Only if you take ‘ten times smarter’ to mean multiplying IQ score by ten. But since the mapping of the bell curve to numbers is arbitrary in the first place, that’s not a meaningful operation; it’s essentially a type error. The obvious interpretation of ‘ten times smarter’ within the domain of humans is by percentile, e.g. if the author is at the 99% mark, then it would refer to the 99.9% mark.
And given that, his statement is true; it is a curious fact that IQ has diminishing returns, that is, being somewhat above average confers significant advantage in many domains, but being far above average seems to confer little or no additional advantage. (My guess at the explanation: first, beyond a certain point you have to start making trade-offs from areas of brain function that IQ doesn’t measure; second, Amdahl’s law.)
I agree, that’s likely what Carrier was feeling when he wrote that sentence. But that doesn’t let him off the hook, because that way is even worse than Logos’! He’s using a definition of “times more intelligent” that is only really capable of differentiating between humans, and trying to apply it to something outside that domain.
I’m not sure if the following could be already encompassed in Amdahl’s law, but I think it was worth a comment. Very intelligent humans still need to operate through society to reach their goals. An IQ of 140 may be enough for you to discover and employ the best tools society puts at your disposal. An IQ of 180 (just an abstract example) may let you recognize new and more efficient patterns, but you then have to bend society to exploit them, and this usually means convincing people not as smart as you are, that may very well take a long time to grasp your ideas.
As an analogy, think being sent into the stone age. A Swiss knife here is a very useful tool. It’s not a revolutionary concept, it’s just better than stone knives in cutting meat and working with wood. On the other hand, a set of professional electrical tools, while in principle way more powerful, will be completely useless since you will have to find a way to charge their batteries before.
To me a more natural interpretation from a mathematical POV would use log-odds. So if the author is at the 90% mark, someone 10 times as smart occurs at the frequency of around 1 in 3 billion.
But yeah. In context, your way makes more sense, if only because it’s more charitable.
Only if you take ‘ten times smarter’ to mean multiplying IQ score by ten. But since the mapping of the bell curve to numbers is arbitrary in the first place, that’s not a meaningful operation; it’s essentially a type error. The obvious interpretation of ‘ten times smarter’ within the domain of humans is by percentile, e.g. if the author is at the 99% mark, then it would refer to the 99.9% mark.
And given that, his statement is true; it is a curious fact that IQ has diminishing returns, that is, being somewhat above average confers significant advantage in many domains, but being far above average seems to confer little or no additional advantage. (My guess at the explanation: first, beyond a certain point you have to start making trade-offs from areas of brain function that IQ doesn’t measure; second, Amdahl’s law.)
I agree, that’s likely what Carrier was feeling when he wrote that sentence. But that doesn’t let him off the hook, because that way is even worse than Logos’! He’s using a definition of “times more intelligent” that is only really capable of differentiating between humans, and trying to apply it to something outside that domain.
I’m not sure if the following could be already encompassed in Amdahl’s law, but I think it was worth a comment. Very intelligent humans still need to operate through society to reach their goals. An IQ of 140 may be enough for you to discover and employ the best tools society puts at your disposal. An IQ of 180 (just an abstract example) may let you recognize new and more efficient patterns, but you then have to bend society to exploit them, and this usually means convincing people not as smart as you are, that may very well take a long time to grasp your ideas.
As an analogy, think being sent into the stone age. A Swiss knife here is a very useful tool. It’s not a revolutionary concept, it’s just better than stone knives in cutting meat and working with wood. On the other hand, a set of professional electrical tools, while in principle way more powerful, will be completely useless since you will have to find a way to charge their batteries before.
Yup, that’s the way I interpreted it too—going from top 1% to top 0.1%.
To me a more natural interpretation from a mathematical POV would use log-odds. So if the author is at the 90% mark, someone 10 times as smart occurs at the frequency of around 1 in 3 billion.
But yeah. In context, your way makes more sense, if only because it’s more charitable.