wolframhydroxide
@wolframhydroxide@sh.itjust.works
- Comment on Just one more square bro 8 hours ago:
Ah, no, it’s that the more efficient packing takes up less space, so the less efficient square is actually slightly larger than the other, compared to the smaller squares.
If the smaller squares are identical in both sets, then the larger square in the less-efficient set will be slightly larger than the larger square in the more efficient set.
- Comment on Just one more square bro 10 hours ago:
Since a link to a wiki article does not an explanation make:
The optimal efficiency (zero interstitial space) is achieved when the ratio of the side length of the larger square to the sides of the shorter squares (called the “packing coefficient”) is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than the packing of n=17 given in the waffle iron, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equivalent to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, the waffle packing (represented by the orangutan) above is not perfectly efficient, leaving interstices. However, the packing coefficient of the suboptimal solution (represented by the girl) is actually 4.707, slightly further from sqrt(17), and thus less efficient, leaving greater wasted interstitial space.
- Comment on I want to replay Skyrim but 1 day ago:
Did you try “beyond skyrim: bruma”? Its only one province of the planned entirety of tamriel, but that was many excellent hours of exploration, and it feels like the plotlines are really going somewhere, whenever they get finished with the rest of cyrodiil. Shame there are some places that feel unfinished (because they involve other provinces), but that mystery made it more intriguing, in my opinion.
Also, it has a soundtrack that I actually like more than the original skyrim soundtrack, and that is saying something.
- Comment on Just one more square bro 1 day ago:
Specifically, the optimal area side length of the larger square for any integer n is the square root of n. The closer your larger side length gets to sqrt(n), the more efficient your packing.
- Comment on Just one more square bro 1 day ago:
I was just answering your question of why someone would want to arrange a prime number of squares. The waffle is clearly a meme.
- Comment on Harvard Places Math Professor Martin Nowak on Paid Administrative Leave Over Epstein Ties 1 day ago:
Precisely. Wilhoit’s Law
- Comment on Just one more square bro 1 day ago:
That candy crush story is, as the commenter said, a lie. I don’t know why they would suggest that adding on a lie is in any way good, since we know that this packing was discovered in the late 1990s. It’s on the wikipedia article for square packing (with sources) but I don’t feel like looking it up again.
- Comment on Harvard Places Math Professor Martin Nowak on Paid Administrative Leave Over Epstein Ties 1 day ago:
I would still say it was a country of laws, but that is not the same thing as a country of justice.
- Comment on Harvard Places Math Professor Martin Nowak on Paid Administrative Leave Over Epstein Ties 2 days ago:
The united states has not been a society of laws since 2017, and anyone telling you otherwise is either blind, stupid, lying, or some combination of the three
- Comment on Just one more square bro 2 days ago:
I mean, the actual answer is severalfold: “sometimes, when you need to fill a space, you don’t end up with simple compound numbers of identical packages” is one,but really, it’s a problem in mathematics which, were we to have a general solution to find the most efficient method of packing n objects with identical properties into the smallest area, we would be able to more effectively predict natural structures, including predicting things like protein folding, which is a huge area of medical research.
- Comment on Honk 2 days ago:
Don’t forget aye-aye
- Comment on Honk 2 days ago:
Olm
- Comment on Just one more square bro 2 days ago:
Precisely. That’s why I wrote the parenthetical about the greater efficiency of 16 as a perfect square. As the other commenter pointed out, this is a meme.
- Comment on Just one more square bro 2 days ago:
Exactly. It is the length of the side of the bigger square, relative to the sides of the smaller identical squares.
- Comment on Just one more square bro 2 days ago:
For the uninitiated: this is the current most - efficient method found of packing 17 unit squares inside another square. You may not like it, but this is what peak efficiency looks like.
