I don’t want to get too into the weeds here. But I think that someone in the top few percent of their school would be smart. The kind of kid who might be feeling without intellectual peers and posting here about it could be the smartest in their school or their town (or they could not). But I don’t think that really changes the conclusions.
You have used the word “feel(ing)” twice. The core question isn’t whether he feels he has intellectual peers he can talk to. It is whether he genuinely does or doesn’t have intellectual peers of his caliber. I believe this high school student when he implies he doesn’t have anyone near his intellect at his school and at other programs he has tried out. You do not. I think this is the crux of our disagreement.
I put so much effort into standard deviations because “smart” papers over a broad range of intelligences. Someone with an IQ of 115 is “smart”. Someone with an IQ of 175 is “smart”. The difference between someone with an IQ of 115 and someone with an IQ of 175 is four standard deviations. Four standard deviations is huge. It is equal to the difference between a PhD in science and someone hovering on the edge of an intellectual disability. It would be absurd for a PhD in science to look for intellectual peers in the same place as someone bordering on the edge of intellectual disability. The same goes for someone with an IQ of 115 verses someone with an IQ of 175.
The difference between someone with an IQ of 115 and someone with an IQ of 175 is four standard deviations. Four standard deviations is huge. It is equal to the difference between a PhD in science and someone hovering on the edge of an intellectual disability.
I’d be careful with this kind of comparison. IQ numbers and SDs may look like cardinal measurements, but they’re actually an ordinal hierarchical system. What one can say is that someone with IQ n+1 is “smarter than” someone with IQ n, who in turn is “smarter than” someone with IQ n-1. But there’s no way, for now, to convert that in a cardinality.
Hence, in an absolute sense of literal, actual intelligence, the difference in between an IQ 175 and an IQ 115 may be either greater or smaller than the difference in intelligence between an IQ 115 and an IQ 55. My personal hunch is that it’s much smaller, although, evidently, I have no way to back that up.
I don’t want to get too into the weeds here. But I think that someone in the top few percent of their school would be smart. The kind of kid who might be feeling without intellectual peers and posting here about it could be the smartest in their school or their town (or they could not). But I don’t think that really changes the conclusions.
You have used the word “feel(ing)” twice. The core question isn’t whether he feels he has intellectual peers he can talk to. It is whether he genuinely does or doesn’t have intellectual peers of his caliber. I believe this high school student when he implies he doesn’t have anyone near his intellect at his school and at other programs he has tried out. You do not. I think this is the crux of our disagreement.
I put so much effort into standard deviations because “smart” papers over a broad range of intelligences. Someone with an IQ of 115 is “smart”. Someone with an IQ of 175 is “smart”. The difference between someone with an IQ of 115 and someone with an IQ of 175 is four standard deviations. Four standard deviations is huge. It is equal to the difference between a PhD in science and someone hovering on the edge of an intellectual disability. It would be absurd for a PhD in science to look for intellectual peers in the same place as someone bordering on the edge of intellectual disability. The same goes for someone with an IQ of 115 verses someone with an IQ of 175.
I’d be careful with this kind of comparison. IQ numbers and SDs may look like cardinal measurements, but they’re actually an ordinal hierarchical system. What one can say is that someone with IQ n+1 is “smarter than” someone with IQ n, who in turn is “smarter than” someone with IQ n-1. But there’s no way, for now, to convert that in a cardinality.
Hence, in an absolute sense of literal, actual intelligence, the difference in between an IQ 175 and an IQ 115 may be either greater or smaller than the difference in intelligence between an IQ 115 and an IQ 55. My personal hunch is that it’s much smaller, although, evidently, I have no way to back that up.