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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

#201

Post by lanstin »

fyrn_ wrote: post #81
aleph_minus_one wrote: post #76

Earlier quoted context omitted.

> 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 - whi…

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.

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.

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

#202

Post by shrx »

Someone wrote: post #159

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, an…

This doesn't hold true for 2 and 3 dimensions, though.

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

#203

Post by ted_dunning »

shrx wrote: post #202
Someone wrote: post #159

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, an…

This doesn't hold true for 2 and 3 dimensions, though.

If it holds for 10 or 20 dimensions, the consequences are still pretty important.

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

#204

Post by ted_dunning »

aleph_minus_one wrote: post #79
Angostura wrote: post #54

Earlier quoted context omitted.

The latter option always comes across as rude. It's a very clear 'piss off you insect'

> 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: wo…

That would be nice.

But it is by far more common that it means "piss off you insect".

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

#205

Post by ted_dunning »

YeGoblynQueenne wrote: post #67
dkarl wrote: post #12

Earlier quoted context omitted.

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…

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.

Of course, there is the unstated second part that you really aren't qualified for a PhD until you can explain it simply.

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

#206

Post by ted_dunning »

zmgsabst wrote: post #114
tbrownaw wrote: post #112

Earlier quoted context omitted.

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?

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.

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".

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

#207

Post by HappMacDonald »

asboans wrote: post #169
Someone wrote: post #159

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, an…

“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…

> (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.

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

#208

Post by rini17 »

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

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.

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

#209

Post by ivanbakel »

HappMacDonald wrote: post #207
asboans wrote: post #169

Earlier quoted context omitted.

“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…

> (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.

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.

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

#210

Post by shakna »

neltnerb wrote: post #182
shakna wrote: post #165

Earlier quoted context omitted.

> 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.

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 under…

That is fine. That's not what has been complained about here. That's invitational, not wall of jargon.
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