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madness

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Very cool paper just out relating fractal geometry to the representation of natural images in visual cortex. The main argument is that brain's representations are as high dimensional as they could possibly be without becoming fractal.

https://www.nature.com/articles/s41586-019-1346-5

I'm curious what the geometers here make of the mathematical results in the supplementary (https://static-content.springer.com/esm/art:10.1038/s41586-019-1346-5/MediaObjects/41586_2019_1346_MOESM1_ESM.pdf). There's a set of theorems relating upper Minkowski dimension to eigenspectrum decay of a manifold (perhaps most interestingly Theorems 3-5). Does this constitute an interesting mathematical development in its own right?

https://www.nature.com/articles/s41586-019-1346-5

I'm curious what the geometers here make of the mathematical results in the supplementary (https://static-content.springer.com/esm/art:10.1038/s41586-019-1346-5/MediaObjects/41586_2019_1346_MOESM1_ESM.pdf). There's a set of theorems relating upper Minkowski dimension to eigenspectrum decay of a manifold (perhaps most interestingly Theorems 3-5). Does this constitute an interesting mathematical development in its own right?

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