What is Fermi Estimation and how is it connected to the Fermi Paradox?
Today we are going to take a dive into Enrico Fermi and discuss one of the most popular topics named after him: The Fermi Paradox. Before we jump into the Fermi Paradox, we must first understand what is Fermi Estimation and its connection to the Paradox!
Goals & Objectives:
- Who is Enrico Fermi?
- Understand Fermi Estimation
- Solve a Fermi Estimation Problem
- Connect Fermi Estimation to the Fermi Paradox
- Understand some of the drawbacks of using Fermi Estimation Techniques
Part 0: Who is Enrico Fermi?
Enrico Fermi (or Fermi for short) was an Italian and naturalized-American physicist who has been called the ‘Architect of the Nuclear Age’ and the ‘architect of the atomic bomb.’
Fermi’s claim to fame was his ability to excel in both Theoretical and Experimental Physics. He held several patents related to Nuclear Power and was also a Physics Nobel Prize Winner for ‘induced radioactivity by neutron bombardment and for the discovery of transuranium elements.’ In addition, his strong presence in Statistical Mechanics is in part what we will diving into today!
If that last part is over your head, don’t worry! We will be explore one of the more accessible topics that he contributed to: Fermi Estimation. He was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb’s yield.
In case you’re wondering, the Trinity test was the first detonation of a nuclear weapon. Using the Fermi method to estimate the bombs yield from Macro Variables, Fermi was able to get surprisingly close to the true yield of the bomb.
Part 1: Fermi Estimation and Example
There are many examples of Fermi Estimation questions being asked in interviews and schools, but the overarching idea is as follows:
Can you come up with a way to answer a broad question that seems unsolvable by using a series of estimations?
- Could you fit $1,000,000 worth of $1 coins in your classroom? What about a billion dollars worth of $1 coins?
- How many cups of water are there in a bath tub? What about in an Olympic pool?
- How many pages would be needed to show a million stars?
- How Many Piano Tuners are in Chicago?
We are going to solve this last question using estimation methods and show how easy it is to use estimates of macro variables to drive correct solutions.
How Many Piano Tuners are in Chicago?
First, lets try to estimate the number of Pianos in the city with the following assumptions:
- 9 Million people in Chicago
- On average 2 people / household
- 1/20 households have a piano
- Regularly tuned pianos are tuned once a year
- A piano takes about 2 hours to tune including travel time
- Every piano tuner works 8–5 M-F for 50 weeks out of the year
This means that the number of Piano Tunings per year in Chicago are 225,000
(9,000,000 persons in Chicago) ÷ (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 225,000 piano tunings per year in Chicago.
We can similarly calculate that the average piano tuner performs: 1000 Tunings per year
(50 weeks/year) × (5 days/week) × (8 hours/day) ÷ (2 hours to tune a piano) = 1000 piano tunings per year.
(225,000 piano tunings per year in Chicago) ÷ (1000 piano tunings per year per piano tuner) = 225 piano tuners in Chicago.
Wow! It is incredible how close we can get to the actual answer without knowing specifics about any of these topics! We where only 24% off from the correct answer!
Part 2: Connection to the Fermi Paradox
Using some of the same techniques as above, we can calculate the number of possible extraterrestrial planets that could host life forms. When this is done, we come up with a very large number of possible planets and this leads us to the Fermi Paradox.
Given that our star and Earth are part of a young planetary system compared to the rest of the universe — and that interstellar travel might be fairly easy to achieve — why have aliens not visited earth yet?
Backing up this claim are the following assumptions:
- There are billions of stars in the galaxy that are similar to the Sun, and many of these stars are billions of years older than the Solar system.
- With high probability, some of these stars have Earth-like planets, and if the Earth is typical, some may have developed intelligent life.
- Some of these civilizations may have developed interstellar travel, a step the Earth is investigating now.
- Even at the slow pace of currently envisioned interstellar travel, the Milky Way galaxy could be completely traversed in a few million years.
In an equation that was devised by Frank Drake (called the Drake Equation) he attempted to find a systematic means to evaluate the numerous probabilities involved in the existence of alien life. This equation, based on some variables that are difficult to measure has widely differing results. In some cases, this equation gives an estimate of 1,000–1,000,000 civilizations in the Milky Way galaxy (Frank Drake & Carl Sagan Estimate). While in other cases, the equation gives a value of much less than 1.
We will not explore the actual calculation, but here is the Drake Equation below:
Paired with the following original estimates:
Using the lower bounds for all the estimates give N = 20 while inserting the maximum value for these estimates puts the number of civilizations at 50,000,000. Based on this Drake has stated there were probably between 1000 and 100,000,000 civilizations in the Milky Way galaxy.
Part 3: Criticism
Criticism of the Drake equation follows mostly from the observation that several terms in the equation are largely or entirely based on conjecture.
This is highly important. Many of the variables that we are estimating are difficult to put an exact number on. Star formation rates for example, are well-known, and the incidence of planets has a sound theoretical and observational basis.
On the other hand, our uncertainties in the evolution of life, intelligence, and civilization, make it difficult to statistically estimate the some of the parameters resulting in a huge margin of error. In our case, we only have one known example of intelligent life which makes statistical estimates impossible.
So are there aliens in our universe? Let me know your thoughts in the comments below!