting and waiting, punctuated by brief periods of foraging. They break camouflage when they forage, so they are exposed to every predator in the ocean that wants to eat them. We speculate that delayed gratification may have evolved as a byproduct of this, so the cuttlefish can optimize foraging by waiting to choose better quality food."</p><p>Given the unique evolutionary tree of the cuttlefish, its cognitive abilities are an example of convergent evolution, in which two unrelated animals, in this case primates and cuttlefish, evolve the same trait to solve similar problems. These findings could help shed light on the evolution of the cuttlefish and its relatives. </p><p> It should be noted that this study isn't definitive; at the moment, we can't make a useful comparison between the overall intelligence of the cuttlefish and the other animals that can or cannot pass some variation of the marshmallow test.</p><p>Despite this, the results are quite exciting and will likely influence future research into animal intelligence. If the common cuttlefish can pass the marshmallow test, what else can?</p>