Category Archives: Williams


It seems that being at Williams College again for only a weekend is enough to prompt a little self-reflection.

Hopkins Gate
Hopkins Gate

I returned to my alma mater for the 2013 commencement exercises. The graduating seniors seemed like a powerhouse of innovation, leadership, and social change. The commencement speaker, Billie Jean King, stood up for gender equality through her career in professional sports. One of the honorary degree recipients, Deogratias Niyizonkiza, went from being a refugee to founding hospitals that provide medical care in impoverished nations. Another honorary degree went to Annie Lennox, who, at a pre-commencement event, condemned material and celebrity culture and spoke about how her visits to Africa inspired her to HIV/AIDS activism.

What, I thought, am I doing to improve the world we live in? Sure, I don’t have the influence power of Lennox – who did acknowledge the irony that her celebrity status and material security enable her to drive activism – but my chosen career is all about building spaceships. What does that do to make the Earth a better place?

I truly believe that it helps. That I am serving a fundamental good.

Imagine this: a group of people have fallen into a hole in the ground. The hole is too deep to get out of, and resources at the bottom of the hole are very scarce. The situation is bleak. What are they to do? Those with liberal inclinations may feel that they can best solve their problems by banding together and coordinating their efforts: cultivating moss and vines on the wall of the hole for sustenance, helping each other out when sickness strikes, and sharing the water that collects in nooks and crannies. The conservatively minded among them might instead think that each denizen of the hole should try to improve their lot individually – if some parts of the hole get more sunlight and water than others, and so some of the people are richer than others, then so be it – because that improves the standing of the people as a whole and the well-off individuals may devote some of their hard-won resources to assist others.

I think that both of these approaches are important ways to improve conditions in the hole. But I also think that there’s another thing that the people in the hole can do.

They can climb out.

They can get together and hoist a representative from among their number higher, and higher, until that person can plant his or her hands on the lip of the hole and breach the horizon.

The struggle to climb out is crucial to meaningful existence inside the hole. Without the idea that the people can climb out, what are they improving life inside the hole for? There needs to be a goal – but more than that, the goal needs to advance. It helps to set the goal high, because in striving to achieve it, we might learn more about our environs and ourselves, and find other ways to improve conditions – ways that we might not have seen at all if we hadn’t started to climb. The people in the hole don’t know what lies above, so they will need to give their climber provisions – and so might develop new and improved ways to cultivate, prepare, or preserve food. They might need hoists to get their climber up to ground level – and so might design mechanisms and machines that save labor in other activities.

Most important of all: once out of the hole, the climber can come back to relate what they see…or to help others follow.

I build spacecraft. I don’t feed the hungry, or clothe the needy, or heal the sick – at least, not to much more or less an extent than the average middle-class person does. I don’t volunteer in the Peace Corps, or tutor in sub-Saharan Africa, or assist in impoverished clinics. I build space ships.

Because of spacecraft and the space industry, though, we have a global positioning system that allows those aid workers to get where they need to go. We have a global communications network that allows those volunteers to coordinate their activities from the most wired national capitals to the remotest wastelands. We have weather data that improves our ability to predict storms, droughts, floods, and climate. We have pictures of the Earth that show us the lay of the land, and how the land is changing.

Because of spacecraft and the space industry, we learn how to make more efficient solar power generators. We learn how to stretch out thin resources into expanded capabilities. We learn basic scientific facts about other worlds, giving us more lenses through which we can look at our own. We learn to build more and more precise scientific instruments. We learn to build more robust and effective machines. Sometimes, we put a human being on one of our spacecraft, and we learn even more. We learn to be better climbers.

I’m only one person, and I can’t do everything to help. I do what I can. One thing I can do is to keep moving the goalposts outward. I can keep us climbing.

To see the fruits of these efforts, I can look everywhere: from the precision medical device on my belt to the way we fundamentally think about the Earth as a planet, the influence of space exploration and industry manifests itself.

We need problem-solvers on Earth. I’m glad to see them. Alongside them, though, to keep making the world a better place, we need climbers.

I know I’m not the first person to say this. I also hope I’m not the last. But, you know, sometimes it needs saying.

What’s the Value of Liberal Arts?

There was an NPR article today about how the pressures of the economy are casting some doubt on the value of liberal arts colleges and liberal arts education.

I have a bit of an opinion on this, since I went to the best liberal arts college in the nation and I found gainful employment in my field immediately after I finished with graduate school.

