[HN Gopher] New sphere-packing record stems from an unexpected s...
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New sphere-packing record stems from an unexpected source
Author : pseudolus
Score : 177 points
Date : 2025-07-07 18:19 UTC (4 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| tomrod wrote:
| Very cool. Sphere packing comes up in a lot of contexts in
| applied problems. Looking forward to reviewing the paper.
| readthenotes1 wrote:
| Earlier today there was an article about neanderthal's rendering
| fat.
|
| The comments pointed out that anthropologist did not know that
| boiling was possible before the invention of pottery. Another
| comment pointed out that science teachers knew that it was
| possible because that was something they would do in class.
|
| Final comment was about how people ReDiscover things in different
| fields - - like the trapezoidal rule for integration being
| discovered by someone studying glucose.
|
| This is just yet another example of how bringing expertise from a
| different area can help.
| ahns wrote:
| The aforementioned trapezoidal rule (Tai's method):
| https://diabetesjournals.org/care/article/17/2/152/17985/A-M...
| pinkmuffinere wrote:
| I haven't read that thread, but I don't believe that
| anthropologists thought boiling was impossible before the
| invention of pottery. Here's one youtube video that demos a
| method for survival scenarios, I'm sure there are many others:
| https://www.youtube.com/shorts/0zun_UxO2vU. I know I don't have
| the context, but unless there are sources for the remarkable
| claim, it just doesn't make sense. It doesn't pass "the laugh
| test"
| knicholes wrote:
| If only there were some sort of expert in everything that we
| could ask, it could pull expertise from all various sciences
| into one response. I think everyone just needs to start using
| LLMs.
| theteapot wrote:
| Noob question: Is the optimal sphere packing correlated with a
| regular lattice? I.e. that's the case for 2D,3D right? If so does
| this extend to ND?
| fiforpg wrote:
| Not necessarily--in 3d there are uncountably many non-lattice
| packings. They all have the same density as the FCC lattice
| though. To construct these packings, shift horizontal layers of
| FCC horizontally with respect to each other.
|
| It is conjectured that in higher dimensions, the densest
| packing is always non-lattice. The rationale being that there
| is just not enough symmetry in such spaces.
| Jaxan wrote:
| Well these new results (denser packings than before) are
| regular lattices which might suggest that the optimal packing
| could be a lattice. (Until the record is broken again by a
| irregular packing ;-)
| jacobolus wrote:
| Besides 2 and 3 dimensions, it's also the case in 8 and 24
| dimensions (The E8 lattice and Leech lattice, respectively).
| These were proven in 2017 by Maryna Viazovska, with some
| collaborators for the second paper.
| https://doi.org/10.4007/annals.2017.185.3.7
| https://doi.org/10.4007/annals.2017.185.3.8
|
| See also
| https://www.ams.org/journals/notices/201702/rnoti-p102.pdf
|
| For other dimensions, this is an open question; it seems
| unlikely to be true in general. For some dimensions the densest
| known irregular packing is denser than the densest known
| regular packing.
| clickety_clack wrote:
| 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'.
| dkarl wrote:
| 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 explanation using jargon that they
| don't understand, which will leave them bored but impressed,
| which is the best of the bad options.
| tomrod wrote:
| I choose the worst of all options and go into excruciating
| detail.
| bell-cot wrote:
| Thereby minimizing how often anyone asks you - which makes
| that the best long-term option?
| EvanAnderson wrote:
| That would only work if you were getting repeat inquiries
| from the same person. Otherwise it's just the longest
| possible option for each new inquiry.
|
| I always opt for excruciating detail because it's what I
| enjoy the most.
| bell-cot wrote:
| > That would only work if ...
|
| Sounds like none of the people you answered, in
| excruciating detail, cared to warn other people about
| what would happen if they asked you.
| EvanAnderson wrote:
| Ahh! I didn't think about the word-of-mouth. Good call.
| 8n4vidtmkvmk wrote:
| My wife's eyes just gloss over. Maybe I should try with
| some other test subjects.
