Cursed
from fossilesque@mander.xyz to science_memes@mander.xyz on 01 Jul 17:24
https://mander.xyz/post/33191678

#science_memes

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janus2@lemmy.zip on 01 Jul 17:25 next collapse

if I ever have to pack boxes like this I’m going to throw up

Midnitte@beehaw.org on 01 Jul 18:17 collapse

I’ve definitely packed a box like this, but I’ve never packed boxes like this 😳

9point6@lemmy.world on 01 Jul 17:40 next collapse

Oh so you’re telling me that my storage unit is actually incredibly well optimised for space efficiency?

Nice!

CuriousRefugee@discuss.tchncs.de on 01 Jul 17:41 next collapse

If there was a god, I’d imagine them designing the universe and giggling like an idiot when they made math.

wise_pancake@lemmy.ca on 01 Jul 17:42 next collapse

Is this a hard limit we’ve proven or can we still keep trying?

rockerface@lemmy.cafe on 01 Jul 17:45 next collapse

It’s the best we’ve found so far

chuckleslord@lemmy.world on 01 Jul 18:47 collapse

We actually haven’t found a universal packing algorithm, so it’s on a case-by-case basis. This is the best we’ve found so far for this case (17 squares in a square).

<img alt="" src="https://lemmy.world/pictrs/image/9ed0ba9e-dcf2-40e2-bdc7-83fdd7090e66.jpeg">

glimse@lemmy.world on 01 Jul 18:55 next collapse

Figuring out 1-4 must have been sooo tough

Natanael@infosec.pub on 02 Jul 19:46 collapse

It’s kinda hilarious when the best formula only handles large numbers, not small. You’d think it would be the reverse, but sometimes it just isn’t (something about the law of large numbers making it easier to approximate good solution, in many cases)

selokichtli@lemmy.ml on 01 Jul 17:49 next collapse

Do you know how inspiring documentaries describe maths are everywhere, telling us about the golden ratio in art and animal shells, and pi, and perfect circles and Euler’s number and natural growth, etc? Well, this, I can see it really happening in the world.

LoreleiSankTheShip@lemmy.ml on 01 Jul 18:00 next collapse

Can someone explain to me in layman’s terms why this is the most efficient way?

Devadander@lemmy.world on 01 Jul 18:06 next collapse

Any other configurations results in a larger enclosed square. This is the most optimal way to pack 17 squares that we’ve found

FelixCress@lemmy.world on 01 Jul 18:19 collapse

Source?

SpikesOtherDog@ani.social on 01 Jul 18:32 next collapse

In the meme.

Acamon@lemmy.world on 01 Jul 21:30 next collapse

Bidwell, J. (1997)

Devadander@lemmy.world on 02 Jul 01:07 next collapse
bstix@feddit.dk on 02 Jul 08:10 collapse

Try this page if you want to read more about it:

erich-friedman.github.io/papers/…/squares.html

FelixCress@lemmy.world on 02 Jul 08:42 collapse

Thank you, that’s very helpful - unlike cretins downvoting me for asking a question.

Upvoted.

SkyeStarfall@lemmy.blahaj.zone on 02 Jul 10:21 collapse

That’s because when you just type “source?” and nothing else people perceive it as you challenging/denying the claim in a slightly hostile manner

Klear@sh.itjust.works on 02 Jul 10:45 collapse

Thankfully the perceived hostility was then dispelled with a followup comment calling people cretins.

…wait.

tiramichu@sh.itjust.works on 01 Jul 18:26 next collapse

These categories of geometric problem are ridiculously difficult to find the definitive perfect solution for, which is exactly why people have been grinding on them for decades, and mathematicians can’t say any more than “it’s the best one found so far

For this particular problem the diagram isn’t answering “the most efficient way to pack some particular square” but “what is the smallest square that can fit 17 unit-sized (1x1) squares inside it” - with the answer here being 4.675 unit length per side.

