Beth Malmskog

Math etc.

More Blog!

Yes, I totally painted that chain rule picture.  Don't everyone order their print at once.

Yes, I totally painted that chain rule picture. 

Hello from my office at Villanova!  I just rearranged to more easily get my students at the blackboard, so look out students.  After being away so much this summer, it feels great to just sit at my office and work on the syllabus for my class.  Except I’m putting off working on the syllabus for a few more minutes to write here…  But I wanted to post here to let you know about my other blog life, which is really just starting today. I just made my introductory post as part of PhD + Epsilon, the early career blog sponsored by the American Mathematical Society.  I’ll be posting there every other week about early career life.  Sara Malec will do alternate weeks.  This blog was started 5 or so years ago by Adriana Salerno, so there is already a huge back catalog of great stuff there about pre-tenure math career issues, in which some of us are of course very interested.

Home for a minute

Back in Philly now after about a month away. I was in Colorado and Wyoming mostly, with a few days up to Ontario for the Computational Number Theory session at the AMMCS-CAIMS meeting. I’m heading out for another trip in a couple days. I’ve been in Philadelphia for about two weeks since the semester ended, and I spent most of that moving from one apartment to another. In the spring and fall I traveled a lot, too; conferences and trips to visit my family and friends, (friends that are spread out all over the world now!). This is great, in a way, but I’m sad to be missing out on my still-kind-of-new home. I want to settle in and look out the same window every day for a few months straight, to find a rhythm of working and feel like I have a routine (if only so I can deviate from it sometimes). I want to practice my accordion! I am dying for what some people think is boring.

Not to say I don’t want to go on any one of these trips. I feel really lucky to have freedom in the summer, not to mention so much flexibility during my school year. And from some perspective my life fits together really well—I can go work on math in Colorado, see my family and friends, then head out for GREAT conference, constantly going from thing that I like to thing that I like. Even the actual transportation has some good points. I read a ton in the airports (twelve Patrick O’Brian books down, nine to go…) and got to take a three-day road trip back to Philadelphia with my parents.

So what is this longing to stay home? Is it just another kind of FOMO (fear of missing out has earned its own wikipedia page)? I don’t know exactly how to reconcile this with all the things I am excited about.

Instead of addressing that difficult question, how about some pictures!?

Did I mention that I learned to solve the cube this spring?!  I am still VERY SLOW.  This is what I did on the train for a while, and boy do the other people look at me strangely.  Nicely, but strangely.

Did I mention that I learned to solve the cube this spring?! I am still VERY SLOW. This is what I did on the train for a while, and boy did the other passengers look at me strangely.

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Did I mention that I spend a huge amount of time on the train? Here’s my platform at Villanova, looking kind of cold and lonesome this spring.

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Did I mention that I ran the Pi-K (actually a pi mile race) at Villanova this March? Here are the student organizers and a few of my competitors. I almost beat them on the home stretch!

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A window in the library at UPenn. I have had a great time attending the Math Department seminars there (and even gave one, very nervously!).

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Spring in Philadelphia was so damn lovely.

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Ben Franklin is my hero these days. Best founding father, hands down.

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Dr. Katie Haymaker and I, on our way to commencement at Villanova. It was SOOOOO HOT in those robes!

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Waterloo, Ontario had a jackalope-themed coffeeshop and whiskey bar called Death Valley’s Little Brother. Did I mention it was really great? Oh wait, it was obviously great given that it was full of JACKALOPE art.

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Crossing the Mississippi at St. Louis on my road trip back to Philadelphia with my mom and dad. Yes, those are dead bugs smeared not the windshield but I actually liked the effect–almost like a sunset!

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My parents at Rodin’s Gates of Hell in Philadelphia.

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My craze of the summer, the Aubrey/Maturin novels.

Math Book Club: “How Not to Be Wrong”

I love book clubs, especially as an idea. I love talking about books, and watching whole new worlds open up from a different reading of the same text. However, absent a really good guide or leader, book talk can be: “I liked that book.” “Admiral Harte is sure a jerk!” “That was boring.” This is actually pretty fun; chatting lightly about shared experiences strikes me as a pretty major human need and creator of community.  I get a spark from realizing someone else heard the same song on the radio as I did, let alone experienced something as lengthy and sometimes heavy as reading the same book. The problem is exactly that, though: some books have a lot in them, and it’s frustrating to stay on the surface of something that feels very substantial. But who knows where to even start? Hence the need for awesome English professors. Plus in some book clubs, coolness prevails in that it is somehow a little shameful to talk about meaning in public. Even though you’re in book club, ostensibly to talk about the book, saying anything heavy is just slightly in bad taste, pretentious, oversharing. Why is it so weird to talk about meaning?!? Maybe because it’s hard, and so we find ourselves saying things that aren’t quite what we want to say. Which is kind of embarrassing. Or maybe we are all kind of insecure and afraid we didn’t really get it. I am in awe of how really good literature teachers can work a discussion, both in providing ways to look at a text and in overcoming all of this social crap that we put in the way of talking about meaning. Anyway, my experience in book clubs has been that people talk for a few about characters they liked and didn’t, and then everybody has some wine and book club becomes essentially planned social drinking! Which is always cool with me. Sign me up for book club.

However, I don’t have one now, and I have been reading a lot of mathy books lately. If it’s hard to find a great book club, how about a great book club that wants to talk about math? So, I guess that’s one reason to have a blog—it can be your pretend math book club! Perhaps we should all pour a glass of wine. Okay, all set on this end. This week we are (um, I am) discussing Jordan Ellenberg’s recent book How Not to Be Wrong.

