Teaching Organic Chemistry in One Comic

Sometimes a comic makes you laugh and feel pride and knocks you down a few notches all at the same time.

This comic, man…so much to unpack. Let’s start with the immaculately drawn phenanthrene on the board. Graphic artists, marketers, and copy editors, take note: if a cartoonist can get it right, you can too! (Actually, now that I’m looking at it, the left-hand ring in the second panel contains an error. But pretty damn close in any case.) I have to believe that behind this structure, perhaps now decades in the past, is a good chemistry teacher.

Next, the looks on the students’ faces. The third panel is absolute perfection. I particularly like the student in the front row looking off in the wrong direction and radiating awkwardness. Between the third and fourth panels, there is an uncomfortable shift of everyone in their seats as the center of gravity in the room shifts to the one student who “understands.” There might as well be laser beams shooting from their eyes. What the teacher says next is key: “I sympathize with your embarrassment,” perhaps? Maybe “I am concerned about your collective ability to explain the shapes”?

And speaking of “explaining the shapes”…yeah. That’s a whole thing. When chemistry teachers get sick of their jobs (it happens to us all at one point or another), teaching feels like little more than playing with shapes. But chemistry is so much more than that, and the re-discovery of that fact is key to crawling out of the burnout hole. Every so often we have to look around and see chemistry everywhere around us. For me, a trip to a brewery or picking up a book on brewing never fails! It’s trickier to keep students from falling into the mistaken belief that chemistry is all about “explaining the shapes.” Students are pulled in so many different directions; if they’re not assessed on anything but “explaining the shapes,” can we blame them for limiting their focus to this?

By the way, if you haven’t see @nathanwpyle‘s Strange Planet comics yet, do yourself a favor and take a look!

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Finance is (Multi)fractal

The older I get, the more I find myself reveling in complexity. Buried within the overwhelming idea that the world is incredibly complex is a kernel of hope: although complexity frustrates our efforts to make predictions, we can still model it. There are lessons in models of complexity that remain hidden from those who lack the disposition to jump in the figurative pool. Without fail, these lessons are less comforting than the platitudes that are proclaimed in formal classrooms, especially at the high-school level and below. Stepping out of that intellectual comfort zone has been part of a long arc of personal growth for me.

My latest stop on that journey has been Benoît Mandlebrot’s book on finance and markets, The (Mis)behavior of Markets. I picked it up on the recommendation of professor-turned-home-math-guru Mike Lawler. The book is a little bit of economics, math (no equations, though!), history, and personal narrative all rolled into an account that challenges the orthodoxy of finance as it is taught in business schools. Mandelbrot is famous as the inventor of fractal geometry and after reading this book, I am starting to see fractals everywhere.

We’ll get back to fractals in a minute, but let’s start with the prevailing (fractal-free) wisdom. Orthodox financial theory assumes that daily changes in the price of a stock are drawn from a Gaussian or normal distribution. Another way to say this is that the “motion” of a stock price is Brownian. Two key ideas emerge from this assumption. The first is that variations in prices are independent of one another, like subsequent flips of a coin. (A patently absurd notion in practice, but “nice in theory.”) The second is that most changes in price are expected to be small. The vast majority are relatively tiny, within two standard deviations of zero. Very few are more than three standard deviations from the mean. Under the standard theory, large price swings should be extraordinarily rare.

The problem, of course, is that they’re not. Distributions of changes in price for a wide variety of stocks have “fat tails,” meaning events on the extremes are much more likely than the standard theory would have the denizens of Wall Street believe. Those with money in the stock market know this just as well as investment bankers. At one point, Mandelbrot shows a figure containing four price charts: two real and two fabricated. If you’ve looked at a lot of stock charts, the fakes are obvious: their ups and downs are too smooth. Plots of the changes with each step illuminate that the fake charts are built from purely Gaussian noise, while the real charts incorporate what the Gaussian perspective would call “shocks” at an alarming frequency. The underlying model that best reflects the economic reality is not a Gaussian distribution. Instead it is a power-law distribution, for which extreme outcomes are significantly more likely—so much more likely, in fact, that the traditional quantities of mean and variance are not defined!

