Relatively Prime: Stories from the Mathematical Domain

This is the final episode of the 2nd season of Relatively Prime. It is also the second chapter of the ongoing series Diegetic Plots. Which means we will once again be exploring the intersection of mathematics and the humanities. This time by exploring what happens when haiku is used to procrastinate from writing a dissertation, how exactly theorems get born, all the possible continuums upon which feelings can be rated, and the executive summaries of some less than successful grant applications.

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Samuel spends a lot of his time searching the internet for cool mathematical things, so you can guess how excited he was when he stumbled on these amazing grant applications.

After hearing the amazing mathematical poems from the first chapter of Diegetic Plots Samuel decided to try his own hand at mathematical poetry. This is what came out of it.

Etta Devine, Gabriel Diani, Tekurah McCullough, and Rob Schultz play Karen, Jeff, Dr. Vittles, and the Narrator in Relatively Prime’s presentation of this piece of mathematically bent theater written by Colin Adams

Courtney Gibbons was just trying to find a way to not write her dissertation. Little did she know that 17 syllables of mathematics would so entrance Helene Tyler, Andrew Gainer-Dewar, and Greg Stevenson that the next thing they all knew they were engaged in a mathematical haiku battle the likes of which the world had never before seen(to be fair the world had probably never seen any sort of mathematical haiku battle before).

Special thanks to Greg Harries for being a great stand-in Greg.

From Courtney:

From Helene:

This piece was written by Rob Schultz with a tiny, tiny, almost minuscule amount of help from Samuel. The character of Murphy was voiced by Etta Devine and Doc was voiced by Rob.

Broke for Free

If you ever want to conduct a quick social experiment on the status of mathematics in the world just get yourself a dating profile and mention on it that you are a mathematician. The messages you get will be quite illuminating:

“I hate to break it to you, but while I appreciate math for its logic and beauty, I don’t think I’ll ever like it. lol TOO many formulas.”

“I got up to AP Calc during my senior year of high school, cheated off my best friend on all the tests and still got 70s in the class, and swore off math from thereon.”

Even when people do not say outright that they despise math the contents can leave a bit to be desired:

“I’m awful at math but it fascinates me–much like historical linguistics and conjugating Russian.”

It is not like it was all bad though. Samuel did once get this message:

“I also really like math and spend a lot of time trying to figure out how to get people to like it more!”

But come to think of it he doesn’t think they actually ended up actually going on a date.

We really shouldn’t be so negative about all of this. Samuel has been told by more than one person that being a mathematician makes him sexy, really he has and it is so validating for him, and he doubts anyone ever turned me down for a date just because he loves mathematics. But given all the times he has received messages with gloomy words about math and how often on a first date some of the first words out of his companion’s mouth is how much they hate math he couldn’t help but wonder if mathematics has impacted my dating life negatively, if only a little bit.

Of course mathematics has never let us down in the past, doubt it is going to start now.

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Andrea Silenzi was the host of Why Oh Why, a radio show about where love and sex meets technology and she was looking for a date. So when Planet Money called her up and asked if she would be interested in getting some dating advice from economist Tim Harford she definitely said yes.

Samuel spoke with Andrea about what it was like to follow an economist’s advice on dating, why we should not treat dating like a job, and where to draw the line when it comes to formulaic dating.

Back in 2009 for the podcast Strongly Connected Components Samuel interviewed Sam Yagan then the CEO and co-founder of an upstart online dating site which was differentiating itself from the competition by putting a real focus on the data side of dating. That little upstart was OKCupid and Sam is now the CEO of Match Group, which includes Match.com, OkCupid and Tinder. They talked about why OKCupid puts such a focus on math and data, how the OKCupid algorithm relies on its users, and why you shouldn’t stress out on having the perfect dating profile photo.

Full Strongly Connected Components Interview:

Mathematics communicator and comedian Matt Parker tells Samuel about the optimal stopping problem, and how it could help him date more effectively.

John Gottman is a psychologist, therapist, mathematician, and co-founder, with his wife Julie Schwartz Gottman, of the Gottman Institute where they do research in order to better understand relationships. For our purposes we are most interested in the work John has done in mathematically modelling marriage, in particular the factors which lead to divorce. John tells Samuel about his research, how he transitioned from mathematics to psychology, and what, mathematically, is the biggest predictor of a lasting relationship.