Some of my recent math reads.  Wine not included in photo.

Some of my recent math reads. Wine not included in photo.

First, the quick and surface pre-wine book club version of my thoughts: “Super awesome book! Math is cool! Jordan Ellenberg is freaking smart.” Okay, now in case you didn’t read the book, (also a hazard of book club), HNTBW is sort of like a tour of great mathematical ideas (subtitle: The Power of Mathematical Thinking). It goes everywhere. Like, scatterplots, the Baltimore stockbroker con, philosophy in mathematics and statistics, error correcting codes, game theory, perspective, voting paradoxes. Picture a book that picks up where Darrell Huff’s How to Lie with Statistics left off and then tours through the country of Burger and Starbird’s The Heart of Mathematics, with the historical color of E.T. Bell’s Men of Mathematics, but with the advantage that the history (I’m pretty sure) is all real. Ellenberg sketches out ideas and stories that are essential to modern scientific thinking. The anecdotes and examples are contemporary, bizarre, funny, and very relevant

The most important thing I learned: statistical significance is shady, shady business. Statistics is how we make sense out of data, so statistics lies at the base of all science.  I think of myself as a logical thinker, a scientist, and I like to use scientific studies to help me make decisions. So how is it that I have never thought carefully about this business.  When I gleefully read  read the aforementioned How to Lie with Statistics as a kid (yeah, I was pretty nerdy), I thought I knew all the tricks and pitfalls.  So wrong.  The second section of HNTBW, entitled “Inference,” was a lesson in what p-values really mean.  If we gather some data from an experiment, and compare two quantities (like height and shoe size), we would think it likely that they could be connected if as one quantity changes, the other seems to change in a predictable way as well.  We are “allowed” to say that the quantities are correlated (the data shows a statistically significant correlation) if there is a probability (p-value) of less than 5% that we would see this relationship in the data by chance if the quantities were actually totally independent (the null hypothesis).

That sounds pretty good—if the two quantities are not correlated, there is less than a 5% chance that we would say they were statistically significantly correlated by looking at a particular data set. But I never really thought about it in this light: say we gathered data on a lot of entirely uncorrelated quantities. Out of every hundred pairs of uncorrelated quantities, five of the pairs of data sets would show statistically significant correlation entirely by chance. Of course if we gathered more new data on these the two seemingly-correlated quantities, there is only a 5% chance this false correlation would show up again. So our false correlation would very likely be debunked. But first there might be a news story about it, because positive results are exciting! And then, when another scientist could not replicate our result, there might be a follow-up piece, but then again maybe not, because negative results are boring. Their non-replication might not be published at all, even in a scientific journal. In fact, it could be that someone else had done the same study years earlier and found no correlation, which would be sort of a pre-non-replication of our study, but we would never have known because this earlier group couldn’t publish their negative results.

Now, despite the beauty and validity of the butterfly effect, I believe that most pairs of quantities in the universe are not meaningfully and predictably correlated. So I’m ready to dismiss claims (based on fMRI images of one out of many, many scanned “subjects”) that dead fish can correctly assess human emotions from photographs (Chapter 7), even though the correlation was statistically significant, based on, well, yeah. However, with complicated biological systems, how can we really apply common sense to say two things are not related? A study that finds a connection between Alzheimer’s and a particular gene is exciting, important, and not at all an implausible connection on the surface. One study finds a statistically significant correlation, and millions of people will factor that in to their decision making. The dead fish example is particularly striking given how much people will believe a story if accompanied by fMRI images.

My mind was totally blown by this previously unconsidered pitfall. Apparently people who were not blind to this have been advocating for the publication of negative results for years. It appears that the advent of open-access online journals may have finally made this possible.

The last part of this book is called “Existence.” If you had any doubts about whether Jordan Ellenberg is willing to talk about meaning, you can lay them to rest right now. I really like the final few chapters of this book. We get voting theory, slime molds and non-Euclidean geometry. And then, the question: what can we say about the truth, and about being right? Drawing on Condorcet’s paradox, that a group’s preferences for various candidates can result in unresolvably cyclical rankings, Ellenberg raises a question. If there is no one true preference of the people, what are elections doing? What can it mean when there is no one right answer, one correct winner for an election, one consistent geometry? If there is no one right answer, then what the hell is math doing? Is it searching for the truth? What if there is no right answer, or if all of the study and data tells you with great certainty that you can not be certain. What is the point of all this, anyway?

This launches a discussion of what mathematical thinking could bring to every person’s daily struggle to decide what is true, and of what it means to be a creative mathematician. He does not shy away from discussing meaning, both in the careful sense of statistical and mathematical meaning and in the more philosophical sense of questions like, why do we do these things? And, if we can choose how to think about the world, why should we think about it like that? He talks about rigorous uncertainty, the inherent contradictions we face in math and in life, the destructive idealization of genius, and how math comes from a whole community. Math is like football? You mean that in a good way? Yeah, in the team sport way (luckily not in the concussion and sweaty dude way), and this actually gave me a really warm feeling about math. Plus there is poetry, David Foster Wallace, my favorite Philadelphian Benjamin Franklin on how annoying mathematicians are, Terry Tao deflating the cult of genius… also F. Scott Fitzgerald, The Housemartins, and Captain Kirk. This could seem like showing off, or just a ham-fisted attempt to synthesize everything and force a moral into mathematics. It does not. Ellenberg really, ahem, scores a touchdown. This is the best discussion of what it means to be a mathematician, and how that relates to big questions in life that I have read. I think this is a book that we should have our first-year math majors read. Or all the first-year students—which would probably mean more math majors, for better or worse.

