by _a_a_a_ on 6/14/23, 8:49 PM
"How far can a stack of n identical blocks be made to hang over the edge of a table? The question has a long history and the answer was widely believed to be of order logn. Recently, Paterson and Zwick constructed n-block stacks with overhangs of order n^1/3 , exponentially better than previously thought possible. We show here that order n^1/3 is indeed best possible, resolving the long-standing overhang problem up to a constant factor."
(from intro)
by trhr on 6/15/23, 7:28 AM
Imagine being this author's parents at parties. "Yes, our son is a Computer Scientist. No, not the well-paid kind, the kind that solves problems. No, not that sort of problem; the ones like how many bricks it takes to make a wall sturdy. No, not a regular wall; a curved one. I don't know who wants a curved brick wall. Yes, I suppose he could just use rebar and mortar."
by f5ve on 6/15/23, 3:21 AM
by mav88 on 6/14/23, 10:19 PM
These diagrams remind me of Lemmings and the builders that would build staircases over gaps you needed to cross.
by omoikane on 6/15/23, 2:47 AM
It mentioned that the harmonic stacks arise from the restriction that the blocks should be stacked in one-on-one fashion. A related restriction might be that the blocks must be stacked one-by-one, i.e. each additional block must maintain balanced state.
I think trying to reproduce some of the diagrams with physical blocks would be difficult unless multiple blocks are placed at the same time.
by stephencanon on 6/14/23, 11:46 PM
by kisonecat on 6/15/23, 1:50 AM
by jojobas on 6/14/23, 11:05 PM
So some scientists get to play with jenga on taxpayers' dime and students' tuition fee.
(I'm not angry, I'm envious.)
by PlunderBunny on 6/14/23, 9:22 PM
I wonder how close the historical examples come to the 20 or 30 block 'ideal'?