Andrea and Samuel had so much fun talking about her economist advised dating experiments that they continued chatting for quite a while. This is eventually where they eventually landed.

Your host Samuel Hansen loves cities. Small Cities, Dense Cities, New Cities, Twin Cities, Reborn Cities, he doesn’t care what type of city cities. He loves them all. This of course made it inevitable Samuel would at some point become interested in the intersection of cities and mathematics, and once he became interested in that intersection it became inevitable he would have to make a podcast featuring stories about it. And now here we are. Cause and effect, it really is a marvelous thing.

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Michael Batty is the chair of CASA, the Centre for Advanced Spatial Analysis . He is also the author of the books The New Science of Cities and Cites and Complexity. Samuel spoke to him about how cities grow, the similarity of cities and trees, and the fractal dimension of cities.

Listen to Samuel’s full interview with Michael Batty:

One truth about living in most cities is traffic, and quite often that truth is slow and all clogged up. As bothersome as all the traffic is, where there is a problem there is often interesting mathematics to do and in this case the mathematics is being tackled by University of Michigan professor Gabor Orosz. Samuel spoke with Gabor about why jams form, if there is any hope in the future for less of them, and what role robots in the hallways of the university play in his studies.

Maths in the City is an outreach program conceived by Marcus du Sautoy which shows groups the mathematics of London and Oxford. Samuel spoke with one of the tour guides, Thomas Woolley about the program and some of the mathematical sights you could see on one of the tours.

If these mathematical city tours sounds interesting to you, but you are not anywhere near London and Oxford do not fret as the Maths in the City website has you covered. There is an entire section where people can post their own examples of mathematics in cities all around the world, and you can easily search to see if there is any notable city mathematics near you.

Lisa Schweitzer is an Associate Professor of Urban Planning at the Sol Price School of Public Policy at USC. Samuel spoke to Lisa about the intersection of urban planning and mathematics, where mathematical tools are the most useful, where they fall short, and what the role of mathematics and statistics will be in urban planning moving forward.

Kolmogorov complexity can be thought of as the smallest amount of computational resources needed to designate some object. Sim City is a computer game where you build and manage cities. Samuel Arbesman is a senior adjunct fellow at the Flatiron Center for Law, Technology, and Entrepreneurship at the University of Colorado. Yes, they do all come together.

Click here if you like spoilers(aka the article Samuel interviewed Samuel about)

Jazz Town

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Mathematician is an insanely broad job title It can encompass everyone from professors to government employees to podcast hosts.

And all of these different types of mathematicians, They do very different work, In very different ways.

Except for that one constant, they all do mathematics.

My friends Jess Charlton, Gabriel Siqueiros, Jen Bokoff, and Mike Wolf called me up and let me know just what it is they think mathematicians do all day.

Anna Haensch is a Professor of Mathematics at Duquesne University, a mathematics writer, and co-host of The Other Half a pocast about the half of mathematics which helps you makes sense of your own life. Oh, and she tweets too.

Kristin Lauter is Principal Researcher and Research Manager for the Cryptography group at Microsoft Research and the President of the Association of Women in Mathematics. She also tweets.

Combinations and Permuations was the first podcast Samuel ever hosted. He in no way thinks you should go back and listen to the inane and vulgar jokes he and his fellow mathematics graduate students made during the shows run, but he know he can’t stop you. For Relatively Prime he got some of the old favorites, Nathan Rowe, Sean Breckling, and Brandon Metz, back together in the mail room of UNLV CDC Building 7 to record an episode all about what mathematicians do all day.

Here is a longer cut of the silliness:

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This episode of Relatively Prime is going to be delving into the humanistic side of mathematics. It is the first chapter in a recurring series Samuel is calling Diegetic Plots. Yes that is a super nerdy joke, and yes Samuel is super proud of it.

Gizem Karaali is an Associate Professor of Mathematics at Pomona College and an editor of The Journal of Humanistic Mathematics, a journal which looks at mathematics as a human endeavor with am emphasis on the aesthetic, cultural, and sociological aspects of mathematics. She read her poem The Colors of Math.

