[HN Gopher] New sphere-packing record stems from an unexpected s...
       ___________________________________________________________________
        
       New sphere-packing record stems from an unexpected source
        
       Author : pseudolus
       Score  : 403 points
       Date   : 2025-07-07 18:19 UTC (1 days 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"
        
           | smallerize wrote:
           | https://www.science.org/doi/10.1126/sciadv.adv1257
           | "Underlining earlier work by Speth (61), experiments recently
           | demonstrated that organic perishable containers, e.g., made
           | out of deer skin or birch bark, placed directly on a fire,
           | are capable of heating water sufficiently to process food,
           | with the advantages of wet-cooking beginning at lower, sub-
           | boiling temperatures than thus far acknowledged (62)."
           | Reference 61 goes to this 2015 paper: https://scholar.google.
           | com/scholar_lookup?title=When+did+hum... "to alert
           | archaeologists and others to the fact that one can easily and
           | effectively boil in perishable containers made of bark, hide,
           | leaves, even paper and plastic, placed directly on the fire
           | and without using heated stones."
        
             | pinkmuffinere wrote:
             | Thanks for the link! Not to be argumentative, but I do want
             | to highlight a couple points that I think may be the root
             | misunderstanding:
             | 
             | 1. The 2015 paper doesn't indicate that it was unknown that
             | you can boil water without pottery. It is meant to alert
             | people to an already known fact. Maybe silly, but I do
             | think there's a distinction here -- it's not that the
             | pinnacle of human knowledge was missing this, it's that
             | common sense was missing it. I'd compare this to the
             | article "things SDEs assume about names". Edit: then again,
             | playing devils advocate against myself, the first paper
             | does say "...sub-boiling temperatures than _thus far
             | acknowledged_" (emphasis mine), which would seem to
             | indicate that this was more than just a common
             | misunderstanding.
             | 
             | 2. The 2015 paper is not about boiling water in general,
             | it's about boiling it in a specific way. (Whereas the
             | initial discussion was about boiling water by any method)
        
           | rukuu001 wrote:
           | I know right? If I, as a yokel kid knew this, it astonishes
           | me people like that wouldn't know it
        
           | stavros wrote:
           | Oh no, did he drink that murky mudwater?! I get it if my life
           | depended on it, but for a demonstration video?! I gagged.
        
         | 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.
        
           | knicholes wrote:
           | By the way, for anyone down voting, ask o3 if humans could
           | render fat before they had pottery. It takes seconds to find
           | the answer.
        
       | 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.
        
           | shkkmo wrote:
           | > 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.
        
             | jacobolus wrote:
             | 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.
        
               | shkkmo wrote:
               | 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.
        
       | 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.
        
               | baobun wrote:
               | It really can go both ways. Was told that "Ask baobun
               | about hacking when you're high" came recommended.
        
               | 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.
        
               | watersb wrote:
               | https://youtu.be/QGw-cy0ylCc
               | 
               | Is this an asynchronous architecture CPU?
        
               | Dylan16807 wrote:
               | It's not. I'm curious what gave you that idea, though?
               | 
               | The belt moves once per cycle, if that wasn't clear? He
               | says the word "cycle" (and measures latency in cycles) a
               | _lot_.
        
               | ZoomZoomZoom wrote:
               | That's how you get a whole population imagining
               | mitochondria as puffy gelatinous beans, instead of
               | network around other organelles.
               | 
               | https://www.nature.com/immersive/d41586-025-00269-y/index
               | .ht...
        
               | 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.
        
               | tbrownaw wrote:
               | Take for example entanglement.
               | 
               | The math that describes it is known precisely. Specific
               | implications of this are known. There's no information
               | transfer, there's no time delay, etc.
               | 
               | And yet lay people keep incorrectly thinking it can be
               | used for communication. Because lay-audience descriptions
               | by experts keep using words that imply causality and
               | information transfer.
               | 
               | This is not a failure of the experts to understand what's
               | going on. It's a failure to _translate_ that
               | understanding to ordinary language. Because ordinary
               | language is not suited for it.
               | 
               | > _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._
               | 
               | We don't have a model of _why_ it works  / if there's a
               | more comprehensible layer of reality below it. But it's
               | characterized well enough that we can make practical
               | useful things with it.
        
               | zmgsabst wrote:
               | > This is not a failure of the experts to understand
               | what's going on.
               | 
               | > We don't have a model of why it works / if there's a
               | more comprehensible layer of reality below it.
               | 
               | Counterpoint:
               | 
               | You've just admitted they don't understand what's going
               | on -- they merely have descriptive statistics. No
               | different than a DNN that spits out incomprehensible but
               | accurate answers.
               | 
               | So this is an example affirming that QM isn't understood.
        
               | tbrownaw wrote:
               | The only descriptive / empirical parts is the particle
               | masses.
               | 
               | But it sounds like your objection is that reality _isn 't
               | allowed_ to be described by something as weird as complex
               | values that you multiply to get probabilities, so there
               | necessarily must be another layer down that would be more
               | amenable to lay descriptions?
        
