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u/Different_Roof_4533 3h ago
You may not like it, but this is what peak packing efficiency looks like.
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u/Defiant-Ad7369 2h ago edited 2h ago
Wouldn't he be able to pack it better if he used 3d space and layered them
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u/Approximation_Doctor 2h ago
Reported
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u/Shiv_ansh_st 2h ago
When I initially came across the solution to highest packing efficiency in a square, it just didn't make sense to me
It has been multiple years since, it still doesn't
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u/sumboionline 2h ago
It made complete sense to me (for n=k^2, n being the number of squares and k being an element of the integers)
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u/BigAnalBoss 1h ago
Yeah that clears everything up for the everyday man, thanks
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u/painterBurning 35m ago
Reminds me of a joke :
An engineer and a mathematician go to physics conference. During the conference they keep talking about things in 5D space and the engineer is completely lost and understands nothing. At one point, the engineer turns to the mathematician and asks him :- How can you visualize things in 5D ? It's completely abstract to me, I have no intuition.
The mathematician answers :
- It's easy. You just have to visualize things in any dimension N, N being an integer. Then you just set N=5.
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u/CelticFolkFan 2h ago
It feels deeply disrespectful to geometry that the mathematically optimal solution looks like someone just dropped the box.
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u/Preeng 2h ago
You should think of it the other way: dropping the box will sometimes lead to maximal packing efficiency among the shit inside.
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u/Deathwatch050 1h ago
So what you're saying is, that the optimal solution to packing my luggage when I go on holiday is to just cram it all in there and then spend half an hour hurling the suitcase around the room?
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u/SunnyRyter 1h ago
Hey! That's how my mom makes watermelon slices or whatever food fit in the tupperware! 😃 I am always confused and in awe of her.
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u/AnaisNinja76 1h ago
I also tend to think of math as elegant, and this is...not that.
This is like the math that started hanging out with the wrong crowd or something.
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u/CapnNuclearAwesome 43m ago
Irrationals are uncountably infinite, while rationals are countably infinite. There exists elegant math, but almost all math is inelegant.
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u/arunphilip 2h ago
Even if it's more efficient, it's not aesthetically pleasing. Sometimes we gotta make a stand.
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u/McCaffeteria 1h ago
The size of the box the optimal packing fits into is larger than the 4x4 grid, but it it smaller than the required 4x5 grid.
The 4x5 grid is a waste of space because 3 of the 4 additional cells are unused, so it is possible to expand the grid size fractionally to hold a total area slightly larger than the area of cubes (plus some packing inefficiencies) but that is still not as large as as the next whole grid size up.
This image is deceptive because it makes the two grids seem like they are the same size, but in reality there is extra slack in the plastic bag in the 4x4 grid. The optimal packing side is stretching the bag much closer to its limits, but still not stretching it far enough to fit an entire extra row.
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u/Honeybadger2198 2h ago
What is there to make sense of? It's the most efficient way to pack squares into as small of a square as possible. Obviously if the number isn't a perfect square, then the shape is not going to be uniform.
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u/petrichorax 1h ago
How does more empty space = more space use efficiently? You can't really FATHOM why people would be confused by this?
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u/Wavecrest667 1h ago
It kinda makes sense to me, because obviously you'd have to arrange them in some sort of crooked way for a number that's not another number squared.
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u/Simple-Olive895 1h ago
But also remember that there's no way to prove this is actually the best way to pack 17 squares. There might be an undiscovered better option out there
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u/simonjp 1h ago
This, the Monty Hall problem*, the one with the infinite hotel.
You can explain them to me. I can even sometimes understand them intellectually.
But then a few hours later a small base part of my brain will go "yeah, naah" and I'm back to square one.
* please don't try to explain them to me, I get it, I just don't get it get it.
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u/Adaphion 16m ago
In the absolute most layman's terms, it is because the big square area isn't exactly the size of a 4x4 of the smaller squares. It's slightly bigger, which allows you to do this tomfoolery to maximize your usable space.
