For everyone who blanches at binomials, cringes at coefficients or detests derivatives: you’re not alone! Even scientists may avoid math if they can, according to a study on the effect of equation density on the likelihood a scientific publication will be cited by other scientists. (Original paper here) The effect is small; for every additional equation per page, a paper is 5% less likely to be referenced. Still, the result is notable because it was observed in the physics literature, a discipline generally associated with mathematical sophistication. A similar finding has been observed for biology papers, but for some reason there was less surprise that biologists avoided mathematics.
We equate math with universal truths like 1+1=2, but math is often expressed in a strongly context-dependent way via ad hoc notation. Research publications often introduce novel notation precisely because their originality. Authors have to invent names and symbols for what they are representing with their equations, or else overload existing symbols with yet another possible meaning. Consequently, there’s a limit to how much understanding can transfer from the math in one paper to the next. It’s like reading a foreign language without ever acquiring a significant vocabulary; you never stop needing to look up terms in the dictionary. Or like reading English and having to remember whether the author is from the US or the UK to know what ‘biscuit’ means.
If our own scientists have trouble reading each others’ math, how will beings from another planet fare? That question is implied by the movie Arrival. It’s an excellent bit of filmmaking I would strongly recommend experiencing for yourself. The challenge of communicating across language barriers with minimal common experience is central to the plot of the film. The task is posed to linguists but also physicists on the assumption that math and science are the universal language. While the movie doesn’t really unpack the cultural context of math specifically, it does explore the ways that culture and experience generally shape our communication and perhaps more importantly what we don’t communicate because we just assume it. Suffice to say, it feels very relevant at a time when those of us in the US are reconsidering just how much ground we actually have in common.
Whether it’s for math, politics, or first contact with aliens, communication requires clarity. That includes a clarity in your reasoning as well as how you express your conclusions. There’s a brief scene in Arrival where the head linguist tells a story about the origin of the word ‘kangaroo’ to persuade an army commander to let her operate a certain way. After he agrees and leaves, she admits that the story is false but it ‘proves her point.’ From a film with plenty of engrossing visuals and gripping dramatic developments, that moment has stuck with me most strongly. It’s a familiar tradeoff between simplicity and accuracy. Yet it might also be a tradeoff between short term communication success and long term distrust. It’s left me wondering what convenient ‘truths’ I rely on and what the cost may be down the road.
Do you encounter this sort of rhetorical shorthand in your discipline? How do you handle it?
About the author:
Andy has worn many hats in his life. He knows this is a dreadfully clichéd notion, but since it is also literally true he uses it anyway. Among his current metaphorical hats: husband of one wife, father of two teenagers, reader of science fiction and science fact, enthusiast of contemporary symphonic music, and chief science officer. Previous metaphorical hats include: comp bio postdoc, molecular biology grad student, InterVarsity chapter president (that one came with a literal hat), music store clerk, house painter, and mosquito trapper. Among his more unique literal hats: British bobby, captain's hats (of varying levels of authenticity) of several specific vessels, a deerstalker from 221B Baker St, and a railroad engineer's cap. His monthly Science in Review is drawn from his weekly Science Corner posts -- Wednesdays, 8am (Eastern) on the Emerging Scholars Network Blog. His book Faith across the Multiverse is available from Hendrickson.
Ethan Ortega says
Great piece Andy. I’m fascinated by mathematics and am continually growing to love it more. I’ve heard that Arrival is an amazing film and I wanna see it asap. I haven’t much pondered on the context of our mathematics but it seems to be that nearly everything we engage in as a species has a context; this idea of some objective absolute may not be as concrete as is often assumed, regarding mathematics and hard sciences. And looking through eyes of faith, it seems that God has vastly many frontiers for us left to explore. Now if only we can put aside our differences and work on ways of getting there together.
Andy Walsh says
Thanks, Ethan! I’m glad you find this post worthwhile. What sort of mathematics do you enjoy? I do a lot of statistical modeling at my day job, but I also have an amateur interest in dynamical systems and number theory.
