I'm a bit confused: as covariance is a kernel, a covariance matrix is always positive semi- definite (proof: https://stats.stackexchange.com/questions/52976/is-a-sample-covariance-matrix-always-symmetric-and-positive-definite), and so the usual random matrix spectral theory doesn't apply, and the top eigenvalue value cannot be negative, and so is not described by the Tracy- Widom distribution. Correlation is also a kernel, so the correlation matrix is also positive semi- definite, and the same applies.
Trying to be maximally charitable to Pinker here, what I think he meant was something along the lines of, sure, g exists, in humans, possibly in other animals, but is there any such thing as a cross-species g that applies to any thinking creature or machine whatsoever? I'm inclined to personally say probably yes, and I'm not totally certain he wouldn't agree even, but then you run into the further problem of how on earth we measure that. I thought that was what this post was gong to address after seeing the title, not whether we can compare non-humans animals to other individuals of their own species, but can be compare individuals of different species?
I still don't think this is necessarily the basis of any kind of strong case if your claim is that talking about intelligence in a general way that applies to all thinking creatures and machines is completely pointless or the word intelligence in itself can't possibly have a generally applicable meaning, but it is at least not obviously contradictory to the belief that g exists and can be measured.
Some more studies looking for g in various species are mentioned in table 1 of Shaw and Schmelz (2017). Cognitive test batteries in animal cognition research: evaluating the past, present and future of comparative psychometrics. https://doi.org/10.1007/s10071-017-1135-1
Do human identical twins satisfy the "positive manifold" criterion, in the sense that if one twin outperforms the other at one cognitive test, they're more likely to also outperform them at a different test?
Is there a way to do a factor analysis (ie, collect data on pairs of identical twins, and then use that data to infer what factors you would see in a single identical 100let), and of yes, what do the resulting factors look like?
If we have a positive manifold for human identical twins, but not for very genetically similar rats, is there some particular explanation for this?
I'm a bit confused: as covariance is a kernel, a covariance matrix is always positive semi- definite (proof: https://stats.stackexchange.com/questions/52976/is-a-sample-covariance-matrix-always-symmetric-and-positive-definite), and so the usual random matrix spectral theory doesn't apply, and the top eigenvalue value cannot be negative, and so is not described by the Tracy- Widom distribution. Correlation is also a kernel, so the correlation matrix is also positive semi- definite, and the same applies.
What am I missing?
Trying to be maximally charitable to Pinker here, what I think he meant was something along the lines of, sure, g exists, in humans, possibly in other animals, but is there any such thing as a cross-species g that applies to any thinking creature or machine whatsoever? I'm inclined to personally say probably yes, and I'm not totally certain he wouldn't agree even, but then you run into the further problem of how on earth we measure that. I thought that was what this post was gong to address after seeing the title, not whether we can compare non-humans animals to other individuals of their own species, but can be compare individuals of different species?
I still don't think this is necessarily the basis of any kind of strong case if your claim is that talking about intelligence in a general way that applies to all thinking creatures and machines is completely pointless or the word intelligence in itself can't possibly have a generally applicable meaning, but it is at least not obviously contradictory to the belief that g exists and can be measured.
Some more studies looking for g in various species are mentioned in table 1 of Shaw and Schmelz (2017). Cognitive test batteries in animal cognition research: evaluating the past, present and future of comparative psychometrics. https://doi.org/10.1007/s10071-017-1135-1
Do human identical twins satisfy the "positive manifold" criterion, in the sense that if one twin outperforms the other at one cognitive test, they're more likely to also outperform them at a different test?
Is there a way to do a factor analysis (ie, collect data on pairs of identical twins, and then use that data to infer what factors you would see in a single identical 100let), and of yes, what do the resulting factors look like?
If we have a positive manifold for human identical twins, but not for very genetically similar rats, is there some particular explanation for this?