by Shane L. Larson
One of the most profound consequences of the development of life on Earth is that the Cosmos has produced complex systems with the ability to question their own existence. We are each of us a collection of atoms that the Universe has stirred together in such a way that we can contemplate the nature of the Cosmos itself. It is remarkable, really. A rock is also a collection of atoms that the Universe has stirred together, but if a rock contemplates the Cosmos, I have no strong notion of what its rocky thoughts might be. Humans, on the other hand, have been given a remarkable gift: we can ask questions, and then we can figure out the answers. This game of questions and answers has a name. We call it science.
There are many questions that we could use the atomic computing engine between our ears to consider, like: how can we grow enough food to feed 10 billion people? will a catastrophic shift in the San Andreas Fault change the geography of California? can I make a jetpack safe enough for sixth-graders to fly to school? anglerfish — what are they all about? why do some tissues develop cancer in the human body and others don’t? Where did the Universe come from?
Questions about life and our own existence often dominate conversations in philosophy classrooms, research labs, and late nights around a campfire. What is the origin of life? Is there life elsewhere? Is there intelligent life (on this planet or others)? These are BIG THOUGHTS — heady questions that have been asked for as long as we have been capable of asking them. Some of them may have answers that can be figured out, and some of them may not. Let’s think about one of these together — is there life elsewhere? This is a question that could be answered by simply looking. Except that looking for life elsewhere is difficult for two reasons: (1) Everywhere else is far away (as I’ve talked about before!) (2) We’re not even sure what life elsewhere might look like! We’re still discovering new life on Earth (like under the Antarctic ice, and even in the deep forests where humans have not tread before).
These points are hindrances to be sure, but that is the nature of this game. Our atomic computing engines are very good at facing down such adversity, and finding ways to answer our questions irrespective of the difficulties we face. For big questions, it is often useful to make an estimate of what the answer could be before you embark on your quest for knowledge. This helps define the boundaries of your quest. One of the defining traits of modern scientists is their ability to make quick, quantitative statements about extremely complex questions using only a few pieces of data that almost everyone agrees upon. These kinds of problems often go by the name “back of the envelope calculations” because they are supposed to be simple enough as to fit on the back of an old bill envelope (though sometimes you may need a manila envelope). They are often called Fermi Problems, after Enrico Fermi who was famous for this skill.
Enrico Fermi was born in 1901 in Rome; he rose to prominence in physics very quickly, completing his laurea (the equivalent of a Ph.D.) at the age of 21. He worked in Italy until 1938, when the Fascist regime passed the leggi razziali (“racial laws”), which threatened his wife Laura, who was Jewish. That same year, he was awarded the Nobel Prize in physics, and after acceptance in Stockholm, took his family to New York, where they applied to become residents of the United States. He famously worked on the world’s first nuclear reactor (“Chicago Pile-1”), and the Manhattan Project.
Fermi was, without a doubt, one of the giants of modern physics. When you first start studying physics, you are regaled with tales of the great minds of physics — their accomplishments as kids, their discoveries early in their careers, and the myriad ways they have transformed the way we view the world. As a young and aspiring physicist, it is incredibly intimidating and almost crippling; fortunately, I had many outstanding mentors. Each of them played a role in calming my doubts and fears; each of them helped me look at great scientists like Fermi and learn something about how to do science from their examples.
One of those things is Fermi problems. Fermi was famous for his ability to quickly estimate the answers to complicated problems. When his answers were checked against precise calculations, his results were amazingly close to the “real” answer! One of the most famous examples was Fermi’s estimate of the strength of the atomic explosion at the Trinity test. Fermi dropped handfuls of paper from a height of 6 feet before, during, and after the blast wave washed over the observation post. Based on the distance the paper spread as it fell, Fermi estimated the explosion to be the equivalent of 10,000 tons of TNT; the strength reported after the test had been fully analyzed was 20,000 tons of TNT.
Calculating the yield of an atomic bomb is definitely a big physics problem; it’s not the kind of thing most of us have to do in our lives. But all of us do Fermi problems every day. Every one of us. Things like: you’re going to watch curling with 4 other friends; how many pizzas should you order? how many bikes can fit in your garage with everything else? what time do you need to leave home to make it to work on time?
The classic problem that Fermi used to introduce this estimation concept is “how many piano tuners are there in your city?” With Google, or the yellow pages (if you are a caveman), this question could easily be answered definitively. But it can also be calculated by using some things you know or can estimate from your own personal experience. Let’s try this together — I’ll do it for Logan, Utah, and you do it for wherever you happen to be right now.
The method is to ask a series of questions upon which the answer must depend, and that you may know the answers to. Questions like: how many people live in your city? how many households are there? how many households have pianos? How often do they tune pianos? if you are a piano tuner, how many days a year do you work? how many tunings can you do in one day? The answers to these questions don’t need to be 100% correct, nor do all of them have to be the same as someone else would guess. All in all, the guessing and errors average out to give about the same answer for everyone. This is a beautiful and elegant method of trying to understand the nature of the world by relying on the fact that your knowledge sometimes does better and sometimes does worse than reality, but overall combines to give something close to the truth. In the figure below, I show the calculation for Logan, Utah. If I check the answer in my phone book, I find that I was pretty close!
The key methods to bear in mind in your quest to become a good Fermi problem estimator are:
- Most problems seem unanswerable when posited, but usually can be broken down into simpler bits which you do know the answer to.
- Rely on numbers you know the value of, or can estimate a reasonable value for.
- Don’t worry about being precise!
- Round relentlessly (“7 is about 10”)
- Combine numbers sloppily (“15 x 6 is about 100”)
- Use everyday experience as averages (“a human masses about 70 kg”)
This is a powerful and robust technique for answering questions. More to the point, you do this every day when you figure out how many cupcakes to make when the cousins are visiting, or when you buy rope to make a new tire swing, or when decide how long before the football game to start mowing the lawn to make sure you are done on time. You could do it for all kinds of other things that may be important in your life and business, like: estimating how much pizza is consumed on a nearby college campus every day, or how many ball point pens are sold in your city each year, or how many car crashes there are in town each month.
For our purposes here, we are going to use this powerful technique to figure out how much life there might be elsewhere in the Cosmos. One of the first people to think about this was astronomer Frank Drake. Drake was a radio astronomer, and made important discoveries regarding the nature of Jupiter’s magnetosphere, and in pulsar astrophysics. In the 1960’s he also began to think about how radio astronomy could be used to search for transmissions from extraterrestrial civilizations, initiating Project Ozma in 1960 to search for possibly intelligent transmissions from the nearby Sun-like stars, Tau Ceti and Epsilon Eridani.
When thinking about life in the Cosmos, and whether we are alone or members of a vast chorus of civilizations spanning the galaxy, Drake asked a specific (but plausibly unanswerable) question: how many civilizations might exist in the galaxy that we could communicate with? The Fermi problem solution to this question is known as The Drake Equation. We’ll examine the Drake equation and its implications next time.
This is the first of two parts. The second part can be read here.
This particular piece was completed while in residence at the Aspen Center for Physics.