Assume an arbitrarily high coefficient of friction between all surfaces. Can you stack the blocks on the table such that at least one block is wholly below the top of the table?
I think I have an answer to this, but I've only worked it through in my head, so there's a good chance I'm wrong!
I think it's also possible for other shapes, all the way up to square blocks. But you need to build a bunch of nested "clamp" arrangements, instead of just one.
Yes but in practice that means using glue, at which point you might as well glue everything together into a single piece.
So you can, for example, have blocks sloping down from the edge of the table by sandwiching one end of them between two other blocks with enough vertical distance between them, and enough weight on top.
I love this kind of writing. It feels like the author is excited to bring me along on a journey — not to show off how smart they are. In this way it reminds me of Turing's original paper that introduced his "computing machine". It presents a fantastically deep topic in a way that is not just remarkably accessible but also conversational and _friendly_.
I wonder why so little modern academic writing is like this. Maybe people are afraid it won't seem adequately professional unless their writing is sterile?
The problem can be perpetuated when e.g. a lecturer sets recommended reading to students. From the lecturer's perspective the selected reading material has clear explanations (because the lecturer understands the subject well), but the students do not feel the same way.
As you say, this takes effort to overcome, both on the author's side and from anyone trying to curate resources - including what we choose to upvote on HN!
That alone would not be problematic. The real problem is that they insist on it, but only evaluate them on their research. That doesn’t create an incentive to spend time on getting better at teaching.
https://m.youtube.com/watch?v=9yPy3DeMUyI&t=913s&pp=ygUSUmVz...
Because essentially the table edge is a fulcrum, as is each block, and the leverage is relative to the center of mass.
https://news.ycombinator.com/item?id=36332136 - The Overhang Problem (2023-06-14, 16 comments)
Whereas a small number of blocks of 2/3 or 1/2 size allows one to sub one into the middle of a stack to adjust fulcrum points without sacrificing the extra mass needed to further stabilize lower layers. Normal bricks are half as wide as they are long and cutting one in half and turning it sideways is absolutely common. And 3:2 ratios aren’t rare. But perhaps more common in tiling.
OgsyedIE•5mo ago
https://chris-lamb.co.uk/posts/optimal-solution-for-the-bloc...
ndsipa_pomu•5mo ago
https://www.youtube.com/watch?v=eA0qGJMZ7vA
JdeBP•5mo ago
ndsipa_pomu•5mo ago