4 ms·
This is a very informative article about the history of manifolds and their significance. Don’t let the title fool you into this being just a definition. It’s
by tetrisgm 1y ago
This is a very informative article about the history of manifolds and their significance. Don’t let the title fool you into this being just a definition.
It’s actually much more well written than the majority or articles we usually come across.
- robot-wrangler 1y agoI'm always surprised more people don't know about Quanta. Seems like it's currently the best science journalism out there, and IMO a very strong candidate for the single best place on the internet that's not crowd-sourced. The mixture of original art and technical diagrams is outstanding. Podcast is pretty good too, but I do wish they'd expand it to have someone with a good voice reading all the articles. Besides not treating readers like idiots, they take themselves seriously, hire smart people, tell good stories but aren't afraid to stay technical, and simply skip all the clickbait garbage. Right now from the Scientific American front page: "Type 1 Diabetes science is having a moment". Or from Nature: "'Biotech Barbie' says ..". Granted I cherry-picked these offensive headlines pandering to facebook/twitter from many other options that might be legitimately interesting reads, but on Quanta there's also no paywalls, no cookie pop-ups, no thinly-veiled political rage-baiting either
- getnormality 1y agoIt's because of their Simons Foundation support, but not only because of that. I mean, I invite anyone to name another billionaire pet project of comparable quality.
- robotresearcher 1y agoCarnegie Libraries, Nobel Prizes, Rhodes scholarships?
- Iwan-Zotow 1y agoClay Mathematics Institute, with its 7 Millennium problems
- robotresearcher 1y agoGood one! Stanford & Carnegie Mellon universities...
- gowld 1y agoMathematica?
- robot-wrangler 1y agoGood game and a hard question, especially if you make "comparable" more explicit. I'd add "noncommercial, open-access", and "modern" in the sense that it happened under the current norms with respect to legacy and the social contract.
- Iwan-Zotow 1y agoClay Mathematics Institute, with its 7 Millennium problems
- BobaFloutist 1y agoI like what MacKenzie Scott is doing in the space of "What it takes to actually spend down billions of dollars"
- drob518 1y agoI agree. I find their articles very enjoyable. And even though they stay technical, they don’t descend into becoming a technical journal. The content is still accessible to a non-expert like me.
- hufdr 1y agoQuanta’s greatest strength is that it doesn’t pretend to be clever. Many tech publications write as if they’re showing off, and you just end up feeling tired after reading them.
- aleph_minus_one 1y ago> Many tech publications write as if they’re showing off, and you just end up feeling tired after reading them. I like this honestly because this shows that I learned something intelligent. On the other hand, if I don't feel exhausted after reading, it is a strong sign that the article was below my intellectual capacity, i.e. I would have loved it if I could have learned more.
- mulmen 1y agoSeems superficial. If a simple concept is presented in a complex way what did you actually learn?
- aleph_minus_one 1y agoOften, if the concept is presented in a more complex way the reason is that the author wants to emphasize and explain how the concept relates in a non-trivial way to some other deep concept; thus you learn a lot more than when the author explains things in the most simple (and shallow) way.
- mejutoco 1y agoIMO the most common reason why something is presented in a more complex way is that it is badly explained. Of course, most common or not, each case is different.
- jaennaet 1y agoAlso speaks to a lack of understanding on the author's part; people who truly understand some subject are generally much more adept at explaining it in simpler terms – ie without adding complexity beyond the subject's essential complexity
- Workaccount2 1y agoQuanta is amazing because it doesn't have to worry about money. It's a publication run by the Simons Foundation, funded with the proceeds of the wildly successful RenTec hedge fund. So they get pretty much full editorial control. For other publications they are beholden to people who haven't figured out ad-block, and your bar needs to be pretty low to capture that revenue.
- jordanpg 1y agoRemarkably, they don't even ask for money anywhere on the site. Now that is a rare thing on the modern internet, especially for high quality writing.
- pferde 1y agoAnd they have a RSS feed, although it's a bit tricky to figure out, since the relevant header tag for that is set up incorrectly, pointing to a useless empty "comments" feed even from their main page. The actual feed for articles is https://www.quantamagazine.org/feed/ https://www.quantamagazine.org/feed/
- lemonberry 1y agoNice find, thank you. Your sleuthing is appreciated.
- tetrisgm 1y agoOh dope. Added to my feedbin!
- Angostura 1y agoAgreed. I'm not a mathematician - and to me a manifold is more familar in the context of engines. But I found both the text and the diagrams very useful.
- ur-whale 1y agoWhen you use the word "engine" on HN, it can be understood as many things that aren't what you think (e.g. game engines).
- idoubtit 1y agoIs that really a good article? I thought it was average. It had some big flaws but was probably still informative for readers with no mathematical knowledge in the domain. For instance, consider the only concrete example in the article: the space of all possible configurations of a double pendulum is a manifold. The author claims it's useful to see it in a manifold, but why? