Penny Pinching at the Grocery Store

When I’m at the grocery store, I almost always compare the prices of different sized packages.  How much less per oz does it cost when I buy twice as much?  Sometimes the price is notably different.  Usually the cost gets cheaper when I buy more.  Here are some quick numbers I pulled from Target about Cheetos.

Cheetos Data
OZ Price $/oz
2.375 1 0.42
3.7 1.49 0.40
8.5 3.39 0.40
17.5 3.99 0.23

Sure enough, as I commit to more Cheetos, the price per oz decreases. This is almost always true! Except when it isn’t. Imagine two sizes of flour: an 8oz and a 16oz.  When the smaller bag costs $2.99 and the larger costs $5.99:


In this situation, you are saving exactly 1 penny if you buy two small bags instead of one large bag. Maybe this isn’t enough to make you change your habits, but I always buy 2 packages of the smaller product when I see this. Always. I’m sure some of you have done this too! Because a penny saved is a penny I have righteously stolen from the grocery store which so vilely priced their products ridiculously!

Actually, I can’t decide if I feel exceptionally clever when I do this… or like I’ve just wasted 5 second of my life over optimizing something trivial.  The opportunity cost of those 5 seconds is surely worth more than a penny? Right?

Well, let’s find out.  If I managed to earn 1 cent every 5 seconds, I would be earning $7.20/hour.  Not bad! But not great.  So maybe it’s not the worst thing to do while I shop.

Now, my dear reader, I have to share with you that this post came out of personal experience.  Yesterday my dad just bought 2 bags of chocolate chips, instead of one, to save a penny. And then he wrote an email to the rest of the family to tell us about it. Does your dad do that too? In his mind: The time spent on the consideration of this penny does not increase the time spent shopping …and he’s going to think about something anyway. So perhaps he is right. It’s a penny saved with zero opportunity cost! And that’s a magical thing by itself. And how often can you say your grocery trip was magical?

But, in all reality, despite the original effort resulting monetary benefit… the accounting of the event is probably not worth much. So now that I have spent time writing emails to my father and even more additional time writing a blog post to you? What have we gained from that effort? Well, maybe we all feel just a little bit better every time we gleefully pick up two tiny packages that magically cost less than the larger version of the same thing.

Posted in Shopping | Tagged , , , | Leave a comment

Hidden Figures

Hidden Figures, the movie, enjoys its wide release today. I got to see the film last night. Janelle Monae, Taraji P. Henson, Octavia Spencer out shine the stars in this beautiful film.  Hidden Figures is based on the book which was released in mid-2016.


The movie was so anticipated, it was actually optioned before the book was even published. 2016 produced two amazing books about female computers and their contributions to the space race: Rocket Girls and Hidden Figures. Rise of the Rocket Girls focuses on the female computers in southern CA at Jet Propulsion Laboratory (JPL). Hidden Figures follows the black women in Langley, Virginia who were computers for NACA and later NASA. Both books are excellent! And I highly recommend both of them. Go get them. Right now. It’s cool, I can wait. Got them ordered? Okay, let’s continue.

Back in the 1930’s women who liked math had limited career options: teacher, nurse, or secretary. These are the same options for all women, excelling math did nothing for you. Except, a woman could, in very particular circumstances, be hired as a computer. Because before computers were machines, computers were people who computed things.  This complicated task often fell to women because it was considered basically clerical. That’s right: computing triple integrals all day long qualified as clerical. And, gosh, how many of us could do that today? Not many! I, for one, can’t do very much without the help of a machine computer. (I have been advocating for the benefits of using calculators for basic math for a while!) Without these highly skilled women putting pencil to paper, we would not be able to complete the most challenging orbital computations of the day.

Karl Zielinski: Let me ask you, if you were a white man would you wish to be an engineer?
Mary Jackson: I wouldn’t have to, I’d already be one.

Hidden Figures, the film

Women often couldn’t move up. Neither to management or to more challenging technical roles like engineering or mathematics. They were forever stuck in their role as a computer. Mary Jackson, one of the key characters in the narrative wishes that she could be an engineer. But “most of the country’s top engineering schools didn’t accept women. …As for black female engineers, there weren’t enough of the in the country to constitute a rounding error.” (Hidden Figures, Pg 144). The film chooses to make this a key plot line. Obviously the issues of today influence this choice, because black women are still struggling to get their fair shake at the jobs white women have worked at for decades.

