The Block Stacking Problem

https://sites.pitt.edu/~jdnorton/Goodies/block_stacking/block_stacking.html

by lisper • 11 months ago

136 36 11 months ago

sites.pitt.edu

OgsyedIE• 11 months ago

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_pomu2• 11 months ago

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).

https://www.youtube.com/watch?v=eA0qGJMZ7vA

JdeBP• 11 months ago

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. (-:

jeffparsons4• 11 months ago

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• 11 months ago

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.

jeffparsons4• 11 months ago

That's basically the direction I was going in my head. I just remembered we have a bunch of Kapla blocks in the house, so I may be able to do this "IRL"!

amelius2• 11 months ago

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.

IAmBroom• 11 months ago

Not glue, necessarily. The coefficient of friction is not about surface adhesion. It is kinetic; glue is an additional static component.

Liftyee• 11 months ago

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).

WithinReason• 11 months ago

Turn the stack from the article by 89°

dooglius• 11 months ago

I don't see how. Consider the block of minimum altitude, what's stopping it from falling?

jeffparsons4• 11 months ago

I didn't specify the challenge clearly. I meant to allow blocks in any orientation, as long as they would be stable.

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.

cluckindan2• 11 months ago

Sure, just use gauge blocks!

jeffparsons4• 11 months 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?

cptroot• 11 months ago

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.

juancn• 11 months ago

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.

Retr0id• 11 months ago

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!

f1shy4• 11 months ago

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.

MontagFTB• 11 months ago

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?

adamschwartz• 11 months ago

That general structure looks somewhat like Edward Tufte’s work.

https://edwardtufte.github.io/tufte-css/

https://github.com/edwardtufte/tufte-css

hinkley4• 11 months ago

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.

hinkley4• 11 months 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.

JKCalhoun• 11 months ago

The video linked to in this thread includes torque.

hinkley4• 11 months ago

"the video" is now a few.

vgb2k18• 11 months ago

Related: "The Best Way to Stack Blocks" Dr. Trefor Bazett (published 1 day ago)

https://youtu.be/eA0qGJMZ7vA?si=jkEmafRhisV5LWnx

omoikane• 11 months ago

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)

hinkley4• 11 months ago

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.

cluckindan2• 11 months ago

What if the blocks are buoyant? Can you construct the same shape upside down if there is a surface to support the part that wants to rise out of the water?

The Block Stacking Problem

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