Ted Chiang is a multiple Hugo and Nebula award winning science fiction author. Among his work is an amazing bit of math-fiction titled, Division By Zero. Samuel talked to Ted about where the idea for the story came from and what it was like to write about such an abstract mathematical idea. You can find the story in Ted’s short story collection Stories of Your Life and Others where you will also find a lot of other wonderful stories to read.

The interview is followed by a reading of Division By Zero by Jess Charlton, Kitty Stoholski, and Samuel.

A black hole appears over Samuel’s desk as he tries to introduce the next segment and what appears is frightening.

Stuart Rojstaczer has been a dishwasher, a college professor, and a grade inflation czar. He is now an author who’s debut novel was published in September 2014. The novel, The Mathematician’s Shiva, is the story of Rachela, the greatest mathematician of her age. It tells the story both of her time in a Soviet Gulag as a child and of the aftermath of her death. Samuel talked to Stuart about how he prepared to write about mathematicians, the importance of balancing all of one’s identities, and a little bit about Navier-Stokes.

JoAnne Growney is a poet and a mathematician. She read her poem A Taste of Mathematics which can be found in her poetry collection Red Has No Reason

Chris Zabriskie (2)

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Mathematics may be the most pure, the most abstract, the most ivory tower of all academic disciplines, but nothing, nothing is beyond the reach of politics. This episode of Relatively Prime looks at how politics effects mathematics and how mathematics can effect politics.

Mathematics does not tend to be the focus of people who are aiming to become president of the United States, which really is not surprising. There are a lot of lawyers among the previous presidents, along with a few economics and business students. All of which do sound like more expected stepping stones to political office than a degree in mathematics. This does not mean they skip mathematical education in its entirety of course. Samuel spoke with Ronald Merritt of Athens State University about his research into the mathematical educations of US presidents and about which president has a proof included in Elisha Loomis’s book of proofs of the Pythagorean Theorem.

Della Dumbaugh of University of Richmond tells us two stories of how Nazi Germany and the Boxer Rebellion changed the lives of individual mathematicians and the effects these life changes had on mathematics more broadly.

Keith Devlin may not have born in the United States, but he is a very proud US citizen. He had only recently received his citizenship when the tragic events of September 11, 2001 came to pass. After the attacks, like a lot of other really smart people, Keith was contacted by the government and asked to lend his expertise to try and stop another attack. Keith talked to Samuel about went into his decision, whether or not he would make the same decision today, and some stuff which went down in Germany in the 70s.

Gerrymandering – the dividing of a state, county, etc., into election districts so as to give one political party a majority in many districts while concentrating the voting strength of the other party into as few districts as possible.

Few aspects of politics are as clearly open to mathematical analysis as gerrymandering. Just looking at district maps seems to scream for geometric analysis, and there really are a lot of different tests out there. Samuel spoke to David Austin about some potential gerrymandered districts and ways to test for them, then things got a bit bizarre. Samuel also sat down with Jonathan Hodge to talk about a technique Hodge helped develop to test for gerrymandering called the Convexity Coefficient.

Not all of the ways to test for possible gerrymandering rely on geometry. Duke University Professor Jonathan Mattingly and his former student Christy Vaughn, she is currently a graduate student at Princeton, decided to use probability theory to check to see if the districts used in North Carolina’s 2012 elections had been drawn fairly. The results were eye opening.

Lowercase n (2)

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We all use mathematics everyday. At least that is what we all like to tell our friends who ask us, “What good is math anyway?” The problem is so much of this everyday mathematics is, how should I say this, non-obvious. No one thinks they are doing mathematics when they figure out the larger peanut butter is not actually a better deal than the smaller size or when they cut across the intersection diagonally to save time or when they decide to ask that friend they don’t really talk to much to spread the word about their new project because that friend has more friends than they do(not that I have any history doing this last one, no history in doing it at all). Sure those are just algebra, geometry, and network analysis problems deep down, but they are also just normal every issues. In this episode of Relatively Prime we look at three regular, everyday problems and use mathematics to make them a bit more comfortable, a bit more pleasant, and, in the case of the first story, a bit more delicious. Oh, and we have a couple quick pieces of advice about how to make pumping gas fun and tipping more secure.