To me, the argument about the value of a liberal arts college seems a bit silly. After all, a huge percentage – if not the majority – of the members of my Williams class majored in physics, biology, chemistry, math, psychology, computer science, or economics – all very practical things that translate directly to various industries and enterprises. A liberal arts college is a tremendous place to study those disciplines: science is a collaborative and inquisitive endeavor, and learning to work with an expert to thoroughly understand scientific principles gave me a much better experience than I think I would have received in the back of a hundreds-seat auditorium getting lectured by a TA.

But Williams did more than give me an incredibly solid grounding in physics, which I could then take towards a doctorate and career in spacecraft engineering. While I studied physics, in very demanding and rigorous classes, I also studied linguistics. And studio art. And history. And even political science. All these things did more than make me a “more well-rounded person.” Study of these subjects gave me exposure to ideas, concepts, and frameworks to help me put all sorts of things in context. So now, when I hear political candidates talk about America’s founders, or invading Iran, or health policy, I have a relevant understanding to evaluate their statements against. When I read about the economy, I have a basic understanding of the principles that govern the situation we face. When I read a good book, or see an engaging film, or view a piece of artwork, I can appreciate the efforts the artists put into those things and understand how they have the effects they do on me. In short: I have gained more than a narrow, vocational perspective on the world – I can approach many subjects from many angles. This is not merely a good thing for its own sake, but it also helps me in my chosen vocation. I’ve used my rudimentary skills as an artist and my experience with writing (Williams grads know what I’m talking about!) quite frequently as an engineer. If this also means that I have a few still lives and unfinished manuscripts in my apartment, well, that’s just icing on the cake.

For the same reasons that I appreciate having a liberal arts background in my academic training, I also appreciate that we have “pure” liberal arts majors in our society. We need historians, writers, artists, filmmakers, and musicians in our society. We need them to remember, curate, create, and teach their liberal arts so that we can keep churning out well-rounded, multi-talented workers instead of narrowly focused drones.

Sol LeWitt

I spent last weekend in Williamstown, MA, with my family for my sister’s Williams Dance Company performance and the super-swanky Mother’s Day brunch at the Williams Inn. (I’m allergic to chicken and turkey, so I passed over the roast duck; but I made sure to grab some brunch swordfish!)

We also went to the Sol LeWitt retrospective exhibition at Mass MoCA. LeWitt is really interesting; first, because he drew his artwork directly on gallery walls, and second, because the artwork consists mainly of a detailed set of instructions describing how to create the drawing. If one museum sells a Sol LeWitt wall drawing to another museum, then they erase the wall, give the new museum the instructions, and that museum carefully follows the plan to reconstruct the wall drawing in a new space. I found this whole process to be quite interesting. (All the images here are from the Mass MoCA web site; click to see them on the original pages.)

Wall Drawing 289 (Mass MoCA)
Wall Drawing 289, Fourth wall: twenty-four lines from the center, twelve lines from the midpoint of each of the sides, twelve lines from each corner. (Mass MoCA)

The precision and care that went into each wall drawing (some on walls that were, maybe, thirty feet wide by eight feet tall) are amazing. Each drawing is the product of work by a number of drafters, some of whom are interns and some of whom are dedicated to Sol LeWitt wall drawing. They develop methods for interpreting LeWitt’s instructions. Some of those instructions even leave parts of the implementation wholly up to the drafters.

Detail from Wall Drawing 305 (Mass MoCA)
Detail from Wall Drawing 305, the location of one hundred random specific points (Mass MoCA)

LeWitt’s method seems to revolve around abstraction – taking something observable and representing it in a symbolic way. The descriptions at Mass MoCA describe how LeWitt was interested in removing the artist from the artwork. This concept resonates for me: here I am, trained as a physicist and engineer, with my livelihood based on constructing, manipulating, and extracting results from mathematical models. Those models are based on the theories that govern physical phenomena; but they never are a full, complete description. Still, we use them to great effect in making predictions or developing new theories. The philosophy of science question here is, are the models conceptually different from the theories they describe? Or are they just a different representation of the same thing? In the same vein, is Sol LeWitt’s art the wall drawing, or the instructions? His opinion seemed to be the latter.

