From: M. Taylor Saotome-Westlake Date: Mon, 4 Jul 2022 05:43:08 +0000 (-0700) Subject: drafting "Useful Approximation" up to numerical envelope X-Git-Url: http://534655.efjtl6rk.asia/source?a=commitdiff_plain;h=d34db8ff33c969b37f7a1e4a5f1cebf41d5c9555;p=Ultimately_Untrue_Thought.git drafting "Useful Approximation" up to numerical envelope I just think I need one mathy graf and one conclusion graf, and then I'm ready to get this eviscerated by Tailcalled. --- diff --git a/content/drafts/the-two-type-taxonomy-is-a-useful-approximation-for-a-more-detailed-causal-model.md b/content/drafts/the-two-type-taxonomy-is-a-useful-approximation-for-a-more-detailed-causal-model.md index 166afc4..a18dc4a 100644 --- a/content/drafts/the-two-type-taxonomy-is-a-useful-approximation-for-a-more-detailed-causal-model.md +++ b/content/drafts/the-two-type-taxonomy-is-a-useful-approximation-for-a-more-detailed-causal-model.md @@ -8,7 +8,7 @@ A lot of people tend to balk when first hearing about the [two-type taxonomy of In some ways, it's a fair complaint! Psychology is _complicated_; every human is their own unique snowflake. But it would be impossible to navigate the world using the "every human is their own unique _maximum-entropy_ snowflake" theory. In order to [compress our observations](https://www.lesswrong.com/posts/mB95aqTSJLNR9YyjH/message-length) of the world we see, we end up distilling our observations into categories, clusters, diagnoses, [taxons](https://lorienpsych.com/2020/10/30/ontology-of-psychiatric-conditions-taxometrics/): no one matches any particular clinical-profile stereotype _exactly_, but [the world makes more sense when you have language for theoretical abstractions](https://astralcodexten.substack.com/p/ontology-of-psychiatric-conditions) like ["comas"](https://slatestarcodex.com/2014/08/11/does-the-glasgow-coma-scale-exist-do-comas/) or "depression" or "borderline personality disorder"—or "autogynephilia". -Concepts and theories are good to the extent that they can "pay for" their complexity by making more accurate predictions. How much complexity is worth how much accuracy? Arguably, it depends! General relativity has superceded Newtonian classical mechanics as the ultimate theory of how gravity works, but if you're not dealing with velocities approaching the speed of light, Newton still makes _very good_ predictions: it's pretty reasonable to still talk about Newtonian gravitation being "true" if it makes the math easier on you, and the more complicated math doesn't give appreciably different answers to the problems you're interested in. +Concepts and theories are good to the extent that they can "pay for" their complexity by making more accurate predictions. How much complexity is worth how much accuracy? Arguably, it depends! General relativity has superseded Newtonian classical mechanics as the ultimate theory of how gravity works, but if you're not dealing with velocities approaching the speed of light, Newton still makes _very good_ predictions: it's pretty reasonable to still talk about Newtonian gravitation being "true" if it makes the math easier on you, and the more complicated math doesn't give appreciably different answers to the problems you're interested in. Moreover, if relativity hasn't been invented yet, it makes sense to stick with Newtonian gravity as the _best_ theory you have _so far_, even if there are a few anomalies [like the precession of Mercury](https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury) that it struggles to explain. @@ -18,7 +18,7 @@ What does this look like for psychological theories? In the crudest form, when w If we notice further patterns _within_ the group of cases that make up a category, we can spit it up into sub-categories: for example, a diagnosis of bipolar I requires a full-blown manic episode, but hypomania and a major depressive episode qualify one for bipolar II. -Is the two-type typology of bipolar disorder a good theory? Are bipolar I and bipolar II "really" different conditions, or slightly different presentations of "the same" condition, part of a "bipolar spectrum" along with [cyclothymia](https://en.wikipedia.org/wiki/Cyclothymia)? In our current state of knowledge, this is debateable, but if our understanding of the etiology of bipolar disorder were to advance, and we were to find evidence that that bipolar I has a different underlying _causal structure_ from bipolar II with decision-relevant consequences (like responding to different treatments), that would support a policy of thinking and talking about them as mostly separate things—even