Furthermore, Mandelbrot goes on to show that price charts look the same at different time scales, reflecting an old Wall Street adage that “all price charts look alike.” That is, whether the time scale is minutes, hours, or days, the zigs and zags of price variations are drawn from probability distributions of the same essential nature. This is where fractals enter the picture.

A fractal is a geometric construct that has the same (or similar) structure at multiple scales. The simplest fractals, such as the Koch snowflake, are constructed by starting with a “trunk” shape and building “branch” structures on the sides of the trunk. The new sides that result are then subjected to the same construction to give a new set of branches at smaller scale. The process is repeated again, and again, and again, infinitely. The resulting structure holds all kinds of insights about complexity in nature (“trunk” and “branches” hold a clue…). For our purposes, the most important is the similarity on multiple scales, a property called self-similarity. In this respect, charts of stock price over time are fractal!

A third insight attacks the assumption that price changes are independent and identically distributed. While a mathematical nicety, this idea is just plain silly in practice. Of course price changes are correlated over time. Bankers see a stock’s price rising and buy more in an effort to cash in by selling high later, pushing the price even higher. Investors sell as they see a stock’s price fall, worried that a further drop in price will cut into their winnings—causing the price to fall even more. Longer-term correlations also play a role: trends in entire industries or the economy as a whole cause large numbers of stocks to move up or down together over long time periods. Such long-term dependence leads to ups and downs at long time scales that the standard model of finance has few satisfactory answers for.

If we combine long-term dependence with the fractal model and a “fat-tailed” power-law distribution of price changes, the result is a multifractal picture of an evolving market with a fugue-like structure. Multiple structures now appear overlaid on one another, each with its own characteristic repeating scale factor. This complex structure can still be reduced to a small number of parameters, just as the musical themes can be distilled from a fugue. We can also work in the other direction, generating the behavior of a market over time starting from a small number of parameters. The result won’t look the same over time (uncertainty and randomness are involved in the “unraveling” process), but all possible price charts will be statistically equivalent.

Mandelbrot argues that the multifractal perspective is a more fundamental approach to modeling markets than the “Franken-Brownian” approach that has emerged from tweaks and adjustments to the standard model. Historically, investment bankers have hit the “real world” with the highly idealized standard model of how markets work that they picked up in business school. To function, they are forced to tweak, adjust, fudge, and essentially torture the standard model until it reflects reality. Why not start from a perspective that better reflects reality? Embrace the complexity, says Mandelbrot.

Speaking of reality, fractals show up in a number of places in nature at a variety of scales: the distribution of galaxies in the universe, growth patterns of plants, even the formation of aggregates in chemistry. It’s not direct evidence for multifractal behavior in markets, but it does hint at some fascinating commonalities between natural phenomena and the global economic system.

On String Cheese and Anisotropy

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String cheese is like an organic transistor…sort of.

A colleague who is a professor and a mom recently said to me, “I eat string cheese every single day of my life. Swear to God it doesn’t taste the same if you don’t pull strings off.” She was of course referring to that perverse group of people who prefer to chomp string cheese like a carrot stick instead of delicately peeling off strings along the long dimension.

Because it’s the kind of person I am, that got me thinking about anisotropy: a fancy word for a common concept, the idea that the properties of a bulk material are different in different directions. Does string cheese really taste different when cut in the longitudinal and transverse directions? It certainly seems plausible…

Anisotropy seems to be the norm in life. For example, we design and manufacture materials so that they have maximum strength along the directions where we need maximum strength, sometimes sacrificing other directions. Often, the very nature of the manufacturing process imposes lasting anisotropies within a material. This is certainly true in the case of string cheese, which is much easier to pull than bite (you’re wasting energy, biters!) in part because of the way it’s made. Could this affect the way our taste receptors respond to compounds in the cheese? Who knows?!

In science, anisotropy makes things complicated (and interesting!) because it forces us to speak of the properties of a material “in a particular direction” rather than “of the material” per se. If we’re measuring in a situation where anisotropy is expected, we have to either work really hard to measure in a specific direction or account as best we can for averaging effects over the measured area or volume.

