EA - Simple estimation examples in Squiggle 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: Simple estimation examples in Squiggle, published by NunoSempere on September 2, 2022 on The Effective Altruism Forum. This post goes through several simple estimates, written in Squiggle, a new estimation language. My hope is that it might make it easier to write more estimates of a similar sort, wider adoption of Squiggle itself, and ultimately better decisions. Initial setup One can use Squiggle in several ways. This blog post will cover using it on its website and in a Google Spreadsheet. An upcoming blog post will cover using it in more complicated setups. squiggle-language.com The simplest way to use Squiggle is to open squiggle-language.com/playground. You will see something like the following: You can write your model on the editor in the left side, and the results will be displayed in the right side. As you make edits, the url in your browser bar will change so that you copy it and use it to refer people to your model. Squiggle Google docs When working with multiple models, I’ve also found it useful to use Squiggle in Google sheets. To do so, make a copy of this spreadsheet, and allow app permissions. Edit the “Main” sheet, and click on “Squiggle” > “Feed into Squiggle” to compute models. If you have difficulties, read the “Instructions” sheet, or leave a comment. So without further ado, the simple example models: Partially replicating Dissolving the Fermi Paradox (complexity = 1/10) Page 2 of the paper defines the factors for the Drake equation: Page 10 of the paper gives its estimates for the factors of the Drake equation: Because Squiggle doesn’t yet have the log-uniform probability distribution, we’re going to have to define it first. A log-uniform is a probability distribution whose log is a uniform distribution. // () loguniform(a, b) = exp(uniform(log(a), log(b))) // Estimates rate_of_star_formation = loguniform(1,100) fraction_of_stars_with_planets = loguniform(0.1, 1) number_of_habitable_planets_per_star_system = loguniform(0.1, 1) fraction_of_habitable_planets_in_which_any_life_appears = 1 // ^ more on this below fraction_of_planets_with_life_in_which_intelligent_life_appears = loguniform(0.001, 1) fraction_of_intelligent_planets_which_are_detectable_as_such = loguniform(0.01, 1) longevity_of_detectable_civilizations = loguniform(100, 10000000000) // Expected number of civilizations in the Milky way; // see footnote 3 (p. 5) n = rate_of_star_formation fraction_of_stars_with_planets number_of_habitable_planets_per_star_system fraction_of_habitable_planets_in_which_any_life_appears fraction_of_planets_with_life_in_which_intelligent_life_appears fraction_of_intelligent_planets_which_are_detectable_as_such longevity_of_detectable_civilizations // Display n This produces the following estimate: The estimate is fairly wide, but the model gives a 10%-ish chance that there is, in expectation, less than once civilization in the Milky Way. After updating on a bunch of observations, the paper raises that probability, hence the conclusion that the Fermi paradox has been “dissolved”. Why did we set fraction_of_planets_in_which_any_life_appears to 1? Well, the paper considers an estimate of 1−exp(−r), where r is distributed as a lognormal(1,50). But because r ranges from very small numbers to very large numbers, they get collapsed to either 0 or 1 when going through 1−exp(−r), which produces some numerical errors when multiplying by 0. In addition, that estimate has been questioned. So following a similar move in the paper, we can set that factor to a high value (in this case, to 1, meaning that all planets capable of life do host life). And then, when we notice that the probability of no other life in the Milky Way is still significant, the Fermi paradox will still have been somewhat dissolved, though to a lesser extent. From here on, we could tweak the ...