Yes, that math checks out (on a skim). Of course it’s not actually possible for this to occur in anything remotely resembling a Western society (which is, I expect, mostly where the data for such theories is sampled); we don’t have many more people dying at age 10 than at age 60. (And several other assumptions of the model are quite unlikely, yes.)
It’s an interesting technical point nonetheless, and a good reminder to be aware of the possibility of non-obvious or unintuitive population-statistics effects.
It wasn’t meant to be a realistic example! But, yes, we are in violent agreement that it isn’t very likely that anything Keganesque would be true without the sort of age correlation you describe. It just seemed worth pointing out that it isn’t a requirement.
A more realistic example might be if the lower stages tended to be almost universally achieved when young, with the higher stages being rare at any age. E.g. I think that of Kegan stages, stage 3 tended to be almost always achieved by early adulthood, while only a very small fraction (1%?) would ever achieve stage 5, with a nontrivial fraction failing to ever achieve stage 4.
In that case there would still be a correlation with age, but it would be pretty weak—if you’re the type that reaches stage 3 at age 18 and then stay there for your whole life, you’ll drag the correlation down, and AFAIK this was claimed to be reasonably common. (This article claims that 65% of the population get stuck at stage 3, though it seems to base its claim on a breakdown that says 65% of the adult population is at stage 3 or lower at any given time, which is not the same thing.)
In order to even describe anything like this as “stages”, you have to motivate it by observing the pre-theoretic facts which I described. @gjm’s comment does that, for his scenario; yours does not. Let’s try to rewrite your scenario without the theory-based assumptions, taking gjm’s comment as a guide:
Suppose everyone has some determinable number associated with them at any given time; let’s call it their “quality”.
(Note that using a number for this implies an interval or ratio scale, but this is not necessary; an ordinal scale suffices, as I say.)
Everyone starts at 1. No one ever goes above 6 5. For a given person, quality only ever increases.
Then from there we stipulate that most people increase to 3 by early childhood; many people at some point increase to 4 (when?); and very few increase to 5 (when?).
Well… I think that calling this scenario “developmental stages” is, actually, kind of nonsensical.
I mean, we named the dimension of variation “quality”, but what if it’s actually… rock climbing skill? Let’s run through our checklist:
Everyone has a certain level of rock climbing skill.
There is a certain maximum level of rock climbing skill that any human has ever achieved.
For a given person, rock climbing skill only ever increases[1].
Everyone starts at the minimal amount of rock climbing skill.
Most people naturally develop a baseline level of coordination and physical ability that lets them climb rocks at a very basic level (at least enough to, say, climb onto a large boulder the size of a small boulder), although a small minority of people can’t even do that.
Some people take rock climbing classes, or generally develop athletic ability, that lets them climb rocks noticeably better than that baseline.
A very few people, at some point in their lives, get really into rock climbing, and become able to climb rocks really, really well.
Do we need a “theory of adult development” to explain the landscape of variation in rock climbing ability…?
I don’t know whether we need one, but it’s not clear that one would be wrong.
In any case, it feels like there’s some misunderstanding between Kaj and Said here. I take Kaj’s comment two steps upthread from here not to be making any particular claim about the correctness or coherence or importance of Kegan’s theory, but only to be saying: if Kegan’s account of things were correct, then we would not necessarily see strong correlations with age. (Implicitly: Hence, it would be a mistake to demand such correlations in order to think such a theory worth investigating.)
So … would the correlation with age be weak, if things were as Kaj describes? I think not very weak. We’d have
everyone starting at 1 …
… and moving to 2 at age, I dunno, somewhere between say 0 and 4 …
… and almost everyone then moving to 3 somewhere between say 12 and 25 …
… and then a substantial fraction of the population moving to 4 between say 20 and 40 …
… and then a small fraction moving to 5 at some point.
That looks to me like it would give a really strong correlation with age. Kaj, do you think I’m missing something here, and if so what?
