Mathematics & Political Geography

Mathematics and Political Geography <Intro Music Plays> SH: Hello everyone, I am Sam Hansen SW: And I’m Sadie Witkowski. SH: And you are listening to Carry the Two, a podcast from the Institute for Mathematical and Statistical Innovation aka IMSI. SW: The podcast where Sam and I talk about the real world applications of mathematical and statistical research. <Intro Music Ends> SH: Welcome to episode four of our season all about the intersection between mathematics and democracy and politics. In this episode we are going to be discussing two different aspects of political geography SW: So, two flavors of Gerrymandering then? SH: Not exactly SW: Ok, so then what (sarcasm) exactly? SH: Well the second aspect has nothing to do with gerrymandering, while the first has to do with redistricting but not the partisan political gain that is the goal of gerrymanders SW: Sam, just tell me what we are talking about SH: Ok, ok we are going to be talking about Communities of Interest, a topic that I learned about at a talk during Career Paths in the Mathematical Sciences an IMSI, Institute for Mathematical Applications and Math Alliance Workshop. The talk was titled A Quarter-Life Crisis: From Commutative Ring Theory to Computational Redistricting and was given by RC: Hi, I am Ranthony Clark. I am a NSF postdoctoral fellow in the Department of Mathematics at Duke University. SW: Oh, I remember Ranthony. She was on our episode about creating a data toolkit for studying Small Town Policing. An episode that you were also featured on as a guest, if I am remembering correctly SH: You are in fact remembering correctly, being a part of that research group was my first introduction to IMSI. SW: Must have been very positive indeed, given that I am now co-hosting this show with you SH: Very much so, but we are not hear to talk about me, even though I like to, we are here to talk about communities of interest SW: Of course, so maybe you could start by letting me know what they are? SH: Sure, Ranthony defines them in two parts RC: The first is that there's some sort of geographic proximity that they have to one another. And the second is that they have some sort of bonding thing that makes them a community. So this could be they share an ethnic identity, a language identity, they share economic interests. SW: Seeing all the cultural variety across Chicago’s neighborhoods like little Italy vs the predominantly Puerto Rican Humboldt Park, that makes sense, but what do they have to do with redistricting? SH: Well it turns out that over half of the states in the USA have language about preserving communities of interest in their redistricting for federal or state congressional districts or both SW: Oh wow, I guess they have a lot to do with redistricting. It makes sense though, since people who live close together from a shared cultural heritage might have shared political views. SH: Exactly, as Ranthony put it RC: Because of this common interest and their shared geographic proximity, then they want to be sort of kept together intact so that they have a chance to elect a representative that speaks to their shared concerns SW: That seems like a totally reasonable goal. Since they are so important for the redistricting process, how are they identified? SH: Now that is where things can get rather complicated RC: This is the thing. There is no uniform way to identify what a community of interest is or isn't. SH: And while the specifics of how a state identifies what the communities of interest are is complicated, there is one traditional stand by that a lot of states use RC: Historically, the information about where a community is, what the people care about has been collected through public testimony. So you might have a town hall or a public hearing, and then you'll have members from the community speak and say, we care about this, and this is my community, and we want to be kept together for the purpose of redistricting. SW: I can just picture it, Leslie Knope is sitting at a folding table and the residents of Pawnee, Indiana are going up one by one giving increasingly bonkers reasons why Eagleton should be in a different district SH: Sadie, would you please work on your Parks and Rec reboot script after the show! SW: Wait, this isn’t where I pitch *my* fanfic? I guess I can put it on hold… SH: Thank you. The testimony approach will always leave something to be desired because not everyone has the ability to attend public hearings, they might be working, they might have to care for a loved one, they might not have transportation SW: That is if they even hear about the meeting in the first place SH: Oh, good point. Not to mention RC: You think about redistricting, it's a very geospatial visual task. And the process of speaking your community does not necessarily translate into where does that community actually live on a map? Can I identify it? Can I draw it? Can I see if it's being split by the districting lines that are being proposed? SW: I am guessing this is where Ranthony’s work comes in? SH: It is. While Ranthony was a postdoc at The Ohio State University her advisor was contacted by the Metric Geometry and Gerrymandering Group, or MGGG, to see if he knew anyone who might be interested in starting to work with them on their redistricting work. RC: And he was like, I have a postdoc who's probably really interested because they've been saying all of these things about how interested and eager they are to do community engaged scholarship and to, you know, sort of do applied mathematics with respect to social justice problems. SH: So while she was not seeking out communities of interest work in particular, it was a perfect fit for the type of mathematics Ranthony was interested