Red Rocks and the Two Body Problem

Roxborough State Park, Colorado (Nov 16, 2013)

There are only two problems in physics that we know how to solve: the pendulum and the planetary orbits. Everything else is calculated either by assuming that behaves like one of the two problems above, or by solving in some approximate way more complicated equations using a calculating device.

The difference between the physics of a pendulum and the one of a planet orbiting the Sun is in the relationship between the force and the distance. In the case of the pendulum there is an attractive force that doubles every time the distance double from the center of the oscillation. Galileo figured that out by looking at the chandeliers swinging in the Cathedral of Pisa. In the case of a planet orbiting the Sun the force on the planet decreases as the square of the distance from the Sun. Double the distance and the force will become one fourth. This was understood by Newton, which also had the epiphany that an apple falling towards the center of Earth would feel the same kind of force as a planet continually falling around the Sun. That's why the theory of gravitation is universal: applies to apples as well as planets.

The rest of physics can generally be approximated as one of these two basic problems. The motion of the atoms in a solid crystal? Nothing else than masses connected by springs; and springs also produce a force proportional to the displacement, making the crystal vibrate like a coupled pendulum. This generalized problem is called "harmonic oscillator". Charges into an electric field? The electric force also goes like the inverse square of distance: exactly like gravity (the only complication is that it can be either attractive or repulsive depending on the sign of the charges). The generalized problem of two masses subjected to a reciprocal force going like the inverse square of distance is called "two body problem". If the masses were three it would be a "three body problem". Four masses? You get it... it keeps going until you get the generic "n-body problem".  The kicker is that we only have an exact solution (the one found by Newton) for the two body problem: higher order problems can only be solved numerically, using a computer. Even worse, for a three (or more) body problem the solution is chaotic: this is a mathematical term that means that even an infinitesimal small change in the initial conditions will cause an unpredictable effect to the solution. You don't believe me? Look at this flash applet that simulates the orbit of one planet (the third body) around two stars.

Roxborough State Park

At this point you may ask what the two body problem has to do with red rocks in Colorado. As it turned out, last time we visited Colorado we met with some friends that work in the University there. Both scientists, a physicist and an astronomer, like Mayli and me. Academic couples are quite common, considering that people tend to pair with the people they socialize with. When you are in graduate school with other future scientists... well these are the people you tend to hook-up. This is all good until you graduate and look for a job. That's when your situation becomes a "two body problem".

Two body problems are not unique to academia, but the difficulty to find two academic positions within commuting distance makes them particularly difficult to solve. A recent article on Scientific American reports the results of a survey of two body problems in and out academia. The results? The large majority of the respondent (90%) said that they either had or think they will have to face a two body problem in the future. Of those that have already found the problem, less than half managed to negotiate a double position to solve it. The others? Either one of them had to leave a dream job to accommodate the career of the spouse, or they accepted to live at a non-commuting distance, with divorce or split-up as most common long term outcome.

Depressing? Well, if you have followed what I have written above, the two body problem (the physics version) is in principle solvable without recourse to chaos. There is hope. We got lucky, and after one failed attempt and two years of separation (Mayli in Chicago while I was still in Boston) we managed to get two positions in the same university. It was not easy, and every case is different, but I know many other couples that have found similar arrangements. What typically works best are mid-sized universities: top University can pick whatever faculty they need, and may not care enough to try creating a spousal accommodation. Too small places may not have the resources to find a solution. It also depends on the culture of the university. In our case we could count on funds that were explicitly set aside for this kind of situations: many university have come to the realization that the two body problems is actually a two body opportunity, a way to attract better candidates by offering a very special perk that fancier institutions would not even dream to contemplate.

