by
Walker Rowe
Photo by Bruno Caimi
“The Avocado Republic of Chile, Because it’s too Cold to Grow Bananas” is Chile’s ultimate tour guide. Laughoutloud funny and insightful. American writer Walker Rowe sick of the pollution and noise in Santiago moves to the country for peace and quiet. What he did not know is when you move to the country, you exchange one set of problems for another.

There is a reason that most of the world’s largest telescopes are located in Chile.
ALMA is the world’s largest telescope array. It is located just above the desert oasis of San Pedro de Atacama. From the town, you can see the building where the European, Japanese, Chilean, and American scientists live, but you cannot see the telescopes.
The people who work there like to point out that the telescope is located at 5,000 meters and in “the world’s driest desert.” This is true for The Atacama Desert: there are large sections where it has never rained, ever. But ALMA is in the high Atacama desert, which is called the Altiplano. In summer it is the Bolivian winter in the Altiplano. That is when humid air blows in from the Amazon Basin. It can pour down rain in San Pedro in the Chilean summer, aka Bolivian winter. Such rains come maybe once per year. Further north, especially in the town of Putre, it rains in the Bolivian winter frequently. Down here in central Chile, we don’t have the Bolivian winter. Here there are no high deserts here, only high mountains, which stops the humid air from coming over.
Still, there is no doubt that it is bone dry in San Pedro and Alma, the occasional flood notwithstanding.
Astronomers are not known for their creativity. ALMA is a radio telescope. An international consortium is building the world’s largest mirrored telescope in Atacama too. The call it the “European Extremely Large Telescope.” Its 39 meter mirror will allow the observer to peer deeper into space much further than its predecessor: the “Very Large Telescope.” How boring. The astronomers should have let a humanities major pick the name.
Until I moved to Curacaví, I did not have much interest in astronomy. In college, I took Astronomy for my science requirement for the same reason that I took Hebrew for the language requirement. Both were said to be the easiest classes. In Hebrew, we did not learn more than the alphabet.
But here in the desert outside Santiago, the stars are so brilliant you have to take note of them. Here you can see the Milky Way, which you cannot see in the city. So I decided to study the stars.
There is a computer program called Stellarium that you can use to draw the night sky given your time and location. The problem with using the Google Sky Map to identify stars is it only points out the bright ones. It tells you where Orion is located and Sirius. But when you point your binoculars skyward, so see much more than is on the map. So you need a star map with high resolution. That is what Stellarium is.
What I have learned so far from my studies is that those of us who live in the Southern Hemisphere are fortunate with regards to star gazing. There are more objects here to look at here than in the Northern Hemisphere. The bulk of the Milky Way, which is the center of our own galaxy, is overhead in winter when the days are longest. That is when the brightest part of the Milky Way is below the horizon in the Northern Hemisphere at night, thus not visible to observers there.
In Chile, you cannot see the North Star, also called Polaris, which people use to find north. Instead here we have the Southern Cross, which points toward the south. Like Polaris, you could use that to navigate. The Southern Cross is 4 stars and not one. They form a cross that points to the south. That’s different than the North Star, which is located due North.
I have been watching the sky here for 5 months. I had to skip a couple of weeks, because bumbling around in the dark I knocked my first pair of binoculars off the porch and they broke. The ground here in the desert is rock hard. But that gave me an excuse to buy a more powerful pair.
The first star that you can see at night this time of year in Sirius. It is the brightest star. Next you can see Canopus. Sirius in summer rises in the east. Orion is to the North. The whole affair has been rotating to the North over these past few months. I was able to see Orion from the comfort of my hammock, lying on my back with binoculars. Now it is blocked by the roof. But now I can see the planet Venus where Orion was. The Southern Cross remains in the same place pointing south.
I saw a satellite or the space station one night. It moved across the sky quickly. It was lit up because it was not in the shadow on the earth. On other nights I have seen shooting stars. Now, having adopted astronomy as a hobby, I put in my calendar when the next shooting star storm is coming. Fortunately, that coincides with a new moon. If the moon is full you cannot see fainter stars, as the bright moon hides them.
The reason we know with such exactitude when shooting stars will appear is because of Sir Isaac Newton. If you will indulge me for a page or two I want to tell you what Newton did and why that matters in Curacaví. If you are not interested in cosmology then feel free skip ahead to the next chapter.
One of my favorite writers is David Foster Wallace. He wrote novels and short stories, but he also wrote a book giving the history of mathematics from Euclid to Cantor. But this was no ordinary history. Instead of talking about the mathematicians, he talked about their work. But he did so in a way that was interesting to read and you could do so without working through the math with a pencil. You only needed to read the formulas and could dispense with the algebra. Someone with some knowledge of calculus could understand what he was saying. I got my bachelor’s degree in math and picked up studying calculus again about 6 years ago when my older son was studying it in high school. We studied together.
The more I studied this book the more I enjoyed it. I learned much more on my own in my own study of math and by reading that book than I ever did in college where I earned a solid C for my efforts.