               | zmgsabst wrote:
               | That's not my point, nor close to what I said.
               | 
               | My point is that their models are fitted
               | tensors/probability distributions, often retuned to fit
               | new data (eg, the epicyclic nature of collider correction
               | terms) -- the same as fitting a DNN would be.
               | 
               | Their inability to describe what is happening is
               | precisely the same as in the DNN case.
        
               | Dylan16807 wrote:
               | If you have a very small neural network, you _can_ fully
               | understand and explain how it works.
               | 
               | As you increase the detail of a description, it reaches a
               | point where nothing is missing.
        
               | zmgsabst wrote:
               | As I pointed out, eg, the high number of correction terms
               | when trying to tune the model to actual particle
               | accelerator data is evidence that our model is missing
               | something. (And some things are plain missing: neutrino
               | behavior, dark matter, dark energy, etc.)
               | 
               | In the same way that a high number of epicycles was
               | evidence our theory of geocentrism was wrong -- even
               | though adding epicycles did compute increasingly accurate
               | results.
        
               | aleph_minus_one wrote:
               | > As I pointed out, eg, the high number of correction
               | terms when trying to tune the model to actual particle
               | accelerator data is evidence that our model is missing
               | something. (And some things are plain missing: neutrino
               | behavior, dark matter, dark energy, etc.)
               | 
               | This is rather a problem of the standard model.
               | Physicists will immediately admit that something is
               | missing there, and they are incredibly eager to find a
               | better model. But basically every good attempt that they
               | could come up with (e.g. supersymmetric extensions of the
               | standard model; but I'm not a physicist) has by now (at
               | least modtly) been falsified by accelerator experiments.
        
               | Dylan16807 wrote:
               | The comment you originally replied to was about
               | entanglement, not the entire standard model. The math
               | there is very simple, not built on correction terms.
        
               | evanb wrote:
               | The standard model has ~20 parameters (depending on what
               | exactly you include as 'the' SM) and it predicts hundreds
               | of thousands of data points.
        
               | tbrownaw wrote:
               | ... So it's about not being able to observe short-lived
               | particles directly, and having to work backwards from
               | longer lived interaction or decay products? Or about how
               | those intermediate particles they have to calculate
               | through also have empirically-determined properties?
        
               | zmgsabst wrote:
               | Most of that is measured corrections, not a theoretical
               | model.
               | 
               | Entanglement is just a statistical effect in our
               | measurements -- we can't say what is happening or why
               | that occurs. We can calculate that effect because we've
               | fitted models, but that's it.
               | 
               | Similarly, to predict proton collisions, you need to add
               | a bunch of corrective epicycles ("virtual quarks") to get
               | what we measure out of the basic theory. But adding such
               | corrections is just curve fitting via adding terms in a
               | basis to match measurement. Again, we can't say what is
               | happening or why that occurs.
               | 
               | We have great approximators that produce accurate and
               | precise results -- but we don't have a model of _what_
               | and _why_ , hence we don't understand QM.
        
               | tbrownaw wrote:
               | > _Entanglement is just a statistical effect in our
               | measurements -- we can't say what is happening or why
               | that occurs. We can calculate that effect because we've
               | fitted models, but that's it._
               | 
               | Bell's theorem was a prediction from math _before_ people
               | found ways to measure and confirm it. A model based on
               | fitting to observations would have happened in the other
               | order.
        
               | zmgsabst wrote:
               | > A model based on fitting to observations would have
               | happened in the other order.
               | 
               | We'd already had models which said that certain
               | quantities were conserved in a system -- and entanglement
               | says that is true of certain systems with multiple
               | particles.
               | 
               | To repeat myself:
               | 
               | > Entanglement is just a statistical effect in our
               | measurements -- we can't say what is happening or why
               | that occurs.
               | 
               | Bell's inequality is just a way to measure that
               | correlation, ie, statistical effect -- and I think it's
               | supporting my point the way to measure entanglement is
               | via statistical effect.
               | 
               | ER=EPR is an example of a model that tries to explain
               | what and why of entanglement.
        
               | ted_dunning wrote:
               | Actually it is just the opposite. QED is comprehensive
               | and, as far as we know, accurate.
               | 
               | But it is impractical to use in most situations so major
               | simplifications are required.
               | 
               | The correction factors that you mention are the result of
               | undoing some of those simplifications, sometimes by
               | including more of the basic theory and sometimes by
               | saying something like "we know that we ignored something
               | important _here_ and it has to have this shape but we can
               | only kinda sort measure how big it might be because it 's
               | too hard to actually calculate".
        
               | teiferer wrote:
               | QM isn't less well understood though than Newton's
               | mechanics. Neither cover the "why". But both provide a
               | model of the world, the model (!) is very precisely
               | understood and it matches observations in certain parts
               | of reality. Like all reasonable scientific theories do.
               | They have limits, and beyond those limits they don't
               | apply, but that doesnt mean they are not understood. It's
               | reality that is not sufficiently well understood and by
               | coming up with more and more refined models/theories, we
               | keep approximating it, likely without ever having a
               | "fully correct" theory encompassing everything without
               | limits. (But that's ok.)
        
