[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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