So I was totally drawn in to DFW’s book “Everything and More.” He walks you through Euclid’s work on geometry where the Pythagorean Theorem is presented. That is the theorem that the length of the hypotenuse of a right triangle squared, which is the long side opposite the 90° angle, is equal to the sum of the squares of the lengths of the other two sides. Then he explains that the Pythagoreans, who were something between a religious cult and a group of geometers, were stumped when they thought about a right triangle with one side of length 2, because it forced them to confront something they had not seen: the square root of 2 is not a rational number. The Pythagoreans could not explain this since all their work was based on ratios of the sides of triangles.
DFW works his way through this, building on the ideas of Archimedes working all the way up to Dedekind and Cantor. What the last two mathematicians did was show that infinity is not the largest number. That is counter intuitive since we were always taught in school there was nothing beyond that number we call infinity. But Dedekind showed with an object he called the schnitt he could construct a number which is in not in either set of numbers when you cut the number line in two. Euclid’s definition of a point is that it has no width. Yet you can cut a number line in two and find a number that, no matter where you cut it, is not in the set to the left of the point where you cut it and nor in the set to the right. But the number line is supposed to include all numbers, an infinite number of them. Yet there are numbers not on this line. So you can find an infinite set of numbers with more elements in it than another set of infinite numbers.
If you grasp what I am talking about, the discovery of transfinite numbers is nothing short of astounding. Like Einstein’s relativity, it too does not make any sense unless you reason through the logic.
So stick with me as I work my way to the sky over Curacaví. Having mentioned Einstein, let me say something about Newton, who you should study first. We know where the stars are located precisely because of Newton. He made the conclusion that an apple falls from a tree, because both the apple and the earth are drawn towards each other by their mass. This we call gravity. Newton took Kepler’s laws of planetary motion—an object in orbit sweeps out equal areas in equal time—and explained exactly why the moon revolves around the sun and the sun around the moon. In his spare time the great man also demonstrated that white light is composed of all the colors we see in a prism. He also solved Galileo’s problem, which was that Galileo’s telescopes showed a halo of light around stars. Newton replaced the lens with a mirror. Galileo was seeing the prism effect so deftly explained by Newton.
I was so carried away with this that I thought I would do what DFW did and explain Sir Isaac Newton’s work in a narrative prose way in a manner that other people could understand. In other words, explain the laws of classical mechanism in a way that is interesting to read and does not require pencil and math.
That is where I got stuck. DFW spent two years working on his book. I picked up Newton’s book “Principia Mathematica,” and spend about 2 weeks on it before giving up. It’s written in a purposely obtuse manner. Even if the Olde English is translated to modern English the problem is Newton used the mathematics of Euclid and Archimedes to explain his ideas. That means all of this was presented and proved using triangles. This 2,200 year old math is impossible for the modern mathematician to understand or impossible for me.
Newton expanded on an idea from Archimedes. Archimedes calculated the area of a circle, pi, by drawing smaller and smaller rectangles inside a circle, whose area is easy to calculate, until added together he came up with the number 3.464 as his estimate of pi, which is very close to its actual value of 3.141… Newton took Archimedes’s idea further and figured out how to draw an infinite number of rectangles under a curve. If you put a dozen rectangles under a curve then you can get a pretty good approximation of the area under the curve by summing the area of each one. But it you increase the number of triangles to infinitely (actually close to infinity) then you can calculate the area under a curve exactly. Today we call this calculus. To Newton this was just a tool, he never even published a paper on that.
So, being stuck on Newton I was happy to find a book called “Newton’s Principia for the Common Reader” written by the Nobel Laureate in Physics S. Chandrasekhar. I expected something like what DFW has written, which was what I wanted to write. Instead it is page after page of mathematics. So the name “common reader” is misleading to say the least. What S. Chandrasekhar does is walk the reader through the ideas and proofs of Isaac Newton, but does so using modern math. That I can understand.
To study the stars and gravity you need to read Einstein too. Einstein wrote books for the laymen and not just books filled with equations. His book “Relativity” is not too hard to understand. Anyone with a little knowledge of calculus can understand it. It that sounds pedantic or if your eyes are rolling, give me a second. Einstein wrote lots of very readable books. He thought mathematics was not at all important. He thought that physics should be so simple that he “could explain it to a child.” Of course he needed math to prove his ideas, but the basic ideas were not complicated, however there are very much counter intuitive.
What Einstein did was also think at the world around him and observe the contradictions in Newton’s work. For example, Newton never explained what caused gravity, whether it was a wave or a particle. Newton also assumed that gravity traveled from one place to another instantly. Einstein knew it could not: it travels at the speed of light. So the gravity that holds the earth in orbit around the sun takes 8 minutes to reach the earth.
Another scientist showed that the speed of light is the same for something standing still as for someone moving. When you take that and apply it to Newton’s work, it means that time is not an absolute value. A clock runs slower for someone who is moving that someone who is standing still.
All of this work: Kepler, Einstein, Newton, Euclid, and Archimedes can be tied right back to the stars and planets circling above Curacaví. Newton said the stars rotated through the sky because objects are attracted to each other because of their mass (size x density). Einstein said that while that appears to be the case, what is actually happening is that space and time are warped, so the moon rotates around the sun, like a marble would rotate around a bowling ball if you put the bowling ball in the bed. Where it makes a dent, the marble rolls around it. Newton’s work is still accurate, because planets do not move fast compared to the speed of light. You have to move near the speed of light before relativity is noticeable.
So I think about all of this when I look at the stars over Curacaví.