Trivially for 16 squares they would fit inside a grid of 4x4 perfectly, with four squares on each row, nice and tidy. To fit just one more square we could size the container up to 5x5, and it would remain nice and tidy, but there is then obviously a lot of empty space, which suggests the solution must be in-between. But if the solution is in between, then some squares must start going slanted to enable the outer square to reduce in size, as it is only by doing this we can utilise unfilled gaps to save space by poking the corners of other squares into them.

So, we can’t answer what the optimal solution exactly is, or prove none is better than this, but we can certainly demonstrate that the solution is going to be very ugly and messy.

Another similar (but less ugly) geometric problem is the moving sofa problem which has again seen small iterations over a long period of time.

cyrano@lemmy.dbzer0.com on 01 Jul 19:09 next collapse

Thanks for the explanation

DozensOfDonner@mander.xyz on 01 Jul 19:28 next collapse

Lol, the ambidextrous sofa. It’s a butt plug.

ouRKaoS@lemmy.today on 01 Jul 20:08 next collapse

For two!

Rusty@lemmy.ca on 01 Jul 23:36 collapse

Now I want to rewatch Requiem for a dream.

ouRKaoS@lemmy.today on 02 Jul 00:07 collapse

Requiem is the best movie that I’ve only wanted to watch once.

CascadianGiraffe@lemmy.world on 01 Jul 21:59 collapse

It’s also a great name for a cover band.

Butt rock covers of gospel songs perhaps?

blackbrook@mander.xyz on 01 Jul 23:03 next collapse

All this should tell us is that we have a strong irrational preference for right angles being aligned with each other.

DominatorX1@thelemmy.club on 02 Jul 16:21 collapse

We have an interpreter in our head. It maps and makes sense of the mysterious whatever. Some of it cultural, some biological. It is vast. There might not even be things and space.

blackbrook@mander.xyz on 02 Jul 19:08 collapse

Well yes, and what it means for “there to be things” is a whole discussion in itself. But the concepts of space and time are rather deep and fundamental (to our mental models regardless of how or if that maps to objective reality). The preference for right angles is much less fundamental and we can see past and get over it.

DominatorX1@thelemmy.club on 02 Jul 19:11 collapse

My point is, when we study our preference for right angles, what we’re studying is the interpreter. It has quirks.

DominatorX1@thelemmy.club on 02 Jul 13:10 collapse

For A problem like this. If I was going to do it with an algorithm I would just place shapes at random locations and orientations a trillion times.

It would be much easier with a discreet tile type system of course

GenderNeutralBro@lemmy.sdf.org on 01 Jul 18:29 next collapse

It’s not necessarily the most efficient, but it’s the best guess we have. This is largely done by trial and error. There is no hard proof or surefire way to calculate optimal arrangements; this is just the best that anyone’s come up with so far.

It’s sort of like chess. Using computers, we can analyze moves and games at a very advanced level, but we still haven’t “solved” chess, and we can’t determine whether a game or move is perfect in general. There’s no formula to solve it without exhaustively searching through every possible move, which would take more time than the universe has existed, even with our most powerful computers.

Perhaps someday, someone will figure out a way to prove this mathematically.

woodenghost@hexbear.net on 01 Jul 19:32 collapse

They proved it for n=5 and 10.

exasperation@lemmy.dbzer0.com on 01 Jul 19:58 collapse

And the solutions we have for 5 or 10 appear elegant: perfect 45° angles, symmetry in the packed arrangement.

5 and 10 are interesting because they are one larger than a square number (2^2 and 3^2 respectively). So one might naively assume that the same category of solution could fit 4^2 + 1, where you just take the extra square and try to fit it in a vertical gap and a horizontal gap of exactly the right size to fit a square rotated 45°.

But no, 17 is 4^2 + 1 and this ugly abomination is proven to be more efficient.

a_party_german@hexbear.net on 01 Jul 18:34 next collapse

It’s a problem about minimizing the side length of the outer rectangle in order to fit rectangles of side length 1 into it.

It’s somehow the most efficient way for 17 rectangles because math.