while they have enough in common to both be kinds of "bipolar". The simple high-level category ("bipolar disorder") is a useful approximation in the absence of knowing the sub-category (bipolar I _vs._ II), and the subcategory is a useful approximation in the absence of knowing the patient's detailed case history. +Is the two-type typology of bipolar disorder a good theory? Are bipolar I and bipolar II "really" different conditions, or slightly different presentations of "the same" condition, part of a "bipolar spectrum" along with [cyclothymia](https://en.wikipedia.org/wiki/Cyclothymia)? In our current state of knowledge, this is debatable, but if our understanding of the etiology of bipolar disorder were to advance, and we were to find evidence that that bipolar I has a different underlying _causal structure_ from bipolar II with decision-relevant consequences (like responding to different treatments), that would support a policy of thinking and talking about them as mostly separate things—even while they have enough in common to both be kinds of "bipolar". The simple high-level category ("bipolar disorder") is a useful approximation in the absence of knowing the sub-category (bipolar I _vs._ II), and the subcategory is a useful approximation in the absence of knowing the patient's detailed case history. With a _sufficiently_ detailed causal story, you could even dispense with the high-level categories altogether and directly talk about the consequences of different neurotransmitter counts or whatever—but lacking that supreme precise knowledge, it's useful to sum over the details into high-level categories, and meaningful to debate whether a one-type or two-type taxonomy is a better statistical fit to the underlying reality whose full details we don't know. @@ -58,33 +58,20 @@ Then the value of the sexual-orientation node is pushing the values of its child (Of course, it's also the case that the component factors in a liability-threshold model would negatively correlate among the population past a threshold, due to the effect of conditioning on a collider, as in the famous Berkson's paradox. But I'm claiming that the degree of bimodality induced by the effects of sexual orientation is substantially greater than that accounted for by the conditioning-on-a-collider effect.) -An advantage of this kind of _probabilistic_ model is that it gives us a _causal_ account of the broad trends we see, while also not being too "brittle" in the face of a complex world. The threshold graphical model explains why the two-type taxonomy looks so compelling as a first approximation, without immediately collapsing the moment we meet a relatively unusual individual who doesn't seem to quite fit the strictest interpretation of the classical two-type taxonomy. +An advantage of this kind of _probabilistic_ model is that it gives us a _causal_ account of the broad trends we see, while also not being too "brittle" in the face of a complex world. The threshold graphical model explains why the two-type taxonomy looks so compelling as a first approximation, without immediately collapsing the moment we meet a relatively unusual individual who doesn't seem to quite fit the strictest interpretation of the classical two-type taxonomy. For example, when we meet a trans woman who's not very feminine _and_ has no history of autogynephilia, we can predict that in her case, there were probably unusually intense cultural factors (_e.g._, internalized misandry) making transition seem like a salient option (and therefore that her analogue in previous generations wouldn't have been transsexual), instead of predicting that she doesn't exist. (It's possible that what Blanchard–Bailey–Lawrence conceived of as a androphilic _vs._ autogynephilic taxonomy, may be better thought of as an androphilic _vs._ not-otherwise-specified taxonomy, if it's not easy to disambiguate autogynephilia from all other possible reasons for not-overtly-feminine males to show up at the gender clinic.) -[TODO— -example: hi femininity + AGP -example: cultural factors -care must be taken to avoid rationalization] +Care must be taken to avoid abusing the probabilistic nature of the model to make excuses to avoid falsification. The theory that can explain everything _with equal probability_, explains nothing: if you find yourself saying, "Oh, this case is an exception" too _often_, you do need to revise your theory. But a "small" number of "exceptions" can actually be fine: a theory that says a coin is biased to come up Heads 80% of the time, isn't falsified by a single Tails (and is