"Most people make the mistake of generalizing from a single data point. Or at least, I do." - SA
When can you learn a lot from one data point? People, especially stats- or science- brained people, are often confused about this, and frequently give answers that (imo) are the opposite of useful. Eg they say that usually you can’t know much but if you know a lot about the meta-structure of your distribution (eg you’re interested in the mean of a distribution with low variance), sometimes a single data point can be a significant update.
This type of limited conclusion on the face of it looks epistemically humble, but in practice it's the opposite of correct. Single data points aren’t particularly useful when you know a lot, but they’re very useful when you have very little knowledge to begin with. If your uncertainty about a variable in question spans many orders of magnitude, the first observation can often reduce more uncertainty than the next 2-10 observations put together[1]. Put another way, the most useful situations for updating massively from a single data point are when you know very little to begin with.
For example, if an alien sees a human car for the first time, the alien can make massive updates on many different things regarding Earthling society, technology, biology and culture. Similarly, an anthropologist landing on an island of a previously uncontacted tribe can rapidly learn so much about a new culture from a single hour of peaceful interaction [2].
Some other examples:
* Your first day at a new job.
* First time visiting a country/region you previously knew nothing about. One afternoon in Vietnam tells you roughly how much things cost, how traffic works, what the food is like, languages people speak, how people interact with strangers.
* Trying a new fruit for the first time. One bite of durian tells you an enormous amount about whether you'll like durian.
* Your first interaction with someone's kid tells you roughly how old they are, how v
