Outside the Ivory Tower

I’ve been outside the Ivory Tower for about a year and a half.  In that time, I have radically changed the way I view the world. MathGuyI’m now asking relatives about their ROI of their time when researching reduced hotel rates instead of asking if they just saved money (b/c time matters!). I have new businessy words for things I would never have thought of previously. I have scoping meetings to prepare for alignment meetings which are preparation for some even greater alignment meeting. I even have new structures for how to solve problems because sometimes explaining my work within the context of DMAIC [ref] is easier to understand than whatever PhD language I learned previously. Sometimes, when I’m doing predictive modeling with a huge parameter space, I feel like my PhD was necessary. Certainly, my breadth and depth of knowledge are useful. But what if I am working on something outside the content of what I learned in graduate school? For these situations, I am still not clear on precisely how having a PhD is helpful in this new world.

Let’s step back in time to when I was a graduate student. In the same way that we say, “youth is wasted on the young”, I clearly didn’t understand how wonderful it was to research in academics.  I didn’t know what I had! In academics, you can be blissfully unconcerned with whether or not your work is intrinsically valuable. What a glorious wonderful haven of intellectual thought! But now I think, “What value is there in creating wonderful research if there is no way to do anything with it?”

In 2009, I wrote about throwing papers over the academic wall and hoping someone picks them up (see left). academic-great-wall-cartoonAt that point, I vaguely understood that there was something interesting about doing useful research. In 2010, I started thinking about how mathematicians were useful in society. Why is it important to have mathematicians outside the Ivory Tower? In 2013, I was thinking about how it was actually better to be outside the Ivory Tower. And in 2014, I learned about why mathematicians (+ data) might be the next big thing in commerce. Then, all of a sudden, I graduated and was working in “the Industry.” (Because that’s what you call everything that isn’t academics.) I went into my new world excited to apply my knowledge to real problems…and I was armed with a PhD in Applied Math.

And I was horrified!  I was so excited to use my math for new applications, but what I found were people who were changing the definition of variance because they didn’t like the result of the model they built with the real definition. I struggled with Industry’s need to bin and bucket different mathematical techniques. I was surprised to learn that I should occasionally not discuss all my project problems because if I discussed them when no one else was, then I looked like the lady who was producing bad results instead of being the only person who was acknowledging a weakness in the inputs. But, within all this cray-cray, I realized my horror for sloppy analytics must be a symptom of something valuable that I learned in my PhD.  But what was it?

Here’s the beginnings of my theory; I spent years beating my head against the side of that Ivory Tower and during those frustrating years I was building stamina and intuition. Every step I took up the ladder was careful and measured. The core of my mathematical faith rests on those building blocks of real analysis, probability theory and dynamical systems. And when someone points at one of those building blocks and says, “That’s not important, I’m going to build it differently because it suits my needs better,” then I get really mad. I am emotionally invested in those ideals. It’s not okay to ignore the building blocks of my field. I’m like a tiny, intellectual paladin ready to solve problems and defeat evil!…umm, what? IvoryTower3

In summary, I poetically claim that every PhD learned how to be an analytical paladin while they were in graduate school. And I’m not sure how it’s a useful skill in Industry, but it has to be part of the PhD toolkit because I’m pretty sure every STEM PhD has that emotional response to bad math. Maybe that is why companies hire us. We get sucked into Industry because of our desire to do something useful. But the reason Industry lets us stay is so they can have their own round table of analytical evangelists? So, while I’m still not sure about all the reasons companies hire PhDs, I believe that our stubbornly held rigorous belief system must be on the list.

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Recreational Math and Wooing Others

Begin with gifts, continue with gifts and end with gifts

                                              -Advice on how to woo a lady

This is a phrase that sticks out in my mind when I think about wooing another person. It was a piece of advice that was given to me some time ago. While, I don’t think that gifts is always the answer for gaining affection, I do think the general principles holds for falling in love with mathematics. Except for math it’s:


My love of mathematics began with a childhood full of puzzles like, “My dad ran a marathon and he won first place! He also got last place. How is this possible?”

Then my love grew when I got to undergraduate and I had a math professor, Jim Henle, who promoted the use of “Doodles” as a valuable and interesting thing to do in a “Math as Art” class. As it turns out, Jim has recently published a lovely book on how doing mathematics is similar to cooking; it’s titled, “The Proof and the Pudding.” I think this is especially relevant because both gifts and cooking are great ways to woo someone!

And while my love of mathematics has not ended, it has continued to continue with my professional research where I consider almost everything to be a “puzzle” or a “game.”  I am an avid board game and video game player. A while back, I even wrote an article about how awesome video game math is.


