EA - Introduction to Fermi estimates by NunoSempere

Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Introduction to Fermi estimates, published by NunoSempere on August 26, 2022 on The Effective Altruism Forum. The following are my notes from an intro to Fermi estimates class I gave at ESPR, in preparation for a Fermithon, i.e., a Fermi estimates tournament. Fermi estimation is a method for arriving an estimate of an uncertain variable of interest. Given a variable of interest, sometimes you can decompose it into steps, and multiplying those steps together gives you a more accurate estimate than estimating the thing you want to know directly. I’ll go through a proof sketch for this at the end of the post. If you want to take over the world, why should you care about this? Well, you may care about this if you hope that having better models of the world would lead you to make better decisions, and to better achieve your goals. And Fermi estimates are one way of training or showing off the skill of building models of the world. They have fast feedback loops, because you can in many cases then check the answer on the internet afterwards. But they are probably most useful in cases where you can’t. The rest of the class was a trial by fire: I presented some questions, students gave their own estimates, and then briefly discussed them. In case you want to give it a try before seeing the answers, the questions I considered were: How many people have covid in the UK right now (2022-08-20)? How many cumulative person years did people live in/under the Soviet Union? How many intelligent species does the universe hold outside of Earth? Are any staff members dating? How many “state-based conflicts” are going on right now? (“state based conflict” = at least one party is a state, at least 25 deaths a year, massacres and genocides not included) How much does ESPR (a summer camp) cost? How many people are members of the Chinese communist party? What is the US defense budget? How many daily viewers does Tucker Carlson have? 1. How many people have covid in the UK right now (2022-08-20)? My own answer Some student guesses 130k 600k 1M to 2M Check To check, we can use the number of confirmed deaths: 2. How many cumulative person years did people live in/under the Soviet Union? My own answer Students guessed pretty much the same. Check Per this graph: the average population seems to have been around 200M, implying 14.8 billion years. 3. How many intelligent species does the galaxy hold? My own answer Probably just one (!?). Student guesses 104 0.4T 0 to 1 Check The dissolving the Fermi paradox paper gives the following estimate: which gives something like a 40% chance of us being alone in the observable universe. I think the paper shows the importance of using distributions, rather than point-estimates: using point estimates results in the Fermi paradox. This is the reason why I’ve been multiplying distributions, rather than point estimates 4. Are any staff members dating? Note: Question does not include Junior Counselors, because I don’t know the answer to that. Own answer The camp has 11 male and 3 women staff members. So the number of heterosexual combinations is (11 choose 1) × (3 choose 1) = 11 × 3 = 33 possible pairings. However, some of the pairings are not compatible, because they repeat the same person, so the number of monogamous heterosexual pairings is lower. Instead, say I’m giving a 1% to 3% a priori probability for any man-woman pairing. How did I arrive at this? Essentially, 0.1% feels too low and 5% too high. That implies a cumulative ~10% to 30% probability that a given woman staff member is dating any man staff member. Note that this rounds off nontraditional pairings—there is 1 nonbinary Junior Counsellor, but none amongst instructors, that I recall. If we run with the 30% chance for each woman staff member: If 10%: So the probability that there is at least one pairi...