Re:Comparing linear and nonlinear effects of cognitive abili...
by ChrisLomont on Saturday November 06, 2021 @12:00AM
(#29127405)
- strongly argue you lose most of the salient information when you try to represent a highly dimensional system with a single numbers.
First you'd have to demonstrate that intelligence is multi-dimensional, at which point you'd still fail since you can represent any point in any number of dimensions by single numbers. Hilbert curves are a trivial mapping. The entire field of manifold embedding exists as a counterpoint to your claim.
And, as others point out, it's also possible that one or a few values capture increasingly larger and larger amounts of the entire effect.
Claiming high dimensional items aren't describable with a single number is simply mathematically wrong.
First you'd have to demonstrate that intelligence is multi-dimensional, at which point you'd still fail since you can represent any point in any number of dimensions by single numbers. Hilbert curves are a trivial mapping. The entire field of manifold embedding exists as a counterpoint to your claim.
And, as others point out, it's also possible that one or a few values capture increasingly larger and larger amounts of the entire effect.
Claiming high dimensional items aren't describable with a single number is simply mathematically wrong.