               | Angostura wrote:
               | 'It's the study how the particles that make atoms
               | interact... it's fiendishly complicated'
        
               | doubledamio wrote:
               | 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 simplifying your work isn't
               | "dumbing it down"; it often sharpens your own
               | understanding too.
        
               | aleph_minus_one wrote:
               | If you have such an opinion, explain some advanced papers
               | of Peter Scholze to me.
        
               | SubiculumCode wrote:
               | 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?).
        
             | 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!
        
               | TimTheTinker wrote:
               | Sounds like an LLM's impression of Feynman.
        
             | 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!
        
               | lupire wrote:
               | Feynman was happy to explain why he couldn't explain how
               | magnets work!
               | 
               | https://m.youtube.com/watch?v=MO0r930Sn_8
        
             | tomrod wrote:
             | Simple terms need not be short terms.
        
               | ykonstant wrote:
               | Huh; now want to write a
               | Supercalifragilisticexpialidocious song for my research
               | topic.
        
               | tomrod wrote:
               | As one must.
        
             | CJefferson wrote:
             | I personally think of this in terms of giving directions.
             | 
             | It's easy to give directions to somewhere near where you
             | currently are -- "Just head down the road, it's the second
             | left, then 3 doors down".
             | 
             | When giving directions to a far-away place you either have
             | to get less accurate "it's on the other side of the world",
             | or they get really, really long. Unless of course they
             | already know the layout of the land -- "You already know
             | Amy's house, over in Algebra Land? Oh, then it's just down
             | the road, fourth left, six doors down".
             | 
             | People often seem cleverer because they know the layout of
             | some really obscure land, but often it's just because
             | people have never been anywhere near it. I have a joke
             | about my research where I say, "A full explanation isn't
             | that hard to explain, it's just long. About 4 hours
             | probably. Are you interested?" So far, I've had 3 people
             | take me up on that, and they all seemed to have an
             | understanding once I'd finished (or, they really really
             | wanted to escape).
        
           | sdenton4 wrote:
           | I kinda love doing the quick+easy explanation... And
           | especially in professional contexts.
           | 
           | "I teach computers what sounds different aminals make."
        
             | pfdietz wrote:
             | As a person who uses the Merlin app regularly, I appreciate
             | this field of study.
        
             | jimbokun wrote:
             | Great pickup line.
        
           | 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.
        
               | Geezus_42 wrote:
               | I think which direction you choose is about knowing your
               | audience. As you mentioned, different people value
               | different things and humans often want to present a
               | different view of ourselves to different people at
               | different times.
        
           | 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.
        
             | Miraste wrote:
             | >extremely uneducated, under-stimulated people, who also
             | have unaddressed insecurities around their own
             | intelligence. But that's not most humans.
             | 
             | This isn't going to be most humans you encounter if you're
             | in the HN demographic, but that's a bubble. It does
             | describe most people in the world.
        
               | dgfitz wrote:
               | This is, in a word, nonsense.
        
             | aleph_minus_one 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).
             | 
             | For me, it's quite the opposite: such a choice demonstrates
             | that they their prior is that I'm sufficiently smart and
             | knowledgable to be likely able to understand this
             | explanation - which I rather consider to be a praise. :-)
        
               | fyrn_ wrote:
               | I think "with strangers" is the important bit. If a
               | nuclear engineer is talking to some lay person and uses
               | hyper specific jargon, then grandparent is correct. If
               | you've established a shared competency with the person,
               | and are therefor no longer total strangers, that's
               | totally different.
        
               | lanstin wrote:
               | True, but however, there are times when I just really
               | need to talk about the extremely detailed bits of some
               | problem I'm thinking about - just the act of speech is
               | really needed; I find this super annoying in other
               | people, but forgivable because I also experience it. I
               | have heard so much about minutiae from my kids that I
               | have to force myself to just semi-actively listen to. My
               | wife has to hear so many things that annoy her as well,
               | when I don't get enough chattering out to co-workers or
               | colleagues.
        
             | xdfgh1112 wrote:
             | Your default position is distrust and anxiety though. Most
             | people aren't wired that way.
        
             | prpl wrote:
             | The correct option is to treat such conversations as a
             | protocol with a negotiation at the onset.
        
               | Hnrobert42 wrote:
               | SYN ACK
        
               | kazinator wrote:
               | RST FIN
        
               | __turbobrew__ wrote:
               | SYN SYN SYN SYN SYN SYN SYN SYN SYN SYN SYN SYN
        
             | zahlman wrote:
             | > or assume they're not emotionally intelligent (because
             | it's a choice demonstrates little respect for the person
             | they're addressing)
             | 
             | Intelligence, in the traditional sense, also involves
             | understanding when to give up. Part of "emotional
             | intelligence" is judging whether the other party actually
             | cares about what you're about to say.
        