in fact _confirmed_ if that Tails happens 20% of the time). -You might ask: okay, but why do I believe this? Anyone can name some variables and sketch a directed graph between them. Why should you believe this particular graph is _true_? +At this point, you might ask: okay, but why do I believe this? Anyone can name some variables and sketch a directed graph between them. Why should you believe this particular graph is _true_? Ultimately, the reader cannot abdicate responsibility to think it through and decide for herself ... but it seems to _me_ that all six arrows in the graph are things that we separately have a pretty large weight of evidence for, either in published scientific studies, or just informally looking at the world. -The femininity→transition arrow is obvious. The sexual orientation→femininity arrow (representing the fact that gay men are more feminine than straight men), besides being stereotypical folk knowledge, has also been extensively documented, for example by [Lippa](/papers/lippa-gender-related_traits_in_gays.pdf) and by [Bailey and Zucker](/papers/bailey-zucker-childhood_sex-typed_behavior_and_sexual_orientation.pdf). - -The v-structure between sexual orientation, erotic target location erroneousness, and autogynephilia has been documented by Anne Lawrence: - - -The autogynehilia→transition arrow has - -The cultural-factors→transition arrow is obvious if you haven't been living under a rock for the last decade. +The femininity→transition arrow is obvious. The sexual orientation→femininity arrow (representing the fact that gay men are more feminine than straight men), besides being stereotypical folk knowledge, has also been extensively documented, for example by [Lippa](/papers/lippa-gender-related_traits_in_gays.pdf) and by [Bailey and Zucker](/papers/bailey-zucker-childhood_sex-typed_behavior_and_sexual_orientation.pdf). The v-structure between sexual orientation, erotic target location erroneousness, and autogynephilia has been [documented by Anne Lawrence](/papers/lawrence-etle_an_underappreciated.pdf): furries and amputee-wannabes who want to emulate the objects of their attraction, "look like" "the same thing" as autogynephiles, but pointed at a less conventional erotic than women. The autogynephilia–transition concordance has been documented by many authors, and I claim the direction of causality is obvious. (If you want to argue that it goes the other way—that some underlying "gender identity" causes both autogynephilia and, separately, the desire to transition, then why does it usually not work that way for androphiles?) The cultural-factors→transition arrow is obvious if you haven't been living under a rock for the last decade. +This has been a qualitative summary of my current thinking. I'm very bullish on thinking in graphical models rather than discrete taxons being the way to go, but it would be a lot more work to try to pin down all these claims rigorously—or, to the extent that my graph is wrong, to figure out the correct (or, _a_ more correct, less wrong) graph instead. But as a gesture of _aspiration towards_ more rigor, we can do some back-of-the-envelope calculations to try to show how a "two types" could emerge quantitatively. [quantifying the two-type effect: -Lippa 2000 "Gender-Related Traits in [...]" -2.70 effect of femininity for gay vs. not-day and 1.07 for "any" vs. "no" attraction to men -mean GD score for non-lesbian women as 0.31; mean score for gay men was 0.30! -—oh, maybe I want to be using Study 2, which had a better sample of gays GD occupations in study 2 gay men are at .48 (.14); straight women at .36 (.13); straight men at .68 (.12) that's d=–1.61 between gay and straight men @@ -93,13 +80,7 @@ whereas a straight man needs to be (.68-.36 = 0.32) 0.32/0.12=2.67 more feminine In percentile terms, 1-norm.cdf(1) = 0.15 of gay men are as feminine as a woman whereas 1-norm.cdf(2.67) = 0.003 of straight men are -that's a likelihood ratio of 50 ... but the prior is not that far from 50:1 in the other direction! They cancel out!! - -For concreteness: what does the Bayes net spit out if 3% of men are gay, and 5% are AGP, and whatever other assumptions I need to make this work? -Suppose gays transition if they're 2-sigma feminine ... - -] +that's a likelihood ratio of 50 ... but the prior is not that far from 50:1 in the other direction! They cancel out!!] -[further implications: as cultural factors increase, the late-onset type becomes more of a "NOS" rather than AGP type] _(Thanks to the immortal [Tailcalled](https://surveyanon.wordpress.com/) for discussion.)_