Skill. A positive manifold might include number of hours of practice, measurable past successes, ability to relax during work, speed and precision of movements, difficulty of current duties, positive references, self-advertisement, employment history, ability to troubleshoot when things go wrong, and detailed preferences for tools, methods, organizational styles, collaborators, and work environment.
Fun. A positive manifold might include smiles, laughter, eye contact, conversation, competition, play, jokes, exclamations, health, youth, higher-pitched and louder voices, physical exertion, large groups of people, intoxication, natural environments, sunny weather.
Artistic taste. A positive manifold might include relationships with artists, attendance at artistic events, ownership of art objects, making art, a range of positive and negative opinions, appreciation of many genres, detailed reasons for preferences, being sough after for one’s opinion.
Nice. Those seem like things that could appear in papers.
Skill. A positive manifold might include number of hours of practice, measurable past successes, ability to relax during work, speed and precision of movements, difficulty of current duties, positive references, self-advertisement, employment history, ability to troubleshoot when things go wrong, and detailed preferences for tools, methods, organizational styles, collaborators, and work environment.
I like this example, because I think you might’ve succeeded in finding three (or more) general factors in one here. Lemme explain, because this is very much the sort of thing I had in mind in the sections about realism and about how meditating on the relationship between the factor and its outputs can be enlightening:
Skill itself is the degree to which people can do things. A lot of the things you mention here are inputs to skill, which make you better at doing things, or (for e.g. detailed preferences) correlates of skill. Interestingly, these inputs still correlate with each other.
The reason for this is that there are other general factors, underneath the inputs; most notably, specialization. That is, if you want to work in a field, that is going to cause a bunch of correlated changes. You might decide to get an education in the field, search for jobs, get practice, etc., which is going to generate successes, knowledge, etc..
Many of the variables tap into not just specialization but also intelligence; given any level of specialization, someone who is smarter is going to have a greater number of successes, better ability to troubleshoot, etc..
So what we essentially have here is something like, (general factor of) skill = (general factor of) specialization + (general factor of) intelligence (probably + other things too). We might draw it as a graph:
Of course this is very simplified. In fact, the graph of the constituents of skill could differ from person to person, depending on what background they’ve had. Anyway a big part of the benefit of general factors is then that because all of the different things end up correlated, a measurement of one will then tend to tell you things about the others, without need for worrying about all of the complexity of how they are connected.
This makes me think of causal networks ala Judea Pearl. The goal is to come up with a causal model (via lifting out general factors) such that the children are conditionally independent given the parent, or at least approximately independent- where most of the correlation comes from the general factor.
Example: In the diagram you made “Seeking education” and “Getting a job” are correlated (both happen when you intend to specialize), but conditional on “Intent to specialize” they’re independent or even anticorrelated if you wouldn’t do both at once.
It’s common to estimate general factors by taking a bunch of correlated variables and assuming they become independent conditional on the general factor, but in reality there are often multiple broad-ranging factors in an area, so in practice the resulting estimates would be some linear combination of all of those general factors.
I think this sort of combo tends to work well for many purposes as it efficiently captures a lot of uncertainty, but sometimes it can “go wrong”, e.g. when one intends to compare the factor across different contexts whose overall levels are produced by radically different combinations of those general factors, or when there are nonlinearities. I’ve been thinking I should write a new framing practicum, about “Mixings”, to better capture this.
Skill. A positive manifold might include number of hours of practice, measurable past successes, ability to relax during work, speed and precision of movements, difficulty of current duties, positive references, self-advertisement, employment history, ability to troubleshoot when things go wrong, and detailed preferences for tools, methods, organizational styles, collaborators, and work environment.
Fun. A positive manifold might include smiles, laughter, eye contact, conversation, competition, play, jokes, exclamations, health, youth, higher-pitched and louder voices, physical exertion, large groups of people, intoxication, natural environments, sunny weather.
Artistic taste. A positive manifold might include relationships with artists, attendance at artistic events, ownership of art objects, making art, a range of positive and negative opinions, appreciation of many genres, detailed reasons for preferences, being sough after for one’s opinion.
Nice. Those seem like things that could appear in papers.
I like this example, because I think you might’ve succeeded in finding three (or more) general factors in one here. Lemme explain, because this is very much the sort of thing I had in mind in the sections about realism and about how meditating on the relationship between the factor and its outputs can be enlightening:
Skill itself is the degree to which people can do things. A lot of the things you mention here are inputs to skill, which make you better at doing things, or (for e.g. detailed preferences) correlates of skill. Interestingly, these inputs still correlate with each other.
The reason for this is that there are other general factors, underneath the inputs; most notably, specialization. That is, if you want to work in a field, that is going to cause a bunch of correlated changes. You might decide to get an education in the field, search for jobs, get practice, etc., which is going to generate successes, knowledge, etc..
Many of the variables tap into not just specialization but also intelligence; given any level of specialization, someone who is smarter is going to have a greater number of successes, better ability to troubleshoot, etc..
So what we essentially have here is something like, (general factor of) skill = (general factor of) specialization + (general factor of) intelligence (probably + other things too). We might draw it as a graph:
Of course this is very simplified. In fact, the graph of the constituents of skill could differ from person to person, depending on what background they’ve had. Anyway a big part of the benefit of general factors is then that because all of the different things end up correlated, a measurement of one will then tend to tell you things about the others, without need for worrying about all of the complexity of how they are connected.
This makes me think of causal networks ala Judea Pearl. The goal is to come up with a causal model (via lifting out general factors) such that the children are conditionally independent given the parent, or at least approximately independent- where most of the correlation comes from the general factor.
Example: In the diagram you made “Seeking education” and “Getting a job” are correlated (both happen when you intend to specialize), but conditional on “Intent to specialize” they’re independent or even anticorrelated if you wouldn’t do both at once.
Yep.
It’s common to estimate general factors by taking a bunch of correlated variables and assuming they become independent conditional on the general factor, but in reality there are often multiple broad-ranging factors in an area, so in practice the resulting estimates would be some linear combination of all of those general factors.
I think this sort of combo tends to work well for many purposes as it efficiently captures a lot of uncertainty, but sometimes it can “go wrong”, e.g. when one intends to compare the factor across different contexts whose overall levels are produced by radically different combinations of those general factors, or when there are nonlinearities. I’ve been thinking I should write a new framing practicum, about “Mixings”, to better capture this.