I’m most familiar with this idea in the context of organic semiconductors, whose electronic properties are often anisotropic because of the way they’re made. Materials scientists and engineers are continuing to study how the microstructure of a material relates to charge-carrier mobility and how we can control the former along desired directions of current flow.

Adventures in Lyon! 6: Reflections

I’ve been back from Lyon for about a month now and had plenty of time to settle back into my usual routine in Atlanta. Spending a month in France was the experience of a lifetime, but I’m glad to be back! In particular, not having a toddler around to keep my sleeping schedule honest was a struggle (not to mention the eighteen hours of daylight and blackout shutters in my apartment in France). It’s nice to sleep soundly again.

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Atlanta is reasonably famous within the US as a city that likes to bulldoze its historical architecture and build something new on top of it. One thing I learned in France is that the old European nations tend to view the entire country this way: as a young upstart still trying to find its way in the world. One the one hand, being steeped in history that runs back over two thousand years leaves one with this constant sense of awe just walking around. You become hyper-aware that millions of other people have walked where you’ve walked. On the other hand, it’s easy to feel small in the midst of all that history: who am I next to the French Resistance in WWII or the revolutionaries?

Stateside, one gets the sense that we’re still in the process of creating our history, of crafting our national story. Monuments are relatively rare and we have debates about destroying some that have been erected. American identity is a fluid concept (and, I think, we like it that way). This can be hard though, as we have little to grasp onto in the way of inspiring national history…leaving many people to define themselves by their work rather than by where they live or those who came before them. Even so, I kind of like it that way. We are still in charge of our own destiny.

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Yes, we tore down a stadium and built a new one right next to it. Why not?

It was fascinating to contrast the organization of the European Union (and what people in France said about it) with the federal system in the United States. Imagine New York began as a sovereign nation and was “asked” to join the United States “Union” as part of a “deal.” What would the “nation” of New York think of the “nation” of Mississippi? It’s difficult to even fathom but it gives one a sense of the language used and the thought process in the EU. The EU is not, and will never be, a country per se as the very notion of Western statehood came into being as distinctions between places like France, Germany, the Czech Republic, etc. emerged. No one within the EU wants to trample on national sovereignty, yet complaints about its economics are common in the rich countries. The disproportionate amount of federal aid going to southern states in the US is an annoyance for us, but France and Germany propping up Greece is an international issue with big implications. Interesting contrast, right?

All in all, Lyon was the trip of a lifetime and I really hope I get the chance to return!

Adventures in Lyon! 5: Exchanges

Last summer, in an event completely unrelated to my trip to Lyon this summer, my wife and I hosted Camille, an exchange student from Lyon, at our house in Atlanta for a month. This summer I was able to repay the favor by visiting her family’s gorgeous home in Francheville, a suburb of Lyon accessible by the C20 bus line. To help orient Atlantans, this is roughly the distance from Mercedes-Benz stadium to Decatur Square. Even so, Francheville has the vibe of a quaint and picturesque French town—things are much more dense in France, where land is at a premium!

In an effort to learn as much as I could about how the “real” French lived, I blasted her father with a barrage of questions: what do you think of the migrant situation? What’s it like for young families? What do you think of Americans? What’s it like being a businessman in Europe? All of his answers are a post for another day; it’ll suffice to say here that he was incredibly open, warm, and downright funny the whole time.

The house was filled with delicious food throughout my stay, including some fruit tarts that will stick in my brain for a while. They don’t have a television on the first floor of their house but do have a large window that looks out onto the rolling hills of the French countryside. It was just as quiet as a typical American suburb…reinforcing in my mind an idea of Hans Rosling that people at similar income levels throughout the world live similarly, regardless of where they are.

Camille’s father was able to score tickets to France’s last friendly soccer match before the World Cup, which happened to be in Lyon and against the national embarrassment US men’s national team. We had a bit too much fun rooting for the USA, to Camille’s annoyance! (We just wanted to see a “close game.” And that’s what we got, as the final was 1 – 1. I consider that a win!)

I visited them once more just before I left to christen their newly installed swimming pool. Camille’s father took me back to my apartment in Vieux Lyon on his Vespa—a rather frightening ride considering that a very large and very steep hill separates Francheville from Lyon. He billed it as an “authentic European experience,” and it certainly was!