I love playing games with math. It’s exciting, interesting and challenging. So when I read this New York Times article, “The Importance of Recreational Math,” I thought, “Right on.” Manil Suri presents a fabulous take on why recreational math is so important.  “This is how math works, how recreational questions can quickly lead to research problems and striking, unexpected discoveries,” writes Suri.

Playing with a toy is a fabulous way for a child to learn things. And, in my experience, playing with a mathematical toy is a fabulous way to get a PhD. I can’t recommend mathematical play highly enough. Here are a few examples of mathematical recreation for you to think about today!

Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. How is this possible?                  <answer>

3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys’ room with $5. On the way the bellboy couldn’t figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?                <answer>

MIT plays a trick on all the incoming freshmen. They line all the students up on one side of the gym and challenge them to run precisely half the length of the gym in 5 seconds. Then they must run precisely 1/2 of the remaining distance in the 5 seconds. All the students who make it to the other wall of the gym will get $1000.  As soon as the challenge is explained, all the mathematicians leave the gym without trying. Why?          <answer>

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Saving Private Martian

Matt Damon

The Martian was released into theaters on Friday. It’s a great film! Yet again, we have put Matt Damon into a dangerous situation that requires a rescue! So, I want to know: How much has makind spent trying to save Matt Damon?


Cost of creating the film Saving Private Ryan is $70M. Then movie goers spent $216.5M in North American theaters, $265.3M abroad and another $44M in disc sales. So that’s 532.8M that Earthlings spent to watch Matt Damon get saved in the 90s. [ref]

Interstellar cost $165M to create. It earned $188M in North America and another $487M abroad. Another $36M on at home video sales. [ref] That brings Interstellar’s total to $876M to watch Matt Damon get saved in 2014.

On Friday, The Martian was released.  It’s hard to say how much it will earn. It cost $108M to create and it’s projected to earn $55M it’s opening weekend. [ref] So we’ve spent at least $163M already.  Now, I’m not a box office predictive analyst, but I think the movie is great. The book is great too. (As an aside, I highly recommend both of them!) And so it is with an optimistic heart that I say: Let’s assume, for the sake of argument, mankind will spend approximately $600M in total on The Martian.

In total, when we combine total production costs, box office profits and at home sales, these three movies have produced more than 2 billion dollars of transactions. To clarify:


If we are so willing to throw that much money at a fake situation, then why don’t we have a real mission to Mars?  Why can’t we really do this?  Surely we could edit together a documentary or reality TV version of astronauts on Mars?

I guess what I’m really asking is: How do these expenses relate to a real situation? Let’s restrict our scope to just having a manned mission to Mars. As it turns out, the cost of an actual Manned Mission to Mars has been computed. NASA estimates the overall expenditures at about $100 billion over 30 or 40 years says Brent Sherwood of NASA’s JPL. Now, if you know the plot, you might argue that The Martian required the resources of 2 manned missions to Mars. Or at least 1.5 missions. So, let’s say we could spend approximately $175 billion to do The Martian for real.

In conclusion, we can fake save Matt Damon 3 times for $2 billion or we could really save him once for $175 billion. Fake saving him costs 1% of the true cost of putting a real human in that real situation.  So until we make 297 more blockbuster movies about saving Matt Damon, we will not get close to reaching the actual cost of space travel. Turns out there is quite a high cost for the actual science; and actual science is not required for a film set!

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Dangerous Animal Meat

CNBC wants you to know that ground beef is going to kill you. Are you sure, CNBC?

Last month, CNBC posted an article which stated that “ground beef is riskier when it comes to containing bacteria that can cause food poisoning.”  Then they included some statistics from Consumer Report which tells us that over a 10 year period (2003-2012), 5 people died from eating tainted beef. FIVE.  So, to clarify.  Five people died by eating beef. Get scared of your grills everyone. Beef is dangerous. Factually, ground beef is more likely than other types of beef to contain E.Coli.  So, since the above statistic is for any type of beef, we know that five or less people died due to eating tainted ground beef. Let’s start there.  How worried should I be about this problem?

