Small differences in the means of a normal distributions cause large differences at the tails.
Motivating example:
East Africans are slightly better at distance running than the rest of the world population, so if a randomly-picked Ethiopian and a randomly-picked someone-else compete in a marathon, the Ethiopian has a better chance of winning, but not by very much. But at the extreme right tail of the distribution (i.e. at Olympic-level running competitions), the top runners are almost all Ethiopians and Kenyans.
In my head I call it “threshold amplification” but I wonder if there’s an official name for this.
I would love a name for this too since the observation is important for why ‘small’ differences in means for normally distributed populations can have large consequences, and this occurs in many contexts (not just IQ or athletics).
The normal distribution can be seen as the sum of lots of independent random variables; so for example, IQ is normally distributed because the genetics is a lot of small additive variables. The log-normal is when it’s the multiple of lots of independent variables; so any process where each step is necessary, as has been proposed for scientific productivity in having multiple steps like ideas->research->publication.
The normal distribution has the unintuitive behavior that small changes in the mean or variance have large consequences out on the thin tails. But the log-normal distribution has the unintuitive behavior that small improvements in each of the independent variables will yield large changes in their product, and that the extreme datapoints will be far beyond the median or average datapoints. (‘Compound interest’ comes close but doesn’t seem to catch it because it refers to increase over time.)
And why was the normal distribution originally chosen? Most of intelligence seems explained by thousands of alleles with small additive effects—and such a binomial situation will quickly converge to a normal distribution.
You seem to be claiming that there are some unspecified underlying other metrics of which IQ is simply a linear combination. If so, then IQ is not the ultimate metric. Which doesn’t contradict my claim (claiming that P is not true does not contradict the claim that P → Q). It does raise the question of what those metrics are.
It does raise the question of what those metrics are.
To expand on what I just said: IQ is a factor extracted from a wide variety of cognitive measures, whose genetic component is largely explained by additive effects from a large number of alleles of small effect with important but relatively small nonlinear contributions. That is, intelligence is largely additive because additive models explain much of observed variance and things like the positive manifold of cognitive tests.
Please be more precise in your comments, or stop wasting my time due to your lack of reading comprehension and obtuseness like you did before in my Parable post.
To expand on what I just said: IQ is a factor extracted from a wide variety of cognitive measures, whose genetic component is largely explained by additive effects
And what are those measures?
That is, intelligence is largely additive because additive models explain much of observed variance and things like the positive manifold of cognitive tests.
As I ALREADY SAID, the word “additive” only makes sense with respect to a particular metric. Saying that intelligence is additive because it’s measured by metrics in which there are additive effects is circular, unless you can show some non-arbitrary source of the metrics. How about you actually address my posts?
Please be more precise in your comments, or stop wasting my time due to your lack of reading comprehension and obtuseness
Given that YOU are failing to be precise, and to articulate what specifically you find erroneous about my posts, that is rather hypocritical thing to say. And I don’t think that personal insults are appropriate.
like you did before in my Parable post.
I have posted another response in that thread (even though you refused to respond to my previous one). In short, you are confusing your inability to write a coherent sentence with a lack of reading comprehension on my part, and you need to get the fuck over yourself. If in cases of miscommunication, you’re not willing to even consider the possibility that you are even partly responsible, then you need to find somewhere else to post, because this website is not for people like you.
You appear to be downvoting my posts due to a vendetta against me from another article, which is rather similar to behavior that got another poster banned. I am not entirely clear on what the community standards are here, but it appears to me that you are likely flouting them.
Do you really not know anything like what tests routinely load or anything about the historical development? If the latter, please go consult Wikipedia or one of many books on the topic. And if it’s Socratic bullshit, just make your point already.
Saying that intelligence is additive because it’s measured by metrics in which there are additive effects is circular, unless you can show some non-arbitrary source of the metrics.
No, it’s not circular. If all the cognitive tests have large fractions of variance explained by purely additive factors, then that large fractions of variance are explained by purely additive factors. If they didn’t, if for example there were some sort of fixed sum of ‘cognition points’ for every person which are zero-sum spread around various domains like verbal vs spatial, or if there were complex nonlinear relationships, then additive factors wouldn’t explain much of anything in cognitive performance and certainly wouldn’t predict anything in the real world. But they do. The positive manifold exists. The correlations with all sorts of real-world results exist. And the underlying genetics is largely additive for the same reason: the additive models explain a lot of variance in IQ, and hence with real world outcomes.