in engaging with. This timing was also perfect because the 2020 census had just been done and the process of redistricting was about to begin and RC: So there are a number of states that had citizen-driven redistricting efforts that wanted to prioritize communities of interest and wanted to do this in a more precise way. SW: And Rathony helped them do it? SH: She did, but it was by no means just her RC: It wasn’t just a group of academics kind of like with our noses down trying to figure out where these communities were. It was a multi-state effort, I believe there were 10 states involved total, I mainly interfaced with four of those states and their data, Missouri, Ohio, Michigan, and Wisconsin. And we were interfacing with community organizations across all these states to try to collect public testimony, right, that we are describing, but in a way where we have not only narrative information about where these communities are, but places, you know, these are churches, these are schools that are really important, these are meeting places for these types of groups. And the important point, having people draw using an app called Districtr, which allows you to go in and actually plot where your community is. So you have a spatial representation of the place that you're describing with your words. SW: Wait, wait, say more about that app Ranthony mentioned? SH: The app was designed by MGGG and is called Districtr, with no e. It is a tool for drawing communities made out of pre-built blocks that come from how the census divides up our geography RC: We had users then go in and build up their communities and their community would be a sort of a polygon is what it would look like to them visually, but that would be comprised of these collections of these blocks that we had pre-designated for that state. And they also had the option to write narrative texts describing their community. SW: So they could collect both the geospatial and narrative data at the same time? SH: Not only that RC: People could also go in and identify important place data, so an important church, a mosque, an important school, an important, I don't know, museum or a dock, something that was of importance to their region. They could actually go in and plot that as geotags on a map. And then lastly, they could include sort of hashtags so that when other people were viewing their submissions, they were centered around common themes. SW: Dant, that could be a rich data set! SH: Right? But as we know just putting something out there is no guarantee that anyone will actually use it SW: [sigh] Too True SH: So this is where the work being with community engagement was so important. In Ohio specifically Ranthony was working with Care Ohio, the Ohio organizing collaborative, the Ohio Citizens Redistricting Commission, and the Kerwin Institute for the Study of Race and Ethnicity at Ohio State RC: The initial meetings looked like first deciding what are the parts of the state that we should focus on in terms of what are the zones in which we need people to try to collect participatory maps and get this data. SW: Once they had decided where to focus, what did they do? RC: So, we used the train-the-trainers model, and then within each of the identified zones, and groups identified by the trainers in those zones, the public participatory mapping effort began. SW: And everything ran perfectly smoothly after that right? SH: Hahaha, Yeah, yeah, you know that nothing is ever perfect. And so did the team doing this work. During the data collection process their were people monitoring what was coming in, both for things like clearly joke maps where people drew shapes and smiley faces, and also issues like areas where the data was not as rich as they hoped RC: Then we reach back out to the community organizations and say, "Hey, we're getting a lot of feedback from this area, but we don't have a lot of feedback from this region. Who can we talk to? How do we get more people drawing maps and using their voice to identify their communities in this part of the state?" SW: What was their hope once they had gathered the data SH: It varied state to state. Some of the data was hopefully going to be used directly in the drawing of new districts, while in Ohio RC: Ohio had a citizens commission that served as a shadow commission, so they weren't able to draw the lines but they were just you know sort of modeling best practices and trying to push the legislative commission to do the right thing and have transparency and a fair process SW: Sure, but how? Were they just going to hand over all the maps and narratives? That seems like a lot for commissions to go through SH: Yeah, that would not have been ideal. RC: The whole point of this is to try and design, you know, mechanisms for collecting community input that are also able to be processed with, mathematical tools so that there's an actual visual representation of community and some sort of description of what they're about. SW: Ah, there it is, we are finally going to get into the math now, aren’t we? SH: Yes, yes we are! And so you can think of the data in two parts. The geographic data and the narrative data. Let’s talk about the geographic data, the maps of communities that citizen’s drew first RC: We can cluster them. We can identify groups of communities of interest. And this is precisely what we did. So we use what's called agglomerative hierarchical clustering. SW: Ok, clustering I get. It is when you gather together similar things. Even hierarchical clustering I get, there are different clusters depending on the amount of similarity at each level of the hierarchy. But you lose me at agglomerative SH: No worries, I think I can help you out on this one. Agglomerative clustering is a