Junk Charts: A Tour

Kaiser Fung’s “Junk Charts” blog is full of treasures, including ones related to the COVID-19 pandemic. Evelyn wrote a post about the blog back in 2017. Please join me on a tour of a few of the posts Fung has written since then.

Pandemic-related posts

This exercise plan for your lock-down work-out is inspired by Venn”

This post includes a Venn diagram with so many compartments that it’s a bit dizzying. The chart came from a Nature article and it’s supposed to show symptoms that users of a UK app reported after testing positive for COVID-19.

It “fails the self-sufficiency test because if you remove the data from it, you end up with a data container – like a world map showing country boundaries and no data,” Fung wrote, adding “If you’re new here: if a graphic requires the entire dataset to be printed on it for comprehension, then the visual elements of the graphic are not doing any work. The graphic cannot stand on its own.”

“The numbers on this graphic add to 1,764 whereas the study population in the preprint was 1,702,” Fung noted. He then comments on the struggle of trying to interpret the information the chart is supposed to convey:

“The chart also strains the reader. Take the number 18, right in the middle. What combination of symptoms did these 18 people experience? You have to figure out the layers sitting beneath the number. You see dark blue, light blue, orange. If you blink, you might miss the gray at the bottom. Then you have to flip your eyes up to the legend to map these colors to diarrhoea, shortness of breath, anosmia, and fatigue. Oops, I missed the yellow, which is the cough. To be sure, you look at the remaining categories to see where they stand – I’ve named all of them except fever. The number 18 lies outside fever so this compartment represents everything except fever.”

 “When the visual runs away from the data” and “Make your color legend better with one simple rule” 

Both of these posts are related to the same pie chart, which is supposed to show survey respondents’ biggest worries about COVID-19. The options were “getting it,” “family getting it” and “the economy.”

In the first post, Fung removed the data from the chart in order to look at how much information the chart actually gives by itself. He calls this exercise a “self-sufficiency test.”

“The idea of self-sufficiency is to test how much work the visual elements of the graphic are doing to convey its message,” he noted. He explains that each of the slices of the pie chart don’t accurately represent the amounts they are supposed to (for instance, “the economy” slice takes up 38% of the pie, but 68% of people responded that the economy was their biggest worry). Furthermore, the data for the three categories add up to 178%, making a pie chart a confusing way of conveying this information. Fung recommends using a bar chart instead.

In the second post, Fung uses the chart to show “why we should follow a basic rule of constructing color legends: order the categories in the way you expect readers to encounter them.” He then recommends re-ordering the legend to better fit the order in which people will likely view the categories.

Other posts

“Too many colors on a chart is bad, but why?”

I usually enjoy colorful charts and graphics, but I agree with Fung here:

“The reason why the coloring scheme backfires is that readers may look for meaning in the colors. What’s common between Iceland, United States and Germany for them to be assigned green? What about Japan, New Zealand, Spain and France, all of which shown yellow? The readers’ instinct is driven by a set of unspoken rules that govern the production of data visualization.

Specifically, the rule here is: color differences reflect data differences. When such a rule is violated, the reader is misled and confused.”

“This Excel chart looks standard but gets everything wrong”

Fung dissects a chart that seems to show global car sales by region. However, he points out that there are at least four major problems with it.

Have an idea we should cover in a future post? Reach out in the comments below or on Twitter (@writesRCrowell).

Posted in Current Events, Data Science, Math Communication, Visualizations | Tagged , , , , , , | 2 Comments

Math in the time of COVID-19

In the past few posts, I’ve been avoiding writing about the current Coronavirus outbreak. Honestly, I’ve been having a hard time coping with the uncertainty and worry about how we are going to survive and move forward from this. Around the blogosphere, there has been an overwhelming amount of post talking about exponential growth, pedagogical tools as we transition to distance learning, ways to keep connected, to keep the research going, to keep moving forward.

I stopped to reflect on what math means at a time like this and came up with many different answers. But the biggest themes of all were empathy, kindness, and a lot of flexibility. For many, this period will be one of collective grieving. During this time some seek to ground themselves with math, others seek to distance themselves from it, both responses should be expected and welcomed as we face this unprecedented challenge. In this post, I want to share a compilation of some of the math-related resources that I’ve found to help me navigate this pandemic. 

As we transition to distance learning, many posts have addressed the challenges not only in supporting our students and faculty but in how grading is promoting/highlighting inequities. In Grading as an issue of justice in this time of transition by Brian Katz and Kate Owens, there is a great discussion on what our concerns and priorities should be. Many of the concerns such as “students’ access to computers, internet, and quiet time/space and equity of this access, the need to adjust goals, changes in our ability to support students, and allowing students to make the hard choices based on their contexts and priorities”, are discussed and some ideas are provided on how to address them.

For example, making the grades this semester “Unsatisfactory/Satisfactory” would ease the pressure on students, if carefully implemented to take into account for “students who need a certain GPA, who can’t have P/NC courses count toward their major, and who might lose NCAA eligibility.” But as mentioned in the post, I think it is crucial (and I cannot emphasize this more) that we put the humanity of our students first, as Owens states,

“If we can’t do something in the best interest of the mental and emotional health of thousands of people because of (obscure regulation), then I maintain the regulation should be expected to adapt, not the people. We are all being forced to adapt to stressors and situations none of us ever imagined a month ago. We need to lighten the burden felt by all of us. Cut the red tape — trust me, it’ll be easier to repair that than emotional baggage when things go back to normal (which I hope is soon).” -Kate Owens

Another great post that provides resources for transitioning to distance learning is “Mathematics Education in time of COVID-19” by David Bressoud, a compiled list of resources by the MAA, “MAA recommendations for COVID-19 response”“Accessible Teaching in the time of COVID-19” by Aimi Hamraie, whose suggestions come from the disability culture and community. This is a great time for conversations about how we perceive accommodations and rethink how to better support students with disabilities.

