Hi Nick, Two smaller replies to what have become two sub-threads:
> On Mar 30, 2026, at 15:42, Nicholas Thompson <[email protected]> wrote: > > DES, EPC, FW > > So far as I understand, the argument flowing from Fisher makes no claims > about the kind of trait that produces reproductive success other than that it > is the kind that produces reproductive success. FW, if that's not a > tautology, it's a pretty tight circle. As usual, let’s decamp to more neutral ground in the hope of having an ordinary negotiation. Suppose that, in your overweening pursuit of the study of metaphor, you never noticed that there is a once/4-year gathering called The Olympics. Also never learned what any of its so-called “events” are, what they are about, how they work, and how one differs from another. My hypothetical here is meant to define a condition of having “very little prior information” about some phenomenon that we can, nonetheless, still reasonably unambiguously circumscribe. But a quick inspection shows that a subset of the participants (who all together seem to be called “athletes”) are given metal disks and stand on some kind of 3-tiered podium, while other athletes do not. Being a statistician — a skill so helpful in the study of metaphor that it was worth taking the time out to learn — you immediately recognize that this is a kind of marking that can be used to partition the athletes. Taking notice, for the first time, of some of the conversation in the society around you, who seem not nearly so devoted to metaphor and thus have time to do other things, you gather that these marked people seem to be called “winners” (or better, “medalists”, this “winning” thing is a finer sub-partition; I’ll mis-use “winner” to label the most salient marking for this little parable). It’s handy to have such a term, for use in later sentences, so they become less tedious than the ones I have been typing so far. You also note that while there is only one 3-tiered podium and metal-disk set per one “event”, there seem to be many such distinct “events”, so some kind of event name gives you a second kind of marking you can put on the athletes. Moreover, interestingly, the “event” label is again a proper partition (or at least seems to be; this one is less cut-and-dried than the observation that everyone carrying a metal disk is not someone not-carrying a metal disk, so we are wary; the event label seems to be a bit more abstract): every athlete is in some “event” set, and it appears that no athlete is in more than one of them. As with the “winners” label, you learn that there are conventionalized names for the events, and you can find a look-up table if you need one or another of them. Now, I can make a list of statements that seem to be of two different kinds (scare quotes here indicate my statisticians’ attribute labels; in my condition of very little prior knowledge, I don’t claim I have any more semantics for them than I listed above): 1. Every “winner" is someone marked as having won something. 2a. Every winner in the “gymnastics” event is shorter than the average over all the participants; 2b. Every winner in the “high jump” event is taller than the average over all the participants; … (we could presumably look for other such summary statistics that seem to be unusually regular and to carry different values in different “events”). I would say sentence 1 is “a tautology”, or close enough to it for the purpose of this negotiation. Maybe I should use EricC’s good, and slighly more flexible term, “truism”. Now you may write a protest email: But the sentences 2a, 2b, have not told me what constitutes “competition” in these “events”: “gymnastics” and “high jump”, and given me the rule book for scoring them. Okay. And they didn’t cook your dinner and do the dishes afterward either. Life is hard. And more a propos (breaking my little 4th wall here), the path to a fully-adequate “causal” theory through statistical inference is like the Road to Heaven: narrow, tortuous, and inadequate to many things one can rightly want to know. That’s what other sciences are then for. But if you claim: The sentences 2a and 2b didn’t give me _any information_ about these “events”, and couldn’t have, because they are tautologies, I would say you made an error. Of course, the real Nick would not say that, so we are all safe. The above parable is, of course, about selection. I didn’t say anything about heredity. But if I had happened to note that height is a fairly heritable trait, I could have spun out a much longer story, and defined some Bayesian-posterior conditional probabilities, which would be shown to have properties such as: the posterior probability, under various ceteris paribus conditions, for a child of a high-jump winner to turn out another high-jump winner is higher than for that child to turn out a gymnastics winner, and so forth. The amalgamation of both of those stories would go in the direction of Fisher’s fundamental theorem. It would leave out all the stuff that Fisher left out of emphasis in his mad pursuit of his covariance term as an analog to the thermodynamic 2nd law (a non-valid analogy, as it turns out to be easy to show), and that Price included didactically (and here, to EricC’s answer): that I didn’t even mention that the tall people might get drafted into wars and put into an infantry to fire rifles over tall dijks, while the short people might be drafted into Special Forces and sent on missions to attack through underground tunnels, and so the number of survivors could depend on many factors about which war their country had started, in what theater, and against what opposition, etc. These are the world of everything-else that Fisher lumped together into “deterioration of the environment”, as Steve Frank (and I think also Price) lays out. They are probably not well-analogized to “mutation”, but in genetics, mutation also goes into the same bin in the Price equation — _outside_ the term of Fisher’s fundamental theorem — as the “deterioration” effects. The accounting identity is flexible enough that we don’t need analogies to use it; we can formulate a version for whatever statistics our phenomenon-of-interest supplies. Anyway; at issue: Seriously, do we have a problem in scientific work, of people being unable to gain partial knowledge about phenomena through sentences of the kinds 2a, 2b, because they can’t tell the difference between those and sentence 1? In the world where I live, I don’t see evidence for this mistake. Eric .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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