Adventures (near) Lyon! 4: Paris and the Pasteur Institute

We hit the road to Paris and paid a visit to the Pasteur Institute. The Institute’s museum is located in Pasteur’s former house and includes several rooms preserved since the 1800’s! One of my favorite rooms contained glassware, instruments, and even chemicals that Pasteur used in chronological order, tracing his work from fermentation to pasteurization to vaccination. The rest of the Institute is a scientific research center, something like an amalgamation of the CDC and National Laboratories in the United States.

Everybody with any interest in science has heard of Pasteur, but to a practicing scientist the myth of Pasteur seems a little too perfect. Pasteur’s productivity was a cut above everyone else’s during his time. To an extent, this was because he had latched onto a deep idea that everyone else had missed. At the same time, the story of Pasteur has a dark side: he kept his notebooks secret for his entire career. Once they became public, it was clear that he had exercised some deception in reporting his discoveries. I suppose we can conclude that in launching the field of microbiology, he was as much a marketer as a scientist. The whole issue of Pasteur’s legacy is interesting because his discoveries directly saved thousands of lives. It’s hard to argue that his deceptions weren’t worth it in the long run.

In the afternoon, we checked out some of the research facilities. I toured the protein crystallography center, where automated machines are used to set up thousands of crystallizations in a matter of a few minutes. The entire process of forming and handling crystals is managed by machines—all the scientist does is examine images and use computer interfaces to “grab” microscopic crystals. Truly amazing, as I can still remember when the process of protein crystallization was extremely painstaking and long winded!

For the rest of our time in Paris, I tried to get off the beaten path as much as I could (can’t stand waiting in lines). There are all kinds of interesting hidden gems in the vicinity of the more popular tourist attractions in Paris. For example, the Crypte Archéologique museum is underneath the Île de la Cité—while people were waiting to see Notre Dame above me, I was exploring Roman ruins unearthed at the center of Paris in the nineteenth century!

Earlier this year, I happened on a neat little book about experiencing Paris and its environs by train. The first chapter mentions several cathedrals that are just a short train ride from the center of Paris. The cathedral of St. Denis, near the end of the no. 13 Métro line, contains the remains of most of the kings and queens of France. In contrast to Westminster Abbey in London, this church is far from the center of Paris, evoking the classic image of the French aristocracy as detached and elitist. Smiling down on the unassuming sarcophagi of Marie Antoinette and Louis XVI is exactly as satisfying as it sounds! The crypt beneath the church also includes an ancient Roman cemetery containing the remains of Saint Denis himself.

 

Adventures (near) Lyon! 3: Grenoble on a Whim

Last Saturday, on a whim (and a waitress’s recommendation) I took a train to Grenoble in southeastern France. The city is just a jump over the mountains from Turin, Italy. It actually reminded me a lot of Denver, in that the city itself is mostly flat but massive mountains are visible just a few miles from town. I was hopeful that without a car, I could still find my way to some hiking trails…thankfully, that was the case!

Upon arriving at the SNCF station in the morning, I hopped out and took a walk through town, aiming to fuel up before hitting the mountains. After grabbing a sandwich I discovered Grenoble’s wonderful cable car, which takes passengers from the city proper up to the Grenoble Bastille, an old military fortress now home to a museum, restaurant, and monument to the famous French geologists of the Alps. Placards point out the names of mountains in the distance and recount the geological history of the region. Can you believe the view of the city from the Bastille?!

The Bastille is also the trailhead for a number of hiking trails heading up Mount Jalla, a peak in the foothills of the Alps. Signs point the way to key landmarks with both distances and estimated times. Near the summit I encountered a monument to the mountain troops of France, which were obviously critical during the World Wars. Lookouts along the trail give even more gorgeous views of the city below!

In case the mountains weren’t enough for you, Grenoble is also sporting a couple of rivers, the Isére and its branch the Drac. Unlike Lyon, the branching occurs somewhat outside of the city. The photo below shows the Drac, the smaller of the two. Not far from that river I found an office of the Communist Party of France: “champagne for the 1%…paid for by the 99%!”