             | ordu wrote:
             | _> 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_
             | 
             | It is just your choice. I'd prefer a short answer full of
             | jargon. It gives people the opportunity to clarify what
             | they want to ask. Do they really want to know details? Or
             | they want a rough idea of an answer? Or they just filling
             | silence with small talk?
             | 
             | Though other times, when I really want to talk about it,
             | I'd go with some ELI5 explanation, while watching people,
             | are they interested or not?
             | 
             |  _> Honestly, I think not appreciating simple explanations
             | indicates both low mathematical /logical and
             | social/emotional intelligence._
             | 
             | It can be. But mostly it is not. People are sending signals
             | by choosing one form of the answer or another, you just
             | need to decode their signals. And it will be better, if you
             | don't jump to conclusions about their persistent
             | psychological traits, based on the first impression.
        
               | shakna wrote:
               | I think the negotiation signal being sent by "all jargon"
               | is "fuck off". It's not an attempt to gauge what level
               | the other person is using. It's a blank wall, being
               | thrust towards them.
        
               | tharkun__ wrote:
               | 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 the other person ask about specific jargon
               | they don't know).
               | 
               | But at the parents dinner party, that other guy may or
               | may not be in your line of work. Just ask them.
        
               | shakna wrote:
               | > 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.
        
               | neltnerb wrote:
               | Maybe it's just me but I feel entirely comfortable asking
               | questions like "how much math did you take? do you
               | remember what a derivative is?" and base my explanations
               | on the response. Turns out fine every time so far... and
               | if they don't remember what a derivative is (or whatever)
               | then I just explain it differently no big deal. I'd
               | almost argue it is easier than not asking, but only if I
               | actually care about them understanding the answer.
        
               | shakna wrote:
               | That is fine. That's not what has been complained about
               | here. That's invitational, not wall of jargon.
        
               | NL807 wrote:
               | Not exactly a bad thing in my books.
        
               | shakna wrote:
               | Maybe so, if that is your choice, but it is not giving
               | "people the opportunity to clarify what they want to
               | ask".
        
             | m463 wrote:
             | I'm reminded of this dilbert cartoon:
             | 
             | https://web.archive.org/web/20230228154639im_/https://asset
             | s...
        
               | falcor84 wrote:
               | and I'm reminded of this xkcd about the pattern of
               | lights:
               | 
               | https://xkcd.com/722/
        
               | dghughes wrote:
               | 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.
        
               | gilleain wrote:
               | 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.
        
             | nurettin wrote:
             | > When I meet people who immediately use hyper-specific
             | jargon with strangers,
             | 
             | That is 90% of the professors I asked questions to. If they
             | go full jargon and don't want to explain any of it, they
             | don't want you near them ( or they want you to improve
             | before even having a conversation ).
        
               | 9dev wrote:
               | That just makes them awful professors. They should stick
               | to WWFD (what would Feynman do!)
        
               | aleph_minus_one wrote:
               | > what would Feynman do!
               | 
               | The counter-camp is "What would Landau and Lifshitz do?"
               | :-)
               | 
               | ---
               | 
               | For those who are out of the loop:
               | 
               | > https://en.wikipedia.org/wiki/Course_of_Theoretical_Phy
               | sics
               | 
               | "The presentation of material is advanced and typically
               | considered suitable for graduate-level study."
        
             | kazinator wrote:
             | > _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.
        
               | SubiculumCode wrote:
               | 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.
        
           | Angostura wrote:
           | The latter option always comes across as rude. It's a very
           | clear 'piss off you insect'
        
             | aleph_minus_one wrote:
             | > The latter option always comes across as rude. It's a
             | very clear 'piss off you insect'
             | 
             | To me, it rather tells: "I consider you to be likely to be
             | sufficiently smart and knowledgable to understand this
             | topic if you put in some effort: do you want to learn some
             | cool stuff which otherwise would demand a lot of literature
             | research to learn? And since I already hinted that I
             | consider you to be smart and knowledgable: would you like
             | to teach me some cool, complicated stuff, too?"
        
               | ted_dunning wrote:
               | That would be nice.
               | 
               | But it is by far more common that it means "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"
        
             | jimbokun wrote:
             | Or "I'm a mathematician. I try really hard to find things I
             | can prove that have no practical application. But
             | frustratingly people keep finding important practical
             | applications for my work."
        
               | ahazred8ta wrote:
               | > No one has yet found any war-like purpose to be served
               | by the theory of numbers or relativity or quantum
               | mechanics, and it seems very unlikely that anybody will
               | do so for many years. - G.H.Hardy, Jan 1940 > A few
               | decades later, we stand waiting for nuclear bombs guided
               | by GPS to be launched when the cryptographic auth
               | certificate is verified. So it goes.
        
           | YeGoblynQueenne wrote:
           | I once told my dad that if the subject of my thesis was
           | something I could easily explain then it wouldn't be
           | interesting enough to do a PhD in. I said it half-jokingly
           | and he laughed about it, but he stopped asking me what I'm
           | studying after that so maybe he did take it more seriously.
        
             | lupire wrote:
             | Hard to explain doesn't make it interesting either.
        
