Continuing the discussion from Examining "Darwin's Doubt":
I have no idea what it has to do with God sustaining the world, but 11 dimensional structures are a real thing. For the mathematically curious a good correlate here is something called: intrinsic dimension.
But those aren’t really 11 physical dimensions, right? I can’t figure out what they actually are, unless they’re what Dan Eastwood said: non-zero principle component axes or something similar, i.e. mathematical abstractions from data.
It is a property of the network connectivity, not the physical dimensions of space. It is real, and in the the 3-D physical world.
Copying my other comment here …
These multivariate methods are useful for data reduction, but orthagonal vectors of data are notoriously difficult to interpret in a non-subsective manner. Social sciences, especially Psychology, use these methods extensively (ie: factor analysis) and have their own terminology for them. We hardly ever use these methods in biomedical data, except for data reduction.
It’s not uncommon for the dimensonallity of data to be less than the number of variables measured, this is due to correlations and redundancy. This is particularly true when making many multiple measurements on a single complex object, like brain activity or motion capture data of physical activity (ex: walking).
I’m not sure their method was PCA.
I wonder how many dimensions would be required to describe cell cycle control in a connectivity model.
It may not be PCA, but there are many variations on methods of multivariate analysis. I haven’t read that paper recently, but I’ll give it another look.
@swamidass, You were correct. Algebraic Topology is not PCA!
But at least I have another area of math to explore now. 