| tomrod wrote:
| One of the classical assessments in strategic behavior is
| "be worse than your roommates at chores so they do them,
| but not so bad they kick you to the curb."
| doubledamio wrote:
| If you can't explain something in simple terms, you don't
| understand it well enough
| thorum wrote:
| 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.
| ars wrote:
| There's nothing wrong with that:
| https://en.wikipedia.org/wiki/Lie-to-children
| pests wrote:
| Reminds me of the old videos on the Mill CPU
| architecture. There is multi hour long video about "the
| belt", a primary concept in understanding the Mill
| architecture and instruction scheduling. It's portrayed
| in the slides as an actual belt with a queue of items
| about to be processed, etc.
|
| Only in the end to reveal the belt is truely
| conceptualized and does not formally exist. The belt is
| an accurate visual representation and teaching tool, but
| the actual mechanics emerge from data latches and the
| timing of releasing the data, etc.
|
| I thought it was helpful.
| jiggawatts wrote:
| Quantum Mechanics is _the_ example of a subject where
| supposed experts don't really understand it either and
| hence can't explain it adequately.
|
| Also, it's hilarious to get comments like this voted down
| by _non-experts_ who assume this must be an outsider's
| uninformed point of view.
|
| I have a physics degree and I studied the origins and
| history of quantum mechanics. Its "founding fathers" all
| admitted that it's a bunch of guesswork and that the
| models we have are arbitrary and lack something essential
| needed for proper understanding.
| Angostura wrote:
| 'It's the study how the particles that make atoms
| interact... it's fiendishly complicated'
| mike_ivanov wrote:
| A horse is just a bunch of chemicals in a skin sack. Gee, I
| understand it!
| IncRnd wrote:
| Hmmmm, what might Feynman say about a horse?
|
| So, what's a horse? Well, you look at it: it's this big
| animal, standing on four legs, with muscles rippling
| under its skin, breathing steam into the cold air. And
| already -- that's amazing. Because somehow, inside that
| animal, grass gets turned into motion. Just grass! It
| eats plants, and then it runs like the wind.
|
| Now, let's dig deeper. You see those legs? Bones and
| tendons and muscles working like pulleys and levers -- a
| beautiful system of mechanical engineering, except it
| evolved all by itself, over millions of years. The hoof?
| That's a toe -- it's walking on its fingernail, basically
| -- modified for speed and power.
|
| And what about the brain? That horse is aware. It makes
| decisions. It gets scared, or curious. It remembers. It
| can learn. Inside that head is a network of neurons, just
| like yours, firing electricity and sending chemical
| messages. But it doesn't talk. So we don't know exactly
| what it thinks -- but we know it does think, in its own
| horselike way.
|
| The skin and hair? Cells growing in patterns, each one
| following instructions written in a long molecule called
| DNA. And where'd that come from? From the horse's parents
| -- and theirs, all the way back to a small, many-toed
| creature millions of years ago.
|
| So the horse -- it's not just a horse. It's a machine, a
| chemical plant, a thinking animal, a product of
| evolution, and a living example of how life organizes
| matter into something astonishing. And what's really
| amazing is, we're just scratching the surface. There's
| still so much we don't know. And that is the fun of it!
| perching_aix wrote:
| How simple? Simple to who?
|
| The quip you're referring to was meant to be inspirational.
| It doesn't pass even the slightest logical scrutiny when
| taken at its literal meaning. Please. (Apologies if this
| was just a reference without any further rhetorical intent
| though.)
|
| It's like claiming that hashes are unique fingerprints. No,
| they aren't, they mathematically cannot be. Or like
| claiming how movie or video game trailers should be
| "perfectly representative" - once again, by definition,
| they cannot be. It's trivial to see this.
| j7ake wrote:
| Not every subject has simple explanations.
| misnome wrote:
| And that's why Feynman was always happy to explain how
| magnets work!
| tomrod wrote:
| Simple terms need not be short terms.
| sdenton4 wrote:
| I kinda love doing the quick+easy explanation... And
| especially in professional contexts.
|
| "I teach computers what sounds different aminals make."