First we need to understand the odds of ground beef sickness. There are approximately 270,600,000,000 lbs of beef consumed by Americans each year. Over the 10 year study, 1144 people got sick- So let’s assume that 114.4 people got sick per year. So the odds of getting sick if you eat 1 lb of ground beef per week is 0.000000042276%.  When you consider how many people died, 5 people over 10 years, we lost 0.5 of a person each year. This leads to a 1.85 x 10-9 % chance of death due to tainted beef (assuming you eat a pound of beef a week). Maybe that seems like a high percentage. Let’s compare it to lightning. There are an estimated 330 who get struck by lightning in a given year. (Thanks NOAA for having an entire webpage dedicated to this!) You are waaay more likely to get struck by lightning than killed by ground beef. And only 33 ultimately die from lightning each year. Suffice to say, it’s SUPER unlikely to get food poisoning from beef. Maybe that’s why more people are inherently more scared of lightning than of a hamburger patty; the patty is not intrinsically dangerous.

But while we are at it, let’s compare ground beef to other dangerous things. Spiders kill 6.5 people/year while centipede’s kill only 0.5 people/year.  Wolves only kill 0.1 people/year. So, I guess that’s interesting! If you have decided to be one of the people who thinks wolves are evil-super-aggressive-creatures-who-should-be-shot-on-sight… then maybe you should be worried about beef consumption. Because beef consumption is actually 5X more dangerous than wolves! This statistic should highlight how non-dangerous beef is… and also how not dangerous wolves are. Because wolves are not dangerous. (On a tangential topic, please don’t shot wolves; they are extremely valuable to nature!)

So why is CNBC writing an article about how horribly dangerous ground beef is? Well, the rest of the article mostly talks about cooking your meat. Because you can kill E. coli quite effectively by cooking your meat to at least medium doneness. So, in some sense, this article is telling us that 5 people died because didn’t know enough to cook their meat!  Inflammatory Internet Statement! CNBC is pushing their well-done agenda on their readers! They are saying, if only everyone cooked their meeting till it was brown, then we wouldn’t have this problem. In seriousness, I think the unfortunate five just liked to eat rare meat and got unlucky with E. coli infested beef.

I don’t prefer rare meat, but if I did, then I would accept this level of risk as part of my life on this planet. As a mathematician, this risk is in the noise. There is no compelling reason to change your habits if you happen to like rare meat. At least not from my frame of reference.

Special Thanks: The article discussed in this post was recommended to me by Bret Weaver, who is a reader of Social Mathematics in Minneapolis, MN. Thank you, Bret, for the great article recommendation and our subsequent discussion about it! If you want to read more from Bret check out on Twitter @WeaverBret. 

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Common Core Check Explained

We can teach math in different ways.  At the moment we are testing something in our schools called common core math.  I’m not an expert in common core math (not even close!), but I do a lot of math, so I feel justified in suggesting an article that is definitely worth reading. There is some guy, who is probably not worthy of all the press he is receiving, who wrote a check using common core math which is getting a lot of press right now.

 And Hemant Mehta wrote a great article titled, “The Dad Who Wrote a Check Using “Common Core” Math Doesn’t Know What He’s Talking About”. The article relates how this guy is fundamentally dismissing something because he doesn’t understand it. And that is a bad tactic to take. Mehta also gives a introduction to common core and explains why it’s more useful than the memorization tactics taught in Elementary schools previous to this. Please take a look, it’s a well written article!

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Social Norms and Other Challenges

If you are drawn to a field that people say you can’t do, then keep pushing against those who seek to limit you. They don’t know what you can do. And, I bet, that you don’t know what you can do.

My senior year of high school, I was in a special program where I took all my classes at the junior college. The program was for people who knew what they wanted to do to. And I wanted to do theater. (spoiler, I now have a PhD in math and love it) But, I had taken my math and science classes thus far and I didn’t see any reason to stop. So I wanted to take Physics 101 as I would have done if I had stayed at my high school for senior year. But in this special program we had a special adviser. And my advisor noticed that the physics class had a “recommended” course of physics for non-physics majors. I didn’t want to take that class. I wanted the class with actual math in it.

My advisor and I got in a fight. She told me to “Go think about my options and let her know when I had reached a conclusion.” I came back and said, “I got an A in calculus. My dad is a computer scientist and he can help me with the homework if I get stuck. I know how to use my resources and I want to take the Physics 101 class.” She told me no. In addition she gave me a veiled threat that she would get me kicked out the program if I continued to try to get into the other class. I’ll never understand that decision of hers.

So I had no choice but to take the thought experiment based physics class where we thought about monkeys falling out to trees.

Classic physics problem about shooting a monkey out of a tree. You can complete this problem with or without math… or so they say!

The class was interesting, but not for me. I wanted the rigor. Because although high school me didn’t realize it at the time, I had an aptitude for math. But no one would tell me that. Probably because I couldn’t subtract numbers to save my life. (Luckily that’s not really what math is about.)