These are the solutions for the numbers next to 17:

<img alt="" src="https://hexbear.net/pictrs/image/ee3a8fe0-2c61-4853-8af4-aa9cf20f2cfa.png">

red_bull_of_juarez@lemmy.dbzer0.com on 01 Jul 18:58 collapse

It crams the most boxes into the given square. If you take the seven angled boxes out and put them back in an orderly fashion, I think you can fit six of them. The last one won’t fit. If you angle them, this is apparently the best solution.

What I wonder is if this has any practical applications.

7bicycles@hexbear.net on 01 Jul 19:33 next collapse

yeah it vindicates my approach of packing stuff via just throwing it in there. no I’m not lazy and disorderly, this is optimal cargo space usage

fox@hexbear.net on 01 Jul 20:19 collapse

There’s very likely applications in algorithms that try to maximize resource usage while minimizing cost

Serinus@lemmy.world on 01 Jul 18:17 next collapse

With straight diagonal lines.

<img alt="" src="https://lemmy.world/pictrs/image/93d9b6ad-78fc-4d3b-9637-1dd17d64f9df.png">

davidgro@lemmy.world on 01 Jul 19:04 next collapse

Why are there gaps on either side of the upper-right square? Seems like shoving those closed (like the OP image) would allow a little more twist on the center squares.

superb@lemmy.blahaj.zone on 01 Jul 19:14 next collapse

I think this diagram is less accurate. The original picture doesn’t have that gap

Serinus@lemmy.world on 01 Jul 19:20 next collapse

You have a point. That’s obnoxious. I just wanted straight lines. I’ll see if I can find another.

Serinus@lemmy.world on 01 Jul 19:22 next collapse
1rre@discuss.tchncs.de on 02 Jul 00:32 collapse

there’s a gap on both, just in different places and you can get from one to the other just by sliding. The constraints are elsewhere so wouldn’t allow you to twist.

davidgro@lemmy.world on 02 Jul 01:33 collapse

Oh, I see it now. That makes sense.

bleistift2@sopuli.xyz on 01 Jul 19:52 collapse

Homophobe!

pyre@lemmy.world on 02 Jul 01:10 collapse

hey it’s no longer June, homophobia is back on the menu

a_party_german@hexbear.net on 01 Jul 18:18 next collapse

https://kingbird.myphotos.cc/packing/squares_in_squares.html

<img alt="" src="https://hexbear.net/pictrs/image/4e473313-a9af-4ba5-8633-af217a3963d0.png">

Mathematics has played us for absolute fools

avattar@lemmy.sdf.org on 02 Jul 01:57 next collapse

If you can put the diagonal squares from the 17 solution in a 2-3-2 configuration, I can almost see a pattern. I wonder what other configurations between 17 and 132 have a similar solution?

WorldsDumbestMan@lemmy.today on 02 Jul 19:21 collapse

Why can’t it be stacked up normally? I don’t understand.

bilb@lemmy.ml on 03 Jul 00:29 collapse

You could arrange them that way, but the goal is to find the way to pack the small squares in a way that results in the smallest possible outer square. In the solution shown, the length of one side of the outer square is just a bit smaller than 12. If you pack them normally, the length would be larger than exactly 12. (1 = the length of one side of the smaller squares.)

Grandwolf319@sh.itjust.works on 01 Jul 18:19 next collapse

But there are 7 squares in the middle with 10 around it, surely that counts for something

fargeol@lemmy.world on 01 Jul 18:25 next collapse

Bees seeing this: “OK, screw it, we’re making hexagons!”

ILikeBoobies@lemmy.ca on 01 Jul 21:13 next collapse

Bestagons*

EpicFailGuy@lemmy.world on 01 Jul 23:20 collapse

Texagons

raltoid@lemmy.world on 02 Jul 00:10 next collapse

Fun fact: Bees actually make round holes, the hexagon shape forms as the wax dries.

starman2112@sh.itjust.works on 02 Jul 18:12 next collapse

But fear not, bees are still smart! Mfs can do math!

raltoid@lemmy.world on 05 Jul 16:44 collapse

Not only can they do math, they can fully percieve time

FiskFisk33@startrek.website on 03 Jul 08:11 collapse

come on now, let them cook, trust the process

brown567@sh.itjust.works on 02 Jul 00:57 collapse

4-dimensional bees make rhombic dodecahedrons

nebulaone@lemmy.world on 01 Jul 18:41 next collapse

To be fair, the large square can not be cleanly divided by the smaller square(s). Seems obvious to most people, but I didn’t get it at first.