bottom up approach where you start with each map being its own cluster and then you let them glom together into clusters based on a similarity cut off. Adding hierarchy into it means that at the bottom level, level 0, you have all the maps as their own clusters and then at the top level you have one cluster that contains all of the maps. SW: I never thought I would hear the word glom in the explanation of mathematics SH: And I never thought I would use it to explain mathematics, but it really is the key word in this case SW: Apparently!, so how did Ranthony and the rest of the team determine which of the maps would glom together? SH: Well in order to explain that, we first need to discuss metric spaces RC: So a metric space is a way to mathematically be very precise about what it means for two things to be close together. So formally a metric space is going to be a set with a collection of things. In this context, our things would be communities of interest, and we want to equip this set with a distance function. So what this distance function is going to do is it's going to take two elements from our set, two members, and it's going to spit out a number that identifies or represents how close those two things are together. SW: So what did they decide to use to measure distance between the maps? SH: They ended up going with the Hausdorff distance of course SW: [pretends to know] Ah yes, of course the Hausdorff distance which is…Ok, you know that you are going to have to explain that to me SH: Alright. In the case of two of these maps to find the Hausdorff distance between them you would look at one of the census regions that make up the first map and then determine the shortest distance from that region to any part of the second map. Once this is done for every region from the first map, it would take the longest of the shortest distances. SW: And that is the Hausdorff distance? SH: Not quite, because you then have to do it for the second map too. And then the longest of the two results would be the Hausdorff distances SW: So they used this Hausdorff distance to create their clusters? SH: Precisely, they would combine maps together in a cluster if the Hausdorff distance between them was less than the max for that level of the hierarchy. This was something they were able to demonstrate visually RA: We can create a representation of this visually. It's called a dendrogram. And at sort of each step of the dendrogram, you can see which communities are clustered with which. SW: I love dendrograms! They look like sideways trees, with branches coming together to form a larger and larger trunk from left to right SH: It is one of my favorite types of visualization too. SW: But how did they decide which level of the hierarchy they would say are the official communities of interests clusters SH: Well, they wanted to make sure the data for the community clusters they put forward was robust and at a level commensurate with the needs of the organizations they were working with RC: We wanted to make sure that each community was supported by a certain number of submissions from the public. So, in Michigan in particular, they might say we want to make sure each community you give us is supported by 60 submissions at least. And so then we can kind of look at our bins and see, okay, at this level, each community has around 60 submissions. And so we're going to just take this level for our communities and maybe there's 14 at that level. So this is how we identified our community clusters. SW: Keeping those community organizations engaged throughout the whole process, I love it. SH: Indeed, as for the second type of data, the narratives, that required a lot more human power SW: How so? SH: Well, if you did just a basic automated keyword analysis it turns out it would not tell you much RC: I mean, if you do a Q&A, keyword, all that really did was sort of group things around geographic place again, because people would say, "This is this region," and they'd give an adjective for the region. And so like maybe in Ohio, the greater metro Columbus region, and so Columbus, Columbus, Columbus. And so if we're clustering around keywords, this is having the same effect as doing a geographic clustering, because everyone is saying very different things about Columbus, but Columbus is the term that's coming up the most. SW: Of course, and the geographic region is already represented by their maps. So how did they end up extracting the descriptive information from the narratives? SH: Very carefully RC: We actually just human read every single submission and came up with a collection of labels. So these could range from policing, agriculture, K through 12, safety, just themes, healthcare. What are the themes that people are describing in these submissions? SW: They read every single one? That is a lot of human power SH: And the result of all of this human power was a set of 0’s and 1’s associated with each map depending on which labels were present SW: Oh, let me guess? You have a set of items, did they again choose a distance measure so they could have a metric space and do a similarity analysis? SH: You are good! They did exactly that, with the distance measure being what is known as Hamming Distance in this case. SW: I may be good, but I am going to avoid “hamming it up” with a silly joke [Sam sighs] and to ask for another explanation here for Hamming distance SH: Of course, Hamming distance takes two strings, or vectors in this case, of the same length and returns a distance based on how many times they have a different symbol or number in the same position SW: Ah, so if there we three labels, say agriculture, k12, and safety, and the first map mentioned all three and the second only mentioned k12 then the