Inequality will be increased not only in our student population but throughout the academic ladder. In this recent post, The pandemic and the female academic, Alessandra Minello talks about how in the world of academic clocks we will see gender inequality exacerbated by during this pandemic, she proposed that the lockdown period is taken as a care leave as a way to support families during this time, particularly single parents who most often tend to be women.  

With the footnote “*Everything is definitely not fine.” , I am very grateful to Piper H for sharing in Everything * is fine” the challenges and thoughts on the human side of this pandemic. I felt very seen especially as we rethink our responsibility as teachers and to each other.

“If we lose a member of our community to illness due to lack of funds, lack of resources, or lack of connection, who cares if we successfully zoomed our lectures?? I’ve heard it said that we have an obligation to our students to provide them what they paid for, but what about our moral obligations to each other? If I’m having breakdowns because I have to navigate caregivers whose exposure I can’t control, whose availability I can’t rely on, and I get a mass mailing with a thousand links about administering exams, all I can think is my workplace doesn’t care if I survive this.

And the worst thing is I know I’m super privileged in this.

Everyone makes connections; reach out to others and let’s remember those who didn’t. I will no longer be intimidated by mathematicians who failed this massive test in decency.” – Piper H

There has been a boom in the number of posts tackling the main features of transmission and spread using mathematics. As a math biologist, I am no stranger to modeling infectious diseases. We see talk about flattening the curve, exponential growth, transmission rates, basic reproduction number, among many other terms used at the intersection of math and epidemiology.

I’ve been so impressed with the efforts to demystify the math behind some of the key features of this outbreak. It might be in your family and friend circles, or also to your students, but I think part of our contribution can be helping the public better understand what these numbers/concepts mean. I really enjoyed Kamuela E. Yong’s, “The mathematics of a pandemic”,  3Blue1bBrown’s on exponential/logistic growth and epidemics , “Coronavirus, by the Numbers” by and “Why outbreaks like coronavirus spread exponentially, and how to “flatten the curve”.

Professional societies have also made available compiled lists of resources such as the American Mathematical Society’s list “AMS Resources & Updates related to COVID-19, the Society for Industrial and Applied Mathematics “Mathematical Resources to Help Understand COVID-19”, Mathematical Association of America’s “COVID-19 Update”, and the Association for Women in Mathematics’ “COVID-19 and the AWM Community. These include lists of online seminars, updates on the status of big community events, resources for teaching, articles of the current research, among others. 

For me, being part of a community is everything and in these isolated times we must find ways to support each other. As Carrie Diaz Eaton discusses in “Community in a time of COVID-19”,

“One of the most beautiful things I’ve seen is the crowdsourcing of help documents and Zoom chat meetups on Facebook and Twitter, the formation of open education communities like the one on MAA Connect and QUBES, and beautiful stories on my email about how my own campus community is helping students and each other through this with as much support as possible. Even without our formal gatherings, our community is still there for us. Don’t do this alone. You don’t have to. Remember that we already are a community, even in a time of COVID-19.” – Carrie Diaz Eaton

At times like this, I am reminded of Francis Su’s words from his 2017 speech at the Joint Math Meetings. 

“Because we are not mathematical machines. We live, we breathe, we feel, we bleed. If your students are struggling, and you don’t acknowledge it, their education becomes disconnected and irrelevant. Why should anyone care about mathematics if it doesn’t connect deeply to some human desire: to play, seek the truth, pursue beauty, fight for justice? You can be that connection.”  – Francis Su

During challenging times, having a connection to others is needed more than ever. Reach out to each other and extend as much kindness as you can, build structures of support for yourself, your students, and others, and stay safe. 

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Resources to share? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)

Posted in Applied Math, Biomath, Blogs, Current Events, Issues in Higher Education, Math Communication, Math Education, Mental Health, women in math | Leave a comment

Logic ForAll: A Tour

From the blog post ‘Vanity Trip’. Translation: Valerria de Paiva: Brazilian Logician and Computer Scientist

While touring the math blogosphere I was very excited to find Logic ForAll’, a blog dedicated to making math accessible by mathematician and computer scientist Dr. Valeria de Paiva. She also writes in another great blog Women in Logic, which is used to organize and keep links to studies and graphs that show the extent of the problem and the tools other people have found to fight it. Women in Logic is also a Facebook group for women in Logic, philosophical, mathematical or computational or any other kind of formal logic that you care about. They have almost 500 members now and as described in the blog “so far, we have been finding it useful to discuss issues that affect us in our daily lives. There is also a Women in Logic spreadsheet with names of female logicians, organized by continent. This is an attempt at showing that there are plenty of female logicians around.”

Back in 2015, Dr. de Paiva was featured in the MAA article where she provides a brief description of her background and research interests.

“I am a Brazilian, from Rio de Janeiro, but I got my doctorate in Mathematics in Cambridge, UK, for work on “Dialectica Categories” written under Martin Hyland’s supervision. Working in Cambridge was a life-changing experience: I am now proud to say that my “academic great-grandfather” is none less than the founder of theoretical computer science, Alan Turing. I have, since my Cambridge days, worked on logical approaches to computation. My research interests include categorical proof theory, type theory, programming languages, logics for knowledge representation, logics of context, linear logic, intuitionistic modal logics and linguistic applications of logic. My work spans several different fields and I like all of my ‘hats’: mathematician, logician, computer scientist, and more recently computational linguist.”

One of the aspects I like most about the blog is the fact that it captures the life of a researcher quite well. Her writing combines a mix of styles that remind me of a mix between a classroom, research seminar, and talking with colleagues. I was curious to know more about the inspiration behind the ‘Logic ForAll’ blog so, in this tour, I hope to give you a glimpse of the blog’s style, content, and insights from Dr. Valeria de Paiva herself!