In other words: The size relation of the squares makes this weird solution the most efficient (yet discovered).

Edit: nvm, I am just an idiot.

<img alt="" src="https://lemmy.world/pictrs/image/762a4ab2-2eaf-4bf8-8e68-03bfc7613e90.gif">

Zwiebel@feddit.org on 01 Jul 21:51 collapse

The outer square is not given or fixed, it is the result of the arrangement inside. You pack the squares as tightly as you can and that then results in an enclosing square of some size. If someone finds a better arrangement the outer square will become smaller

Melatonin@lemmy.dbzer0.com on 01 Jul 18:58 next collapse

I love when I have to do research just to understand the question being asked.

Just kidding, I don’t really love that.

RustyNova@lemmy.world on 01 Jul 19:39 next collapse

Not complete without the sounds

Zerush@lemmy.ml on 01 Jul 19:51 next collapse

It is one prove more, why it is important to think literally out of the box. But too much people of this type

i.vgy.me/UVG654.gif

schnokobaer@feddit.org on 01 Jul 20:15 next collapse

That tiny gap on the right is killing me

friendly_ghost@beehaw.org on 02 Jul 05:23 collapse

That’s my favorite part 😆

Psaldorn@lemmy.world on 01 Jul 20:52 next collapse

You may not like it but this is what peak performance looks like.

Lionel@endlesstalk.org on 01 Jul 21:07 next collapse

Unless I’m wrong, it’s not the most efficient use of space but if you impose the square shape restriction, it is.

cooligula@sh.itjust.works on 01 Jul 22:15 collapse

That’s what he said. Pack 17 squares into a square

Lionel@endlesstalk.org on 02 Jul 00:26 collapse

My point was that it doesn’t break my brain at all when considering there’s an artificial constraint that affects efficiency and there’s just not going to be a perfect solution for every number of squares when you consider the problem for more than just 17 squares

treesapx@lemmy.world on 02 Jul 01:10 collapse

That’s what makes it a puzzle. That’s what a puzzle is.

JoeTheSane@lemmy.world on 01 Jul 22:39 next collapse

I hate this so much

Squalia@sh.itjust.works on 01 Jul 22:40 next collapse

Here’s a much more elegant solution for 17

<img alt="" src="https://sh.itjust.works/pictrs/image/32b9bf97-9af0-4c05-b98e-f7fc101e1b8c.png">

peteypete420@sh.itjust.works on 02 Jul 01:26 next collapse

Is this confirmed? Like yea the picture looks legit, but anybody do this with physical blocks or at least something other than ms paint?

crmsnbleyd@sopuli.xyz on 02 Jul 09:36 next collapse

Proof via “just look at it”

CheeseNoodle@lemmy.world on 02 Jul 09:44 next collapse

Visual proofs can be deceptive, e.g. the infinite chocolate bar.

peteypete420@sh.itjust.works on 03 Jul 00:18 collapse

I feel like the pixalation on the rotated squares is enough to say this picture is not proof.

Again I am not saying they are wrong, just that it would be extremely easy make a picture where it looks like all the squares are all the same size.

crmsnbleyd@sopuli.xyz on 03 Jul 06:25 collapse

I was joking about the proof but there’s a non-pixelated version in the comments here

deaf_fish@midwest.social on 02 Jul 12:30 collapse

It is confirmed. I don’t understand it very well, but I think this video is pretty decent at explaining it.

youtu.be/RQH5HBkVtgM

The proof is done with raw numbers and geometry so doing it with physical objects would be worse, even the MS paint is a bad way to present it but it’s easier on the eyes than just numbers.

Mathematicians would be very excited if you could find a better way to pack them such that they can be bigger.

