> Agreed, but there is plenty of utility that can be harvested, if we can direct our attention adequately.
Only for problems no worse than O(n^m) where m is not much more than 1.
Greenend (the domain name in the link) is, or so goes local legend, named after an actual street in Cambridge, quite close to where I was working a decade ago; one particular job, we'd just changed a file format for a mobile app, and the upgrade process was taking 20 minutes on test devices. The other engineer insisted it couldn't possibly be improved despite the two observations (1) it was fine before the upgrade, and (2) it was fine once the upgrade was complete. After a bit of digging, I found an O(n^2) operation we didn't need, and turned 20 minutes into 200 ms.
Increase the available compute by a factor of 1024 in an O(n^2) task, only compensates for n growing by a factor of 32.
Only for problems no worse than O(n^m) where m is not much more than 1.
Greenend (the domain name in the link) is, or so goes local legend, named after an actual street in Cambridge, quite close to where I was working a decade ago; one particular job, we'd just changed a file format for a mobile app, and the upgrade process was taking 20 minutes on test devices. The other engineer insisted it couldn't possibly be improved despite the two observations (1) it was fine before the upgrade, and (2) it was fine once the upgrade was complete. After a bit of digging, I found an O(n^2) operation we didn't need, and turned 20 minutes into 200 ms.
Increase the available compute by a factor of 1024 in an O(n^2) task, only compensates for n growing by a factor of 32.