1. VRQ: Can you tell our readers a bit about yourself and your blog?

Valeria de Paiva: “Sure. I am a mathematician, an AI scientist and a computational linguist. I did my PhD in Cambridge, UK on Category Theory and I was a professor of Theoretical Computer Science at the University of Birmingham, UK, until I moved to the Bay Area, some twenty years ago. Here I have worked for some nine years at Xerox PARC and then in a series of other enterprises, like Nuance Communications and Samsung Research America. Along this way I have accumulated several different lines of research, so now I do work on several things, with different people. My blog started when I was teaching “baby logic” at Stanford and Santa Clara Universities and wanted to give students things to read. But nowadays its main function is to help me keep balancing these different projects. A sketchy description of the projects in the blog simply gives names to the buckets of things I do: Categorical Structures for (Linear) Logic, Constructive Modal Logics and IMLA, Lexical Portuguese Resources and OpenWordNet-PT, Lean Logic and Entailment and Contradiction Detection (ECD). This is in vaguely chronological order, but I actually work most when I have collaborators to play mental ping-pong with: I have an idea, you don’t like a bit of it, we try again, and the game goes on until we decide that we have a nice story of making a dent on our common ignorance.”

2.VRQ: What is the inspiration behind your blog?

Valeria de Paiva: “I’ve got inspiration from many mathematicians that I see trying to make mathematics more accessible to everyone. The name of the blog is “Logic ForAll”, now this is what I want, all people using logic formalized or not in the daily activities. But the name is also a pun, because in Brazilian Portuguese we have a dance and a style of music called “forro’ “. I only realized very late that the music (which is great and very danceable) comes from a mispronunciation of the English expression “for all”. So I wanted my blog to be like the music, fun and enjoyable and for all. Also, if possible full of little puzzles and games that it didn’t matter if you didn’t get them. It’s not about competition, it’s about fun!”

3.VRQ: What is the most interesting thing you’ve learned through blogging?

Valeria de Paiva: “I think I learned a while back that I only understand things when I am able to explain it to others — wherein others, I include myself. Once it’s written, it looks like another person did it, so I can debate it and discuss it all over again. I think one of the first posts in my blog, (I’m afraid I don’t remember where I copied it from) shows what I mean well 

From the webcomic Abstruse Goose.

You don’t just read mathematics, you fight it. An attitude that we should carry over to all kinds of things we read, right?”

4. VRQ:  Do you have advice for other mathematicians interested in creating their own blog?

Valeria de Paiva: “I do not think that I am good enough at this job, to be giving advice. My blog is a mess, I cannot keep the number of posts reasonable. I cannot find things I need that I know are there. I cannot write latex in it, I end up in a latex pidgin, where some things are their latex symbols, some others whatever name I prefer to give them, etc. But I’d suggest that any amount of demystification that we can do of mathematics is a good thing. It’s not rocket science, actually not even rocket science is rocket science, you just have to put the effort to understand it. And, as Barbara Fantechi was saying in Twitter the other day “most mathematicians aren’t like the gentlemen in this picture (Erdos and Tao). We’re not geniuses, just honest workers, motivated by a love of beauty, and patterns, and discovery. Most of us cover a variety of social roles, and not all of our time is for maths. We all count.” But we count more when we’re not impenetrable, when we have pictures and drawings, when we make our ideas more accessible, even if they do get a tiny bit less precise. It’s worth the trade-off, I say. Also, if English is not your first language (like it’s the case for me) using some grammar and spelling software does wonders for you (and your prepositions!).”

Some of her recent blog posts include:

“SICK (the data set) in these trying times” 

Here Dr. de Paiva describes her work with colleagues involving the Sentences Involving Compositional Knowledge (SICK) data set, provides a list of references, and shares her future research directions. In particular, she shares her article “Textual Inference: getting logic from humans, and her belief that their systems should learn from datasets that agree with human experience and how the single implication cases in SICK, they expected to find many problems. She mentions a few directions of the work towards addressing these problems.

“Artifacts in NLP”

In this post, Dr. de Paiva shares the work that is being done to track the progress (i.e. frameworks, tasks, and datasets) in the area of Natural Language Processing (NLP). She explains that in the area of Natural Language Inference (NIL) which  “is the task of determining whether a “hypothesis” is true (entailment), false (contradiction), or undetermined (neutral) given a “premise””. As she remarks, many of the results reported on the NLI task seem to be the outcome of biases on the datasets constructed to detect inference, and these are called artifacts.  I really enjoyed reading this post and learning about the growing literature regarding NLP and modeling inference and its challenges.

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)

Posted in Applied Math, Artificial Intelligence, Blogs, Category Theory, Math Communication, Mathematics and Computing, Theoretical Mathematics, women in math | Tagged , , , , , , | 2 Comments

Joyful Learning in the Early Years: A Tour

With schools shutting down for weeks or the rest of the semester in response to COVID-19, many guardians are concerned about how to support or even direct their children’s education from home. This seems particularly true when the children are young enough that online classes might not be feasible (or the school district has opted not to offer them).

Deanna Pecaski McLennan’s Joyful Learning in the Early Years blog offers educational resources for folks with young children.  McLennan “is an educator in Southern Ontario who is greatly influenced by the Reggio Emilia approach to Early Childhood Education. She believes in a play-based, exploratory, democratic learning environment,” according to her profile on the blog. (If you’re like me and don’t know much about the Reggio Emilia approach, the Compass School in Illinois has a blog post explaining a bit about that child-centered approach.) Here are a few interesting posts that could help parents and other caregivers keep their kids engaged with learning math during this stressful time.

“Spring Math”

“In times of uncertainty, helping one another is one of the best ways to get through the stress and worry of what awaits. I know that many educators and families right now are wondering how to help support children even when we can’t be together physically,” Pecaski McLennan wrote. She created the post “to continually provide ideas for how children can explore math in their natural world.”

“The CDC is asking us to engage in social distancing and being aware of what is recommended is important. Right now being outdoors in our yards, on trails, and in gardens is still safe and encouraged. I realize that some of us are limited by our personal circumstances and not everyone has access to a yard or natural trail. I will try my best to vary activities in order to meet as many circumstances as possible. I will also tweet ideas for math learning on a regular basis @McLennan1977,” she added.