| imoreno wrote:
| >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.
|
| What is the problem with this?
|
| Most jobs, when simplified, sound like "anybody can do it". I
| think it's generally understood among adults who have been in
| the workforce that, no, in fact anybody cannot do it.
| pcthrowaway wrote:
| There is no problem with it, but I assume there are many
| people who will look upon you favourably if they think you
| do a highly skilled job. While many of us may not care to
| impress those people, there are certainly those who do
| (possibly people with similar attitudes who care more about
| validation from people who think like them)
|
| A somewhat ungenerous characterization of the attitude may
| be something like the Rocket Scientist vs Brain Surgeon
| sketch - https://www.youtube.com/watch?v=THNPmhBl-8I
|
| But we should also acknowledge that there's an entire
| culture built around valuing people and their time relative
| to one's perception of their "importance", that this
| culture can influence one's earning potential and
| acquisition of material possessions, and that many people
| do care about things like "seeming important" or moving
| upwards in this hierarchy as a result.
| bravesoul2 wrote:
| Or tell them about the bit of the job they understand. "I
| teach maths to adults".
| pseudocomposer wrote:
| 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 things simply) might make your
| job sound easy to a very small minority of _extremely_
| uneducated, under-stimulated people, who also have
| unaddressed insecurities around their own intelligence. But
| that's not most humans.
|
| Moderately-to-very intelligent people appreciate how
| difficult (and useful) it is to explain complex things
| simply. Hell, most "dumb" people understand, recognize, and
| appreciate this ability. Honestly, I think _not_ appreciating
| simple explanations indicates both low mathematical /logical
| and social/emotional intelligence. Which makes explaining
| things simply a useful filter for, well... people that I
| wouldn't get along with anyway.
|
| With all that said, I prefer to first explain my job in an
| "explain like I'm 5" style and, if the other party indicates
| interest, add detail and jargon, taking into account related
| concepts that may already be familiar to them. If you take
| _them_ into account, they won't get bored when you go into
| detail.
| Angostura wrote:
| The latter option always comes across as rude. It's a very
| clear 'piss off you insect'
| xorcist wrote:
| > You can give a quick explanation in terms they understand,
| which makes your job sound easy
|
| This is always the right answer. It is the only answer that
| respects the listener and contains a seed to further
| conversation.
| jvanderbot wrote:
| I don't see what's hard about threading the needle, or maybe
| I'm completely lacking in EQ
|
| "I'm a mathematician, I study how shapes fit together, which
| surprisingly, is being used for new methods of secure
| communication by so and so university, but I just love the
| math"
| dekhn wrote:
| At least in the case of sphere packing it's closely related to
| some core problems in information theory that helped make the
| Bell phone system so reliable.
|
| (not sure about convex shapes)
| binarymax wrote:
| "I'm an electron wizard. I write spells and magical constructs
| appear on the mirror slate"
| zem wrote:
| betjeman's delightful poem "executive" had a great humorous
| take on this:
|
| You ask me what it is I do. Well, actually, you know,
|
| I'm partly a liaison man, and partly P.R.O.
|
| Essentially, I integrate the current export drive.
|
| And basically I'm viable from ten o'clock till five.
| lawlessone wrote:
| shapes that exist on higher dimensions we can't mentally
| comprehend.
| Workaccount2 wrote:
| I have my own micro business where I make equipment for high
| energy physics machines.
|
| I have yet to figure out a way to tell people what my business
| is in a way that is even slightly accessible. Everything about
| it is so esoteric and multiple steps removed from regular life.
| It's not necessarily complex, it just contains a ton of details
| that the average person has no familiar contact with, and don't
| really have everyday analogues.
| wasabi991011 wrote:
| Isn't "I have my own micro business where I make equipment
| for high energy physics machines" a good description already?
| xorcist wrote:
| > I make equipment for high energy physics machines
|
| > I have yet to figure out a way to tell people what my
| business is in a way that is even slightly accessible.
|
| You ... just did? In a remarkable short, concise, and very
| accessible way. I can ask as many follow up questions as I
| want and we might even have an engaging conversation. Sounds
| interesting!