The problem of audience—David Foster Wallace brought this up in his essay “Rhetoric and the Math Melodrama.” What reader is this book written for? I can’t un-love math, so I of course I can’t say how this book would speak to people who don’t love math. I would guess that it is aiming for an interested but not specifically mathematical audience, and that it will speak incredibly well. Ellenberg has a great knack for being casual and conversational but never sloppy, and he starts with topics that people care about for their own sake (slipping in the cool math and the hard, unanswered questions after your interest is solid). He comes across as a hell of a guy to have in your book club. If he had time for book clubs, that is, what with a family and a billion speaking engagements and writing for the New York Times and like, proving stuff. But, hey, if he was in book club, we could look forward to more lines like this:

“The moment, early in the Italian Renaissance, at which painters understood perspective was the moment visual representation changed forever, the moment when European paintings stopped looking like your kid’s drawings on the refrigerator door (if your kid mostly drew Jesus dead on the cross) and started looking like the things they were paintings of.”

Conspiracy theories are “like the multi-drug-resistant E. coli of the information ecosystem. In a weird way you have to admire them.”

On a study finding that women were more likely to say they would vote for Mitt Romney during the most fertile part of their ovulatory cycle: “I was disappointed to find that this study has not yet spawned any conspiracy videos coming that Obama’s support of birth control coverage was aimed at suppressing women’s biological drive to vote GOP during ovulation.  Get on the stick, conspiracy video producers!”

“It’s not wrong to say that Hilbert was a genius. But it’s more right to say that what Hilbert accomplished was genius. Genius is a thing that happens, not a kind of person.”

“If I’m going to pay a college kid to superimpose dancing cutlery on all my pages, I want to know not only whether it works, but how well.”

“Here, ‘Swedishness’ refers to ‘quantity of social services and taxation,’ not to other features of Sweden such as ‘ready availability of herring in dozens of different sauces,’ a condition to which all nations should obviously aspire.”

And all good book clubs, as well.

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A few of the many varieties of delicious fish that I sampled at a smorgasbord at the European Women in Mathematics summer school on Apollonian Circle packing in Stockholm last summer (2014).

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Anna Haensch and Amy Feaver, who also marveled at Sweden’s incredible wealth of smoked fish.

And did I mention we saw James Blunt in Sweden?

And did I mention we saw James Blunt in Sweden?

Both Math and Not

I’m pretty much in a constant, random walk-type state of reading Both Flesh and Not, the collection of essays by David Foster Wallace. As has become a pattern for me with hip things that turn out to be truly amazing, I’m somewhat late to the party.[i]

The problem with taking this long to catch on to David Foster Wallace (he died in 2008, Infinite Jest came out in 1996) is that I missed out on those years of having his voice in the mix inside my head. His work is so goddamned smart, funny, sad, and ultimately generous, and has lately taken such a space in my mind and heart, that I feel I must hurry up and tell everyone about it so they don’t miss out too. I’m trying to hold my evangelism back in daily life, because I don’t think anyone wants to hear about it. I mean, I read a lot and like to hear about books, but there are only a few people in my life from whom I enjoy unsolicited book tirades.

But that’s one of the good reasons to have a blog. It’s all about just saying what I want!  Nobody has invested anything in this piece, or is obligated to read about it any longer than they want to.  But then, would anybody read this unless they already knew? Or would the reader just glaze over and click on something else? Who would actually read this blog entry about David Foster Wallace and (as you can guess) math unless they were already pretty into either DFW[ii] and math, and probably a friend of mine as well (or my mother—she reads these things too, hi Mom!)? So am I not writing only for an audience that either doesn’t care, or one that not only knows everything I am going to tell them but will probably think I am mangling something that is legitimately beautiful and very close to their heart? This kind of writing has an audience problem.

This dilemma of audience is the crux of the problem of fiction about math, as DFW points out in “Rhetoric and the Math Melodrama” which originally appeared in Science in 2000. “Rhetoric and the Math Melodrama” takes a critical look at two math novels of twenty-ish years ago: Uncle Petros and Goldbach’s Conjecture by Apostolis Doxiadis (1992) and The Wild Numbers by Philibert Schogt (2000). Critical in both senses, one pleasure of this essay is sort of like as a really good bad movie review. Plus DFW can be totally hilarious.  Though he doesn’t actually pan Uncle Petros in the end, he does let us savor some weak points. Reaching beyond these two books, DFW takes what he calls the “Math Melodrama”.

Math Melodrama is the pop culture trope of mathematician as “a kind of Prometheus-Icarus figure whose high-altitude genius is also hubris and Fatal Flaw.” At the time of his writing, Good Will Hunting and Pi were still pretty fresh at the video store and the movie version of A Beautiful Mind (2001) would soon appear in the theatres (and then a year later in the VCRs of May classrooms of AP calculus classes across the country). Math was granted laurels as a creative endeavor, and with that came the trage-glamourization (totally made up that word) of mathematicians.

This Melodrama is nothing new for musicians and writers.  The title character of the movie Frank is an eccentric, creative, driven musician who wears a giant fake head all the time. He is talented, exciting, charismatic. The other characters variously value him, envy him, want to be like him, and push him to realize their own ambitions. This is all fun in the beginning but darkens, culminating in an Icarus moment at South by Southwest.  Sounds like Music Melodrama in action, but it’s not Frank who has the Fatal Flaw. It’s the main character, the musically limited but driven keyboard player, Jon, who ignores Frank’s obvious deterioration and in his quest for recognition and winds up humiliated. Frank isn’t in great shape at this point and retreats to his parents’ home. When Jon tracks him down there, he is trying to understand what went wrong in Frank’s life, what terrible event was the key to Frank’s genius and suffering. Frank’s parents offer maybe our one bit of insight into Frank, and something that helps take this film past the easiest answers. Frank’s dad: “Nothing happened to him. He’s got a mental illness.” “The torment didn’t make the music,” his Mom says. “He was always musical; if anything it slowed him down.“ This conclusion asks us to reject the notion of talent or genius linked to insanity, viewing the two as independent.