(Of course, 16 squares has a packing coefficient of 4, compared to this arrangement’s 4.675, so this is just what peak efficiency looks like for 17 squares)
- Comment on Little scritchy 5 days ago:
IIRC, this is from the worst case scenario survival handbook, but has been edited. This is a method of fishing, and you’re supposed to hook the gills like that.
- Comment on No More Neutral ⚛ 1 week ago:
“Wish granted. Electrons, being a human construct, have now always been defined slightly differently. Just as Franklin got the polarity wrong and you still use his labeling system, J.J. Thompson will now have fundamentally misunderstood the nature of the electron, leading to a cascading assumption by later scientists that the number of electrons in a neutral atom is one greater than the number of protons. Even though this completely breaks the math of quantum mechanics, everyone is just used to subtracting one at this point. This is a significantly worse world, and as a bonus, every physicist who sees you will now be preternaturally certain that you are personally to blame. You’re welcome.”
- Comment on Liminal Space 1 week ago:
Science didn’t give us the guillotine, no matter which scientific method or forbear you’re using to determine scientific nature. At best, engineering gave us the guillotine, but I rather doubt there was any actual engineering design going on when they first made the Halifax Gibbet.
- Comment on Small little shenanigans 1 week ago:
All excellent points. I concede to your deeper consideration.
- Comment on Small little shenanigans 1 week ago:
Zinc has a characteristic blue tint and oxidizes to white.
- Comment on Small little shenanigans 1 week ago:
Except that they’re clearly zinc shot. I think the poster made a funny without realising that they aren’t steel.
- Comment on Small little shenanigans 1 week ago:
These aren’t bearing balls. They’re zinc shot.
- Comment on Small little shenanigans 1 week ago:
And that’s zinc shot.
- Comment on Small little shenanigans 1 week ago:
But that’s zinc shot… It doesn’t even look like steel. It shouldn’t be attracted to a magnet.
- Comment on Say no to BAYES 2 weeks ago:
I believe that they contribute to understanding, because human minds are wired to engage with stories. If your chemistry teacher was worth their salt, they’d teach you Gay-Lussac’s law by telling you about how, when the hot air balloon was first invented, Gay-Lussac was seen as mad by all of the older scientists for wanting to go up in one. Well, not only did he nearly die making measurements, he also showed that, at higher altitudes, there was lower pressure and lower temperature. Then, your chemistry teacher should pull out a spray-can of keyboard cleaner, invert it, spray the liquid into a beaker, and let everyone feel the adiabatic temperature depression from expansion.
- Comment on Say no to BAYES 2 weeks ago:
Quality shit post, but the naming thing is true of virtually everything in mathematics, with good reason, because otherwise you’d just be talking about “that slightly different combination of arbitrary letters by which we do something very similar, but measurably distinct, from the use cases of the other three equations like it”.
See:
- Pythagorean theorem (geometry)
- Dijkstra’s Algorithm (graph theory)
- Fermat’s last theorem (number theory)
- Peano axioms (formal logic)
- For that matter, the word “Algorithm” comes from the Latinised name of the dude who invented algebra, and the word “algebra” is just an overly a truncated version of the title of that dude’s book.
This is also doubly true in science, where there are 5000 different “laws” and “theorems” surrounding something like gas behaviour, so at some point, you have to differentiate them based on their history, rather than what they do. Hence “Charles’ law”, “Boyle’s law”, “Gay-Lussac’s law”, “Bernoulli’s principle”, the “navier-stokes theorem”, etc…
- Comment on 2 kool 4 skool 2 weeks ago:
And, of course, “Delta P”:
- Comment on vibes based astronomy 2 weeks ago:
The moon isn’t in this image. You’re looking at mercury.
- Comment on vibes based astronomy 2 weeks ago:
Neptune’s great dark spot is clearly visible, and thus immediately identifies it as such.
- Comment on it's just science 2 weeks ago:
Well, all you need to do is travel at a significant fraction of the speed of light. That will let you fast-forward the rest of non-relativistic reality. Then it’s just a matter of slowing down again.