Many of the activities discussed in the post could also be adapted to be done indoors if safe outdoor options aren’t available. At the end of the post, Pecaski McLennan shares a link to a free Kindle version of her Spring Math Walk book.

“Virtual Math Question”

“In our school hallway we have a dry erase board that asks rich, low floor high ceiling questions. Students and staff that walk by are encouraged to consider the question for a few days and then contribute their ideas using dry erase markers,” Pecaski McLennan wrote. For instance, she shares the question “If 24 is the answer, then what might the question have been?” By asking questions such as this, caregivers could give kids of multiple ages and levels of math background something to think about. After pondering the question for a few hours or days, the family could come together to discuss their varied answers to the question.

“Printable Pentominoes”

Pecaski McLennan shares a set of printable pentominoes. (She recommends printing them on cardstock and laminating them, but for easy, temporary, at-home use, they could also just be printed on ordinary printer paper and used without lamination.)

She describes these manipulatives as “an essential tool for any early childhood classroom,” because they encourage a positive attitude toward math, inspire children to cooperate and collaborate and “promote math thinking in a variety of areas including spatial reasoning (logic when solving puzzles, symmetry, reflection, rotation, design), measurement (considering the area and perimeter of designs), and number sense (counting the number of tiles or squares in a design, calculating the total number of squares using the anchor of 5).”

However, these tools can also be used in activities with older children. For instance, there are pentomino activities for middle schoolers on the

“Cereal Stringing”

While this activity isn’t inherently math-related, there are definitely ways to make it so. For instance, a caregiver and kids could each make a secret pattern using cereal on a pipe cleaner. Then the children could guess what pattern the adult created and if they can’t guess it, the adult could give them clues until they guess the pattern correctly. Each kid could then explain the pattern they created on their own bracelet. Alternatively, parents could play a game with kids in which everyone makes a bracelet without counting the number of cereal pieces they use. After the bracelets are made, everyone could make their own guess about how many pieces are strung on each bracelet, explain how they reached their guesses and then count the actual number of pieces together.

I also like this activity because it only requires a few materials and those can be easily swapped out. (Don’t have pipe cleaners at home? Use string or strips of fabric instead. Don’t have cereal? Use beads or help your kiddo thread stale popcorn onto string.)

The Joyful Learning in the Early Years blog abounds with other ideas that could be adapted to meet the needs of guardians educating their own children during the pandemic, even if outdoor access isn’t available or if the children they’re educating are older than the kindergarteners that Pecaski McLennan teaches.

Looking for additional ideas? The Bedtime Math website and app offer free activities. The new “Cabin Fever Math” section focuses on non-screen math activities that families can do together.

Thank you for reading! If you have ideas or feedback to share, please reach out in the comments or on Twitter (@writesRCrowell).

Posted in Book/App, Current Events, Interactive, K-12 Mathematics, Math Communication, Math Education, Mathematics and the Arts | Tagged , , , , , , , , , | Leave a comment

Old and New Math Celebrations

With all the news about the coronavirus, the uncertainty, and stress many are currently facing, I wanted to write a post with some levity ¹. What better day than this! Today is both the first International Day of Mathematics (IDM) and Pi Day. These two celebrations cause great joy in math enthusiasts and give space to learn new (and old) exciting facts.

International Day of Mathematics Logo.

Proclaimed by UNESCO back in November,  the goal of the IDM is to  “explain and celebrate the essential role that mathematics and mathematics education play in breakthroughs in science and technology, improving the quality of life, empowering women and girls, and contributing to the achievement of the Sustainable Development Goals of the 2030 Agenda (SDG1-17) of the United Nations.”

This lofty goal is hoped to be achieved by worldwide events for all in schools, museums, libraries, and other spaces. This year’s International Day of Mathematics theme is “Mathematics is Everywhere” and there is a great website dedicated to exploring many examples of this theme available in seven different languages. Among my favorite examples on the page is “Search for Alien Life”, “Predicting Weather”, and “Epidemic Analysis”. Fun fact, in “Search of Alien Life”, they talk about the famous Arecibo Message sent from Earth to space back in 1974 from Puerto Rico. As explained in Arecibo Message” by the SETI Institute,

“The message consists of 1679 bits, arranged into 73 lines of 23 characters per line (these are both prime numbers, and may help the aliens decode the message). The “ones” and “zeroes” were transmitted by frequency shifting at the rate of 10 bits per second. The total broadcast was less than three minutes. A graphic showing the message is reproduced here. It consists, among other things, of the Arecibo telescope, our solar system, DNA, a stick figure of a human, and some of the biochemicals of earthly life. Although it’s unlikely that this short inquiry will ever prompt a reply, the experiment was useful in getting us to think a bit about the difficulties of communicating across space, time, and a presumably wide culture gap.” – SETI Institute

Through their Twitter account, IDM also shared this really neat collective video featuring submissions from all over the world in many languages showcasing all the places you can find math around you.

The fact that this was the first celebration of the International Day of Math made me curious about the history of Pi Day. I was surprised to find that it started in 1988 and it was founded by physicist Larry Shaw. The first celebration was at the Exploratorium interactive science museum and consisted of a circular parade and eating fruit pies. You can still celebrate Pi Day at the Exploratorium by joining online and checking out some of their fun $\pi$ inspired activities.

The symbol for pi wasn’t used until the 1700s. As described in PiDay.org, before the symbol was used it was described as  “the quantity which, when the diameter is multiplied by it, yields the circumference” and other long, roundabout descriptions. In the 1700s, the Swiss mathematician and physicist named Euler formalized the use of the Greek lowercase letter, π, as the notation for pi. This is the first letter of the Greek word, perimetros, which loosely translates to “circumference.”

In “Getting Ready for Pi Day, and also the Playful Math Blog Carnival”, Joseph Nebus shares a few some of his Pi day content in his archive including “Six or Arguably Four Things for Pi Day” on different ways to compute $\pi$ and a great list of comic strips from previous years. In the Crooked Pencil blog, Priya Narayanan writes about Ramanujan: He who had the Pi & ate it too!