The two books DFW reviews are similar to Frank in that their main characters are not the undeniable geniuses of the world. These books are not about Ramanujan or Gauss or Archimedes. They are about people who do pretty well but who want desperately to be the best; people who want to win the prize of outside acknowledgement and inner peace that they think will come with solving an officially hard problem or a triumph at South by Southwest. And in all cases this doesn’t work out, because they don’t win. Which makes for decent and worthwhile stories in the case of Frank and Uncle Petros (I haven’t read Wild Numbers), but I am also interested in the case of what happens when people do win. This is one of the plot points not totally at the center of the Melodrama, but is essentially the other half of the same story. Are these people unhappy because they reached too far and failed? Does failure make people miserable? Does ambition make people miserable? Does talent make people happy? Does success make people happy?

There are plenty of places where this is taken on (we could work on this through Frank, for example) but this very gnarly dilemma is touched beautifully in DFW’s Infinite Jest, as the main character Hal contemplates own position in light of his wildly and broadly successful father and his disappointed and embittered grandfather: “Have a father whose own father lost what was there. Have a father who lived up to his own promise and then found thing after thing to meet and surpass the expectations of his promise in, and didn’t seem just a whole hell of a lot happier or tighter wrapped than is own failed father, leaving you yourself in a kind of feral and flux-ridden state with respect to talent.”  This is not the thing that the ambitious characters in the melodrama are thinking about, but it is worth thinking about.

My own thoughts on this problem drift back to the lives of both David Foster Wallace and Jack Kerouac. These were two writers who won. Who succeeded artistically and professionally and had everything any daydreaming writer could hope for.  However, I assume that by the ends of their lives, David Foster Wallace and Jack Kerouac were not happy.  Reading Big Sur hurts because Kerouac has laid it out for us, how winning does not necessarily feel how we think it will feel, or doesn’t feel that way for all that long. Reading “This is Water” hurts too, because it is about the way we are tragically complicit in our own suffering, but also about how we can find at least a little relief. It addresses truth and meaning in life and seems to give a few answers, but when read in the knowledge of David Foster Wallace’s later suicide it can seem like a manual for a hopeless and futile struggle.  I have no idea why DFW killed himself or why Jack Kerouac could not stop drinking.  We could assume that the force that made these two people intensely creative was the same force that drove them to desperation.  However, I have to believe that these are independent.  Everybody struggles in life, but some people are almost randomly struck with depression, mental illness, vulnerability to alcoholism.  Everybody is good at something, and some people are great because they work super hard and/or have talent, and some people are almost randomly struck with exceptional creative vision or intelligence and the drive to pursue it.  Some people are struck with both the creativity and the despair.

This is oversimplified, I know, and I feel like the relationship between ambition, success, and happiness is much more complicated than this.  But these stories remind me in a very concrete way that winning, or getting what I want, would probably not solve my problems or be the key to lasting happiness.  Which is a good thought to have on hand as a mathematician, because I very frequently do not get what I want.  My method fails, my paper is rejected, my students stare blankly at me, my grant application is denied, and on and on and on.  There’s no way I could keep doing this if I had to win to enjoy it.

I’ve gotten away from “Rhetoric and the Math Melodrama” here. The essay says a lot that I won’t re-say, but I do want to go back for just a moment to the problem of audience. The thing about math and mathematicians in novels that a little bit of technical sounding gibberish can lend a mathy feeling which is a legitimate spice for a story. Science fiction math gibberish often serves a real narrative purpose. And if it works there, that means there’s no ironclad rule against math gibberish in a good story, so maybe it could work anywhere. The problem is, though, if math is really central to the plot, there’s going to be this problem of audience. The people who see math as a draw are probably going to know enough math that nonsense or oversimplification is really annoying. But if the story is full of real math, it’s going to lose non-mathematicians pretty quickly unless its also super compelling otherwise.

The movies mentioned above didn’t have any trouble finding an audience—they were good enough or formulaic enough beneath the mathy surface that people liked them. And maybe people liked thinking a little bit in the few places where the math glinted though. But who will actually sit down and read a novel involving math, with all the extra time that reading a book involves? Someone who loves novels, someone who loves math, or, most likely, someone who loves both. Which means your novel better to a really good in at least one of two ways—as a novel (usually a story about people) with math providing some color, or as a study of real mathematics (a story about mathematical ideas) with people providing some color. Or else it’ll be doomed to reach only an unsatisfied audience of people who love both math and novels, and are desperate enough to try about anything to get both in one go, and are very often disappointed by their endeavors. That is totally me.

