If folks are interested, I recently published a paper [1] demonstrating that fMRI activity in the visual cortex is remarkably high-dimensional!

Specifically, using a linear approach (like PCA, but slightly fancier), we find that stimulus-related information is present along many, many dimensions of the neural response---much more than previously expected/reported.

[1] https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...