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New sphere-packing record stems from an unexpected source

quantamagazine.org

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Re: New sphere-packing record stems from an unexpected source

#191

Post by somethingsome »

dkarl wrote: post #12
clickety_clack wrote: post #7

I have trouble explaining to my parents how my job is a real thing. I can only imagine trying to explain ‘I study shapes, but only ones that don’t jut inwards’.

I've found it's best to explain my job using unintelligible jargon. There are three choices, really: You can give a quick explanation in terms they understand, which makes your job sound easy and makes them wonder how anybody gets paid to do it. You can explain what you do and why it's important in terms they understand, but it'll take so long they'll get bored and wish they hadn't asked. Or you can give a quick expl…

I work at many levels and on many different projects, so usually I give a very simple explanation of the most interesting one, in very simple terms, and add, 'that's a small part of my job'.

People that are interested can ask either to give more details on what I have explained, or what about the rest. If they are not interested, they say something and I usually ask what about them, no hard feelings.

It works smoothly for me.

Re: New sphere-packing record stems from an unexpected source

#192

Post by gilleain »

dghughes wrote: post #179
falcor84 wrote: post #177

Earlier quoted context omitted.

and I'm reminded of this xkcd about the pattern of lights: https://xkcd.com/722/

I've often thought how my cat must think I am insane. I sit in from of a medium-sized glowing rectangle, I occasionally look at a small glowing rectangle, then in the evening stare at a really large glowing rectangle.

Other options are :

1) Cats do not really think that much about us at all, except for thoughts like - "oh no! it's about to attack! wait no, it's fine, relax..." or "will it feed me if I shout at it?" or "it's sitting down, perhaps I feel like sitting on it"

2) Their thoughts about us revolve around our weird lack of fur, the strange way we never clean ourselves by licking, and how bad we are at catching small animals to eat.

Re: New sphere-packing record stems from an unexpected source

#194

Post by tsunamifury »

paintbox wrote: post #173
tsunamifury wrote: post #138

Why does this seem incredibly obvious to me?

Probably because you overestimate your knowledge.

This doesn’t follow at all. In fact it’s an admission of not understanding. Did you struggle to figure that out?

Re: New sphere-packing record stems from an unexpected source

#195

Post by [deleted] »

shakna wrote: post #165
tharkun__ wrote: post #158

Earlier quoted context omitted.

It seems like dumbing it down or immediate heavy jargon with people you don't know are just both equally bad options. What's wrong with asking their level of experience with the topic? Sure, with parents you know the level. I'm talking "other strangers" you meet outside of a context where some familiarity would be expected (like at a conference one might assume at least some form of knowledge and ability to just have…

> What's wrong with asking their level of experience with the topic? Nothing. That's precisely the point. Giving a wall of jargon, isn't asking if someone is familiar.

[deleted]

Re: New sphere-packing record stems from an unexpected source

#196

Post by SubiculumCode »

kazinator wrote: post #145
pseudocomposer wrote: post #50

Earlier quoted context omitted.

When I meet people who immediately use hyper-specific jargon with strangers, I either distrust them, or assume they’re not emotionally intelligent (because it’s a choice demonstrates little respect for the person they’re addressing). It also projects that they may be compensating for some emotional insecurity on their own end, trying to assert intellectual “superiority” in some way. The first option (explaining thing…

> Hell, most “dumb” people understand, recognize, and appreciate this ability. That remark reminds me of all the praise heaped by commenters onto videos that explain complex topics glibly. Like "I've been struggling to understand this for 20 years, until this video", etc.

Except, when, which is often the case in mathematics, there is actual way to reduce the complexity of a topic to be understandable to most people without sacrificing veracity for digestible half truths.

Re: New sphere-packing record stems from an unexpected source

#197

Post by SubiculumCode »

doubledamio wrote: post #153
thorum wrote: post #26

Earlier quoted context omitted.

Some ideas are too complex to explain accurately in simple terms. You can give someone a simple explanation of quantum chromodynamics and have them walk away feeling like they learned something, but only by glossing over or misrepresenting critical details. You’d basically just be lying to them.

To me, every profession—from software engineering to farming—has its complexities, yet most professionals can explain what they do in clear terms. When academics say they can’t offer a basic explanation, it often feels like an attempt to protect their status or avoid the effort—if not a kind of intellectual arrogance. Yes, the topics are challenging—you don’t need to throw in quantum buzzwords to convince me—but simp…

I encounter this idea too much..the idea that complex topics can always be explained in a way to make everyone understand it...and that just isn't true. There is usually a point on any topic where further reduction/compression is no longer lossless. Yes, I think the analogy of image compression works pretty well. Lossless compression can only go so far. Further reduction introduces loss, but the image may still be understandable, but at a certain point, the loss from compression prevents understanding of the image, and may even mislead (Is that a bear, or uncle Robert?).

Re: New sphere-packing record stems from an unexpected source

#198

Post by shkkmo »

jacobolus wrote: post #122
shkkmo wrote: post #85

Earlier quoted context omitted.

> For some dimensions the densest known irregular packing is denser than the densest known regular packing. I thought that was one of the important results from the paper, the most efficient packing for all dimensions is symmetrical again and this increase was significant enough it seems unlikely that existing non-symmetrical methods will be able to beat it.

Perhaps so. If you hunt you might be able to find a new summary table somewhere (I didn't find one in a very brief skim around). My impression was this new work was more about high-dimensional cases than necessary a dramatic improvement for every low-dimensional example.

I mean, it says it directly in the article:

> His result has also revived a debate in the field about the nature of the optimal packing in arbitrarily high dimensions. For a while, mathematicians considered highly symmetric, lattice-based packings to be the best way to arrange spheres as densely as possible. But in 2023, a team found a packing that didn’t rely neatly on a repeating lattice; before Klartag’s result, it was the record to beat. Some mathematicians saw it as evidence that more disorder was needed in the search for an optimal sphere packing.

Clearly, this improvement doesn't apply to the few dimensions for which we already proven optimal packing, but the proof was general.

Re: New sphere-packing record stems from an unexpected source

#199

Post by kibwen »

sota_pop wrote: post #184
asboans wrote: post #169

Earlier quoted context omitted.

“Fill less than 1% of its space” becomes a very counter intuitive statement in any case when discussing high dimensions. If you consider a unit n-sphere bounded by a unit cube, the fraction occupied by the sphere vanishes for high n. (Aside: Strangely, the relationship is non monotonic and is actually maximal for n=6). For n=100 the volume of the unit 100-sphere is around 10^-40 (and you certainly cannot fit a second…

I’m familiar with this example of hyper-geometry. Put more abstractly, my intuition always said something like “the volume of hyper geometric shapes becomes more distributed about their surface as the number of dimensions increases”.

There's a great 3blue1brown video that demonstrates this unintuitive result in a relatively intuitive way: https://youtube.com/watch?v=zwAD6dRSVyI

Re: New sphere-packing record stems from an unexpected source

#200

Post by lanstin »

dkarl wrote: post #12
clickety_clack wrote: post #7

I have trouble explaining to my parents how my job is a real thing. I can only imagine trying to explain ‘I study shapes, but only ones that don’t jut inwards’.

I've found it's best to explain my job using unintelligible jargon. There are three choices, really: You can give a quick explanation in terms they understand, which makes your job sound easy and makes them wonder how anybody gets paid to do it. You can explain what you do and why it's important in terms they understand, but it'll take so long they'll get bored and wish they hadn't asked. Or you can give a quick expl…

I think about things and then type in stuff that makes them work better.
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