On top of societal prejudice, there was also legal bounds holding these black women back. Segregation in all public life was standard at that time. And being that Virginia is in the south, segregation was even more ingrained in the laws and society. This was one of the pieces of magic that took place at Langley, in Hidden Figures. “Unlike public schools, where minuscule budgets and ramshackle facilities exposed the sham of “separate but equal,” the Langley employee badge supposedly gave Mary access to the same workplace as her white counterparts.” (Hidden Figures, pg 108) But, despite that, the women have to fight for each and every injustice to be removed. And I do mean each and every.  For example, they wage a silent battle lasting many months where the ladies remove the “colored” sign from the lunch table everyday only to have it return the next day. In the film, this particular injustice wasn’t highlighted, instead the film focused on the immense challenges of colored bathrooms for Katherine Goble (later Katherine Johnson).

In this way, Hidden Figures gives beautiful insights into what it was like to be a female mathematician 50+ years ago. Hidden Figures has the added layer of communicating was it was like to a black female mathematician. “Compared to the white girls, [Mary] came to the lab with as much education, if not more. She dressed each day as if she were on her way to a meeting with the president.” (Hidden Figures, pg 108). I believe the film highlights this imbalance beautifully with their costume design. There is a fabulous scene where a large group of male scientists are gathered and every one of them has on a long sleeves white shirt with a thin black tie. Katherine Johnson is with them and is wearing a modest green dress. Despite it’s modesty, she stands out of a crowd with her color, style, and poise.

The film is sharp, witty and surprisingly optimistic. If you only see 1 movie in 2017, see this one. While there are other recent films about mathematicians (e.g. The Man Who Knew Infinity), Hidden Figures has the heart to make it a classic. Because if you are black or female or a mathematician or a fan of space, this film will speak to you.  And if you aren’t any of these things… that’s okay! I won’t hold it against you.  Go see this movie to learn more about life at Langley during the biggest and only race to space there ever was.

Paul Stafford: There’s no protocol for women attending.
Katherine Johnson: There’s no protocol for man circling the earth either, sir.

Hidden Figures, the film


Posted in Movies & Books, Social Mathematicians | Tagged , , , , , , , , , , , , , | 2 Comments

Indexical Visualization

Indexical Visualization is about visualizing something by looking at the actual thing.  Most of the time we take the event and turn it into numbers (data), then we take those numbers and create a visualization out of them. The idea of indexical visualization is to skip the numbers part all together.

Here is a great indexical visualization to show how fast olympic swimmer Katie Ledecky was in her 800 meter Freestyle race.  But instead of just giving you the final times, the visualization is actually a recreation of the entire race.

Data Stories podcast presented a variety of wonderful uses of this idea within their fabulous interview with Dietmar Offenhuber about his work with indexical visualization. I really love the idea of removing the middle man, the numbers. How can we describe and visualize the information we need without translating to numbers first?

Below is another great indexical visualization of the microbes on an 8 year old’s hands after playing outside. This visualization was made by Tasha Sturm of Cabrillo College.Lastly, I want to call out the Pinterest board with more great examples of indexical visualizations. The tag line/description they use is, “physical embodiment of information, traces, evidence.”

What examples of indexical visualization can you think of? Is there anything that is easier to understand through indexical visualization? Or perhaps some things that are harder to understand if we don’t translate them into numbers first?


Posted in Art, Communicating Math, Exercise, Nature | Tagged , , , , , , , | 2 Comments

Math in the Media: October 2016

The internet had lots of great and terrible uses of math and mathematical visualizations in October 2016! This is our opportunity to applaud the winners and be confused by the blunders. Here are a few of my favorites:

1. The Gold Star goes too…

Without a doubt, this month’s Gold Star goes to the white house panel of “Math and Movies” that took place on October 28th. I have so much to say about this, that I wrote an entire article. Please check it out! My favorite quote in the whole panel was US Chief Data Scientist, DJ Patel speaking about math:

“It’s about the art. It’s about the humanity of making creativity come alive. It’s not the stodginess of just a set of formulas and equations.” -DJ Patel

Check out my whole article here.

2. Odd Use of “Mathiness”

Usually this is the “terrible use of mathiness” section, but the article I want to feature here isn’t particularly terrible math. I mean, maybe it wasn’t even terrible at all… But it certainly was odd. Very odd.  Chandra Kant Raju is an Indian professor who knows a fair bit about the history of mathematics. His work seems to revolve around crediting the correct person and how the societal pressures of the West stifled and altered the history of mathematics.

I found his current article published to The Wire. The Wire had republished it from The Conversation. And the weirdest part of the story is that The Conversation withdrew the article soon after it was published, citing editing standards. The Wire decided to continue to offer the version they published, but the back and forth of publication, withdraw, republication makes the article an oddity already.

In the actual article C.K. Raju presents arguments behind the bold title: To Decolonise Maths, Stand up to Its False History and Bad Philosophy. The article seems to call for a complete re-write of the history of mathematics, which is rather audacious. And C.K. Raju mostly sites his own publications as evidence. Which, I guess is what you have to do when no one else agrees with you? …But, it’s also something you do when you are really old and famous for a particular topic. So I don’t know what to make of that.