I think you are right to say that nearly everything we engage in has a context. While I think math and science are useful tools for exploring an objective reality, we can easily overlook how they are also human endeavors shaped by our tendencies and biases as individuals and as a species. For starters, there are potentially infinitely many questions we could ask about the world and yet we only have time and resources to ask and try to answer a finite number of them. What we choose to ask or not ask can’t help but influence the answers we get.
Allow me to second your enthusiasm for exploring all the frontiers God has created for us, and the hope that as many people as possible will join us in that adventure. Next week I hope to reflect a little more on how we can better work together. I’d be glad to hear more of your thoughts on that challenge.
Ethan Ortega says
Great to hear from you Andy!
Hmmm, here are a few thoughts of mine regarding that last paragraph:
Observing the landscape of the U.S. currently, it seems evident that division is still far too powerful in many aspects. So how do we go about working towards unity? Maybe it starts with finding the common ground we share with those who we find opposed to us, taking things down to a very basic human level and then building up again with understanding. As Christians, shouldn’t we always be about the ministry of reconciliation? I think that extends to every facet of our lives. Too often, I believe that people are so guarded and ready with a list of defensive bullet points on issues of division that they rarely take the time to actually listen to people’s hearts and try to get a more intuitive perception of why people believe so strongly about things.
Something crucial that I have come to understand in my Christian faith is the emphasis on humility. Often times, I feel like in America we are encouraged to have this radical, defensive mindset with our faith vs “the world”, but the Jesus I see in the Gospels was all about humility and identifying with all sorts of people from all sorts of walks of life. In fact, that strikes me as the most compelling aspect of Christ, is this God who identifies with me and meets me where I am. I think that’s where reconciliation, unity, starts: humility. And we of faith should, in my opinion, be the first ones going about the hard process of healing what is broken, seeking ways of working together with others. It’ll take time, to be sure. But I know firsthand the redeeming power of the Savior’s love; healing is certainly possible.
Regarding mathematics, I am very much a novitiate, but I am endlessly fascinated by the simple and profound in all the many wondrous ways we can use mathematics. I am an aspiring screenwriter, and so I make up for my paltry grasp of mathematics by often writing characters who are preeminent math geniuses and who have this profound mathematical intuition. Helps me to explore the realm in some creative way.
Peace of Christ.
Andy Walsh says
Absolutely, humility is essential to unity. We each have to be willing to admit we are not complete unto ourselves, and then also trust that someone else has what we are lacking. And I think you’re right, the tendency of American Christians to feel, if not persecuted, then at least beset on all sides by antagonistic forces makes it challenging to show anything resembling weakness. At the same time, we occupy a place of substantial cultural influence, and that kind of power also is an obstacle to being humble. Fortunately, as you note we have hope in Christ. Jesus had greater power than any of us, and he had every reason to be defensive in the face of persecution during his ministry on Earth, yet he exemplified humility in every facet of his life. So at least we have a model to follow.
I love the idea of using fictional characters to explore a new field of inquiry. And naturally I like the idea of more movies with mathematician characters. Do you have any favorite fictional mathematicians? One of my favorite books is Neal Stephenson’s Crytponomicon which is about both fictional mathematicians and fictionalized versions of historical ones like Alan Turing. The book is full of fascinating little excursions into various corners of math, computer science and technology. And I’ve used the clip of Jeff Goldblum as Ian Malcolm explaining chaos theory in Jurassic Park to introduce the topic of nonlinear dynamics for a Sunday school class on strange attractors and grace.
Ethan Ortega says
First off, Jeff Goldblum as Ian Malcolm is one of the greatest fictional characters of all time and one of the greatest on-screen presences in cinema history (side note, are you a fan of Goldblum’s ’86 The Fly?). I love the idea of more mathematician characters in literature, film, and television. And they need good representation; not as villains, not as sidekicks. I feel like we need mathematicians and scientists at the forefront, and with emotions and depth, not as the stereotypical stony depiction.
And especially for younger audiences, I feel like we need good role models of mathematics and science. I find that all too often, there’s been a heavy emphasis in teen dramas to focus on the athletic world and paint an unflattering picture of the academics. In one of my series I’m working on, the main characters are heavy into STEM and are taking advanced calculus classes and yet they’re in a punk rock band and reading Huxley and Plath. I’m really pushing for this new depiction of the intelligent character where in high school, they join the Mathletes and listen to underground rock music. There’s a much greater field of diversity and a stark abandonment of the “nerd” stereotype.
