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.
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.
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?
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!
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!
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 whitehouse.gov.