Samuel was talking to Matt Parker, on of the nerds in The Festival of the Spoken Nerd and author of Things to Make or Do in the Fourth Dimension which sadly is only a three dimensional book, and asked him if he had any everyday tasks which mathematics could make better. His answer will change how you pump gas forever.

Say you are living in a new city and you haven’t made any new friends yet and your birthday is coming up. This was the exact situation Samuel was in last year. He still wanted to have a cake though, but as he was by himself Samuel was worried if he cut his cake in the traditional way it would go stale. Enter Alex Bellos, Guardian Columnist, author of Here’s Looking at Euclid, The Grapes of Math, and, with Edmund Harriss, the math coloring book Snowflake Seashell Star, to tell Samuel about Sir Francis Galton’s perfect cake cutting technique.

Of course since Samuel recorded the interview with Alex before his birthday something was going to have to happen to make it not relevant. In this case it was a happy occurrence, Samuel actually made a friend with whom he could celebrate his birthday. Which was awesome, except it meant Alex’s cake cutting method wasn’t going to be too useful. Samuel wasn’t going to have a birthday without a mathematically appropriate cake cut though so he called up Steven Brams to determine how to fairly divide his cake between him and his new friend.

Of course this meant Samuel needed to go get his birthday cake, and in order to do that he was going to need to find himself a parking spot. For most people this is an everyday problem, but since Samuel usually rolls out of bed and lands in front of his microphone he needed some help to choose the best spot to choose when buying his cake. Thankfully Laura Mclay, who writes the blog Punk Rock Operations Research, had his back or he would probably still be driving around the bakery’s parking lot.

Imagine this: It is a Thursday night and the pub a few blocks away has an Irish music night you really like, but it is a small pub and when there are a lot of people there you don’t enjoy yourself. Should you go to the pub or should you stay home? This is the exact problem W. Brian Arthur found himself having in Santa Fe with the El Farol Bar in the early 90s and being trained in economics and mathematics Brian did the logical thing, he wrote a paper on it.

Music:

The Three R’s, Reading Writing and ’Rithmetic, have formed the basis of formal education for centuries, at least since they were mentioned by Sir William Curtis in 1795, even if he probably used Reckoning instead of ‘Rithmetic. Most of the time though the three R’s can be simplified down even further to the two Glyphs, Letters and Numbers.

For most people ‘Rithmetic or reckoning or mathematics or what ever you want to call it, falls directly under the umbrella of numbers. That is not incorrect. Numbers are very much mathematics brand. Numbers are how mathematics is represented to children from a young age and when you show an aptitude for the subject you are often branded a numbers person. There is even a youtube channel featuring videos about cool mathematics called Numberphile.

But mathematics is more than numbers, and before you go making a joke about how of course it is otherwise we could never solve for x, mathematics is more than individual letters too. Letters, and that thing you get when you put a bunch of letters together and make them into words and then you take those words and you put them together according to some set of rules called language, plays a very important role in mathematics. This episode of Relatively Prime, The Lexicon, explores this role.

Lynne Murphy is an American born, University of Sussex employed linguist. This made her the perfect person to talk to about the linguistic fight which destroys more Anglo-American mathematical friendships than which type of breakfast pastry to serve at a conference: Is it Math or is it Maths? (Ed. Note: It is math, I do not care at all what the story actually concludes)

One of the things about the language of mathematics is a lot of it comes from language, like from the languages that we speak. To be fair not the actual languages we speak, at least not that we speak anymore. Unless you just happen to be a scholar of Greek, Latin, or Arabic.

This is where Anthony Lo Bello’s Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots comes in. Samuel was joined by Anthony for a conversation about the dictionary and some of the origins therein.

A discussion of mathematical language which only touched on mathematical words would be really unsatisfying. It would probably feel like only one half of a dialogue. This is of course because it would be skipping over half of what constitutes mathematical language, it would be skipping over symbols.

Today symbols are just as much part of the language of mathematics as words. This is a surprisingly recent development. For example, when Algebra was first being developed it was entirely in prose. Joseph Mazur wrote about how symbols were developed and integrated into mathematics in his book Enlightening Symbols and he spoke to Samuel about the evolution of symbols and how they have changed mathematics.

