Those Topologists…


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Older and wiser


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Ugly Fact


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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.

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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


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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?


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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!

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