> I'll assume you understand the difference between a 1D line, a 2D plane
IQ isn't linear because it is not superposable. A 100 IQ person isn't twice as clever, within the definition of cleverness IQ measures, as someone with a 50 IQ. (An 8' man is twice as tall as a 4' child.) If you need to force it into a geometric analogy, the distribution IQ rests on cannot be described by a line.
> IQ isn't linear because it is not superposable. A 100 IQ person isn't twice as clever, within the definition of cleverness IQ measures, as someone with a 50 IQ.
You appear to be thinking of a uniform distribution as compared to a normal distribution.
Nominally both height and IQ approximate a normal distribution (sans the infinite tails, leaving aside discrete ordinal bucketing).
"Linear" (see the O.E.D. for example) is a word with many meanings, mostly pertaining to lines and things resembling a line.
You can line up people by height or by IQ score, you cannot line up people by "intelligence", it's a partial order at best.
> the distribution IQ rests on cannot be described by a line.
You're the only one of us that connected the scalar IQ distribution to a line .. I've been aware of the central limit theorem for 45+ years now.
The geometric analogy is that mapping people by intelligence to a line is a poor fit, to a plane or higher space would make more sense.
You probably meant that there doesn't exist a total order for comparing intelligence and/or that it isn't a scalar quantity like height, but "linear" didn't convey that meaning.
Intelligence clearly isn't a scalar quantity like height, the implication is that a faux scalar quantity like IQ or other ordinal scale doesn't well describe intelligence.
I agree, I think any test that gets you a meaningfully different result if you take it twice or are coached beforehand isn't measuring something intrinsic or meaningful, I'm just trying to help bridge a miscommunication.
Ranking people by "intelligence" is compounded by it being multifactored, language skills and numerical skills can differ independently, spatial skills are a third vector unaligned with either.
What is your issue here?