In short, you are confusing your inability to write a coherent sentence with a lack of reading comprehension on my part, and you need to get the fuck over yourself.
There must be many charitable and intelligent people here to read all my stuff despite my inability to write a coherent sentence.
because this website is not for people like you...I am not entirely clear on what the community standards are here
What a peculiar claim; quite aside from my karma, I helped make this website from the start.
You appear to be downvoting my posts due to a vendetta against me from another article, which is rather similar to behavior that got another poster banned
You flatter yourself that your comments aren’t bad enough that other people will downvote them… I don’t bother with mass downvotes of idiots.
Do you really not know anything like what tests routinely load or anything about the historical development? If the latter, please go consult Wikipedia or one of many books on the topic. And if it’s Socratic bullshit, just make your point already.
I asked for metrics, not tests.
You made a claim. The burden of proof is on you to support it. “Go read a book” is not a valid citation.
So you think that asking questions to clarify a position is “bullshit”?
No, it’s not circular. If all the cognitive tests have large fractions of variance explained by purely additive factors, then that large fractions of variance are explained by purely additive factors.
So, in other words, if a large fraction is additive, then a large fraction is additive. Do you not understand what the word “circular” means?
If they didn’t, if for example there were some sort of fixed sum of ‘cognition points’ for every person which are zero-sum spread around various domains like verbal vs spatial, or if there were complex nonlinear relationships, then additive factors wouldn’t explain much of anything in cognitive performance and certainly wouldn’t predict anything in the real world.
You’re arguing for a position by contradiction, but your contradiction is only one alternative hypothesis. That is fallacious. Your responses show you don’t even understand what my objection is, and therefore all your attempts at refutation fall flat.
What a peculiar claim; quite aside from my karma, I helped make this website from the start.
When someone says “if A, then B”, it’s not very honest to quote them as saying B. And what do you mean by “I help make this website”? Does having a lot of karma give you the right to ignore basic civility? Was this website constructed by going around being rude to people? Or is that a recent development on your part?
You flatter yourself that your comments aren’t bad enough that other people will downvote them… I don’t bother with mass downvotes of idiots.
I didn’t say that I was dismissing all other hypotheses, only noting that of all the posters, you are the most likely candidate to have downvoted.
Tests yield metrics. More quibbling. Good job there convincing me you’re asking questions in good faith. I can really see that you’ve bothered to read anything on the topic.
You made a claim. The burden of proof is on you to support it. “Go read a book” is not a valid citation.
Yes, it is, when you’re criticizing an entire century-old well-developed field with an abundance of materials online. At this point, the burden is not on the person talking about intelligence. Go educate yourself, stop wasting my time with your captious quibbling about whether ‘tests’ are ‘metrics’ (to point out your latest crap); if you actually cared about the topic, you wouldn’t be saying any of this, you’d be reading Jensen’s textbooks or hell, even a Wikipedia article.
So you think that asking questions to clarify a position is “bullshit”?
Given all your previous comments, yes.
So, in other words, if a large fraction is additive, then a large fraction is additive. Do you not understand what the word “circular” means?
I see you didn’t understand the point of that. Think a little harder, and also think a little bit about what circular arguments are. (Hint: they don’t take the form ‘A, therefore, A’.)
You’re arguing for a position by contradiction, but your contradiction is only one alternative hypothesis. That is fallacious. Your responses show you don’t even understand what my objection is, and therefore all your attempts at refutation fall flat.
Sigh.
When someone says “if A, then B”, it’s not very honest to quote them as saying B. And what do you mean by “I help make this website”? Does having a lot of karma give you the right to ignore basic civility? Was this website constructed by going around being rude to people? Or is that a recent development on your part?
Let me try again: when a newcomer and an oldtimer disagree on what is appropriate for a site, when the oldtimer was around before the site existed, helped make it, and is a major contributor by comments, articles, and karma, which is more likely to be correct? I’m thinking… it’s probably not the newcomer, and that arguing that is astoundingly presumptuous of them.
I didn’t say that I was dismissing all other hypotheses, only noting that of all the posters, you are the most likely candidate to have downvoted.
Nice walk back there. ‘I never said he was a communist, I was merely noting he was the most likely candidate to be a communist.’
So to reiterate my previous question—you know, since you’re totally not trolling or anything, and you’re definitely arguing in good faith, and you’re surely not going to reply with just some more rhetoric and attempts to shame or nitpick irrelevant wording, in this thread or others—what is your actual problem with these concepts? Do you have data which refutes the relevant concepts entirely? Or what?