(For what it’s worth, I also don’t see anything in this scenario that makes it unrealistic to describe it as “developmental stages”. Whether that description is reasonable or not depends on details that, for the moment, we’ve abstracted away—how discretely people move from one “stage” to the next, how consistently the various features of each stage go together with one another, etc. And, in view of Said’s final comment, perhaps also how much of the alleged progression is something that any reasonable person would guess on their own after a few minutes’ thought. Rock climbing doesn’t do very well by those criteria, but that doesn’t tell us much about whether Kegan’s theory does.)
I take Kaj’s comment two steps upthread from here not to be making any particular claim about the correctness or coherence or importance of Kegan’s theory, but only to be saying: if Kegan’s account of things were correct, then we would not necessarily see strong correlations with age.
I endorse this interpretation.
That looks to me like it would give a really strong correlation with age. Kaj, do you think I’m missing something here, and if so what?
No, you’re right. My intuitive sense of how the distribution would line up was off, I get correlation coefficients around 0.5 on few synthetic datasets that I had Claude generate now (eyeballing the scatterplot, I think the code generating the datasets has some bugs, but I think fixing those is more likely to increase the correlation than to decrease it).
I take Kaj’s comment two steps upthread from here not to be making any particular claim about the correctness or coherence or importance of Kegan’s theory, but only to be saying: if Kegan’s account of things were correct, then we would not necessarily see strong correlations with age.
But “Kegan’s account of things”, as I’ve seen it described (and as Kaj describes it), is an account of “things” in terms of his theory (with the “stages” and so on). What is the formulation of “Kegan’s account of things” prior to having any concept of “stages” of “adult development”, before we have any reason to think that there’s any such thing as “development” that takes place in “stages”?
So the antecedent—“if Kegan’s account of things were correct”—is something that can’t even be formulated, in the pre-theoretic setting. (At least, as I have seen the account given. This comment claims that there was motivating experimental data to begin with, but no reference or elaboration has yet been given, so I can’t comment on that.)
(Your comment re: strength of the correlation seems correct.)
(For what it’s worth, I also don’t see anything in this scenario that makes it unrealistic to describe it as “developmental stages”. Whether that description is reasonable or not depends on details that, for the moment, we’ve abstracted away—how discretely people move from one “stage” to the next, how consistently the various features of each stage go together with one another, etc. And, in view of Said’s final comment, perhaps also how much of the alleged progression is something that any reasonable person would guess on their own after a few minutes’ thought. Rock climbing doesn’t do very well by those criteria, but that doesn’t tell us much about whether Kegan’s theory does.)
Well, yes, it does depend on the details, but what I’m saying is that describing things that fit such a pattern as “stages of adult development”, or any such thing, isn’t the default. Rock climbing is one example, but of course there are many others—many kinds of skill, to name the obvious category; many kinds of understanding or knowledge (e.g. “how well does this person understand basic mechanics” or “how much does this person know about lizards”). If the way people move between clusters is by deciding to learn or practice something, or by reading something, etc., then talking about “stages of development” (which we need some theory to account for) is obviously farcical.
Once again I think your objection is to something other than what I take Kaj to have been saying. That is: you’re saying that Kegan’s theory specifically isn’t sufficiently clearly defined to make it meaningful to talk about what “stages” it might or might not involve, etc. That might be true. But Kaj isn’t (here, in this thread) arguing about that. He’s saying (I paraphrase): “I think that if all the rest of it turns out to make sense, the relationship between age and stage according to Kegan’s theory has such-and-such a shape, in which case the correlation wouldn’t be very strong; therefore it would be a mistake to insist on strong age/stage correlations before taking such a theory seriously”. And so far as I can see, this is a reasonable kind of argument to make, even if it might turn out that actually “Kegan’s theory” fails to be clearly definable, or something of the sort. (In that case, making the argument would turn out to have been wasted effort, but that’s OK.)