vectors would be 111 and 010 with a Hamming distance of 2 SH: See, I said you were good SW: Thanks, and what did they end up using these distances? RC: And the end result was, you know, a collection of community submissions and in some cases, sub-clusters, each with sort of a description narratively of what the themes were in that particular area. SW: And the narratives were driving these subclusters? SH: They were. SW: What a useful way to present the results of all of that data they gathered. I bet the redistricting commissions found them super useful. SH: Speaking of that, there is one last part of the work that Ranthony wanted to make sure we talked about SW: What is that? SH: The dynamics between the math and data team and the community organizations they were working with RC: My mind is going to be captivated both by the social implications of the work that I'm doing, but also the math. And so I go into this meeting and at that point, I think we were thinking about how to incorporate the narrative sub-clustering process. And so I go into the meeting and I kind of update them on what we're doing. And some people were like, great. And some guy was like, yeah, but like, who cares? Like really, like why are you caught up on whether or not there's a church in this region and a school in that region, like there's a, like a right now-ness energy that I felt and like also sort of like a, I want to like a, I don't want to say like a lack of interest, but sort of a, hey, like this is a great, like I recognize that maybe you're stuck on this technical thing, but like rein it in. Like we got people to represent here. We have a fair districting process that we're trying to influence and model, you know, like democracy is at stake, reign it in little birdie. Like we, like, it's not your, your technical concern or where you're held up on. It's nice to know, but just keep it focused. SH: This was an important experience for Ranthony RC: Doing community engaged scholarship, yes there are really cool mathematical problems that arise. There are tools, like tools you get to utilize that it's, I mean, what a cool application, right? And I think that like my mathematical scientific mind was just really just bursting with energy. But like when you reign that in and think about what you're really doing, like this matters, you know, like these, the things that you are doing or the tools that you're using, yes, they're cool, but you are there to support this community partnership. SW: Yeah, what a great take away SH: And not one that many mathematicians and statisticians get the chance to have, since we spend so much of our time not engaged with the public. SW: There is one last thing that I want to know about Rathony’s work though SH: Ok, what is it? SW: What happened with all of those Ohio communities of interest?!? SH: Well… RC: I also went to their public hearing to see how they presented the analysis that we did and what they had been doing. And that was also really interesting because it wasn't a paper, right? Like the grand finale was this public hearing that the actual legislative commission did in Ohio. And so I got to see them describe, we did a community participatory mapping effort. Here are these clusters and this is what this graph means. And I know what it means specifically, quantitatively, like those are nodes on the graph of a district and we use the Hausdorff distance to do this and that. But hearing them talk about it in a big picture way is part of a collective process to model a fair redistricting and transparent process like, that’s citizen engaged was really important. SW: And were those the maps the commission went with? SH: Umm… RC: It's very eye-opening to see that these sorts of analyses are one part of a much bigger puzzle of trying to push for a fairer democracy. And there's a lot of work to be done, and it's not necessarily work that's going to be embraced with open arms. And I think that I, it's my first time, you know, like the meme, and I was just floored by the level, the lack of transparency in some regards that we experienced. And I just really thought we've shown them that this could be done in a fairer way. We've shown them that, you know, you can do this participatory mapping effort, that you can modify these maps to make them different than what's being proposed. And it didn't, it didn't hit the way I thought it would hit the first time around. And so that's also a part of this work that I've had to kind of settle myself in is that this is a marathon, this is not a sprint and that the progress is measured, is going to be measured differently. And that there's a level of stamina for being engaged in this long-term that one has to develop less crumble and under the weight of it all, you know? SW: Soooo, no? SH: No, the maps the citizen’s redistricting commission put together with the communities of interests that Ranthony and the MGGG team helped gather were not used by the legislative commission in OH. But don’t worry, Ranthony is planning to keep going RC: I don't see this project as a one-off. I see it as the beginning of something to really take a long, hard look at how to better quantify this really fuzzy, but really important principle in redistricting, because there are so many states that say, we want to keep communities of interest together for the purpose of redistricting. And no one knows where those are. And there's no streamlined version of how to identify them. And it needs to stop. And we had a beautiful start of this journey of how to quantify these and think about them more intentionally from both a qualitative and a quantitative perspective. And I just want to iterate that that work is just beginning. And I am very excited about the next