Writing well about mathematics (fiction or nonfiction) is just ridiculously hard to do well, but there are so many beautiful ideas in mathematics that people just want SO BAD to get them across. So people keep writing about math, and I keep reading it, but only a few writers can really reach beyond the small intersection audience of people who just love to read and who already know a pretty fair amount of math.[iii] Even fewer can use math in a story about people and create something magical, transcendently wonderful writing that talks real math but is so great either you understand the math or, if you don’t, the math becomes like so many of the Spanish passages in Cormac McCarthy’s books—meaningful even in obscurity. It’s a language you don’t speak but it still speaks to you and puts you in the place and mood of the story.[iv]

“Rhetoric and the Math Melodrama” is not about math, exactly, but it is an outstanding piece of writing about writing about math. As a piece of criticism it succeeds beautifully in reaching beyond its raw material, to speak about issues meaningful to people who haven’t read the books and probably don’t even care about math. Regarding Both Flesh and Not, I’m probably the odd one that came for the math narrative criticism and stayed for the prose poems and Roger Federer (not to mention buying a ticket for Infinite Jest) but I’m damn glad I came for something. David Foster Wallace is an Astonishingly Good Writer.

[i] Please enjoy or at least forgive the tribute footnotes. My first favorite footnotes in fiction were Manuel Puig’s in Kiss of the Spider Woman, but David Foster Wallace makes footnotes seem indispensible, like how could anybody write a focused but interesting and layered and natural piece without them? But anyway, another example is Wilco. I mean, it’s been years since loving Wilco was really hip or edgy, but there was a time! And I was behind it. Throwing hipness out the window, that was actually great, like discovering some incredible TV show and finding 4 seasons of it waiting for you on Netflix. Or realizing that there are

[ii] Please forgive the tribute abbreviation of David Foster Wallace as DFW. By the way, I learned recently that these are not acronyms unless they are pronounced as words in their own right. So like STEM is an acronym but DFW if probably not.

[iii] My first favorites in this were Journey Through Genius by William Dunham and The Code Book by Simon Singh. But my favorite right now, which I will write about soon if I get time, is Jordan Ellenberg’s newish book How Not to Be Wrong.

[iv] . What writer can do this for math? Maybe DFW in Infinite Jest? I loved that book but I need to give it a second read to think more about how the math in it works. Everything and More (a book about infinity, and of course more) would also be a natural place to look, but needs another look, too, because I didn’t finish it. My whole fascination with DFW started a few years ago when I randomly read his Kenyon College commencement speech (adapted into the essay This is Water), and I started Everything and More expecting something like the speech and was disappointed. Here was this Great Writer writing about math so I ought to love it but it left me cold. I remember that I was just pummeled flat by the number of words the man could put in a sentence. He seemed to be using way too many words to say things, things that were hard but even harder when he put it that way. That’s honestly what I thought (though I feel funny saying that now because I was completely won over by Both Flesh and Not and Infinite Jest so I figure I must have been mistaken about Everything and More). In the essay, DFW also points to some (he thinks well done) math-heavy narratives I haven’t read—Ratner’s Star by Don DeLillo will be on my next library list, and of course Gravity’s Rainbow.


My favorite math joke and other random notes.

My favorite math joke is:

Three logicians walk into a bar.  The bartender says, “Do you all want a drink?”

The first logician says, “I don’t know.”

The second logician says, “I don’t know.”

The third logician says, “Yes.”

My WIN3 project group, April 2014: Me, Wei Ho, Renate Scheider, Christelle Vincent, Padmavathi Srinivasan, and Irene Bouw, our fearless leader.

My WIN3 project group, April 2014: Me, Wei Ho, Renate Scheider, Christelle Vincent, Padmavathi Srinivasan, and Irene Bouw, our fearless leader.

Our Women in Numbers 3 project group recently submitted a paper!  

Yay! Philly’s theatre scene has math and physics fever, with productions of Arcadia, Proof, and QED this fall.

William Penn, my friend!

William Penn, my friend!

It’s not always sunny in Philadelphia, but it is always humid

What Rocky saw when he turned around after running up those stairs...

What Rocky saw when he turned around after running up those stairs…

“Philadelphia Freedom! I lo-o-o-o-ove you, yes I do.”  My friend Rodney has been singing Philadelphia Freedom by Elton John for the last 6 months, every time I talk about my new job.  So now I have a mental soundtrack that begins anew whenever someone says the word Philadelphia.  Yes, I just moved to Philly, and I do love it here.  The city is beautiful.  Things are happening everywhere, great food, great music.  Killer art museums.  And the public transportation totally works!  I LOVE YOU SEPTA!  SEPTA is Philly’s transit system, which I take 30 minutes each way every day to get to my job.  People are nice on the trains.  There is no pushing to be first on or off. The conductors will wait for you if they see you running to the train (I have tested this in repeated trials).  

 

Here are difficult things: everything is paved, it is super humid right now, packages get stolen off your porch, my family is very far away, my house has 3 rooms on 3 floors and I keep tripping on the “cute” circular staircase.  Haven’t tried going upstairs after a couple of glasses of wine yet but I see disaster looming.  

Here are more wonderful things: radio stations (WHYY and WXPN are both incredible!), coffee shops, tons of murals, constantly tripping over historic sites, good bike culture, my new job.

 

I moved to Philadelphia for an Assistant Professor Position at Villanova University, in the NW suburbs of Philadelphia.  The faculty and students here are incredibly kind and dedicated to service.  The students are smart, work hard, and show up to class.  And sometimes they think I’m funny when I am actually trying to be funny, which is nice.  After 2 weeks of class, the first round of students came to my office today.  I was so happy to see them!  Coming from Colorado College, which I would guess has as much student-professor interaction as any college in the world, I miss talking to students as individuals and connecting with them as people.  I guess I just need to trick these guys into coming to my office more often.  Surely I will get to know them better as the class gets more difficult.

 

From the Rodin Museum here in Philadelphia

From the Rodin Museum here in Philadelphia.  This is not what I look like when I am doing research, however.

