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New sphere-packing record stems from an unexpected source

quantamagazine.org

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

#151

Post by stavros »

pinkmuffinere wrote: post #10
readthenotes1 wrote: post #3

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…

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 laug…

Oh no, did he drink that murky mudwater?! I get it if my life depended on it, but for a demonstration video?! I gagged.

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

#152

Post by wyan »

fcanesin wrote: post #99

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.

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.

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

#153

Post by doubledamio »

thorum wrote: post #26
doubledamio wrote: post #17

Earlier quoted context omitted.

If you can't explain something in simple terms, you don't understand it well enough

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

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

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

#154

Post by kristopolous »

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

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

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

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.

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

#155

Post by adityaathalye »

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.”

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

#156

Post by yorwba »

lupire wrote: post #82
dsp_person wrote: post #66

> 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?

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

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 π^(n/2) (1/2)^n / Γ(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 Γ(n/2 + 1) / π^(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.

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

#157

Post by rando234789 »

fcanesin wrote: post #99

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.

check out the idea of a habilitation: https://en.wikipedia.org/wiki/Habilitation at least in germany, it is pretty much what you describe

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

#158

Post by tharkun__ »

shakna wrote: post #149
ordu wrote: post #102

Earlier quoted context omitted.

> 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 othe…

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.

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.

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

#159

Post by Someone »

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.

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

#160

Post by aleph_minus_one »

9dev wrote: post #132
nurettin wrote: post #130

Earlier quoted context omitted.

> 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 ).

That just makes them awful professors. They should stick to WWFD (what would Feynman do!)

> 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_Physics

"The presentation of material is advanced and typically considered suitable for graduate-level study."

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