“While Ramanujan’s formulae were progressively more and more accurate, what is more important to us today is his approach to the calculations, which provided the foundation for the fastest- known algorithm that, in 1987, allowed mathematician and programmer Bill Gosper to use the computer to churn out the value of π to around 17 million decimal places. Later, mathematicians David and Gregory Chudnovsky used his formulae as the basis of their own variants that allowed them to calculate the value of π to an astounding 4 billion decimal places using their homemade parallel computer.”

The number $\pi$ has a really interesting history. In his book, Tales of Impossibility, David Richeson discusses how “compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia.” A review of the book in The Math Less Travel blog, describes the chapters as follows,

“Alternating with the “regular” chapters, Richeson includes a number of “tangents”, each one a short, fascinating glimpse into some topic which is related to the previous chapter but isn’t strictly necessary for driving the story forward (e.g. toothpick constructions, Crockett Johnson, origami, the Indiana pi bill, computing digits of pi, the tau vs pi debate, etc.). Even though none of them are strictly necessary, taken as a whole these “tangent” chapters do a lot to round out the story and give a fuller sense of the many explorations inspired by the problems of antiquity.”

You also find many cool facts in this short article, “Here’s how pi matters every day not just March 14“, in particular, what is the current Guinness World Record for computing $\pi$.

“The Guinness World Record for a calculation of pi was set in 2019 by Emma Haruka Iwao using Google cloud software. She calculated pi to 31,415,926,535,897 digits.”

Pretty amazing! You can hear from Haruka herself on how she achieved this here. Another really interesting find was that IBM has released a new tutorial as part of its open-source online textbook to estimate $\pi$ on a quantum computer.

“The thing we’re trying to do here is to stay away from computing a million digits of Pi and more to use the theme of Pi Day to educate people on what quantum algorithms look like.” – Abraham “Abe” Asfaw, Global lead of quantum education at IBM.

But what makes Pi so interesting? As explained by Tom Crawford in “Make your Own Pi” it turns up in many important theories like Heisenberg’s Uncertainty Principle, Einstein Field Equations, and Newton’s Gravitational Constant to name a few.

“You may know it in terms of circles, but it has the rather fantastic knack of cropping up in the most unexpected places… Quantum Theory? Check. Einstein’s Theory of Relativity? Check. Newton’s Law of Gravity? Check. Three of the most important theories we use to explain the universe, and each of them has a formula containing the number Pi.”

Whether you celebrate International Mathematics Day and/or Pi Day, stay safe! Have ideas or feedback to share with us? You can reach us in the comments below or on Twitter (@MissVRiveraQ)!

¹ Note: Though I will recommend watching this great video from 3Blue1bBrown’s on exponential/logistic growth and epidemics and this recent article “Coronavirus, by the Numbers”.

Posted in Applied Math, Current Events, History of Mathematics, Math Communication, Mathematics and Computing, Recreational Mathematics | 1 Comment

A Tour of Intersections: Poetry with Mathematics

I don’t know about you, but between coverage of the coronavirus outbreak and political discussions looking ahead to this year’s presidential elections, I have been encountering a lot of stress-inducing content lately. Reading poetry is a welcome break from that, so here is a roundup of a few of my favorite posts from the last few months on the Intersections: Poetry with Mathematics blog.

“A MATH WOMAN acrostic poem”

In this short post, JoAnne Growney challenges readers to “describe a MATH WOMAN in 9 words? and, what if those words’ first letters must spell MATH WOMAN?”

After all, March is still Women’s History Month.

I’m still thinking of ideas for my poem.

“Those trains in word problems — who rides them?”

This post is about the poem “A Problem in a Math Book” by Yehuda Amichai. The poem was originally written in Hebrew before being translated into more than 40 other languages, Growney’s post notes.

If I had to pick a favorite line from the poem, it would be this part (about two trains in a math problem): “And no one ever asked what happens when they meet.”

“Learning slowly . . savoring difficulty . . .”

Growney shares one of her own poems called “Reflection,” which is about her mathematics learning process.

I relate deeply to this line. ” My notes were three times as long as what I had read.”

“Poetically exploring the the invention of ‘i'”

Featuring an except from “The Mathematical i” by Punya Mishra.

“Dogs Know . . . Mathematics”

This piece explores the poem “Dogs Know” by Larry Lesser, which first appeared in the Journal of Humanistic Mathematics and was also featured on NPR. I really enjoy the section of the poem that talks about the dog solving a packing problem, but I think my favorite phrase from the poem is:

My dog knows trigonometry, tracking
periodic rhythms
of moon
and heart.

Finally, Growney’s blog also has two posts (this one and this one) about the three winning poems in the 2020 AMS Math Poetry Contest: “Outlier,” by Sabrina Little, “The Number Won,” by Austen Mazenko and “x² + y² = 1(ife),” by Chenyu Lin, Colorado Christian University.

Have ideas or feedback to share with us? You can reach us in the comments below or on Twitter (@writesRCrowell)!

Posted in Current Events, Math Communication, Math Education, Mathematics and the Arts, people in math, Recreational Mathematics, women in math | Tagged , , , , | 2 Comments

The Joy of x Podcast: A Tour

The Joy of x podcast logo.