Roxborough State Park, Colorado (Nov 16, 2013)

The Diaspora of the Italian Astronomers

The Loch, Rocky Mountain National Park, Colorado (May 29, 2003)

It takes about two hours to get from The Denver International Airport to Estes Park, in the heart of the Rocky Mountain National Park. It actually takes less than that, in normal circumstances, if you rent a car and drive up on Interstate 25, and then west on Route 66. That's the smart choice that avoids Boulder, and saves time. But when I went there I was a postdoctoral fellow on a budget, going to a conference on the Astrophysics of Dust. I took the bus.

In case you wonder, yeah there is plenty of dust in space. Mostly, is in the form of fine microscopic particles of sooth or quartz-like material, and fills the interstellar space. Near stars, though, it concentrates in larger particles. The ones that make shooting stars when falling on Earth. Some are even bigger, much bigger. Like asteroids. Some are humongous, like the one you are sitting on at precisely this moment. Planetary size dust grains. This is all stardust: blown out from stars as they die.

The bust was actually chartered by the conference organizers, and as such it was full of astronomers. It was an international conference, so the astronomers were arriving from all over the world. I must really look italian, though, because I didn't even have time to set my bag in the rack that I saw somebody pointing to the seat next to mine, saying: "'che è libero questo posto?". This inevitably proved that my nationality had been discovered, and that of all possible astronomers on the bus, the one that was going to sit next to me for the two hours trip was another italian.

Finding another italian astronomer in the US is not that rare. The diaspora of italian scientists, and astronomers in particular, is a well known fact. Italy has an excellent and free educational system, producing first class scientists at a much higher rate that it can absorb. Well, the production rate is maybe not that high: the problem is on the low employment rate side of the equation. Italy invests in science less than 1.3% of its Gross Domestic Product, which is well below the world average, and less than half than the US (2.8% of GDP). Italian scientists (and a lot of astronomers among them) get their education and leave to sunnier pastures: many try to stay in Europe (France and Germany the preferred destinations) but US is also a favorite place to go. Of all my classmates in graduate schools, none remained in Italy: three of us are in the US, one in Switzerland, the last one went back to his native China. He is the one that had the most successful career.

A not-italian ground squirrel

Of the foreign contingent in my old institution (the Harvard-Smithsonian Center for Astrophysics) the largest community is the italian one. That is particularly true in the high energy division, the realm of X-ray astronomy. The italian dominance is not surprising, because the division was funded by Riccardo Giacconi, the italian X-ray astronomy pioneer that won the Nobel prize in 2002. It was not difficult to find italians at CfA. Among them Cesare, a true "toscanaccio". An excellent guy, always with strong and astute opinions, and colorful ways to express them, as typical in the people from the region of Dante. I remember that he was very unhappy with his run-of-the-mill Windows laptop (he didn't like Bill Gates too much) and wanted to install Linux on it to "stick it to the man". We spent hours to coerce that poor computer to run what at the time was a "rebel" operating system until we managed to have everything working properly, including the internet and Netscape (yes I am that old). Then he returned to Italy. I later learned that when he got home to Florence he sat at the dinner table with a large bowl of soup and the computer in front of him. Ready to finally browse the web without the tyranny of Internet Explorer. It didn't last long: as soon as the first page was slowly loading at dialup speed he got so excited that he bumped into the bowl, all the soup launched at orbital speed to fall back right on the laptop, seeping inside the keyword with fizzling sounds. Despite heroic efforts, the computer was pronounced dead by the time it was brought at the repair store. It is said that Cesare took it quite well, given the circumstances: "it could have been worse" it is believed he said; "instead of soup, it could have been wine".

PS: it turns out that my italian companion on the bus to Estes Park was nobody else than the old thesis advisor of Cesare. We spent the whole trip bitching about how americans do everything wrong (that's another trait of toscanacci, explaining how "everything is wrong and needs to be done over". All in a very strong tuscan accent, totally impenetrable to any english-speaking passenger on the bus (thankfully). The photos were taken after the conference ended: I stayed a few more days to hike in the beautiful rockies and try out my first DSRL. These are the first photos I took with my Nikon D100 camera, that served me well for many years since.

View from Estes Park, Colorado (May 28, 2003)