redistricting cycle and to continue staying engaged in this type of work. <Ad Break Music> SH: Hello, Carry the Two listeners. I just wanted to pop in to let you know about a podcast that I appeared on talking more about mathematics and politics. That podcast is called Mathematical Objects, and hosts Katie Steckles and Peter Rowlett go through various objects throughout the world, like novels and games and cards and dice, and talk about their mathematical aspects. From the Aperiodical, which you can find at aperiodical.com, or on any of your podcast listening apps of choice, find Mathematical Objects, and you can hear me on it. And also, if you’re enjoying the discussions we’re having on this program, here’s another University of Chicago podcast network show you should check out. It’s called The Pie. Economists are always talking about The Pie – how it grows and shrinks, how it’s sliced, and who gets the biggest share. Join host Tess Vigeland as she talks with leading economists about their cutting-edge research and key events of the day. Hear how the economic pie is at the heart of issues like the aftermath of a global pandemic, jobs, energy policy, and much more. <Ad Music Ends> SW: So what non-gerrymandering or redistricting aspect of political geography did you bring me? SH: I bring to you an analysis of how well polling locations are covering some US cities SW: Ohhh, that’s exciting. You know, I'm going to be a poll worker this year. SH: I had no idea. That's going to be so much fun. SW: Ugh, 5 a.m. to 7 p.m. Let's go. SH: Well, Chicago polls were even a part of this research. So let's get into the work that this research team did by having the two members of the team I got on the line introduce themselves to us. MP: Okay, so my name is Mason Porter. In terms of salutations, I go by Mason. I am a professor of mathematics at UCLA. And then I also have a 0% appointment in sociology and I'm an external professor at Santa Fe Institute. JL: Yeah, so my name is, I guess my legal name is Jiajie Luo. I go by Jerry. I've gone by Jerry for most of my life.I just finished my PhD in the mathematics department at UCLA, and I think I'll probably just end with that. SW: And what did Jerry and Mason find out about polling locations? SH: Calm down, calm down. You know how this works, before I give you any results I want to give you the best part, the mathematics that they used to get them SW: Dinner before dessert… Alright, go ahead SH: I’m sorry, this is desert before dinner. First up, I want to talk with you about Topological Data Analysis, or TDA JL: I would say that topological data analysis is basically an area of data analysis that uses tools from topology to understand the quote unquote shape of data. SW: Data has a shape? SH: Maybe not in the way we typically think of shapes, but yes it does. One way to think of it, is that the data can be turned into a ordered set of values which can be plotted out as a cloud of points and it is those points that are being studied topologically at different scales MP: You fix a certain scale, and you say what is the topology at that one scale but you also fix a scale a little bit different and you ask what is the topology at that scale and you fix a scale a little bit different you ask what is the topology of that scale. So, given a scale you can say something about the topology. The point of doing what you do in topological data analysis is that you try to do it at all scales. Okay, I guess air quotes can only show up in video and not in audio. You try to do it at all scales simultaneously. SW: I guess I can see where they are coming from with this. For the polling location analysis what data were they looking at across all these scales? SH: There was a lot of different data that the combined, but the geographic data, specifically the locations of the polling places, was of strong importance MP: Some of the geographical work has been in a series of papers that I and others have been involved in, and that we were doing this sort of construction of changing scales. So scales is now going to mean something different in this context than it would in the normal TDA context. And there was a need to think about how does it make sense to do something geographically. SH: In particular they used a tool called from topological data analysis called persistent homology. Which allowed them take the location of polling sites and create coverage areas for those sites, based on some metric, to determine where holes in the coverage of polling sites were and if they persisted as that scale, or coverage area, changed SW: I follow everything there, but you seem to have been a bit non-specific about what the metric they used was SH: That was because I was hoping you might be willing to guess what a possible metric for determining polling site coverage would be SW: Great, a guessing game. Let me think… Hmm, I know that there is a rule in India about there needing to be a polling station within 2 km of all voters so let’s go with distance SH: Yeah, that is the rule that explains why in the state of Uttar Pradesh there are 200 million residents and over 160,000 polling stations. And it is one that Mason, Jerry, and their collaborators thought about. But they did not ending up using it, with good reason MP: Five miles in Los Angeles is not the same as five miles in cities in Montana. Right. It's just not. SW: As a Chicago resident who is regularly stuck in traffic, I feel that so much. So, if not distance, what metric did they end up using? JL: We actually use time to, you know, because we believe that's a more accurate measure of accessibility. You can live, you know, like a mile away from a polling site but if you want to drive there and it's like, you know, rush hour in LA, then