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wolframhydroxide

@ wolframhydroxide @sh.itjust.works

Posts
3
Comments
582
Joined
2 yr. ago

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  • 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 bigger than the larger square in the more efficient set.

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  • 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 (let's call it 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.

  • What's a TV series that you really, really liked and would enthusiastically recommend?

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  • I haven't! It's shockingly tough to find anywhere

  • What's a TV series that you really, really liked and would enthusiastically recommend?

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  • I agree. Admittedly, NDT does say "keep in mind, Bruno didn't have any evidence for his claims. He was not a scientist." But still, that scene came off as somewhat less appropriate. I think that, on balance, it's about showing that entrenched systems of power and authority have an active disincentive to take progressive stances, or even allow radical voices to exist. Even if Bruno did have evidence on his side, the church still would have burned him. Were I making that episode, I would have made it more clear that there were good reasons for him being laughed out of Cambridge. He had no evidence, but the scientists' arguments highlighted were mostly arguments from authority "but Aristotle said", or "but the bible says", rather than demands for evidence and argumentation. Even scientists can fall to the trap of entrenched ideas and authority.

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  • Specifically, the optimal side length of the larger square for any natural number of smaller squares 'n' is the square root of n (assuming the smaller squares are unit squares). The closer your larger side length gets to sqrt(n), the more efficient your packing.

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  • I was just answering your question of why someone would want to arrange a prime number of squares. The waffle is clearly a meme.

  • Science

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  • Much like monarch butterflies, those are actually two separate species. The species of Curling Stone which returns to Scotland is actually on the IUCN Red List.

  • What's a TV series that you really, really liked and would enthusiastically recommend?

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  • Cosmos (the NDT series) - my overall favourite series. If you like Cosmos a lot, consider watching the archives of the Royal Institution's Christmas lectures

    The Good Place - Existential Philosophy and Ontology 101, the TV Series. Hilarious, dramatic, and one of the most touching stories I've ever encountered

    Person of Interest - Basically "What You'll Learn on Lemmy: The TV Series", about all of the wondrous horrors of the digital surveillance state in which we all live.

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  • Precisely. Wilhoit's Law

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  • 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.

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  • I would still say it was a country of laws, but that is not the same thing as a country of justice.

  • He probably just forgot

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  • Downvote for AI on principle, even if the office space reference is appropriate.

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  • The united states has not been a society of laws since at least 2020, and anyone telling you otherwise is either blind, stupid, lying, or some combination of the three

    (I count the supreme court overturning settled law and all branches of government abetting treason as the actual final point of breakdown of the rule of law in this country)

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  • 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. Simple, seemingly inapplicable cases can often be generalised to more specific cases, and that's how you get the entire field of applied math, as well as most of scientific and engineering modeling

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  • 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. This is only the most efficient packing method for 17 squares. It's the packing efficiency equivalent of the spinal tap "this one goes to 11" quote.

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  • Exactly. It is the length of the side of the bigger square, relative to the sides of the smaller identical squares.

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  • 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)

    Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square's side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when 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 this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions "is it possible to prove that a given packing is the most efficient possible packing for that value of n" and "does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?"

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  • 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.

  • TIL pediatricians are being used as a great source of antibodies.

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  • At least one of us is still wearing a p100 respirator every day...