             | guicen wrote:
             | There's something bittersweet about that moment when
             | someone you love stops asking about your research. It's a
             | quiet kind of respect, but also a reminder of the
             | communication gap academia often creates.
        
             | ahazred8ta wrote:
             | Introduce him to the annual Dance Your PhD contest:
             | 
             | https://duckduckgo.com/?q=dance+your+phd&ia=videos&iax=vide
             | o...
        
             | coderatlarge wrote:
             | i once got excited to explain to my father what i did at a
             | research lab after grad school. he listened patiently for
             | about 30 minutes then he said "oh, so you build software
             | for big business?"
        
             | ted_dunning wrote:
             | Of course, there is the unstated second part that you
             | really aren't qualified for a PhD until you can explain it
             | simply.
        
           | dsaalgo wrote:
           | > There are three choices
           | 
           | There is another:
           | 
           | Give away as little information as you can about it.
           | 
           | Don't say or agree that it's secret or that you can't talk
           | about it- just be tight-lipped, and don't divulge.
           | 
           | If you do it right, you will seem mysterious.
           | 
           | If you do it wrong, they probably won't talk to you much
           | again.
           | 
           | Win-win.
        
             | volemo wrote:
             | _-- Hi, and what do you do?
             | 
             | -- What's your security clearance?_
        
           | eru wrote:
           | There's more choices than three.
           | 
           | Eg you can focus on what you actually do, or you can focus on
           | the benefits you bring to other people.
        
           | dietr1ch 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's wrong with this? Making it look easy is why you get
           | paid for it.
        
           | johnfn wrote:
           | The way I think about it is this. There are roughly two
           | groups of people:
           | 
           | - Some people will not care / be dismissive of what I have to
           | say. I probably don't want to talk to these people much.
           | 
           | - Some people will be interested! I probably will like these
           | people.
           | 
           | If I use technical jargon, I am optimizing to impress people
           | I don't really care about impressing - and I will be pushing
           | away the people that I would actually be interested to spend
           | time with.
           | 
           | If I speak respectfully, i.e. the simple explanation, it will
           | resonate more with the people I like. I will push away the
           | people who don't care, but I didn't really want to talk with
           | them anyways.
        
           | ykonstant wrote:
           | >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.
           | 
           | Yes, don't fall into this trap. The other two options are
           | still better. Everyone says, "no, no, I really want to know"
           | and then tunes out two minutes later; then four minutes later
           | they start doing the George Carlin lean: "Surgery! I am
           | having my _ears sewn shut!_ ".
        
           | teiferer wrote:
           | I'll bite: What is your job?
        
             | tengwar2 wrote:
             | Chief Dexitroboper.
        
           | kristopolous wrote:
           | Really? When I see that all I think is it's one of "them" -
           | the kind that takes some kind of perverse pleasure in
           | needlessly mystifying, complicating, and obfuscating things
           | as much as possible - especially the trivial.
           | 
           | Blowing smoke around simple things to gatekeep them is not
           | impressive and not cute.
        
           | mkehrt wrote:
           | I think you can explain the _product_ you work on rather the
           | what you actually do.
           | 
           | I personally say I work on Bluetooth support for Google Home
           | assistant devices. "It's like Alexa, but Google.
           | 
           | Even if you work on some absurdly down stack thing, this
           | seems to work. You work on making sure the internet is as
           | fast as possible, or files are stored in the cloud properly,
           | or the graphics on your computer are displayed correctly.
        
           | ericol wrote:
           | I don't have that problem ("I work with computers / I am a
           | computer programmer") but I usually follow with "I'm a race
           | driver. I drive the car as fast as I can, I don't change the
           | tires nor the oil in it" when I get the usual "can you fix my
           | computer?" request.
           | 
           | For reasons that I care not to ask people get seriously
           | annoyed by that.
        
           | somethingsome wrote:
           | 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.
        
           | lanstin wrote:
           | I think about things and then type in stuff that makes them
           | work better.
        
         | 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)
        
           | contravariant wrote:
           | Yeah I'd definitely explain that one as "I study ways to make
           | wifi faster", doesn't cover all the nuance, but it's
           | definitely better than the alternative.
           | 
           | Convex shapes, well, annoyingly it's too broad. It has _way_
           | more applications than sphere packings but it 's hard to pick
           | a good example. It's like trying to explain you design
           | screwdrivers to someone who doesn't know what a screw is.
        
         | 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.
        
               | grogenaut wrote:
               | Help me that you're not a doctor a lawyer accountants
               | software engineer working for a large company. It tells
               | me you're a small business owner and you work on advanced
               | things. You're not manufacturing knick knacks or toys.
               | 
               | Really if we're at a party that's more than enough unless
               | I want to ask you more and you want to talk more about
               | it. If you were a lawyer I'd probably ask what area of
               | law that I probably stop and talk about something else.
               | So I agree with others that you said was a very good
               | distillation of what you do to the level that most people
               | probably care about
        
               | stavros wrote:
               | "I have a small business that creates parts for machines
               | used to do physics research" is perfectly understandable,
               | though.
        