that one mile actually might take, you know, a very significant amount of time. But it's also the case where it's like you could actually like live next to a polling site but then if its lines are, you know, long, like incredibly long, then, yeah, sure, you can walk there but, you know, like, but essentially, like, you know, like, you're still going to spend a significant amount of time voting as opposed to someone who might live, let's say, two miles away or five miles away even but they can get there and then they can vote immediately and then be out, you know, on their way. MP: In L.A., if you live one mile away, you probably want to walk. I love how there was the assumption of driving with one mile away, which is, I will point out is very much an LA perspective on the world. SW: [Laughs] So they needed a lot more than just polling locations didn’t they? SH: Indeed, they needed travel time JL: We looked at three different forms of travel. One is by car. One is public transportation, so like bus and that sort of thing. And the third is walking. So for the first two, we used Google Maps API to get travel distances. And for the walking distance, what we've done is we used basically an OpenStreetMaps-- yeah, we used OpenStreetMaps, essentially. Oh, yeah. I'm sorry. I should have actually said, I actually did not mean distance I meant time SH: Though they did not necessarily get all the travel times they wanted JL: Yeah, there was a monetary cost using the Google API. SW: Oh yeah, I bet they could have wracked up a healthy bill if they weren’t careful SH: Thankfully for their wallets they were careful. As for waiting times they used estimates from a study by Chen, Haggag, Pope, and Rohla. By combining those two types of data they were able to then use persistent homology to determine where there were holes in polling site coverage and at what times those holes went away SW: Now can I ask what they found out? SH: You may, but only with this caveat from Jerry JL: I want to like caution against like necessarily just, you know, straight up using those results and making comparisons directly because oftentimes you might end up with some holes that for example, in New York, we have like a, one of the big holes are over, you know, it's over water and that hole you might not necessarily want to take as seriously as, you know, some of the other ones. SW: But what about the mermaids, don’t they also deserve a quick voting experience? SH: As soon as I find one, I will be sure to ask. SW: Fair enough SH: As for what their study found, with that caveat in mind, for the cities they studied, Atlanta Metro , Chicago, Jacksonville (Florida), Los Angeles County, New York City, and Salt Lake City holes tended to persist for the longest in Atlanta, New York, and Salt Lake and the shortest times in Chicago and Jacksonville. Though long and short here are very much relative, even in Jacksonville the median time it took the holes to disappear was around three quarters of an hour or a full hour, depending on the specifics of the homology classes SW: Oof that’s still a really long time that people may have to wait SH: Yeah, yeah it is, and they are much closer to the longest times of just over 80 minutes than they are to no wait at all. Which is why Jerry thinks there is a much better use for their work than comparing city wait times JL: In my opinion, I think one of the more important things is that by doing persistent homology, we can actually plot where some of these holes are, and that gives us a visual interpretation of where we might want to maybe add in polling sites in the future. SW: Yeah, let’s do that. Using math to help facilitate better access to polling places might be one of my favorite applications ever SH: From your lips to election commission’s ears! [outro music] SH: Don’t forget to check out our show notes in the podcast description for more about Ranthony, Jerry, and Mason including links to their work we discussed on this episode SW: And if you like the show, give us a review on apple podcast or spotify or wherever you listen. By rating and reviewing the show, you really help us spread the word about Carry the Two so that other listeners can discover us. SH: And for more on the math research being shared at IMSI, be sure to check us out online at our homepage: IMSI dot institute. We’re also on twitter at IMSI underscore institute, as well as instagram at IMSI dot institute! That’s IMSI, spelled I M S I. SW: And do you have a burning math question? Maybe you have an idea for a story on how mathematics and statistics connect with the world around us. Send us an email with your idea! SH: You can send your feedback, ideas, and more to sam AT IMSI dot institute. That’s S A M at I M S I dot institute. IM: We’d also like to thank Blue Dot Sessions for the music we use in Carry the Two. SW: Lastly, Carry the Two is made possible by the Institute for Mathematical and Statistical Innovation, located on the gorgeous campus of the University of Chicago. We are supported by the National Science Foundation and the University of Chicago. Go Vote! SH: Not only that, I am just going to give myself SW: Not only that Both: Not only that, not only that, not only that SH: Hausdorff distance? Actually, I think it is Hausdorff. SW: Now I'm confusing you. SH: Yeah. No, no, no. I think you were right and I said the wrong thing. So let's… SW: I assume it's Hausdorff. SH: Yeah. Hausdorff. Hausdorff. SW: Hausdorff. SW: It feels real, but not correct. SW: This one no that's you wow not me oh i'm just trying to talk SH: Uh not to be confused with pda personal data analysis SW: I was thinking personal displays public data analysis [outro music ends] SH: Do-dodo-dodo do-do-do-do Do-dodo-dodo bwah-wah SW: [laugs]