| Workaccount2 wrote:
| It doesn't really tell you much, and frankly my audience is
| mostly non-tech people. And no doubt some people really are
| curious and keep asking questions, but most people you can
| kinda see their head uncomfortably spin.
|
| I also obfuscated it a bit by giving the most general name
| just for privacy reasons since not many people do it. But
| rest assured it is a "Retro Encabulator" type machine, and
| as you add details it just becomes more and more alien.
|
| This is not at all what I do, but its similar esoteric-ness
| to "I make differential gear sets for calibrating ion trap
| interferometry systems". A collection of words where every
| one of them the average person struggles to place.
| DonHopkins wrote:
| Joey Chestnut?
| Scene_Cast2 wrote:
| Neat. I spent a month trying to use sphere packing approaches for
| a better compression algorithm (I had a large amount of vectors,
| they were grouped through clustering). Turned out that
| theoretical approaches only really work for uniform data and not
| any sort of real-world data.
|
| EDIT: groped -> grouped
| Gregaros wrote:
| _May_ be a case for extending out what has been explored by
| theory to cover more useful ground (or not, depending on
| whether real-world usecases like yours are too heterogenous for
| effective general techniques).
| soulofmischief wrote:
| You really shouldn't grope your vectors.
| dotancohen wrote:
| Roger, Rodger. Over, Oveur.
| GuinansEyebrows wrote:
| you're Kareem Abdul-Jabar!
| dotancohen wrote:
| I'm sure you've already explored this, but is there some
| precompression operation that you could do to the vectors such
| that they're no longer sparse, and therefore relatively
| uniform?
| Scene_Cast2 wrote:
| They weren't sparse, they were dense but the "density" was
| quite non-uniform (think typical learned ML vectors). Not too
| far from an N-dimensional gaussian (I ended up reading
| research on quantizing Gaussian distributions, but that
| didn't help either as we didn't have a perfectly gaussian
| thing).
| sdenton4 wrote:
| VAE objectives are useful for pushing embeddings into a
| Gaussian distribution.
|
| Here's some work on low-latency neural compression that you
| might find interesting: https://arxiv.org/abs/2107.03312
| layer8 wrote:
| This should have practical applications for cow packing in
| physics.
| NooneAtAll3 wrote:
| does anyone know at what lowest dimension does this construction
| beats known best packing?
| imoreno wrote:
| This was a very confusing article, full of filler. I couldn't
| stand to read the "detective story" style.
|
| Sounds like the technique is for high-dimensional ellipsoids. It
| relies on putting them on a grid, shrinking, then expanding
| according to some rules. Evidently this can produce efficient
| packing arrangements.
|
| I don't think there's any shocking result ("record") for literal
| sphere packing. I actually encountered this in research when
| dynamically constructing a codebook for an error-correcting code.
| The problem reduces to sphere packing in N-dim space. With less
| efficient, naive approaches, I was able to get results that were
| good enough and it didn't seem to matter for what I was doing.
| But it's cool that someone is working on it.
|
| A better title would have been something like: "Shrink-and-grow
| technique for efficiently packing n-dimensional spheres"
| bGl2YW5j wrote:
| "Shrink-and-grow technique for efficiently packing
| n-dimensional spheres" isn't obtuse enough.
|
| I think something like "Hypertopological Constriction-Expansion
| Dynamics in Quasistatic R^n-Ball Conglomeration" would be even
| more apt.
| bGl2YW5j wrote:
| I hated maths as a kid, now I love this stuff; pure maths for its
| own sake. Super impressive! It's a dream of mine to discover
| anything useful in the field.
| dsp_person wrote:
| > For a given dimension d, Klartag can pack d times the number of
| spheres that most previous results could manage. That is, in
| 100-dimensional space, his method packs roughly 100 times as many
| spheres; in a million-dimensional space, it packs roughly 1
| million times as many.
|
| Those numbers sound wild. For various comms systems does this
| mean several orders of magnitude bandwidth improvement or power
| reduction?
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