New sphere-packing record stems from an unexpected source
65 comments
·July 7, 2025clickety_clack
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
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.
pseudocomposer
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.
imoreno
>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
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.
jvanderbot
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"
tomrod
I choose the worst of all options and go into excruciating detail.
bell-cot
Thereby minimizing how often anyone asks you - which makes that the best long-term option?
Angostura
The latter option always comes across as rude. It's a very clear 'piss off you insect'
sdenton4
I kinda love doing the quick+easy explanation... And especially in professional contexts.
"I teach computers what sounds different aminals make."
xorcist
> 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.
bravesoul2
Or tell them about the bit of the job they understand. "I teach maths to adults".
Workaccount2
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
Isn't "I have my own micro business where I make equipment for high energy physics machines" a good description already?
xorcist
> 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
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.
dekhn
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)
lawlessone
shapes that exist on higher dimensions we can't mentally comprehend.
binarymax
“I’m an electron wizard. I write spells and magical constructs appear on the mirror slate”
null
zem
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.
Scene_Cast2
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
dotancohen
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
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
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
soulofmischief
You really shouldn't grope your vectors.
Gregaros
_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).
bGl2YW5j
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.
layer8
This should have practical applications for cow packing in physics.
NooneAtAll3
does anyone know at what lowest dimension does this construction beats known best packing?
theteapot
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?
jacobolus
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.
fiforpg
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
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 ;-)
tomrod
Very cool. Sphere packing comes up in a lot of contexts in applied problems. Looking forward to reviewing the paper.
readthenotes1
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
The aforementioned trapezoidal rule (Tai's method): https://diabetesjournals.org/care/article/17/2/152/17985/A-M...
pinkmuffinere
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
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.
gbxyz
[flagged]
DonHopkins
Joey Chestnut?
imoreno
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
"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.
> 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?