The other thing I ended up thinking about while strolling through the wall drawings was how the implementation of the drawings corresponded to realizations of models in the science and engineering world. We can come up with incredibly complex models for how the universe works, but when constructing a simulation or making a prediction, we often choose to use only a small part of the model. For instance, Einstein’s theory of General Relativity describes how objects move under the influence of gravity (or, equivalently, how they move through curved spacetime). But for a great many applications, Newton’s single equation for gravitational attraction between two bodies is enough: The force is attractive, proportional to the product of the masses of the bodies, and inversely proportional to the square of their separation. Then for yet another large subset of applications, the simple high-school physics expression F = -mg is quite sufficient. In a sense, both of these simplifications are realizations of General Relativity, in the presence of certain simplifications that let us “zoom in” on part of the model. When the drafters have a LeWitt wall drawing instruction sheet, they must match the instructions up to the wall space they have to work with. The instructions seems to be written in reference to relative measurements on the wall (the midpoint of the left side, the corner, the center of the wall, etc), which means that the same instructions – the same idea, the same “theory” can produce very different realizations on different walls. (And, speaking of relativity, I wonder if LeWitt ever took a look at the math behind Einstein’s theories. It would have been neat to see something like this wall drawing as viewed by an observer traveling at 0.5c!)

Not only do the spaces shape the wall drawings, but the drafters themselves may be left with choices in how to interpret and then implement LeWitt’s instructions. Take this wall drawing:

Wall Drawing 386 (Mass MoCA)
Wall Drawing 386, stars with three, four, five, six, seven, eight, and nine points, drawn with a light tone India ink wash inside, an India ink wash outside, separated by a 6-inch (15 cm) white band. (Mass MoCA)

I spent a little while thinking about that three-pointed star. Without that, it’s obvious how the progression works: the nth star is centered in the middle of each square, its points are evenly spaced about a circle, they all extend to the same radius, and the border of the star comes in between each point so that the shape is concave. But that three-pointed star breaks all those rules! It need not have – it could have been just like the four-pointed star, only with three points. Instead, it is a triangle with one concave side. Here, I do not know: was this in LeWitt’s instructions, or did a drafter determine how to construct this three-pointed star?

Some of the wall drawings definitely did have ambiguity built in. My favorite of MoCA’s drawings was 146A:

Wall Drawing 146A (Mass MoCA)
Wall Drawing 146A, all two-part combinations of arcs from corners and sides, and straight, not straight, and broken lines within a 36-inch (90 cm) grid. (Mass MoCA)

The instructions for this drawing specify that the drafters make “not straight” lines. Okay…so we define the line by what it isn’t, and leave a still-infinite space of possible lines that meet this description. The drafter can make “not straight” lines as un-straight as they like. They can make lines that wander as much as they want. They can choose to tie their “not straight” lines in to the “not straight” lines in the rest of the drawing or not. If you take a look at the timelapse video of this wall drawing being drafted, you can see how each drafter does each “not straight” line differently.

Were I Sol LeWitt, I think it would have been interesting to create a set of wall drawing instructions that contained intentional contradictions. Some drawings might have tiny contradictions, some might seem like egregious errors. What would the drafters do? Would they prioritize the instructions, and satisfy the most important ones first? Would they try to satisfy both constraints equally? Would they push back at all the instructions for the wall drawing, going for the most “average” level of meeting the instructions? That would sure be an interesting way to comment on our artistic, geometric, scientific, or philosophical methodologies. In an exhibition with many drafters and many walls, giving them all the same set of contradictory instructions would likely turn up some very interesting results!

Wall Drawing 692 (Mass MoCA)
Wall Drawing 692, continuous forms with color ink washes superimposed. (Mass MoCA)

Some of LeWitt’s later wall drawings were just plain fun. Drawing 692, above, was also one of my favorites – I liked how it gave the impression of different planes, and how the vibrant colors made the painting stand out as if with its own light. It was like looking through a windowpane onto another stained-glass window. Remember – this image doesn’t convey it, but I stood only a little taller than the second black line from the floor!

Then, of course, there were wall drawings like Splat, the intentionally impossible-to-look-at Loopy Doopy, Whirls and Twirls, and some cool experimentation with glossy and matte paints.

Wall Drawing 824 (Mass MoCA)
Wall Drawing 824, a black square divided in two parts by a wavy line. One part flat; one glossy. (Mass MoCA)

But of course, being a Williams guy, I had to like Wall Drawing 852 best of all.

Wall Drawing 852 (Mass MoCA)
Wall Drawing 852, a wall divided from the upper left to the lower right by a curvy line; left: glossy yellow; right: glossy purple. (Mass MoCA)

The Sol LeWitt Retrospective is a very cool exhibit. I didn’t always like the art at Mass MoCA, but I’ll happily recommend a trip to see this!