What metric to apply to a test is a completely nontrivial issue, and the fact that you refer to such a crucial issue as “quibbling” shows how little you understand about the issue.
Yes, it is, when you’re criticizing an entire century-old well-developed field with an abundance of materials online.
I’m not criticizing the field. I’m asking you to answer a simple question, and you’re refusing.
At this point, the burden is not on the person talking about intelligence.
Simply declaring yourself to not have the burden of proof does nothing.
I see you didn’t understand the point of that.
And so, instead of explaining, you’re simply telling me to “think a little harder”.
(Hint: they don’t take the form ‘A, therefore, A’.)
“A, therefore A” is a circular argument. Most people put more effort into disguising the circular nature of their arguments, but that doesn’t mean that yours is not circular.
Let me try again: when a newcomer and an oldtimer disagree on what is appropriate for a site, when the oldtimer was around before the site existed, helped make it, and is a major contributor by comments, articles, and karma, which is more likely to be correct? I’m thinking… it’s probably not the newcomer, and that arguing that is astoundingly presumptuous of them.
I think it is astoundingly presumptuous for you to dismiss any criticism of your behavior with “I’ve been around here longer than you and have lots of karma”. Your behavior is at blatant odds with what I understand to be the goals of this website. Either you are indeed acting contrary to those goals, or I have a deep misunderstanding about the goals of this website.
Nice walk back there.
I am not walking anything back. I deliberately included the word “appear” in my original post in recognition that this was merely the most likely explanation.
So to reiterate my previous question—you know, since you’re totally not trolling or anything, and you’re definitely arguing in good faith, and you’re surely not going to reply with just some more rhetoric and attempts to shame or nitpick irrelevant wording, in this thread or others—what is your actual problem with these concepts? Do you have data which refutes the relevant concepts entirely? Or what?
So, it’s “bullshit” when I ask you to clarify what you mean, but it’s okay for you to ask me to clarify what I am saying, even though you’ve made it absolutely clear that you have no intention whatsoever of listening to my point of view, have already made up your mind that I am wrong and refuse to listen to any contrary arguments, interpret everything I say through the filter of presuming bad faith, and are here simply to insult me? A discussion is a cooperative process. I can’t explain something to someone whose motive isn’t to understand, but to attack.
So to reiterate my previous question—you know, since you’re totally not trolling or anything, and you’re definitely arguing in good faith, and you’re surely not going to reply with just some more rhetoric and attempts to shame or nitpick irrelevant wording, in this thread or others—what is your actual problem with these concepts? Do you have data which refutes the relevant concepts entirely? Or what?
So, it’s “bullshit” when I ask you to clarify what you mean, but it’s okay for you to ask me to clarify what I am saying, even though you’ve made it absolutely clear that you have no intention whatsoever of listening to my point of view, have already made up your mind that I am wrong and refuse to listen to any contrary arguments, interpret everything I say through the filter of presuming bad faith, and are here simply to insult me? A discussion is a cooperative process. I can’t explain something to someone whose motive isn’t to understand, but to attack.
Tell you what, tell me what you meant by “Um, no, because the USSR had no reason to think and be correct in thinking it served a useful role for the USA which meant the threats were bluffs that were best ridden out lest it damage both allies’ long-term goals.” and I’ll try to explain what my issue here is.
And no, we’re not done here. You have been extremely rude, and that needs to be addressed.
No, we’re done. Conversation with you has proven on several topics to be a frustrating waste of my time. I think it’s better for both of us if I simply ignore you from now on on all topics. Maybe you’ll improve, but I doubt it.
I can remember one occasion, taking a shower with my wife while high, in which I had an idea on the origins and invalidities of racism in terms of gaussian distribution curves. It was a point obvious in a way, but rarely talked about. I drew the curves in soap on the shower wall, and went to write the idea down. One idea led to another, and at the end of about an hour of extremely hard work I found I had written eleven short essays on a wide range of social, political, philosophical, and human biological topics. Because of problems of space, I can’t go into the details of these essays, but from all external signs, such as public reactions and expert commentary, they seem to contain valid insights.
(It is a little interesting, & amusing, to see someone inferring the “invalidit[y] of racism” from an observation more often used as a justification for racial hereditarian attitudes!)
General case:
Small differences in the means of a normal distributions cause large differences at the tails.