So it’s not like there is no way to improve it. It’s just that we haven’t found it yet.

TimewornTraveler@lemmy.dbzer0.com on 02 Jul 11:31 next collapse

the line of man is straight ; the line of god is crooked

stop quoting Nietzsche you fucking fools

SpongyAneurysm@feddit.org on 02 Jul 14:01 next collapse

Now, canwe have fractals built from this?

mEEGal@lemmy.world on 02 Jul 16:01 next collapse

“fractal” just means “broken-looking” (as in “fracture”). see Benoît Mandelbrot’s original book on this

I assume you mean “nice looking self-replicating pattern”, which you can easily obtain by replacing each square by the whole picture over and over again

psud@aussie.zone on 03 Jul 18:13 collapse

Fractal might have meant that when Mandelbrot coined the name, but that is not what it means now.

Lemmisaur@lemmy.zip on 02 Jul 22:07 collapse

Say hello to the creation! .-D

<img alt="" src="https://lemmy.zip/pictrs/image/7f27470e-96da-4501-9eba-38d357642506.webp">

(Don’t ask about the glowing thing, just don’t let it touch your eyes.)

SpongyAneurysm@feddit.org on 02 Jul 22:31 collapse

Good job. It’skinda what I expected, except for the glow. But I won’t ask about that.

BowtiesAreCool@lemmy.world on 02 Jul 22:51 collapse

The glow is actually just a natural biproduct of the sheer power of the sq1ua7re

bitjunkie@lemmy.world on 02 Jul 19:01 next collapse

It’s important to note that while this seems counterintuitive, it’s only the most efficient because the small squares’ side length is not a perfect divisor of the large square’s.

jeff@programming.dev on 02 Jul 19:21 next collapse

What? No. The divisibility of the side lengths have nothing to do with this.

The problem is what’s the smallest square that can contain 17 identical squares. If there were 16 squares it would be simply 4x4.

Natanael@infosec.pub on 02 Jul 19:42 next collapse

He’s saying the same thing. Because it’s not an integer power of 2 you can’t have a integer square solution. Thus the densest packing puts some boxes diagonally.

bitjunkie@lemmy.world on 03 Jul 15:31 collapse

And the next perfect divisor one that would hold all the ones in the OP pic would be 5x5. 25 > 17, last I checked.

sga@lemmings.world on 02 Jul 19:24 next collapse

this is regardless of that. The meme explains it a bit wierdly, but we start with 17 squares, and try to find most efficient packing, and outer square’s size is determined by this packing.

curiousaur@reddthat.com on 03 Jul 06:38 collapse

Did you comment this because you think the people here are stupid?

dream_weasel@sh.itjust.works on 03 Jul 11:20 next collapse

Bro, the people here, like the people everywhere, ARE stupid.

It’s always better to be explicit. I’m one of the stupid people who learned some things reading the comments here and I’ve got a doctoral degree in aero astro engineering.

bitjunkie@lemmy.world on 03 Jul 15:37 collapse
NigelFrobisher@aussie.zone on 03 Jul 07:43 next collapse

Why doesn’t he just make the square bigger? That’d be more efficient.

EddoWagt@feddit.nl on 03 Jul 10:43 collapse

That’s not more efficient because the big square is bigger

JackbyDev@programming.dev on 03 Jul 20:46 next collapse

I think people have a hard time wrapping their heads around it because it’s very rare to have this sort of problem in the real world. Typically you have a specific size container and need to arrange things in it. You usually don’t get to pick an arbitrary size container or area for storage. Even if you for something like shipping, you’d probably want to break this into a 4x4 and a separate single box to better fit with other things being shipped as well. Or if it is storage you’d want to be able to see the sides or tops. Plus you have 3 dimensions to work with on the real world.

NigelFrobisher@aussie.zone on 03 Jul 22:31 collapse

See, that’s the problem with people nowadays?They want to minimalise everything.

They should just slow down and breathe.

Admetus@sopuli.xyz on 04 Jul 12:20 collapse

Initially I thought 4x4 square but this is a square of 4.675 sides. Reasonable. Clever maths though.