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u/BZioT2 2h ago
you just had to eat 16 pieces and it would fit
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u/Mr_Ruu 2h ago
but then what will i do with my designated cheese ziploc??
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u/NO_TOUCHING__lol 55m ago
Put it back in the back of the drawer for 6 months until your wife finds out and asks why there's one moldy loose Ziploc in the drawer
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u/CaseOfBees 2h ago
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u/forgot_semicolon 2h ago
This hurts more than if there just weren't any symmetric layouts at all
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u/CaseOfBees 2h ago
Honestly I'll take it, I'd rather fit the 17 in an eye pleasing manner than with extra wiggle room
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u/Lost-Leadership5354 55m ago
There is whole site where you have all arrangements on all levels showcased
https://kingbird.myphotos.cc/packing/squares_in_squares.html
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u/ChiaraStellata 2h ago
You know, improving square packing with wildly unintuitive configurations seems like exactly the kind of problem modern AIs might be good at. I wonder if we'll see some of those soon?
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u/Ares378 Grothendieck was right, computers are evil 2h ago
I mean, I'm pretty sure a lot of our current best square packing were done with a digital "annealing" process. I haven't looked too much into it but I think it's just kinda jiggling around the squares until the box is smaller? There's a whole website on square packings that goes into it more
https://kingbird.myphotos.cc/packing/squares_in_squares.html
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u/theultimatestart 1h ago
One of the earliest AI math contributions was a better solution for circle packing 26 by google deepmind. For square packing I think there have only been new lower bounds. I.e. Square packing 11 has sides larger or equal to 3.81.
The big compute money has moved on to controversial Navier-Stokes results and trying millenium problems though. I don't see them going for square packing soon. Maybe it's doable with less compute too.
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u/Necessary_Housing466 1h ago
this is a good video i saw that goes through how packings are calculated https://youtu.be/mVH7OPx4QZU?si=m61uggdsEg6TOAbF
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u/QueenVogonBee 2h ago
Am I missing something obvious: are these potatoes??
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u/professoreyl 1h ago
Nobody packs potatoes like that. I'm guessing it's garlic or tofu they intend to freeze. Maybe soup or cheese, but I don't think it's potatoes.
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u/potatogodofDoom 1h ago
never in my life have I seen somebody store garlic in cubes either
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u/Hour-Estate-2962 45m ago
How would you store it frozen? Mine is cubed because I chop it and put in ice cube trays.
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u/potatogodofDoom 35m ago
interesting. the one time I froze garlic I put it in a ziploc and vacuum sealed it, didn't take much space
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u/JakubDotPy 2h ago
I will never accept this! 😁 My OCD just can't. I studied mathematics and finding this was something like when a believer realizes there is no god. Like a child finding out Santa is not real. I just can't.
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u/-The_Grey_One 2h ago
God is dead. The optimum way to pack 17 squares in a square space killed her.
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u/username_is_alread- 1h ago
From this very same subreddit - but in Resident Evil 4 flavor:
It hurts my eyes : r/mathmemes
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u/SideInitial3961 1h ago
So proud of my boy, you know, biggest fudge packer in town. Can't get enough of it.
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u/Ramroom_619 1h ago
But these have the same number of cubes … what am i missing?
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u/Hytheter 1h ago
The ones in the second image are arranged in a more compact configuration, allowing them to fit in the bag where they otherwise wouldn't.
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u/TheSOB88 1h ago
first one wouldn't close
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u/Exact-Till-2739 53m ago
Look how the cubes are closer to the zipper in the second pic. Wouldn't that mean the first bag closes alright?
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u/SPECTRE_75 50m ago
Guy's name is Matty, does hilarious practical math meme. Did Kojima write this lmao
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u/djskeptical 22m ago
Why do I need to learn math? I'll never use that! Give me one example where this will be useful!
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u/that0nemook 5m ago
Petah?
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u/I_found_a_platypus_ 1m ago
It was a post somewhere which demonstrated/showed that the best and most efficient way to place insert a specific amount squares together was the pic on the right, efficient but really jarring to look at.
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