There are two words which can elicit a groan in almost any mathematics classroom, word problem. Thankfully this does not have to be the case. Tharanga Wijetunge and Kirthi Premadasa are here with the solution. Their research has shown that using different language to frame the problems can help students not only enjoy the problems more, but also better recall the mathematics.

Tim Chartier is a person who spends half of his life trying to find stories within mathematics and the other half telling those stories in as many ways as possible. While this would be a hard enough task if Tim just wrote books, made videos, and gave podcast interviews. All of which he does, but Tim, along with his wife, have gone one step farther and now tour the world tell mathematical stories without any words at all. That is right, they do mathematical mime.

Mime-matics – The Plunger from Tim Chartier on Vimeo.

Mime-matics – the infinite rope from Tim Chartier on Vimeo.

Mime-matics – The Tube (with Topology discussion) from Tim Chartier on Vimeo

It hardly seems that a week can go by without seeing another newspaper story or television report about the decline of the American Educational Establishment. Particularly in respect to mathematics. As a product of said establishment Samuel Hansen can not say that he thinks that it is as bad as the doomsayers would have us all think, but that is not to say that he thinks everything is peachy keen either.

There are problems, ranking 25th, out of 34 countries, on the mathematical section of the OECD’s International Student Assessment test, a score they refer to as being Statistically significantly below the average makes that clear. As does the general populace’s ill will towards the subject.

The problems are not insurmountable though, in fact Samuel may have spoken to some the people who will help solve them.

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The Teacher:

Dan Meyer is a PhD student at Stanford University. He has also spent 6 years teaching high school math, a year as a Cirriculum Fellow at Google, and is the man behind the popular mathematics education blog dy/dan. Samuel first heard about him from the TEDx talk that spread like wildfire across the internet mathematics community.

The Organization:

Math for America is a non-profit that has made its mission since 2004 to improve the state of USA mathematics education by creating a corps of top notch educators and leaders. In order to accomplish this goal they have created fellowships to support new teachers, established teachers, and mathematics teachers that are going into administration. Samuel spoke with the president of Math for America, John Ewing, in their New York offices. He also spoke with Math for America Fellows Meredith Klein and Patrick Honner.

The Innovator:

Keith Devlin is the Executive Director of Stanford’s H*STAR institute, a mathematician, an author, an educator, and a World of Warcraft player. When you put all of those things together you get a man both qualified and inclined to think about how video games can be used in mathematics education.

Music

This episode is all about the forgotten mathematical tool of numbers. Ok, forgotten may be a bit strong, but after a certain point in mathematics numbers seem to lose a bit of their importance. For the first few years after you start to learn math it is all add these numbers, divide this number by that one, or find that number. And then it morphs into for all numbers or let x be an arbitrary number or for epsilon greater than zero and numbers start to lose their power.

Well not on this episode. Samuel Hansen has found stories about amazing properties of numbers, how a person started collecting collections of numbers, how research can lead to a number horde which can then lead to more research, and all about favorite numbers.

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Follow ACMEScience on twitter, and Samuel Hansen too, for Updates on Relatively Prime, and our other shows

Numbers Gossip:

Tanya Khovanova is a freelance mathematician and mathematical entertainer currently working as a research affiliate at MIT. She is also the mind behind Number Gossip, a website for finding out surprising things about numbers. Her son Alexey Radul helped design Number Gossip, and his son Lev helped give background noise for our interview.

Sequence Encyclopedia:

Neil Sloane started collecting sequences in 1964 as a graduate student at Cornell. His collection was first published in 1973, then again in 1995, and then became the Online Encyclopedia of Integer Sequences in 1996. He also managed to fit 43 years of work at AT&T in there somehow. Samuel caught up with Neil Sloane at the 2012 Joint Mathematics Meetings in Boston

0% of All Real Numbers:

Michael Shamos is the Distinguished Career Professor in the School of Computer Science at Carnegie Mellon University. His career has included mathematics, computer science, law, business, and pool. He is the author of “The Catalog of Real Numbers”

Which is Your Favorite:

Alex Bellos is a journalist and author. His most recent book Here’s Looking at Euclid(Alex’s Adventures in Number Land in the UK) is all about the world of mathematics. He is also the mind behind the Favourite Number Project.

The Favorite Number Gang:

David Spiegelhalter

Music:

Soap and Foam