IQ is renormalized to the bell curve by definition, so multiplying it by 10 isn’t guaranteed to be a meaningful operation. And since we have no other way to measure intelligence, it’s not clear what Carrier meant by “10 times smarter”. For some easy interpretations (e.g. 10x serial speed or 10x parallelism) his claim seems trivially wrong.
It is a simple way of expressing “a lot,” but it’s also one that immediately raises the question “is there any meaningful sense in which anyone that smart has actually existed?”
Of course, when Carrier claims that the most remarkably intelligent people do not tend to be the most productive, while it’s clear what kind of individuals he has in mind, the obvious next question is “can we design machines that use their intelligence more productively than humans?” Considering how human brains actually work, this sounds like much less of a tall order than making AI that are more intelligent in a humanlike way.
Well, central limit theorem says it’s mostly a bell curve among humans (you could make a case for a bigger tail on the low end, but still mostly a bell curve). And you can always identify “0” with a random number generator. So multiplying by 10 seems okay to me.
Not that major. The assumptions are that there are many small, independent things that affect intelligence. These assumptions are wrong, in that there are many things that do not have a small effect at all. But to the extent that these (mostly bad things) are rare, you’ll just see a bell curve with slightly larger tails.
Why can we assume that all the little things affect intelligence independently? Are synergies obviously rare, and how rare do they have to be for the central limit theorem to apply? In the simplest alternative model I can think of, incremental advances could be multiplicative instead of additive, which gives a log-normal distribution instead of a bell curve. This case is uninteresting because you could just say you’re measuring e^intelligence instead of intelligence, but I can imagine more complicated cases.
Side note: I think it is not well known that for the quintessential normally distributed random variable, human height, the lognormal distribution is in fact an equally good fit. And on the other end of the variance spectrum: I became biased toward the lognormal distribution when I observed that it is a much better fit for social network degree distributions than the much-discussed power-law. It is a very versatile thing.
IQ is renormalized to the bell curve by definition, so multiplying it by 10 isn’t guaranteed to be a meaningful operation. And since we have no other way to measure intelligence, it’s not clear what Carrier meant by “10 times smarter”.
Well… IQ is meant to be a direct quantification of raw “intellectual capacity”. So while its distribution is relative given the history of tests thus far, it still remains a quantification. But, that being said, this only further exascerbates the point I’m really getting at here: the ‘logic’ the man used is… fuzzy.
IQ is meant to be a direct quantification of raw “intellectual capacity”.
No it isn’t; it is a framework for relative rankings. Developing some means of “direct quantification” would be a major intellectual achievement, which as a first step would require a good definition of intelligence. I have been thinking about this and while there are quite a few useful definitions of intelligence out there, they each have notable weaknesses, we are a long way from a good definition.
Just as thermometers are a tool that measures temperature as relative degrees, and a serious understanding of and definition of heat waited on the development of the statistical theory of molecular motions.
Just as thermometers are a tool that measures temperature as relative degrees,
Amusing—those are a direct quantification of temperature. Degrees Celsius for example goes to degrees Kelvin rather well. They use arbitrarily fixed points above zero K—but the IQ scale does not do this.
Now, of course, IQ is not g. And we have no means of quantifying g.
I think maybe you are under the misapprehension that by “intellectual capacity” I was saying “intelligence”. If I had meant “intelligence” I would have said “intelligence”.
IQ is renormalized to the bell curve by definition, so multiplying it by 10 isn’t guaranteed to be a meaningful operation. And since we have no other way to measure intelligence, it’s not clear what Carrier meant by “10 times smarter”. For some easy interpretations (e.g. 10x serial speed or 10x parallelism) his claim seems trivially wrong.
“10 times” just means “a lot”. I’m more curious about what Carrier meant by “smart”.
It is a simple way of expressing “a lot,” but it’s also one that immediately raises the question “is there any meaningful sense in which anyone that smart has actually existed?”
Of course, when Carrier claims that the most remarkably intelligent people do not tend to be the most productive, while it’s clear what kind of individuals he has in mind, the obvious next question is “can we design machines that use their intelligence more productively than humans?” Considering how human brains actually work, this sounds like much less of a tall order than making AI that are more intelligent in a humanlike way.
Well, central limit theorem says it’s mostly a bell curve among humans (you could make a case for a bigger tail on the low end, but still mostly a bell curve). And you can always identify “0” with a random number generator. So multiplying by 10 seems okay to me.
Only subject to some major assumptions.
Not that major. The assumptions are that there are many small, independent things that affect intelligence. These assumptions are wrong, in that there are many things that do not have a small effect at all. But to the extent that these (mostly bad things) are rare, you’ll just see a bell curve with slightly larger tails.
Why can we assume that all the little things affect intelligence independently? Are synergies obviously rare, and how rare do they have to be for the central limit theorem to apply? In the simplest alternative model I can think of, incremental advances could be multiplicative instead of additive, which gives a log-normal distribution instead of a bell curve. This case is uninteresting because you could just say you’re measuring e^intelligence instead of intelligence, but I can imagine more complicated cases.
Side note: I think it is not well known that for the quintessential normally distributed random variable, human height, the lognormal distribution is in fact an equally good fit. And on the other end of the variance spectrum: I became biased toward the lognormal distribution when I observed that it is a much better fit for social network degree distributions than the much-discussed power-law. It is a very versatile thing.
Good point.
Well… IQ is meant to be a direct quantification of raw “intellectual capacity”. So while its distribution is relative given the history of tests thus far, it still remains a quantification. But, that being said, this only further exascerbates the point I’m really getting at here: the ‘logic’ the man used is… fuzzy.
No it isn’t; it is a framework for relative rankings. Developing some means of “direct quantification” would be a major intellectual achievement, which as a first step would require a good definition of intelligence. I have been thinking about this and while there are quite a few useful definitions of intelligence out there, they each have notable weaknesses, we are a long way from a good definition.
Just as thermometers are a tool that measures temperature as relative degrees, and a serious understanding of and definition of heat waited on the development of the statistical theory of molecular motions.
Amusing—those are a direct quantification of temperature. Degrees Celsius for example goes to degrees Kelvin rather well. They use arbitrarily fixed points above zero K—but the IQ scale does not do this.
Now, of course, IQ is not
g. And we have no means of quantifyingg.I think maybe you are under the misapprehension that by “intellectual capacity” I was saying “intelligence”. If I had meant “intelligence” I would have said “intelligence”.