The Joy of x podcast is a series of conversations with a wide range of scientists about their lives, work, and what fostered their passion. It is hosted by Steven Strogatz in collaboration with QuantaMagazine. The format of this podcast makes it seem like you are joining an intimate session where you are privy to the interviewee’s lived experiences and how it has influenced their journey so far. Steven Strogatz, an applied mathematician, and author, really sparks the curiosity of listeners by displaying his own joy for discovery and scientific quests. In each episode, you get a clear sense of the joy behind the search for answers for the big questions these mathematicians tackle. As said by Strogatz in Why I’m Hosting The Joy of x Podcast,

“Through this podcast, I’ve been learning about the inner lives of some of the most intriguing mathematicians and scientists working today. A few are old friends and colleagues, while others are people I’ve still never met in person: Until their voices came through my headset, I knew them only through their research. But in every case, I wanted to know what makes them tick. I wanted to know why they do what they do, what they’ve discovered, and why it matters to them and to the world.” – Steven Strogatz

In the press release, QuantaMagazine Launches new podcast ‘The Joy of x’, we get the full line-up of this series which will have 12 episodes (one per week) that run from 40 to 75 minutes each and features a fantastic group of scientists and mathematicians including “mathematical physicist Robbert Dijkgraaf, mathematical biologist Corina Tarnita, mathematician Alex Kontorovich, neurobiologist Leslie Vosshall, mathematician and retired NFL player John Urschel, theoretical cosmologist Janna Levin, mathematician Tadashi Tokieda, neurobiologist Cori Bargmann, astrophysicist Brian Keating, mathematician Moon Duchin, mathematician Rebecca Goldin, and psychologist Brian Nosek.” 

So far, the podcast has released six episodes featuring Priya Natarajan (Yale University), Alex Kontovorich  (Rutgers University), Leslie Vosshall (Rockefeller University), Robbert Dijkgraaf (Director of the Institute for Advanced Study in Princeton), Corina Tarnita (Princeton University), and John Urschel (Massachusetts Institute of Technology). There is a great variety in the fields represented by the interviewees. If you enjoy exploring all sorts of areas of science and knowing the minds behind interesting questions, this podcast is for you. You can listen to the trailer below!

For me, the power of this podcast is listening to people share their stories. This adds a new dimension to them that is missed in how we talk about science and math. In this post, I review and give a glimpse of the latest three episodes.

John Urschel: From NFL Player to Mathematician

In this episode, we listen to mathematician and former NFL football player John Urschel. Currently, he is a Ph.D. Candidate at MIT where he studies topics in Convex Geometry, Graph Theory, Machine Learning, and Numerical Analysis. He shares the pressures of “living two lives” as an NFL football player and graduate student. For example, how qualifying exams can feel like the only chance to prove that you belong in the fields and how strategic quitting can be a valuable skill. From a very young age, he discovered the joy in solving challenging puzzles which turned into a passion for math. While his work has many applications, what he really enjoys is “digging out the math that makes the machine work”. This translates into going from a real-world problem, moving it to a more abstract yet beautiful representation and towards a generalization. You can read more about his journey in this interview about his upcoming book “Mind and Matter: A Life in Math and Football”. 

Corina Tarnita and the Deep Mathematics of Social Insects

In this episode, we listen to Corina Tarnita a mathematical biologist with a passion for patterns. She nurtured her mathematical ability by tackling problem-solving from a young age through the encouragement of her mother and participation in math olympiads. Her love for math sparked a love for biology. As she elegantly put it, “there is something remarkable about the diversity of solutions that nature has found for this unbelievable complex problems.” Using mathematical models, she discovered that termite colonies and plant competition for resources drive the patterns that can be seen like “pepperoni slices on a pizza” in the grasslands of Namibia. What I enjoyed the most about this interview, what of course the connection between the math, the biology, and also a bit of chance. I won’t spoil the story but sometimes, even when math points in the right direction, it takes being in the field to connect the dots. You can read more about Tarnita’s story and work in A Mathematician Who Decodes the Patterns Stamped Out by Life.

Robbert Dijkgraaf on Exploring Quantum Reality

In the episode, we listen to Robbert Dijkgraff a mathematical physicist who rediscovered his passion for physics through art. Through his career, even as a young scientist, he valued the power of collaboration. He retells how collaborating with his childhood friend allowed them to use both their strengths to make discoveries. He spent two years at an art school in the Netherlands, where it brought him a new perspective, “it’s about how adventurous are you, are you willing to go to other fields?… You could just explore, explore, explore.” This allowed him to bring this sense of adventure to what it means to be a research scientist. He works in the field of string theory, a field that hopes to bring together the theory of general relativity (i.e. the theory of the very large) and quantum theory (i.e. the theory of the small). Matrix models, which have symmetry at its core, can be used to build strings, gravity, and space-time. What I loved about this interview is the great commentary on how we experience time and space differently as humans. You can read more about Dijkgraff’s views on mathematical conjectures in his recent post, “The Subtle Art of the Mathematical Conjecture”.

Do you have suggestions of topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me at @MissVRiveraQ.


Posted in Applied Math, Biomath, Current Events, Math Communication, Physics, Podcast | Leave a comment

ThatsMaths: A Tour

“The Great Wave off Kanagawa” by Katsushika Hokusai is discussed in a ThatsMaths post about rogue waves. Woodblock print by Katsushika Hokusai. Wikimedia Commons image credit: Meidosensei/CC

ThatsMaths is a blog by Peter Lynch, an emeritus professor of the University College Dublin’s School of Mathematics and Statistics. Many of the posts on the blog are articles that Lynch has written for the Irish Times. Please join me on a tour of some exciting ThatsMaths posts from the last several months.

“An English Lady with a Certain Taste”

In the early 1900’s, Dr. Muriel Bristol told two statisticians — Ronald Fisher and William Roach — that she could taste the order in which ingredients were added to tea.

Shortly after Fisher had moved to Rothamstead Research Station in 1919, he poured a cup of tea and offered it to Bristol. She declined, saying that she preferred the milk to be poured first. The arrogant young Fisher scoffed at this, insisting that it could not possibly make any difference, but Bristol maintained her stance, assuring him that she would always know the difference. Overhearing this exchange, another scientist, William Roach said, ‘Let’s test her,'” Lynch wrote.

He describes how statistics and combinatorics were used to determine if Bistol could actually taste the order in which ingredients were added to her cup of tea.

“Simple Curves that Perplex Mathematicians and Inspire Artists”

This post covers the Jordan Curve Theorem (including an extension of the theorem to higher dimensions), the traveling salesman problem and their intersections with art.