(As I said above, I think that in fact Kegan-as-described-by-Kaj does predict a strong correlation between age and stage. But that’s an entirely separate matter.)
I agree that describing things that fit such a pattern as “stages of development” isn’t and shouldn’t be the default. I don’t know what evidence (anecdotal or scientific) Kegan and others have, or think they have, to support using such a term for the psychological changes Kegan professes to have observed. But (for what it’s worth) my impression is that they aren’t just saying that anything that changes over time should be called “stages of development”. I think they think (rightly or wrongly) that the “stages” are fairly well demarcated, that it’s not common for someone to be “in stage 3 as regards X and Y but in stage 4 as regards P and Q”, that it’s usual to spend much more time unambiguously in a particular stage than in any sort of transitional state, etc. Whether any of that’s true, I don’t know. Whether in fact Kegan “stages” can be defined clearly enough for the question to have a definite answer, I don’t know. But (so far as I can make out) the Keganites are purporting to describe something different from rock-climbing in such a way that (if they’re right) talking about “stages of development” and seeing them as needing some kind of explanatory theory makes more sense for what they’re talking about than it would for rock-climbing.
Well, regardless of what the “Keganites” are saying, I want to see the pre-theoretic facts before I’m going to be particularly interested in their model of “stages” etc.
Now, one way to read objections like Kaj’s is that my account of precisely which pre-theoretic facts would motivate an “adult developmental stages” theory is flawed. That’s a reasonable sort of objection. (I haven’t seen any evidence yet that any such objection is right, but there is no a priori reason why none can be.)
In such a case, if the objector wishes to substitute some different set of pre-theoretic facts, make the case that those facts constitute a state of affairs that can meaningfully be described as “there sure seem to be stages of adult development”, and then make the conditionally reasonable claim that a theory thereof is thus motivated—by all means, I would be interested to see such a thing.
But that argument isn’t going to involve any mention of any element of any existing theory at all. If it does, then the point has been thoroughly missed.
My interpretation of what Kaj wrote was indeed that he disagrees about exactly what pre-theoretic facts would suggest looking for an “adult developmental stages” theory, on the grounds that he thinks there could be such a theory (and indeed a basically-Kegan-shaped one) in which the strong age/stage correlation isn’t present.
The fact that the particular pattern of stage-transitions Kaj describes is basically-Kegan-shaped isn’t relevant to the validity of the objection, except in so far as it indicates that the pattern in question isn’t somehow the wrong sort of pattern to be part of an “adult developmental stages” theory.
For what it’s worth, my notion of what the pre-theoretic facts ought to look like isn’t exactly the same as yours. I’d want to see something like: 1. a specific set of psychological characteristics that 2. each exhibit a consistent pattern of progression through an individual’s life, 3. in such a way that we can put matching labels on all the progressions and see that people generally have most or all in consistently-labelled states, 4. (slightly optionally; if this fails then “developmental” is a misleading term) such that later-reached bundles of states are generally better in some sense than earlier-reached ones, and 5. (slightly optionally; if this fails then “stages” is a misleading term) a smallish discrete set of labels sufficing in the sense that most people most of the time have most of those characteristics in states corresponding to a single one of those labels. In particular, I don’t think I care whether the characteristics in question all pertain to a single “domain” in any sense, and I don’t think anything’s gained by introducing the possibility of correlations with other characteristics besides age, when later in your list you’re specifically going to demand correlation with age. And what I want to see is progression within each individual’s life, not a population-level correlation with age.
And what I want to see is progression within each individual’s life, not a population-level correlation with age.
I think I agree that this is a better criterion, yeah. I’m not prepared to be sure about this without thinking about it some more, but I definitely lean toward being convinced.