Motivating example:
East Africans are slightly better at distance running than the rest of the world population, so if a randomly-picked Ethiopian and a randomly-picked someone-else compete in a marathon, the Ethiopian has a better chance of winning, but not by very much. But at the extreme right tail of the distribution (i.e. at Olympic-level running competitions), the top runners are almost all Ethiopians and Kenyans.
In my head I call it “threshold amplification” but I wonder if there’s an official name for this.
I would love a name for this too since the observation is important for why ‘small’ differences in means for normally distributed populations can have large consequences, and this occurs in many contexts (not just IQ or athletics).
Also good would be a quick name for log-normal distribution-like phenomenon.
The normal distribution can be seen as the sum of lots of independent random variables; so for example, IQ is normally distributed because the genetics is a lot of small additive variables. The log-normal is when it’s the multiple of lots of independent variables; so any process where each step is necessary, as has been proposed for scientific productivity in having multiple steps like ideas->research->publication.
The normal distribution has the unintuitive behavior that small changes in the mean or variance have large consequences out on the thin tails. But the log-normal distribution has the unintuitive behavior that small improvements in each of the independent variables will yield large changes in their product, and that the extreme datapoints will be far beyond the median or average datapoints. (‘Compound interest’ comes close but doesn’t seem to catch it because it refers to increase over time.)
IQ is normally distributed because the distribution of raw test scores is standardized to a normal distribution.
And why was the normal distribution originally chosen? Most of intelligence seems explained by thousands of alleles with small additive effects—and such a binomial situation will quickly converge to a normal distribution.
The phrase “additive effects” doesn’t make sense except in reference to some metric. If your metric is IQ, then that’s circular.
No, it’s not, because IQ is itself extracted from a wide variety of cognitive measures.
You seem to be claiming that there are some unspecified underlying other metrics of which IQ is simply a linear combination. If so, then IQ is not the ultimate metric. Which doesn’t contradict my claim (claiming that P is not true does not contradict the claim that P → Q). It does raise the question of what those metrics are.
To expand on what I just said: IQ is a factor extracted from a wide variety of cognitive measures, whose genetic component is largely explained by additive effects from a large number of alleles of small effect with important but relatively small nonlinear contributions. That is, intelligence is largely additive because additive models explain much of observed variance and things like the positive manifold of cognitive tests.
Please be more precise in your comments, or stop wasting my time due to your lack of reading comprehension and obtuseness like you did before in my Parable post.
And what are those measures?
As I ALREADY SAID, the word “additive” only makes sense with respect to a particular metric. Saying that intelligence is additive because it’s measured by metrics in which there are additive effects is circular, unless you can show some non-arbitrary source of the metrics. How about you actually address my posts?
Given that YOU are failing to be precise, and to articulate what specifically you find erroneous about my posts, that is rather hypocritical thing to say. And I don’t think that personal insults are appropriate.
I have posted another response in that thread (even though you refused to respond to my previous one). In short, you are confusing your inability to write a coherent sentence with a lack of reading comprehension on my part, and you need to get the fuck over yourself. If in cases of miscommunication, you’re not willing to even consider the possibility that you are even partly responsible, then you need to find somewhere else to post, because this website is not for people like you.
You appear to be downvoting my posts due to a vendetta against me from another article, which is rather similar to behavior that got another poster banned. I am not entirely clear on what the community standards are here, but it appears to me that you are likely flouting them.
Do you really not know anything like what tests routinely load or anything about the historical development? If the latter, please go consult Wikipedia or one of many books on the topic. And if it’s Socratic bullshit, just make your point already.
No, it’s not circular. If all the cognitive tests have large fractions of variance explained by purely additive factors, then that large fractions of variance are explained by purely additive factors. If they didn’t, if for example there were some sort of fixed sum of ‘cognition points’ for every person which are zero-sum spread around various domains like verbal vs spatial, or if there were complex nonlinear relationships, then additive factors wouldn’t explain much of anything in cognitive performance and certainly wouldn’t predict anything in the real world. But they do. The positive manifold exists. The correlations with all sorts of real-world results exist. And the underlying genetics is largely additive for the same reason: the additive models explain a lot of variance in IQ, and hence with real world outcomes.
There must be many charitable and intelligent people here to read all my stuff despite my inability to write a coherent sentence.
What a peculiar claim; quite aside from my karma, I helped make this website from the start.
You flatter yourself that your comments aren’t bad enough that other people will downvote them… I don’t bother with mass downvotes of idiots.
I asked for metrics, not tests.
You made a claim. The burden of proof is on you to support it. “Go read a book” is not a valid citation.
