The Block Stacking Problem
7 comments
·August 18, 2025jeffparsons
juancn
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.
cptroot
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.
OgsyedIE
Even better solutions which are interesting to visualize were proved optimal in 2007.
https://chris-lamb.co.uk/posts/optimal-solution-for-the-bloc...
ndsipa_pomu
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).
jeffparsons
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!
cousin_it
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.
> 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?