“The Jordan Curve Theorem states that every simple closed curve, no matter how complicated or convoluted, divides the plane into two regions, an inside and an outside. The theorem appears so trivial that it does not require a proof. But results like this can be much more profound than a first glance might suggest and, on occasions, things that appear obvious can turn out to be false,” Lynch wrote.

He then discusses Bernhard Bolzano’s work. (Lynch has also written a separate post focusing on Bolzano’s life and work.) “He claimed that, for a closed loop in a plane, a line connecting a point enclosed by the loop (inside) to a point distant from it (outside) must intersect the loop. This seems obvious enough, but Bolzano realized that it was a non-trivial problem,” Lynch wrote.

“For general curves it is quite difficult to prove since “simple” curves can have some bizarre properties, such as being jagged everywhere with no definite direction, or as being fractal in nature like the boundary of a snowflake. This makes it difficult to distinguish which points are inside and which are outside. The proof uses advanced ideas from the branch of mathematics known as topology,” he added.

“Hokusai’s Great Wave and Roguish Behaviour”

In this post, Lynch wrote about “The Great Wave off Kanagawa” woodcut by Katsushika Hokusai, rogue waves, non-linear modeling and the study of rogue waves in laboratory tanks.

“In recent decades, many enormous sea waves have been observed, removing all doubt about the existence of rogue waves. These waves have heights more than double the surrounding waves. In January 2014, the height of a wave off Killard Point in Co. Clare was measured at almost 30 meters. Although they are quite rare, rogue waves are part of the normal behaviour of the oceans,” Lynch wrote.

Lab studies on rogue waves utilize “mathematical theory, computer simulations, wave-tank experiments and observations” to “determine the critical factors for the formation of rogue waves. Mariners’ lives depend on their ability to avoid them, and new theoretical descriptions may enable us to anticipate their likely occurrence. Despite progress, many questions about rogue waves remain unanswered and research continues. The pay-offs include greater accuracy of wave predictions and saving of money and of lives,” Lynch noted.

“Chase and Escape: Pursuit Problems”

This piece describes the mathematical study of pursuit problems, beginning with the work of Pierre Bouguer, who, around the year 1730, produced “the first comprehensive treatment” of the subject, according to Lynch.

“From cheetahs chasing gazelles, through coastguards saving shipwrecked sailors, to missiles launched at enemy aircraft, strategies of pursuit and evasion play a role in many areas of life (and death). From pre-historic times we have been solving such pursuit problems. The survival of our early ancestors depended on their ability to acquire food. This involved chasing and killing animals, and success depended on an understanding of relative speeds and optimal pursuit paths,” he wrote.

The rest of the piece focuses on cyclic pursuit problems (more specifically, the N-bug problem).

Want to get in touch to share feedback or ideas for future posts? We welcome your comments below or on Twitter (@writesRCrowell).

Posted in Applied Math, Biomath, Blogs, History of Mathematics, Mathematics and the Arts, people in math, Statistics | Tagged , , , , , , | Leave a comment

In honor of Black History Month

February 1 marked the beginning of Black History Month. Its origin trace back to 1926, when the historian Carter G. Woodson pioneered “Negro History Week” in the second week of February because it coincided with the birthdays of former US president Abraham Lincoln (February 12) and abolitionist Frederick Douglass (February 14). Later, during the United States Bicentennial in 1976, President Gerald Ford recognized Black History Month, reminding Americans to “seize the opportunity to honor the too-often neglected accomplishments of black Americans in every area of endeavor throughout our history”.

In last year’s post, “On Mathematical Superpowers and Black History Month“, Rachel listed some of the great posts that have been published across many of the AMS blogs and highlights “some power problems that need to be addressed to make the mathematics community a more welcoming and opportunity-filled one for Black mathematicians and students.” Last year, SIAM News highlighted some of the African American heroes in mathematics in “Celebrating Black History Month” including Mary Jackson, Charles L. Reason, J. Ernest Wilkins Jr, Annie Easley, Katherine Johnson, Elbert Frank Cox, Dorothy Vaughan, and David Blackwell. Knowing their history, the power behind their pursuit of knowledge, and the trail the left for others to follow is a way to honor their place in our community. To preserve and share the stories of African American Elders, the National Visionary Leadership Project has recorded two video series featuring interviews with David Blackwell, the first African-American member of the National Academy of Sciences, and Evelyn Granville, one of the first African-American women to earn a Doctorate in mathematics.

This month’s Notices of the AMS features articles that showcase the research and contributions of Black mathematicians to the mathematical community. In “A word from…” by Robin Wilson, he summarizes the topics covered in this issue and emphasizes that the history of Black mathematicians is a part of the history of the American Mathematical Society, one not always centered around inclusion.

“Black history is American history, and the history of Black mathematicians in the United States is a part of the history of the American Mathematical Society. As with the history of the United States, the history of the AMS has not always been one of inclusion. With this special issue in honor of Black History Month, we shine light on some of that history, as well as uplift the efforts of mathematicians and institutions to redirect this tide of history and create equity in the field.” – Robin Wilson

A piece that caught my attention was Jesse Leo Kass, “James L. Solomon and the End of Segregation at the University of South Carolina”. In the article, he provides an overview of the impact segregation had on mathematics and how James L. Solomon, a former math graduate student, was one of the first three African American students to desegregate the university in 1963.

“The professional trajectories of African American mathematicians were profoundly shaped by legalized segregation and other exclusionary policies. Not only did such measures make it difficult for African Americans to obtain a college education, but those who persevered and wanted to work as professional mathematicians faced limited job opportunities. While HBCUs employed largely African American faculty, many other universities had formal or informal policies against hiring African Americans. Moreover, those who did secure academic positions still struggled to participate fully in academic culture. The career of William Claytor vividly illustrates these challenge.” – Jesse Leo Kass

In “Black and Excellent in Math”, Haydee Lindo writes for the MAA Math Values blog about the implicit and overt aggression that students and faculty of color face and how it is a key source of disparity in black mathematical achievement. She highlights the work of Ebony McGee, in search of navigating these challenges.

