Right, and updates are also O(32 log32(n)) rather than O(2log2(n)), rather than O(1) for arrays. It’s a bit more complicated when you think about cache lines being updated but mutable arrays massively win on cache
It is meaningless mathematically. It’s as meaningless as the parent talking about log32(n) because of course log32(n) = log n / log 32, so there is just a constant of 1 / log 32 being put at the front.
I think the subtext is really a statement about constant factors. The parent is saying “if trees are wide then lookups are cheap” and I am saying “if trees are wide then updates may be expensive” (to update an immutable binary tree of size n, you must allocate log2(n) nodes of size (say) 3. To update a 32-ary tree you need log2(n) / log2(32) = log2(n) / 5 nodes of size 33 so, as 33/5 = 6.6 > 3, the wider tree requires more allocation for updates.)
