The Block Stacking Problem
sites.pitt.edu112 points by lisper 3 days ago
112 points by lisper 3 days ago
> My goal here is to develop an intuitive sense of comfort with the behaviors of these stacks. If I succeed, you will not just understand that the physics allows the stacks to be stable, but you will feel that it is proper and just.
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?
It's really hard to achieve. It takes an awful lot of work and being able to put yourself in the shoes of somebody who doesn't know everything you know.
A lot of writing suffers from the problem of "this explanation only makes sense if you already understand it", and I think it's the default - if the author is essentially explaining the problem to themselves, of course it makes sense to someone who already understands it.
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!
Sadly many Universities have lots of professors who just copy books in the blackboard. Those books that asume you already know.
Partially because Universities insist on making professors both teach and perform research (for the most part a few do have a real distinction between teaching and research but most still require at least a token class from most of their researchers) which isn't what most people go into a PhD program to do.
> Partially because Universities insist on making professors both teach and perform research
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.
That's not universal, it factors in at some points at least at some universities, my wife is going through her reappointment after her first year as a professor at an R2 HBCU and teacher evals are part of it from what I've heard of the process there and she was definitely hired as principally a research oriented professor.
What helps is explaining it to many people, and carefully listening the questions asked by them. It of course help also to have a deeper understanding of the subject matter.
It is more likely that it is exceedingly difficult to write like this, even for simple topics like this balancing blocks problem. The further you get into an academic subfield, the less likely it is that you can even describe what you are pondering in plain English.
Even better solutions which are interesting to visualize were proved optimal in 2007.
https://chris-lamb.co.uk/posts/optimal-solution-for-the-bloc...
Coincidentally, I happened across a block stacking YouTube video yesterday that discusses the limits of the standard Lire tower solution, the "optimal" spine solutions and the "better" parabolic solutions (more overhang although may not be optimal for any particular number of blocks).
It is even possibly not a coincidence that someone has delved into this and brought an article to Hacker News less than 24 hours after a Trefor Bazett video. (-:
I hadn't noticed that it was a new video and I wasn't aware of Trefor Bazett either - I like his presenting style so will likely watch some of his other videos
If you like the Block Stacking Problem, the Overhang Problem is similar, but without the one-block-per-level restriction.
https://news.ycombinator.com/item?id=36332136 - The Overhang Problem (2023-06-14, 16 comments)
Has anyone done this work with multiple sizes of blocks? It looks to me that some of the solutions fail because (n + 1)/2 % 1 = 0.5 which puts each block ready to fall over at the slightest breeze.
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.
How about this one:
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 don't see how. Consider the block of minimum altitude, what's stopping it from falling?
If the blocks are thin enough, I think it's possible. Stack three blocks. Position the left edge of the stack on the edge of the table, so it's hanging downward at a slight angle, and stack enough blocks on top that it holds. Now slide the middle block 2/3 of the way out. The friction should still hold.
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.
> Assume an arbitrarily high coefficient of friction between all surfaces
Yes but in practice that means using glue, at which point you might as well glue everything together into a single piece.
The difference is that glue can withstand tension which changes a lot. Even infinite friction still requires a non-negative contact force (i.e. the surfaces are not being pulled apart).
Not glue, necessarily. The coefficient of friction is not about surface adhesion. It is kinetic; glue is an additional static component.
Related: "The Best Way to Stack Blocks" Dr. Trefor Bazett (published 1 day ago)
Am I right in thinking that this problem ultimately boils down to how much torque you can apply to an object before it moves?
Because essentially the table edge is a fulcrum, as is each block, and the leverage is relative to the center of mass.
I love the layout of the article, where the images are allowed to bleed into the margins, and the footnotes are immediately to the right of the paragraph. Is this an open or well known format?
On of my many disappointments is that when I learned of this phenomenon I could now convince any of the children in my life that this was amazing.