Since this article was written in 2005, multiple attempts have been made to establish non-rectangular UIs. The mentioned Daisy Disk delights in its hierarchical view. Ça. 2010 there was an initiative for an entire phone UI based on this kind of concept. This went nowhere but Android 4 tried to incorporate as slide in from the side circular menu. [1] Most recently HTC incorporated this kind of UI in their U11 phone launcher. [2]

Forgoing the entire concept of rows and columns of pixels to render a UI though is just asking for trouble as all assumptions about arrangement go out of the window. With sufficiently high resolutions screens (we've achieved that) an arbitrarily shaped UI can be displayed. Masterfully demonstrated here in Neil Sardesai s UI experiments [3]

As for having the menu separate from the content canvas, foldables are currently a great experiment platform for this, see Samsungs "flex mode" [4]

[1]https://www.androidauthority.com/is-google-aiming-for-a-ui-m... [2]https://www.htc.com/us/support/htc-u11/howto/opening-edge-la... [3] https://twitter.com/neilsardesai/status/1381241571895615491 [4] https://www.bgr.in/news/youtube-app-update-brings-improved-s...