I don’t think I care whether the characteristics in question all pertain to a single “domain” in any sense
I don’t necessarily care about that either, but clustering and progression that is parallel across multiple domains is an additional fact, which is not necessary to motivate a theory of the relevant sort. And treating domains separately is useful because we may well have, for example, a case where the data that indicates clustering/progression in one domain is weaker than the data which indicates it in another domain; we want to retain the ability to say “well, I’m not sure about the claim that people exhibit this pattern with respect to rock climbing skill and knitting skill and desire for broccoli, but at least the first one is clearly true, and so we’d like a theory that explains that even if it doesn’t also explain the other stuff”.
In general, there’s not really a good reason not to keep domains conceptually separate here; we can always decide later that a pattern that holds across domains requires a unified theory (or we can notice that a theory that explains the pattern in one domain also explains it in other domains). In the meantime, keeping our claims narrowly scoped seems prudent.
Yes, that math checks out (on a skim). Of course it’s not actually possible for this to occur in anything remotely resembling a Western society (which is, I expect, mostly where the data for such theories is sampled); we don’t have many more people dying at age 10 than at age 60. (And several other assumptions of the model are quite unlikely, yes.)
It’s an interesting technical point nonetheless, and a good reminder to be aware of the possibility of non-obvious or unintuitive population-statistics effects.
It wasn’t meant to be a realistic example! But, yes, we are in violent agreement that it isn’t very likely that anything Keganesque would be true without the sort of age correlation you describe. It just seemed worth pointing out that it isn’t a requirement.
A more realistic example might be if the lower stages tended to be almost universally achieved when young, with the higher stages being rare at any age. E.g. I think that of Kegan stages, stage 3 tended to be almost always achieved by early adulthood, while only a very small fraction (1%?) would ever achieve stage 5, with a nontrivial fraction failing to ever achieve stage 4.
In that case there would still be a correlation with age, but it would be pretty weak—if you’re the type that reaches stage 3 at age 18 and then stay there for your whole life, you’ll drag the correlation down, and AFAIK this was claimed to be reasonably common. (This article claims that 65% of the population get stuck at stage 3, though it seems to base its claim on a breakdown that says 65% of the adult population is at stage 3 or lower at any given time, which is not the same thing.)
In order to even describe anything like this as “stages”, you have to motivate it by observing the pre-theoretic facts which I described. @gjm’s comment does that, for his scenario; yours does not. Let’s try to rewrite your scenario without the theory-based assumptions, taking gjm’s comment as a guide:
(Note that using a number for this implies an interval or ratio scale, but this is not necessary; an ordinal scale suffices, as I say.)
Then from there we stipulate that most people increase to 3 by early childhood; many people at some point increase to 4 (when?); and very few increase to 5 (when?).
Well… I think that calling this scenario “developmental stages” is, actually, kind of nonsensical.
I mean, we named the dimension of variation “quality”, but what if it’s actually… rock climbing skill? Let’s run through our checklist:
Everyone has a certain level of rock climbing skill.
There is a certain maximum level of rock climbing skill that any human has ever achieved.
For a given person, rock climbing skill only ever increases[1].
Everyone starts at the minimal amount of rock climbing skill.
Most people naturally develop a baseline level of coordination and physical ability that lets them climb rocks at a very basic level (at least enough to, say, climb onto a large boulder the size of a small boulder), although a small minority of people can’t even do that.
Some people take rock climbing classes, or generally develop athletic ability, that lets them climb rocks noticeably better than that baseline.
A very few people, at some point in their lives, get really into rock climbing, and become able to climb rocks really, really well.
Do we need a “theory of adult development” to explain the landscape of variation in rock climbing ability…?
Setting aside injury or disease; but then, injury or disease can affect mental characteristics too, so that’s not a flaw of the example.
I don’t know whether we need one, but it’s not clear that one would be wrong.
In any case, it feels like there’s some misunderstanding between Kaj and Said here. I take Kaj’s comment two steps upthread from here not to be making any particular claim about the correctness or coherence or importance of Kegan’s theory, but only to be saying: if Kegan’s account of things were correct, then we would not necessarily see strong correlations with age. (Implicitly: Hence, it would be a mistake to demand such correlations in order to think such a theory worth investigating.)