The drastic change in teaching format and amount has given me some much needed freedom, too.  Freedom in the sense that I have much more time to spend on my research.  Research life is exciting right now.  This spring and summer, Chris Rasmussen and I worked hard to finish our paper classifying Picard curves with good reduction away from 3.  We now have a little time to consider how we can build on this work, to classify curves of higher degree or to choose a different prime.  In August, I led a project group at Sage Days 62 to generalize our code an create Sage functions to compute bounds involved in this classification.  This was my first time leading a project in this setting and I was really really hoping it would go alright.  Thanks to my kick-ass group (Alejandra Alvarado, Christelle Vincent, and Mckenzie West) we created some good code that generalized on what Chris and I had written for our project.  Also, my project group from Women In Numbers 3 has been hard at work writing a paper about the automorphism groups and Jacobian varieties of some particular Artin-Schreier curves.  This is a really impressive group of women (Irene Bouw, Wei Ho, Renate Scheidler, Padma Srinivasan, and Christelle Vincent) and I am honored to work with them on this project.  

I miss you, Arlo!

I miss you, Arlo!

The last thing I want to say today is actually really sad.  Arlo, my much-loved and wide-traveling dog, died last week in Laramie.  He was nearly 16 years old and lived a really full life and, according to my mom, died almost in his sleep.  Arlo lived with me in 10 houses in 4 different states and was the best companion I could imagine.  He was a good dog.  The hardest thing about moving to Philadelphia was leaving him behind for the first time in all my moves, because he was simply so old that I didn’t think he would survive the trip.  I have been missing him every day here and I miss him all the more now.  I am very grateful for all the years that we spent together.

Beth–The Missing Years

Okay, it’s just one year, but I don’t often get a chance to reference John Prine so there you go.  I said last time that I’d fill in some of the gaps since my last post with pictures, and somehow my computer’s feeling frisky enough to upload photos today.   I decided to post something from every month I missed.  Mostly math related but a few others just to show I have *some* other life.  Here goes.

January 2013:

My good friend and now CC colleague Rodney James at the 2013 Joint Meetings in San Diego.

My good friend and now CC colleague Rodney James at the 2013 Joint Meetings in San Diego.

Winter break cross country skiing with Mom, east of Laramie.

Winter break cross country skiing with Mom, east of Laramie.

February:

CC Tiger hockey!  I think this was my first game, now I'm hooked.

CC Tiger hockey! I think this was my first game, now I’m hooked.

Another math trip to Connecticut, another picture of the lego replica of Mark Twain's house in the Hartford airport.

Another math trip to Connecticut, another picture of the lego replica of Mark Twain’s house in the Hartford airport.

March:

Accordion moments with my good friend Dee.

Accordion moments with my good friend Dee.

April:

Colin visited in April, resulting in this colorful math explosion! It's the action of F and V on the deRham cohomology of the Suzuki curve, in case you were wondering.

Colin visited in April, resulting in this colorful math explosion! It’s the action of F and V on the deRham cohomology of the Suzuki curve, in case you were wondering.

May:

Excellent student presentations from my block 8 Calculus 3 class.

Excellent student presentations from my block 8 Calculus 3 class.

June:

Super Moon from the Laramie airport as I flew out to Connecticut in June.

Super Moon from the Laramie airport as I flew out to Connecticut in June.

My cell phone text cheers to my collaborator Chris Rasmussen after a lot of hard work and major shifts of perspective on our project.

My cell phone text cheers to my collaborator Chris Rasmussen after a lot of hard work and major shifts of perspective on our project.

July:

Women in Sage!  This was an incredible week in Seattle working with really wonderful math women on the computer algebra system Sage.  And oh, yeah, we cooked a hell of a lot of great food (thank you Alina and Michelle for taking charge in the kitchen).

Women in Sage! This was an incredible week in Seattle working with really wonderful math women on the computer algebra system Sage. And oh, yeah, we cooked a hell of a lot of great food (thank you Alina and Michelle for taking charge in the kitchen).

View from the way to the top of Pike's Peak.  Had some good friends from my time at Wesleyan out for a visit at the end of July.

View from the way to the top of Pike’s Peak. Had some good friends from my time at Wesleyan out for a visit at the end of July.

August:

Relaxing with math friends after the Algebraic Curves and Applications workshop at the University of Calgary.  Team USA got trounced at Darts by both Team Canada and Team Australia.

Relaxing with math friends after the Algebraic Curves and Applications workshop at the University of Calgary. Team USA got trounced at Darts by both Team Canada and Team Australia.

September:

Back to school at CC.  Snow on the peak already.  This is the view form my office window, by the way.

Back to school at CC. Snow on the peak already. This is the view form my office window, by the way.

Got to add this one from my block-break trip to Laramie, of Dad and his misbehaving bloodhound.

Got to add this one from my block-break trip to Laramie, of Dad and his misbehaving bloodhound.

October:

Hannah and Chidinma show off their trig sub skills.  They kick ass at integrating!  Now to go back to the original variables...

Hannah and Chidinma show off their trig sub skills. They kick ass at integrating! Now to go back to the original variables…

My friend Rachel and I at a CC Hockey game, taking a trial run with our Halloween costumes.  Our friend Dee's sister (see above for Dee) made these amazing Valkyrie hats by hand.

My friend Rachel and I at a CC Hockey game, taking a trial run with our Halloween costumes. Our friend Dee’s sister (see above for Dee) made these amazing Valkyrie hats by hand.

November (aka this month):

Middletown fall!

Middletown fall!

Boston public library, paying homage to the muse of Newton et al.

Boston public library, paying homage to the muse of Newton et al.

