Basically just to see if they can. We can think of the problem from multiple angles. The general problem is: “if we have a larger square with side length of a, what’s the maximum number of smaller squares (with side length of b) that we can fit into that larger square?”. If we have a larger square with side length of 4, then we can fit 16 squares in. If the larger square had a side length of 5, then we can fit 25 squares in. So this means that if we want a neat packing solution, and we can control how large the outer square is (in relation to the inner squares), then we want each side of the larger square to be a whole number multiple of the smaller square’s side length.

But what if that isn’t our goal? The fact that packing 25 squares into a 5x5 square is an optimal packing solution with no spare space means that it will be impossible to fit 25 smaller squares into a square that’s less than 5x5 large. But what about if we do have awkward constraints, and the number of smaller squares we have to pack isn’t a square number? The fact that this weird packing solution in the OP has 17 squares isn’t because 17 is prime, but rather that 17 is 1 more than 16 (it’s just that 17 happens to be prime).

This is a long way of saying that because packing 16 squares into a square is easy, the natural next question is “how large does the larger square need to be to be able to pack 17 squares into it?”. If this were a problem in real life where I had to pack 17 squares into a physical box, most people would just get a box that’s at least 5x5 large, and put extra packing material into all the spare space. But asking this question in terms of “what’s the smallest possible box we could use to pack 17 squares in?” is basically just an interesting puzzle, precisely because it’s a bit nonsensical to try to pack 17 squares into the larger square. We know for certain we need a box that’s larger than 4x4, and we also know that we can do it in a 5x5 box (with a heckton of spare space), so that gives us an upper and lower bound for the problem — but what’s the smallest we could use, hypothetically?

As a fellow autistic person, I relate to your confusion. But I’d actually wager that there were a non-zero number of autistic people who were involved in this research. It sort of feels like “extreme sports” for autistic people — doing something that’s objectively baffling, precisely because it feels so unnatural and wrong

The optimisation objective is to fit n smaller squares (in this case, n=17) into the larger square, whilst minimising the size of the outer square. So that means that in this problem, the dimensions of the outer square isn’t a thing that we’re choosing the dimensions of, but rather discovering its dimensions (given the objective of "minimise the dimensions of the outer square whilst fitting 17 smaller squares inside it)

Oh my God, I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised. However, I love that someone went to the effort of making a waffle iron plate for this. High effort shitposts like this give me life

Thanks for sharing that talk, it’s pretty good.

I always find his talks interesting, because it often feels like it’s the same core talk each time, but changed through iterative refining of his ideas and rhetoric due to how often he gets the chance to talk about these issues.

Even though I’ve seen many of his talks before, I am surprised at how skillfully he is able to weave in new angles and themes. I mean, he has been doing this stuff for literal decades, but still, it’s impressive.

“Most of us have been in your shoes, with the same amount of fear, confusion and helpless feelings. So…uh…welcome to our little club. We get together sometimes and hang out (mostly virtually, admittedly).”

This exactly. I felt such an overwhelming sense of solidarity when reading this post because I have been in this position so many times before. Hell, I still occasionally get like this — although I am way more confident in solving most of my technical problems nowadays, that additional knowledge just makes it all the more frustrating when I run into something that makes me feel confused and overwhelmed.

I’m not going to give you any technical advice because there’s already a lot of suggestions already. I just wanted to leave a comment in solidarity.

I am the techiest person in my fairly techy group of friends, and even I often end up making silly mistakes that mess up my system sometimes. It’s easy to get overwhelmed, especially when there seems to be solutions to my problems that I’m not able to understand.

Trust me when I say that you’re not stupid for not getting this. This shit is difficult. I have been in your position so so many times before — right down to the despair making me feel suicidal. It’s hard when you desperately need to fix a thing, but the more you throw yourself at the problem, the harder it gets. Take as much of a break as you need to, and come back to some of the answers that sound promising, but you’re struggling to understand, and ask questions. You’re not dumb for not understanding — you’re new at this, and that’s okay.

I can’t speak for other people in this thread, but I know that when I’m giving technical advice to people, it often feels like I’m getting practice at communicating things in an accessible way. I want more people to be able to participate in this hobby that I enjoy, but I’ve been steeping in this environment for so long that sometimes, the advice that I give is overly dense, or it assumes knowledge that the person needing help doesn’t have. That’s an unfortunate mistake to make, because it makes the person reading my reply feel stupid, and that’s the last thing I want. I’ve found that giving technical advice online is often a mutual learning process — the person I’m helping is learning the tech stuff, and I’m learning how to communicate better. If you revisit some of the comments in this thread, bear that in mind — it’s not all on you.

On the topic of wishing you were stronger, I can relate to that — like I said, I’m pretty prone to getting myself into a spiral of shame when I don’t understand a thing and everything I do keeps getting worse. For what it’s worth, I think that asking for help as you have done here is something that requires a lot of strength; it’s hard to be vulnerable when you feel like you’re messing things up. It also takes strength to recognise that you’re getting overwhelmed enough that you need to take a step away. It’s valid to want to be stronger than you are now, but I hope you’re able to recognise your small achievements.

Finally, a small bit of practical advice that I’d give is that if you’re entering terminal commands or changing settings to try fix this, it’s super useful to make a note of what you’re doing. Sometimes when I have a complex problem and I try one potential solution that doesn’t end up working, the changes made in that solution can conflict with steps involved in attempting a second solution. It can make it easier to keep track of what you’ve tried so far, especially if you have to undo stuff later. It’s okay if you haven’t done this so far, but it can help going forward. I find that when I’m panicking and desperate for a solution, that makes me more likely to just attempt basically everything, and those are the times when keeping track of what I’ve done is especially important.

Don’t feel guilty for asking for help, or for needing clarifications. We’re all here of our own free will. Many of us have been in your position before, and only got to the point where we are now because of the patient help of kind online nerds. That’s a big part of why I try to chip in when I find someone with a problem I can help with — it feels like giving back to the community that helped me to learn back when I was new to this.

I know it doesn’t feel like it, but you’re doing well. Keep trying, and I promise things will get easier. Don’t beat yourself up for needing to take breaks, or for feeling overwhelmed. How you’re feeling right now is within the range of what’s normal for new people running into a difficult technical problem like this. You’re not stupid, this stuff is just hard.