No one noticed that I never used to my calculator and said, “Hey, by not using your graphing calculator, you are forcing yourself to really learn how to graph and understand it. Thus making this class harder and not easier. I bet you secretly like math.” In fact it was the opposite. There were people activity pushing me away from the subjects I was interested in. Why had my otherwise nice adviser forced me to take the class she felt was appropriate? Was it because she had me pegged as a theater major and she couldn’t accept that I could do something else? Was it because I was female?

If you have faced challenges, then know that you are in good company. This morning a reader recommended this great clip of Neil deGrasse Tyson (below) which reminded me that acknowledging the struggle is valuable. I always appreciate when people who have “made it” admit to the challenges they faced. No one has succeeded without struggles. Succeeding without challenges is a probability zero event.

PS: If for whatever reason the clip below starts at the beginning then skip to time 1:01:30 to just hear the most relevant portion of the Q&A. Thanks!

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Hunger statistics and click bait rant.

I have a bit of a issue with an article came out a while ago on Cracked.com titled, “6 Insane True Statistics That Laugh In The Face of Logic”. While the title is total click-bait, and I recognize that, it still makes me angry. Statistics don’t laugh in the face of logic. The fact that statistics are logical is kind of the whole point of mathematics. Perhaps they are not intuitive and/or not obvious, but they are certainly logical.


The article has several examples of probability & statistics brain teasers that most students will see in an undergraduate Intro to Probability course. This article could have been titled, “6 unintuitive examples your professor will use to stump you on an exam”. I also think it could be called, “A statisticians take on Hunger Games”. Let’s look at the “Insane True Statistics” they cover through the lens of someone who has taken a few math classes.

1. Probability Dictates that “miracles” are routine.

The odds of me winning the lottery twice in a row are tiny (especially since I don’t buy tickets). But the odds of someone winning the lottery twice in a row are pretty good. The odds of Katniss’s little sister being pulled into the Hunger Games were small (she only had one token in the bowl after all). But the odds that someone from district 12 was going to the Hunger Games are 100%. Sample Size is important. With a large enough sample, lots of things with small probability will happen.


Did you ever hear the idea that if you put enough monkeys in a room with enough typewriters that eventually they will produce Hamlet? Theoretically, if one ignores all the tasks of training/feeding monkeys, would this be possible?

2. The odds of two people sharing a birthday in a small group is almost a certainty.

This is a feature that happens in groups due to the fact that there are only 365 days a year. It has to do with Independent vs Dependent variables. It has a wikipedia page. I have nothing else to add.

3. The probability that a man’s sibling is also a male is one in three (not 50-50)

The solution to this is Conditional Probability. If you know the definition of conditionally probability, you too can compute this. 

4. You can rig a game of coin flips just by going second

Here too, the solution is to use Conditional Probability.  As it turns out, conditional probability is a great source of non-intuitive puzzles. But thankfully, mathematics has rules for this kind of thing and statisticians figured this stuff out a long time ago. Back to de Moivre in in the 18th Century or perhaps even  Pascal and Fermat in in the 17th Century. So I’m not sure if this should really “laugh in the face of logic”. Perhaps it merely laughs in the face of people who haven’t seen conditional probability. But that seems like a far cry from fundamentally deposing logic! While these problems are not obvious, I believe that they are totally solvable with persistence.

5. Pi can be calculated by randomly dropping a bunch of paper clips.

Okay, I admit, this one is awesome and seemingly magical even when you understand what is happening. This is true and a very cool experiment called Buffon’s Needle!  In my Intro to Probability class, I did an equivalent experiment by dropping toothpicks onto a grid. I remember completing a big, complicated proof to show that it really was pi.  Advanced note: If you are working your way towards an undergraduate math major (or maybe you already have one) can prove the relationship using a probability density function and double integrals.

If you want to know and/or try your hand at a simulated version of Buffon’s Needle: Science Friday did a write up on it:

Science_Friday6. Lastly, when you shuffle a deck of cards, you’re creating a sequence that has never existed before.

This is a problem that you might consider at the beginning of a statistics course. Understanding how many combinations or permutations a certain set of objects can have is integral to doing probability and statistics. Unlike the odds in problem #1, the number of possibilities is really really big. So while you can’t truly “prove” that it has never existed before, the odds are ever in your favor.

So the next time you are stuck in the middle of a statistics or probability course and frustrated with the unintuitive nature of the problems. Don’t worry. The entire rest of the world is with you. And mathematicians have been thinking about this stuff for a long time. So while it may not feel intuitive, it’s definitely logical.


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