           | fuzzy_biscuit wrote:
           | My cousin has his own metrology business, and it took me a
           | long time before I understood how he was doing so well
           | financially. Kinda get it now.
        
           | Izikiel43 wrote:
           | I make gear for machines that throw energy
           | beams/lightning/lasers?
        
         | jimbokun wrote:
         | I describe myself as a plumber but with systems for moving
         | around masses of data instead of water.
        
         | Izikiel43 wrote:
         | I practiced with my wife. Now I can describe my job as a
         | service for making services.
        
         | volemo wrote:
         | I usually struggle not with the "what is it you do?" question
         | but with the following "how is it useful/applicable?"
         | 
         | How do I concisely describe the long chain between a
         | fundamental research and something tangible?
        
         | m4tthumphrey wrote:
         | I just say "I work with computers". I get the nod of "oh right
         | nice" and that's it. Done.
        
           | aleph_minus_one wrote:
           | > I just say "I work with computers".
           | 
           | This is a suitable description of possibly 70 % of all jobs.
        
         | noworld wrote:
         | "You know what?"
         | 
         |  _convex hulls your car_
        
         | Scarblac wrote:
         | While making it clear that packing spheres, which are also
         | shapes that don't jut inwards, is a completely different field.
        
         | ncr100 wrote:
         | There is a way to explain to neophytes and it's generally to be
         | more emotional problem-solving and intuitive, and less logical
         | or scientific. There's a toxicity that can rise up in talking
         | in a seemingly over-specific manner which puts people off.
         | 
         | Explain it from the perspective of, "well, in order to get XYZ
         | done, we are frustrated by it being hard, so we make an easy
         | guess .. we try thinking about the problem in this crude way
         | way because that's easy to think about, and then we make ABC
         | because we know about ABC's ... and we are excited when using
         | it gets us closer to working than anything else we've tried
         | before".
         | 
         | Emotion-laden explanations are a viable way to explain to non-
         | techs. They may be more comfortable thinking emotionally,
         | whereas we are steeped in the logic and sometimes mathematics
         | of our practice. So we must reintroduce emotion into the
         | explanations.
         | 
         | It worked for me, explaining to my family, they followed on and
         | actually understood.
        
       | DonHopkins wrote:
       | Joey Chestnut?
        
         | vanderZwan wrote:
         | I'm afraid I don't get the reference :)
        
           | wmeredith wrote:
           | He is the world champion of eating hotdogs. He can eat 73 or
           | something. The joke is that he's packing them into his
           | stomach.
        
       | 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
        
             | dotancohen wrote:
             | I see, thank you.
             | 
             | Another thing that I'm sure you explored, and I'd love to
             | hear how it went, would be to rearrange the elements in the
             | vectors such that perhaps the denser parts could be more
             | contiguous, and the sparser parts could be more contiguous,
             | on average. That sounds like something that would be easier
             | to compress. Were the distributions such that a
             | rearrangement like this might have been possible? Or were
             | they very evenly distributed?
             | 
             | I.e. could you have rearranged a Gaussian-like distribution
             | into a Poisson-like distribution?
        
               | Scene_Cast2 wrote:
               | What ended up launching is a fancy product quantization
               | based on k-means. Some of the tricks were storing
               | magnitude separately (i.e. removing the mean) and
               | rearranging dimensions based on variance (and/or rotation
               | based on PCA) for PQ to work better.
               | 
               | I also remember trying to fit a distribution so that I
               | can generate synthetic data (not for a lack of data, but
               | more for understanding the problem space better). The
               | synthetic data quantized pretty differently - my guess is
               | that it's because of random areas of density and
               | sparsity.
               | 
               | I'm not quite following your exact rearranging idea
               | though. Not sure if the above answers the question.
        
               | dotancohen wrote:
               | I was just wondering, it seems like an interesting
               | problem to explore.
        
             | derf_ wrote:
             | If you start from N-dimensional Gaussian-distributed
             | vectors and normalize them, you wind up with uniformly
             | distributed vectors on an (N-1)-dimensional hypersphere. Of
             | course, sphere-packing on the surface of a hyperspehere is
             | its own fun problem, and if your data is not actually
             | Gaussian may still not be exactly what you want, but coding
             | the vector magnitude separately from the vector direction
             | is probably a good start.
        
         | lupire wrote:
         | It's usually the case that the low hanging fruit in a decades
         | old commercially valuable field have already been picked.
        
         | hansvm wrote:
         | The usual trick is to use domain-specific knowledge to
         | translate that asymmetry to uniformity.
         | 
         | E.g.: Suppose the data has high-order structure but is locally
         | uniform (very common, comes about because of noise-inducing
         | processes). Compute and store centroids. Those are more uniform
         | than your underlying data, and since you don't have many it
         | doesn't really matter anyway. Each vector is stored as a
         | centroid index and a vector offset (SoA, not AoS). The indices
         | are compressible with your favorite entropic integer scheme (if
         | you don't need to preserve order you can do better), and the
         | offsets are now approximately uniform by assumption, so you can
         | use your favorite sphere strategy from the literature.
        