Lunch with the wonderful Billy Chan.  He knows where to get all the best food (if by food you mean meat--do not ask for a vegetarian suggestion!).  Excellent pho at Pho Boston in West Hartford (weird, right?).

Lunch with the wonderful Billy Chan. He knows where to get all the best food (if by food you mean meat–do not ask for a vegetarian suggestion!). Excellent pho at Pho Boston in West Hartford (weird, right?).

Looking this over, a lot of this happened in the context of my work so I guess that means it’s pretty awesome being a math professor.

Hello Again from the Middletown Inn

I’m out in Connecticut working on some math with the wonderful Chris Rasmussen.  We started this great project when I was working out here and we keep making progress, but somehow the stunning conclusion just keeps getting further away.  It’s like watching Mad Men.  I mean, it seems to me that Don Draper has just got to fully collapse and/or be redeemed one of these days and the story will run out.  But no!  There he is again, drinking in the morning and eyeing another dame.  I keep thinking that these binary forms/s-unit equations/curves of genus 3 are just going to give it up and fall down dead under the weight of their rock and roll lifestyle.  However, they survive and somehow seem to thrive in their folly, suavely dodging all attempts to pin them fully down, somehow gaining my sympathy and drawing me back to Middletown again and again.  I guess this is somewhat less glamourous than a date with Don Draper, though come to think of it, maybe the better bargain.  

This is my way of easing back into this blog after nearly a year off (I am finding it hilarious/pathetic that my last blog entry was entitled “Reintroduction”).  It has of course been a big year and it would be too much to try to say much about it, except I can’t get my head around where all the time went.  I’m deep into my second year at Colorado College (which I love!) and now on my second house in Colorado Springs (I’m really good at moving these days).  Just before this trip I was in Fort Collins visiting Rachel Pries, along with Colin Weir.  Suzuki curve fever.  Also an excellent Halloween.  

Hmm, I was going to post some pictures but my poor computer has too much going on to open iphoto… I’m pushing this six year old computer to its edge and am taking my digital life in my hands every time I use it.  Yes, of course I backed everything up (four years ago).  So pictures will have to wait for next time while my computer cools down a bit.  But now that I’ve taken the edge off I hope to have another post soon.

 

Reintroduction

This is me, reintroduced to writing and guarding my winter meal with bared fangs.

This is not only a wolf, reintroduced to Yellowstone: this is me, reintroduced to writing and guarding my winter meal with bared fangs. Clearly that elk shouldn’t have made such a ridiculous claim about the cable bill.  Photo from PBS.org.

Wow, it’s time to reintroduce myself to writing.  By which I mean writing about whatever I want to write about.  The last 3 months have been incredibly full of math, speaking, writing on the board, writing lesson plans, emails, website updates for my classes, research and teaching statements, applications–all the standard stuff.  But I haven’t posted for quite a while.  I haven’t sent my energies this way.  However, something truly inspiring happened at my parents’ kitchen table in Laramie over Thanksgiving break, something that revitalized my blogging desire.

I saw a terrible cable commercial.

It claimed you could reduce your cable bill by 150% with their bundle.

I’m guessing that nobody wants to hear the bitter rant that emerged from my until then mild-mannered, turkey-stupored person.  It involved swear words and a lot of contempt.  Come on, you can’t reduce a cable bill by 150% unless the cable company is going to pay you to have cable!! 100% of your bill is your whole freaking bill.  150% of your bill is your whole bill and then half again!  Is this company going to send you a freaking check every month? Seriously!  Does no person in the entire advertising department understand percentages?  Does no person in the entire company understand percentages?  If they do, are they crazy, or do they think that there are actually 0 Americans who both understand percentages and haven’t learned to TIVO everything they could possibly want to watch on television?    Am I all alone in the whole world?!?!

But on the upside:

1) That terrible commercial got me writing about it, which is already fun.

2) In my agitated state I forgot every detail of what they were advertising, so when wanted to find it, I called my mother in Laramie to ask if she remembered.  My 11-year old niece Gabby answered the phone and we talked for a while about her hockey practice, and tennis practice, and when I was coming home for Christmas, and what I should be considering as a Christmas present for her and her brother Nick.  (She said “A science set.”  My heart leapt with joy.  Though she’s the kind of sweet kid that would say that just because she knew it would make my heart leap with joy.) I described the commercial to her and asked her if she’d seen it, and if so could she remember what company it advertised.  She hadn’t seen it but she did ask me all kinds of relevant questions, impressing me with her engagement and problem solving skills.  Then she handed the phone off to my mom, who remembered the rant but not the company.  But while we were chatting I got to hear Gabby in the background, explaining to Nick: “You can’t reduce somebody’s debt by 150% unless you’re going to pay them.  100% is the whole bill.  Nobody’s going to pay you to watch TV.”

3) I searched many variations on “save 150%” to see if I could find the commercial online. I didn’t, and I was reassured that this claim doesn’t seem to appear all over the internet for all kinds of products, as I had feared that it might.  I was getting paranoid about America’s math skills and advertising ethics.  This sold-out item is the only product I found which featured the exact “save 150%” claim.  So, at least on this count, the whole world has not fallen into darkness.