At first, I couldn’t decide if I wanted to feature it in Math in the Media because I wasn’t sure I wanted to provide it more press. But it’s was such a strange experience to read. I couldn’t not write about either. So, if you want to read something strange, then I recommend this article by C.K. Raju.

3. Math Graphic of the Month

My favorite graphic of October is actually the collection of infographics about treats for pets on Facebook by American Veterinary Medical Association. It’s adorable and very meaningful! The infographic does a great job of presenting a relationship that their viewers can relate to. It’s amazing!avma_healthy_weight_infographic

Did you have a favorite experience with math on the internet in October? Share it in the comments below! Until next time, have a mathy November!

Posted in Communicating Math, Internet Math | Tagged , | 1 Comment

Math and Movies: White House Panel

On October 28, 2016, the white house hosted a panel on “Math and the Movies” where they spoke with DJ Patil, US chief data scientist, Andrea Hariston,  applied mathematician from NSA, Jeremy Irons, cast member from “The Man who knew Infinity”, and Ken Ono, the math advisor on the film. After the panel, they screened, “The Man who knew Infinity.”

“The Man who knew Infinity” is a film chronicling part of the life of Srinivasa Ramanujan, the Indian mathematician who is famous for 3 books of beautiful equations that he wrote down with no proofs. This film focused on Ramanujan’s struggle to break into Western mathematics. Whatever you may feel about the portrayal of mathematicians in this film, there are many things about this film which are to be lauded. For example, one cannot argue with the real struggle to be accepted by the mathematics community. I think this is something the film features quite well. It highlights the different backgrounds of the characters and gives some dimension to their struggles.

“An equation has no meaning unless it expresses a thought of God.” -Srinivasa Ramanujan

The screenwriter/director, Matthew Brown, was especially concerned about presenting the movie from an non-western point of view. In fact, “Colonialism and that white savior ideas are things Dev Patel, Jeremy Irons, and myself wanted nothing to do with, ” said Brown in a Tribeca interview. The panelist talked about this as well. How can we change culture to open up mathematics to more people? How do we draw young people into mathematics?

Ken Ono spoke about a recently created program, The Spirit of Ramanujan Talent Search. They have been searching the planet for undiscovered math talent. Their website is up and taking in applications. In fact, they have already found several young mathematicians to give awards to.

And just between you and I, panelist DJ Patel is amazing. He’s actually my new favorite person because he studied theater in undergraduate just like me! On mathematics, DJ Patel said, “I can’t imagine a more powerful foundation on which you can build so many different things.”  He spoke passionately about how mathematics can teach someone “how to be clever”, how to solve problems in creative ways.

“It’s about the art. It’s about the humanity of making creativity come alive. It’s not the stodginess of just a set of formulas and equations.” -DJ Patel.

Patel spoke passionately about changing the culture of mathematics. For those we see who have an interest in mathematics, Patel says that we should take a moment to say, ‘that’s cool. That’s awesome.’ because “that is going to systemically change the trajectory about how we think about [mathematics]”. I couldn’t agree more.  Let’s celebrate our mathematicians instead of marginalizing their talents. So DJ Patel, if you are reading this, can we be friends?

DJ Patel also presented first math homework problem to be given by the white house. They call it out with the twitter handle: #mathmovies. Actually, this is an amazing hashtag where you can find some fabulous gems like this response to a RedBox post about math movies:


Math culture is unique. There are problems associated with the culture of genius. “One of the biggest misconceptions in mathematics is that you have to be a genius to be a mathematician,” said panelist Andrea Hariston.  There are also problems associated with Western culture of rigor and structure.

“I think I’m a successful mathematician mostly because I’m resilient.” -Andrea Hariston

The panelists also call out the upcoming movie, “Hidden Figures.” Hidden Figures (trailer out now!) is about young female african american mathematicians who work with NASA to get Americans into space. As Andrea states, “Representation Matters.” From a personal stand point, I can not tell you how excited I am for the release of Hidden Figures.

Speaking of films, Jeremy Irons, the actor who portrayed G.H. Hardy in the film said,  “pure mathematics is rather similar to poetry…it’s something you search for.” Irons said he learned this from reading some of Hardy’s essays. And this is something that I find amazing. How an actor can, without any previous interest in mathematics, see the beauty in the math? Or perhaps I should say, he can see the beauty of mathematical thought and passion despite the mathematics. I think this is very similar to Ramanujan’s awe of mathematics, “An equation has no meaning unless it expressed a thought of God.” Those are Ramanujan’s words.