“How do we make ourselves bulletproof? We can’t. […] One of the key ideas seems to be this: when we are younger our attraction to Mathematics is often fueled by external encouragement from our teachers, high scores on tests, etc. As we grow more mature, black mathematicians and engineers remain successful by progressing, from being preoccupied with attempts to prove stereotypes wrong to adopting more self-defined reasons to achieve.”  – Haydee Lindo

Lindo also emphasizes the importance of cultivating affirming environments. For example, attending Historically Black Colleges and Universities (HBCU), taking courses with faculty of color, attending conferences with a focus on the success of minority STEM students, and moving towards culturally sustaining pedagogies. Giving back to the community through mentorship, service, and outreach plays a huge role in preparing future generations. In “Mathematics: The Key to Empowering Tomorrow’s Workforce”, Tanya Moore describes it elegantly.

“In the African-American tradition there is a phrase, Each One, Reach One, that reflects the value of bringing along others once you have acquired a certain level of knowledge or success. In the context of the mathematics community, this value is often reflected in the math-related activities and events that happen outside the classroom to prepare the next generation for their chosen educational and career paths. As technology promises to change the way we work by altering the landscape of the labor market, mathematics will take on a new level of importance. The role of service and outreach and the willingness for Each One to Reach One to increase mathematical engagement will matter even more.” – Tanya Moore

The workforce is also changing as data plays a bigger role in many career paths and in our lives. An amazing group that has data at its center is Data for Black Lives. This group of activists, organizers, and mathematicians are “committed to the mission of using data science to create concrete and measurable change in the lives of Black people”. During this month, “Mathematically Gifted & Black” highlights the contributions and lives of Black mathematicians. This website was founded in December 2016 by  Erica Graham, Raegan Higgins, Shelby Wilson, and Candice Price. Its name was inspired by the song “To Be Young, Gifted and Black” sung by Nina Simone and co-written by Weldon Irvine. I was so excited to read the profiles of the honorees of this year which so far include Asamoah Nkwanta, Felicity T. Enders, Kwame Okrah, Shea D. Burns, Kevin Corlette, Caprice Stanley, Abdul-Aziz Yakubu, Aissa Wade, Lorin Crawford, Omayra Ortega, Christopher C. Jett, and Loni Philip Tabb.  What I love about this website is summarized perfectly in “The Mathematically Gifted and Black Website“:

“The power of the personal story is helping people better understand one another and shred stereotypes. The mathematicians spotlighted were able to tell their stories in their own words, to discuss their proudest moments, in mathematics and in life, and to include personal stories of struggle along with inspirational anecdotes. All were allowed to be themselves, unapologetically.”

Do you have suggestions of topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me at  @MissVRiveraQ.

Posted in Black History Month, Blogs, Current Events, History of Mathematics, Math Education, people in math, Publishing in Math, women in math | 2 Comments

Mathematical Enchantments: A Tour

Mathematical Enchantments, or “Jim Propp’s math blog” is about “adventures in fantastic realms you can build inside your head.” The blog has been discussed a few times on this blog in recent years. Welcome to my tour of a few interesting posts on the blog.

“Why this blog?”

I appreciate when the purpose and focus of a blog are well-defined, and this post really delivers on that front.

Propp wrote about math as “a consolation for living in a world without magic.” As someone who never believed in magic (even as a child) but wished for its existence, I relate to that sentiment.

“Lots of people (most notably Martin Gardner and more recently Arthur Benjamin, Persi Diaconis, Ron Graham, and Colm Mulcahy) have written and talked about the links between math and magic tricks, but hardly anyone talks about the way that math, for many people who do research in it, satisfies a craving for the fantastic that most of us haven’t outgrown (even if we’ve persuaded ourselves that we have). Indeed, I think that most children get glimpses, all too easily forgotten, of math as a wondrous ticket to other worlds,” Propp wrote.

“My goal in Mathematical Enchantments is to reawaken in my readers this childlike relationship to the subject, and to make this view of math enticing and even natural. And if you are an actual child, or an actual mathematician, and your sense of mathematical wonder is already awake and active, all the better! There’ll be lots of new games you can play. These things are fun, and fun is good,” he added.

“The Paintball Party Problem and the Habit of Symmetry”

Propp wrote about time he was “the showrunner” of his son’s ninth birthday party. He had to decide how to configure seven games of two “four on four” paintball teams so that each boy attending the party would be on his son’s team the same number of times, and ideally, would also be teammates with each of the other party attendees the same number of times.

He describes how the notions of randomness and quasirandomness, the geometry of cubes, finite fields and other mathematical ideas informed his solution. The team schedule “took me under five minutes, if you leave out the time I spent learning abstract algebra and coding theory thirty-plus years earlier,” Propp wrote.

“Knots and Narnias”

This post starts with the idea of portals similar to those in The Chronicles of Narnia books by C.S. Lewis and the His Dark Materials trilogy by Philip Pullman. Propp then shows how to use “mathematical scissors and glue” to construct different types of wonky, complex portals. His post includes a link to an older video of Bill Thurston (1946-2012) discussing similar ideas.

“Time and Tesseracts”

I love A Wrinkle in Time (the classic book by Madeleine L’Engle and the 2018 film), so this post especially appeals to me. Propp begins with a discussion of forth dimensional space, which he defines as “a space that at every points admits four mutually perpendicular lines, in no particular order, but not five.” He then delves into a discussion of tesseracts, hypercubes and music as a tool for thinking about higher dimensions.

Want to get in touch with feedback or to share ideas for future blog posts? Reach us in the comments or on Twitter (@writesRCrowell)!

Posted in Blogs, Interactive, Math Communication, Mathematics and the Arts, people in math, Recreational Mathematics | Tagged , , , , , , , , | 1 Comment