Seems you and Spencer Greenberg (whose piece you linked to) are talking past each other because you both disagree on what the interesting epistemic question is and/or are just writing for different audiences?
Spencer is asking “When can a single observation justify a strong inference about a general claim?” which is about de-risking overgeneralisation, a fair thing to focus on since many people generalise too readily
You’re asking “When does a single observation maximally reduce your uncertainty?” which is about information-theoretic value, which (like you said) is moreso aimed towards the “stats-brained”
Also seems a bit misleading to count something like “one afternoon in Vietnam” or “first day at a new job” as a single data point when it’s hundreds of them bundled together? Spencer’s examples seem to lean more towards actual single data points (if not all the way). And Spencer’s 4th example on how one data point can sometimes unlock a whole bunch of other data points by triggering a figure-ground inversion that then causes a reconsideration of your vie seems perfectly aligned with Hubbard’s point.
That said I do think the point you’re making is the more practically useful one, I guess I’m just nitpicking.
Also seems a bit misleading to count something like “one afternoon in Vietnam” or “first day at a new job” as a single data point when it’s hundreds of them bundled together?
From a information-theoretic perspective, people almost never refer to a single data point as strictly as just one bit, so whether you are counting only one float in a database or a whole row in a structured database, or also a whole conversation, we’re sort of negotiating price.
I think the “alien seeing a car” makes the case somewhat clearer. If you already have a deep model of cars (or even a shallow one), seeing another instance of a Ford Focus tells you relatively little, but an alien coming across one will get many bits about it, perhaps more than a human spending an afternoon in Vietnam.
Seems you and Spencer Greenberg (whose piece you linked to) are talking past each other because you both disagree on what the interesting epistemic question is and/or are just writing for different audiences?
Spencer is asking “When can a single observation justify a strong inference about a general claim?” which is about de-risking overgeneralisation, a fair thing to focus on since many people generalise too readily
You’re asking “When does a single observation maximally reduce your uncertainty?” which is about information-theoretic value, which (like you said) is moreso aimed towards the “stats-brained”
Also seems a bit misleading to count something like “one afternoon in Vietnam” or “first day at a new job” as a single data point when it’s hundreds of them bundled together? Spencer’s examples seem to lean more towards actual single data points (if not all the way). And Spencer’s 4th example on how one data point can sometimes unlock a whole bunch of other data points by triggering a figure-ground inversion that then causes a reconsideration of your vie seems perfectly aligned with Hubbard’s point.
That said I do think the point you’re making is the more practically useful one, I guess I’m just nitpicking.
From a information-theoretic perspective, people almost never refer to a single data point as strictly as just one bit, so whether you are counting only one float in a database or a whole row in a structured database, or also a whole conversation, we’re sort of negotiating price.
I think the “alien seeing a car” makes the case somewhat clearer. If you already have a deep model of cars (or even a shallow one), seeing another instance of a Ford Focus tells you relatively little, but an alien coming across one will get many bits about it, perhaps more than a human spending an afternoon in Vietnam.