           | tsunamifury wrote:
           | Intelligence is compression
        
       | 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.
        
         | lupire wrote:
         | The delight of pure maths is in its uselessness :-)
        
       | 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?
        
         | lupire wrote:
         | I think not, because moving to a higher dimension is
         | exponentially worse (density ~ n^2/2^n) than this linear
         | improvement.
         | 
         | So it's only helpful for naturally high dimensional objects.
         | Digital objects do not have a natural dimension (byte length),
         | so you can choose a small dimension.
         | 
         | https://en.m.wikipedia.org/wiki/Sphere_packing
        
           | tonetegeatinst wrote:
           | The addition of a dimension can be thought of as adding
           | another variable or "axis" in simpler terms.
           | 
           | Due to the added variable aka axis, you have increased the
           | size of complexity.
           | 
           | 2d shapes packed in a 2d boundary vs 3d objects in 3d space.
           | The difference is fitting quarters on a paper vs marbles in a
           | perfect cube.
           | 
           | Now imagine having to find the most optimal method of packing
           | for objects of Nth degree in Nth constraint. For example
           | packing object that have 256 dimensional or variables into a
           | constraint that also is 256 of complexity.
           | 
           | I feel as your dimension aka variable increases....the amount
           | of information to compute grows quite quickly.
           | 
           | We can rule out some things as non optimal or non perfect,
           | but we can also get close to perfection via trial and error.
           | I see this as an example of the traveling salesman issue.
           | 
           | Do you stick with a randomly selected answer, do you go with
           | the current most optimal solution, or do you invest time and
           | effort into finding a new solution but you risk finding a
           | worse solution. At the end of the day is the packing
           | efficient gains worth the computational complexity of N
           | dimension of N constraint given it will take an unknown
           | amount of time to find a more efficient packing solution, and
           | the new solution could be anywhere from 0.1% to 80% more
           | efficient.
        
           | yorwba wrote:
           | That density is the volume density. For most applications,
           | you care about the density in terms of number of hyperspheres
           | instead. The largest hypersphere that fits inside an
           | n-dimensional unit hypercube has radius 1/2 and volume
           | p^(n/2) (1/2)^n / G(n/2 + 1),
           | https://en.wikipedia.org/wiki/Volume_of_an_n-
           | ball#Closed_for... so the number of hyperspheres in a given
           | volume scales as n^2 G(n/2 + 1) / p^(n/2). Of course the
           | dominant term is the factorial growth of the Gamma function,
           | so even without the recent improvement by Klartag, using more
           | dimensions to encode multiple values simultaneously was
           | already preferable.
        
           | rini17 wrote:
           | Error-correcting codes in signal processing are naturally
           | high dimensional object, also mentioned there. Don't see any
           | reason why this research would not be applicable, we haven't
           | found optimal error correcting code for 100 bits yet.
        
       | teleforce wrote:
       | > The answer matters for potential applications to cryptography
       | and communications
       | 
       | Someone can take this challenge to provide a more secure and
       | reliable communication systems hopefully with more energy
       | efficiency, very much an exciting research direction.
        
       | deadbabe wrote:
       | Can't you just montecarlo the hell out of this thing?
        
         | slwvx wrote:
         | I don't think so. You can't just "Montecarlo the hell" out of a
         | post-quantum cryptographic scheme [1] which are also based on
         | lattices. Even if that analogy isn't quite apt, I don't think
         | looking for a good random lattice is a good way to find the
         | densest possible lattice [2].
         | 
         | [1] https://en.wikipedia.org/wiki/Post-quantum_cryptography
         | 
         | [2] https://en.wikipedia.org/wiki/Random_close_pack#For_spheres
        
         | crazygringo wrote:
         | According to the article, that's precisely what he did.
         | 
         | But he did it in a better way, randomly expanding ellipses. And
         | when you're dealing with hundreds of dimensions, it's
         | incredibly easy to be montecarlo-ing in the wrong directions...
        
       | fcanesin wrote:
       | I feel like mathematicians should be able to do a second
       | doctorate level degree a few years after their first PhD, that
       | must be in a adjacent field of their own, but not the same.
        
         | vanderZwan wrote:
         | I feel like most sciences should have this, it would accelerate
         | science a lot via the cross-pollination of ideas and
         | techniques.
         | 
         | But I can imagine that drawing connections between different
         | branches of maths would be especially powerful, yes
        
         | karmakurtisaani wrote:
         | It's possible! From somewhat famous mathematicians, at least
         | Bela Bollobas has 2 PhDs: one in discrete geometry and one in
         | functional analysis.
         | 
         | Try doing that in the modern academic environment tho..
        
         | wyan wrote:
         | The purpose of a PhD is to certify that you're able to do
         | independent research. Many researchers retrain (or just add a
         | research interest) in adjacent fields during their postdocs or
         | later. At that point it's just research.
        