The recording of the panel is also available at

Posted in Communicating Math | Tagged , , , , | 2 Comments

Trade agreements of dining out

Social Mathematics can sometimes be considered Economics. And here is a lovely explanation of how two countries (or people) can share food when dining out. Enjoy!

I am eternally astonished to find not only that many couples I know failed to discuss this key area before they marched up to the altar, but also that many of them still have not developed a joint dining strategy even after 10 or 20 years together. This is madness. You are placing undue stress on your relationship, and you are very probably having a suboptimal dining experience, thereby wasting time and money and missing out on deliciousness. As a romantic economist might put it in a wedding-reception toast, couples have the chance to jointly move to a higher utility curve.

There is all kinds of math about sharing.  Mathematicians have carefully considered how best to fairly split a cake at many levels. We know that between two people the “you cut, I chose” method works fairly. But we also have studied how to cut a cake when it has multiple flavors and multiple people receiving pieces.

Conversing about and understand the various options of dining experiences is important! You want to understand the ordering options before you chose! Enjoy the complete article about dining out on Bloomberg.



Posted in Communicating Math | Tagged , , , | Leave a comment

Math in the Media: September 2016

The internet had lots of great and terrible uses of math and mathematical visualizations in September 2016! This is our opportunity to applaud the winners and be confused by the blunders. Here are a few of my favorites:

1. The Gold Star goes too…

Henry Segerman for his amazing 3D mobius transformation henry_segerman_terdragon_smallartwork. In particular, I want to call out his Stereographic projections. A Stereographic projection is a mapping (that is, a function) that projects a sphere onto a plane. In the case of Segerman’s art, you can shine a light from above to make the projection appear.


Stereographic projections have a strong and beautiful connection to moebius transformations. Moebius (or Möbius, like the Moebius band!) transformations have a key part to play in understanding complex analysis. In particular, they encompass a particular type of mappings (functions) that map the complex plane back onto itself. Stereographic projections have the power to make something really complicated appear relatively simple. To really understand why stereographic projections are so meaningful, I recommend the “Moebius Transformations Revealed” by University of Minnesota professor, John Rogness. I promise that there are almost no equations and you’ll probably learn something:

Do you need one of these in your life?

2. Terrible Use of “Mathiness”

My least favorite mathematical graphic from September has to be the Bloomberg BusinessWeek’s visualization on income. Income is a really important topic. And the idea that “everybody thinks they’re middle class” is an important piece of the puzzle to understanding why income inequality is growing over time.  However, I strongly disagree with the way they presented the material.

First, let’s take a moment to wonder at the title: “Everybody thinks they’re middle class.” The visualization gives only 5 individual’s opinions, and yet we presume to call this a representation of “everyone”? In high school I learned that three points make a line… but hopefully we all realize that a 5 person sample out of more than 300 million Americans does not a statistical sample make! And since, with a sample size of 5, it’s not providing scientific insights, then I’m left to believe that it’s goal has to be emotional insights to the nontechnical audience… which is also does poorly.

How well does it communicate with a nontechnical audience member? The article is basically one big visualization with a little bit of text:

bloomberg_middle_class This is a visualization showing the annual income of Americans. Annual income is on the x-axis against the percentage of the population who have that income level on the y-axis. How to read it? Well, one can learn that approximately 10% of the population makes $30k and about 4% of the population make $100.  Basically, this visualization is like a histogram with a million little rectangles… drawn as a continuous line. However, it obfuscates what percentage of the total population are above and below each data point.

Our society has been very focused on the top 1%. So, when I look at this graphic, I want to understand where in this visualization the top 1% is. I’m also curious about other things, like: what is the mean income of this study? It’s really hard to tell when you look at the Bloomberg graphic. What I really want is something more like a Pareto chart or a cumulative distribution curve:

Here we get the histogram AND information about the cumulative values. So I can visually see when I’ve reached 50%, 80%, or 98% of my population sample by reading the right y-axis. Ultimately I think the Bloomberg visualization falls short of providing insights to anyone in both content and visualization. Better luck next time, Bloomberg!

3. Math Graphic of the Month

I’m guessing that if you are reading this website, you probably believe in math and science. Thus, I think you will also appreciate that science (and math!) do not have political agendas. Simply put, mathematics is a tool to learn about and communicate the facts of the world. In our social climate, I think it’s important to remember that there is a division between science and state. They have different goals and different aims. And math, if math had opinions and emotions (which is doesn’t!)… anyways, if it did, Math couldn’t care less about which way you vote. In short, I think this is a beautiful reminder:

You can buy yours here.

Did you have a favorite experience with math on the internet in September? Share it in the comments below! Until next time, have a mathy October!

Posted in Art, Communicating Math, Media | Tagged , , , , , , | 3 Comments