So … would the correlation with age be weak, if things were as Kaj describes? I think not very weak. We’d have
everyone starting at 1 …
… and moving to 2 at age, I dunno, somewhere between say 0 and 4 …
… and almost everyone then moving to 3 somewhere between say 12 and 25 …
… and then a substantial fraction of the population moving to 4 between say 20 and 40 …
… and then a small fraction moving to 5 at some point.
That looks to me like it would give a really strong correlation with age. Kaj, do you think I’m missing something here, and if so what?
(For what it’s worth, I also don’t see anything in this scenario that makes it unrealistic to describe it as “developmental stages”. Whether that description is reasonable or not depends on details that, for the moment, we’ve abstracted away—how discretely people move from one “stage” to the next, how consistently the various features of each stage go together with one another, etc. And, in view of Said’s final comment, perhaps also how much of the alleged progression is something that any reasonable person would guess on their own after a few minutes’ thought. Rock climbing doesn’t do very well by those criteria, but that doesn’t tell us much about whether Kegan’s theory does.)
I endorse this interpretation.
No, you’re right. My intuitive sense of how the distribution would line up was off, I get correlation coefficients around 0.5 on few synthetic datasets that I had Claude generate now (eyeballing the scatterplot, I think the code generating the datasets has some bugs, but I think fixing those is more likely to increase the correlation than to decrease it).
But “Kegan’s account of things”, as I’ve seen it described (and as Kaj describes it), is an account of “things” in terms of his theory (with the “stages” and so on). What is the formulation of “Kegan’s account of things” prior to having any concept of “stages” of “adult development”, before we have any reason to think that there’s any such thing as “development” that takes place in “stages”?
So the antecedent—“if Kegan’s account of things were correct”—is something that can’t even be formulated, in the pre-theoretic setting. (At least, as I have seen the account given. This comment claims that there was motivating experimental data to begin with, but no reference or elaboration has yet been given, so I can’t comment on that.)
(Your comment re: strength of the correlation seems correct.)
Well, yes, it does depend on the details, but what I’m saying is that describing things that fit such a pattern as “stages of adult development”, or any such thing, isn’t the default. Rock climbing is one example, but of course there are many others—many kinds of skill, to name the obvious category; many kinds of understanding or knowledge (e.g. “how well does this person understand basic mechanics” or “how much does this person know about lizards”). If the way people move between clusters is by deciding to learn or practice something, or by reading something, etc., then talking about “stages of development” (which we need some theory to account for) is obviously farcical.
(Anyhow, I think we mostly don’t disagree here.)
(I agree that we mostly don’t disagree here.)
Once again I think your objection is to something other than what I take Kaj to have been saying. That is: you’re saying that Kegan’s theory specifically isn’t sufficiently clearly defined to make it meaningful to talk about what “stages” it might or might not involve, etc. That might be true. But Kaj isn’t (here, in this thread) arguing about that. He’s saying (I paraphrase): “I think that if all the rest of it turns out to make sense, the relationship between age and stage according to Kegan’s theory has such-and-such a shape, in which case the correlation wouldn’t be very strong; therefore it would be a mistake to insist on strong age/stage correlations before taking such a theory seriously”. And so far as I can see, this is a reasonable kind of argument to make, even if it might turn out that actually “Kegan’s theory” fails to be clearly definable, or something of the sort. (In that case, making the argument would turn out to have been wasted effort, but that’s OK.)
(As I said above, I think that in fact Kegan-as-described-by-Kaj does predict a strong correlation between age and stage. But that’s an entirely separate matter.)