         | rando234789 wrote:
         | check out the idea of a habilitation:
         | https://en.wikipedia.org/wiki/Habilitation at least in germany,
         | it is pretty much what you describe
        
         | aleph_minus_one wrote:
         | Beside the habilitation example of rando234789
         | (https://news.ycombinator.com/item?id=44498702), in Russia (and
         | Ukraine) there indeed exist two "doctorate levels": kandidat
         | nauk [Candidate of Sciences] and doktor nauk [Doctor of
         | Science].
        
       | vanderZwan wrote:
       | > _Klartag is convinced that this makes them extremely powerful:
       | Convex shapes, he argues, are underappreciated mathematical
       | tools._
       | 
       | I agree with this and I'm not even a mathematician, I've seen
       | convex hull algorithms pop up in unexpected places to solve
       | problems I would never have thought of using convex hull
       | algorithms for, like a paper on automatic palette decomposition
       | of images.
       | 
       | https://www.rose-hulman.edu/class/cs/csse451/Papers/DILvGRB....
        
       | tsunamifury wrote:
       | Why does this seem incredibly obvious to me?
        
         | paintbox wrote:
         | Probably because you overestimate your knowledge.
        
           | tsunamifury wrote:
           | This doesn't follow at all. In fact it's an admission of not
           | understanding. Did you struggle to figure that out?
        
         | ncr100 wrote:
         | Perhaps because the challenge was explained well? Or because
         | "the devil is in the details".
         | 
         | The article does mention that phenomenon, deceptive simplicity.
        
       | adityaathalye wrote:
       | I wonder; is this essentially _why_ LLM tech is useful for
       | certain Fields-medal level problems? i.e. _because_ the LLM
       | search construct has no barrier between sub-fields; nor between
       | distant ones? Only multiple likely paths?
       | 
       | In context of packing problem, it's a bit meta to me...
       | 
       | An LLM contains a k-dimensional packing of known knowledge. This
       | packing is highly inefficient because it has holes and unbridged
       | dimensions. By injecting random seed (prompts) into the LLM
       | probability space, it gets perturbed. Sometimes this perturbation
       | fills a hole in the packing and/or connects two adjacent units in
       | way nobody thought of before because it wasn't fashionable any
       | more, or wasn't top of mind. Thus new knowledge is created
       | _within the same k-dimensional box_ through a novel joining-of of
       | existing know-how.
       | 
       | From the article:
       | 
       | > Klartag had broken open a central problem in the world of
       | lattices and sphere packing after just a few months of study and
       | a few weeks of proof writing. "It feels almost unfair," he said.
       | But that's often how mathematics works: Sometimes all a sticky
       | problem needs is a few fresh ideas, and venturing outside one's
       | immediate field can be rewarding. Klartag's familiarity with
       | convex geometry, usually a separate area of study, turned out to
       | be just what the problem required. "This idea was at the top of
       | my mind because of my work," he said. "It was obvious to me that
       | this was something I could try."
        
       | Someone wrote:
       | FTA: _"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"_
       | 
       | Nice example of how weird large-dimensional space is. Apparently,
       | when smart minds were asked to put as many 100-dimensional
       | oranges in a 100-dimensional crate as they could, so far, the
       | best they managed to do was fill less than 1% of its space with
       | oranges, and decades of searching couldn't find a spot to put
       | another one.
        
         | asboans wrote:
         | "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 sphere in this cube...) so its not surprising that the
         | gains to be made in improving packing can be so large.
        
           | sota_pop wrote:
           | 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".
        
             | kibwen wrote:
             | There's a great 3blue1brown video that demonstrates this
             | unintuitive result in a relatively intuitive way:
             | https://youtube.com/watch?v=zwAD6dRSVyI
        
           | HappMacDonald wrote:
           | > (Aside: Strangely, the relationship is non monotonic and is
           | actually maximal for n=6)
           | 
           | For this aside I crave a citation.
           | 
           | When n=1 the sphere fit is 100% as both simplex and sphere
           | are congruent in that dimension. And dismissing n=0 as
           | degenerate (fit is undefined there I suppose: dividing by
           | zero measure and all that) that (first) dimension should be
           | maximal with a steady decline thereafter thus also monotonic.
        
             | ivanbakel wrote:
             | This looks to have been a conflation by the GP between the
             | volume of the unit sphere itself and its ratio to the
             | volume of its bounding cube (which is not the unit cube.)
             | The volume of the sphere does top out at an unintuitive
             | dimension, but indeed the ratio of the two is always
             | decreasing - and intuitively, each additional dimension
             | just adds more space between the corners of the cube and
             | the face of the sphere.
        
         | shrx wrote:
         | This doesn't hold true for 2 and 3 dimensions, though.
        
           | ted_dunning wrote:
           | If it holds for 10 or 20 dimensions, the consequences are
           | still pretty important.
        
       | cellular wrote:
       | It said his proof was basically by example. He proved more were
       | possible.
        
       | fraserphysics wrote:
       | Don't Shannon's channel coding theorem and rate-distortion
       | theorem establish bounds on possible sphere packing?
        
         | meindnoch wrote:
         | That's in Z_{2}^n, not in R^n.
        
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