Do you have any suggestions of some fictional mathematicians or scientists I should check out?
Hannah Eagleson says
Hi Andy and Ethan, I’m an editor here at ESN and couldn’t resist the last question about fictional mathematicians. Have either of you seen Tom Stoppard’s *Arcadia*? It’s a fictional play set in the same English country house in two periods of time, the early 1800s and probably somewhere in the 1990s. It plays around with literary and mathematical ways of thinking about life, and I think both are actually important to the plot. I couldn’t speak to how well it addresses the actual math, but it’s a pretty impressive play that is trying to take storytelling and math and science literally. It’s often featured in interdisciplinary colloquia trying to bring humanities and science conversations together.
I’d love to hear other people’s thoughts!
Andy Walsh says
Confession: I’ve not seen The Fly. I have no good excuse; it’s just a hole in my cultural experience that I guess I need to rectify.
I’m right with you on the need for more diverse portraits of mathematicians and scientists in popular culture — diverse in personality, world view, ethnicity, gender, the works. I think there have been some positive trends lately, but there’s still plenty of room for further expansion. The stories you are working on sound fantastic. My apologies if I should be able to answer this for myself, but are any of them available somewhere to read/see?
Here are some of my other favorite fictional scientists and mathematicians; hopefully at least one will be someone new for you to discover.
Murph from Interstellar, played by Jessica Chastain as an adult, offers a neat chance to see a character grow from a childhood aptitude for curiosity and experimentation into a professional scientist. The film also has a rich cast of other scientists and engineers as well.
Little Man Tate is about a child math savant that I think speaks to some of the trials and challenges of growing up as a gifted kid, as an introvert, and as someone with unpopular interests.
Big Hero 6 has a whole team of college students who use applied science to fight crime. Not the deepest film, but a fun introduction for younger viewers.
Contagion is the closest I’ve ever found to a movie about what I actually do for a living and the things I studied as a graduate student. It’s also a pretty realistic look at the politics and the logistics of science.
Neal Stephenson’s books often feature scientists and mathematicians as leads. His most recent book, Seveneves, covers a whole range of disciplines from orbital mechanics to robotics to evolutionary biology. I haven’t read Anathem yet, but that’s about a future monastery devoted to mathematics. Stephenson’s books can be intimidating in length, but I personally enjoy the level of detail.
Calculating God by Robert J Sawyer is about a paleontologist who makes first contact with aliens and is somewhat surprised and appalled that they believe in God because of their advanced science.
Dr. Nemesis is an X-Men character in the mold of a mad scientist but who is also, if not exactly a hero, at least an ally of the heroes. He’s been in a couple of different stories, but the X-Club mini-series is a good self-contained story to start with, and the whole cast are scientists from different disciplines.
Age of Ultron #10 A.I. is this odd little postlude of a comic that’s really an amazing portrait of Hank Pym, a celebration of the creativity inherent in science and a compelling argument for not requiring all science to be driven by practical application.
Unbeatable Squirrel Girl is a delightfully charming series whose heroine is a college student studying computer science who does some squirrel-themed superheroing. Her computer science studies feature prominently in detailed but accessible ways.
Oh, and Hannah – thanks for reminding me of Arcadia! I’ve never actually seen the play, but I have read it a long time ago; I should probably revisit it. Stoppard’s Rosencrantz and Guildenstern are Dead also has some mathematical elements, particularly about probability and statistical inference.
Ethan Ortega says
Hi Hannah, welcome to the conversation! 🙂
I’ve never heard of Arcadia but I’m definitely going to look into that! Sounds amazing. I love whenever STEM and the Humanities meet and hang out together. That’s what we need much more of, in my humble opinion.
Thanks for this list. I’m gonna do some research. It’ll help me with my writing for sure. And thank you for your interest in my screenplays. As of now, I’m still in the very nascent stages of things, but if you’d like to look at some of my work, I could email you a treatment or a PDF of a short sci-fi that I’ve written sometime.