So you think that asking questions to clarify a position is “bullshit”?
So, in other words, if a large fraction is additive, then a large fraction is additive. Do you not understand what the word “circular” means?
You’re arguing for a position by contradiction, but your contradiction is only one alternative hypothesis. That is fallacious. Your responses show you don’t even understand what my objection is, and therefore all your attempts at refutation fall flat.
When someone says “if A, then B”, it’s not very honest to quote them as saying B. And what do you mean by “I help make this website”? Does having a lot of karma give you the right to ignore basic civility? Was this website constructed by going around being rude to people? Or is that a recent development on your part?
I didn’t say that I was dismissing all other hypotheses, only noting that of all the posters, you are the most likely candidate to have downvoted.
Tests yield metrics. More quibbling. Good job there convincing me you’re asking questions in good faith. I can really see that you’ve bothered to read anything on the topic.
Yes, it is, when you’re criticizing an entire century-old well-developed field with an abundance of materials online. At this point, the burden is not on the person talking about intelligence. Go educate yourself, stop wasting my time with your captious quibbling about whether ‘tests’ are ‘metrics’ (to point out your latest crap); if you actually cared about the topic, you wouldn’t be saying any of this, you’d be reading Jensen’s textbooks or hell, even a Wikipedia article.
Given all your previous comments, yes.
I see you didn’t understand the point of that. Think a little harder, and also think a little bit about what circular arguments are. (Hint: they don’t take the form ‘A, therefore, A’.)
Sigh.
Let me try again: when a newcomer and an oldtimer disagree on what is appropriate for a site, when the oldtimer was around before the site existed, helped make it, and is a major contributor by comments, articles, and karma, which is more likely to be correct? I’m thinking… it’s probably not the newcomer, and that arguing that is astoundingly presumptuous of them.
Nice walk back there. ‘I never said he was a communist, I was merely noting he was the most likely candidate to be a communist.’
So to reiterate my previous question—you know, since you’re totally not trolling or anything, and you’re definitely arguing in good faith, and you’re surely not going to reply with just some more rhetoric and attempts to shame or nitpick irrelevant wording, in this thread or others—what is your actual problem with these concepts? Do you have data which refutes the relevant concepts entirely? Or what?
What metric to apply to a test is a completely nontrivial issue, and the fact that you refer to such a crucial issue as “quibbling” shows how little you understand about the issue.
I’m not criticizing the field. I’m asking you to answer a simple question, and you’re refusing.
Simply declaring yourself to not have the burden of proof does nothing.
And so, instead of explaining, you’re simply telling me to “think a little harder”.
“A, therefore A” is a circular argument. Most people put more effort into disguising the circular nature of their arguments, but that doesn’t mean that yours is not circular.
I think it is astoundingly presumptuous for you to dismiss any criticism of your behavior with “I’ve been around here longer than you and have lots of karma”. Your behavior is at blatant odds with what I understand to be the goals of this website. Either you are indeed acting contrary to those goals, or I have a deep misunderstanding about the goals of this website.
I am not walking anything back. I deliberately included the word “appear” in my original post in recognition that this was merely the most likely explanation.
So, it’s “bullshit” when I ask you to clarify what you mean, but it’s okay for you to ask me to clarify what I am saying, even though you’ve made it absolutely clear that you have no intention whatsoever of listening to my point of view, have already made up your mind that I am wrong and refuse to listen to any contrary arguments, interpret everything I say through the filter of presuming bad faith, and are here simply to insult me? A discussion is a cooperative process. I can’t explain something to someone whose motive isn’t to understand, but to attack.
Exactly as predicted. I think we’re done here.
Tell you what, tell me what you meant by “Um, no, because the USSR had no reason to think and be correct in thinking it served a useful role for the USA which meant the threats were bluffs that were best ridden out lest it damage both allies’ long-term goals.” and I’ll try to explain what my issue here is.
And no, we’re not done here. You have been extremely rude, and that needs to be addressed.
No, we’re done. Conversation with you has proven on several topics to be a frustrating waste of my time. I think it’s better for both of us if I simply ignore you from now on on all topics. Maybe you’ll improve, but I doubt it.
I think that “multiplicative” or “geometric” describes such phenomena.
I’ve suspected for a long time that that was the insight Carl Sagan had while high and showering with his wife:
(It is a little interesting, & amusing, to see someone inferring the “invalidit[y] of racism” from an observation more often used as a justification for racial hereditarian attitudes!)