This is the kind of graph you'd better be able to show me if you want to make a claim like that.  What's that you say, cable company?  Nothing?  That's what I thought.  Image credit: Santhanam, et al. ©2012 American Physical Society

This is the kind of graph you’d better be able to show me if you want to make a claim like that. What’s that you say, cable company? Nothing? That’s what I thought. Image credit: Santhanam, et al. ©2012 American Physical Society

4) As usual, I found a lot of things I wasn’t seeking.  My searches brought me to something about “230% efficient light production,” which turned out to be an article about a (bad pun that you will get in a second) “extremely cool” recent feat of physics/engineering: an LED that emits more light energy than it takes in as electrical energy.  It apparently gets the rest of the energy by absorbing heat from its surroundings.  I love this in so many ways!  Claims with percentages that are justified? Yes!  Counterintuitive greater than 100% efficiency that actually makes sense?  Yes!  Energy efficient light production? Yes! It’s December in Colorado and the temperature has been over 60 degrees every day for two weeks.  That’s the forecast weather for the Joint Mathematics Meetings in SAN DIEGO!!  Colorado’s ski industry desperately needs these LEDs.  Though it looks like they currently can only produce very small quantities of light, and that it needs to be 135 degrees celsius for this efficiency to happen.  But still.

5) The cooling lights brought to mind laser cooling, a (note to self: don’t use the cool pun again here!!), a process which won the Nobel prize in Physics and has applications to creating Bose-Einstein condensates (macroscopic quantum phenomena).  I heard about laser cooling when I wrote about Dr. Jacob Roberts work for the school paper during graduate school.  Which leads (because scientists have used lasers to cool/slow particles down enough to trap them for use in quantum computers) to quantum computing.  Something I am especially stoked about because, if a quantum computer is ever built, the kind of cryptosystems that I studied at Microsoft Research will be really useful. In any case, this made me look up the really recent Nobel prize in Physics that was given Serge Haroche and David Wineland for their related contributions to quantum computing.  Which led me to a New York Times Opinion piece about quantum computing, and how great is it that the NYT has opinion pieces about quantum computing?  My search-walk then brought me to a fancy new press release from MIT about very recent advances in the mathematics of quantum computing.  Thanks, Peter Shor and company.  They have proven that the entanglement necessary for quantum computing on a practical scale can be produced in a much simpler situation that researchers feared.  This makes a practical quantum computer much more imaginable.  What if all online transactions were suddenly insecure?  This is what all my back to the land / money in a coffee can / stockpiling guns on their compound friends are worried about (these are three different sets friends, by the way).  EXPLOSIONS!  CRAZY STUFF!

7) Another recent advance which did not win a Nobel prize in Physics that but has applications in my life (this January in San Diego): how to build really tall sandcastles.

This is 10 feet high.  Could they do better after reading this new study?  Public domain photo from Guy King, via Wikipedia.

This is 10 feet high. Could they do better after reading this new study? Public domain photo from Guy King, via Wikipedia.

 

8) In the course of our discussions about this awful commercial, by non-math-loving but very sensible mom pointed out that the ridiculous claim of saving 150% on your cable bill could even make sense if they are considering your cable bundled with your internet.  Idea being that if you look at your current cable and internet bill, you could by bundling with their company get a combined cable and internet bill that is less than your current combined bill by 150% times your current cable bill.  This seems like a pretty weak premise for the claim, it does give the company some room to argue that they are not baldly lying.  So I can to get off my soap box now.  And grade some calculus exams.

Latin square love affair

This is what you get when you google “sexy quilt.” Can you believe it?? My faith in the essential wholesomeness of the internet (which should never have existed in the first place) has not been restored, but I do love surprises.

I am writing today about a problem that I described in my last post about how a group of 5 people could pass 5 quilts around so that each person works on every quilt and no person ever passes to the same other person twice.  And of course, I used Latin squares to model the problem, and I am now a little bit in love with Latin squares.  So the exciting thing for today is my new mathematical crush on Latin squares and a solution to the problem at the end of this post.

But first, let me share a few updates about my life.

School is just about to start here at Colorado College. CC has a very unusual course structure.  The academic year is organized into eight three-and-a-half week blocks.  During each block, students take a single course and professors teach a single course.  Classes are intense but the structure gives the opportunity for lots of creativity in teaching and amazing field trips.  I am really looking forward to teaching on the block schedule.  My first class is good old Calculus I, starting Monday and running through September 24.  So goodbye to all my decadent ways.  Goodbye, sleeping late.  Goodbye, reading novels all afternoon.  Sigh. But really tt’s about time I got back to work.  I’m pretty sure I have the best job around so I’m not going to whine (any more) about not being able to sit home and read The Hunger Games all day.

And… forget work, there is another extracurricular activity to take up my time.  I finally visited KRCC 91.5 FM here in Colorado Springs and had a great time talking with Mike Procell and Vicky Gregor.  Did I mention how much I really love that station?  It was one of the (many) things that made me decide to take the job here at CC.  I will go in tomorrow to sit in with Vicky and start training! The prospect of getting on-air at KRCC is totally thrilling.  So wish me luck.  And, I also get to learn about my health insurance tomorrow.  Did I mention how much I love being out of grad school and having health insurance?

I couldn’t resist sticking in a gratuitous picture of this incredibly beautiful place. I work here!

Here is one of the sweet quilts that Judy and her group worked on, though without the passing sequence they dreamed of.

Back to the problem. In the interest of laziness, I will link directly to a pdf of my solution and response to Judy: quiltproblem.

My favorite part about this problem is that it is a real-life problem that is modeled with very useless-seeming mathematics.  I love abstraction and mathematics for the sake of fun and beauty, and I love solving problems, but its not every day that these two loves come together for me.  And this problem promises to be a good source of united fun for a while.  So, I have determined that the quilts can be passed as desired if there are an even number of people.  It is not possible if there are 3 or 5 people.  What about other odd numbers?  That’s my next question: for what sizes of groups is it possible to find a good way to pass the quilts?

I’ll post whatever I figure out.  But probably not until block break.