I agree that describing things that fit such a pattern as “stages of development” isn’t and shouldn’t be the default. I don’t know what evidence (anecdotal or scientific) Kegan and others have, or think they have, to support using such a term for the psychological changes Kegan professes to have observed. But (for what it’s worth) my impression is that they aren’t just saying that anything that changes over time should be called “stages of development”. I think they think (rightly or wrongly) that the “stages” are fairly well demarcated, that it’s not common for someone to be “in stage 3 as regards X and Y but in stage 4 as regards P and Q”, that it’s usual to spend much more time unambiguously in a particular stage than in any sort of transitional state, etc. Whether any of that’s true, I don’t know. Whether in fact Kegan “stages” can be defined clearly enough for the question to have a definite answer, I don’t know. But (so far as I can make out) the Keganites are purporting to describe something different from rock-climbing in such a way that (if they’re right) talking about “stages of development” and seeing them as needing some kind of explanatory theory makes more sense for what they’re talking about than it would for rock-climbing.
Well, regardless of what the “Keganites” are saying, I want to see the pre-theoretic facts before I’m going to be particularly interested in their model of “stages” etc.
Now, one way to read objections like Kaj’s is that my account of precisely which pre-theoretic facts would motivate an “adult developmental stages” theory is flawed. That’s a reasonable sort of objection. (I haven’t seen any evidence yet that any such objection is right, but there is no a priori reason why none can be.)
In such a case, if the objector wishes to substitute some different set of pre-theoretic facts, make the case that those facts constitute a state of affairs that can meaningfully be described as “there sure seem to be stages of adult development”, and then make the conditionally reasonable claim that a theory thereof is thus motivated—by all means, I would be interested to see such a thing.
But that argument isn’t going to involve any mention of any element of any existing theory at all. If it does, then the point has been thoroughly missed.
My interpretation of what Kaj wrote was indeed that he disagrees about exactly what pre-theoretic facts would suggest looking for an “adult developmental stages” theory, on the grounds that he thinks there could be such a theory (and indeed a basically-Kegan-shaped one) in which the strong age/stage correlation isn’t present.
The fact that the particular pattern of stage-transitions Kaj describes is basically-Kegan-shaped isn’t relevant to the validity of the objection, except in so far as it indicates that the pattern in question isn’t somehow the wrong sort of pattern to be part of an “adult developmental stages” theory.
For what it’s worth, my notion of what the pre-theoretic facts ought to look like isn’t exactly the same as yours. I’d want to see something like: 1. a specific set of psychological characteristics that 2. each exhibit a consistent pattern of progression through an individual’s life, 3. in such a way that we can put matching labels on all the progressions and see that people generally have most or all in consistently-labelled states, 4. (slightly optionally; if this fails then “developmental” is a misleading term) such that later-reached bundles of states are generally better in some sense than earlier-reached ones, and 5. (slightly optionally; if this fails then “stages” is a misleading term) a smallish discrete set of labels sufficing in the sense that most people most of the time have most of those characteristics in states corresponding to a single one of those labels. In particular, I don’t think I care whether the characteristics in question all pertain to a single “domain” in any sense, and I don’t think anything’s gained by introducing the possibility of correlations with other characteristics besides age, when later in your list you’re specifically going to demand correlation with age. And what I want to see is progression within each individual’s life, not a population-level correlation with age.
I think I agree that this is a better criterion, yeah. I’m not prepared to be sure about this without thinking about it some more, but I definitely lean toward being convinced.
I don’t necessarily care about that either, but clustering and progression that is parallel across multiple domains is an additional fact, which is not necessary to motivate a theory of the relevant sort. And treating domains separately is useful because we may well have, for example, a case where the data that indicates clustering/progression in one domain is weaker than the data which indicates it in another domain; we want to retain the ability to say “well, I’m not sure about the claim that people exhibit this pattern with respect to rock climbing skill and knitting skill and desire for broccoli, but at least the first one is clearly true, and so we’d like a theory that explains that even if it doesn’t also explain the other stuff”.
In general, there’s not really a good reason not to keep domains conceptually separate here; we can always decide later that a pattern that holds across domains requires a unified theory (or we can notice that a theory that explains the pattern in one domain also explains it in other domains). In the meantime, keeping our claims narrowly scoped seems prudent.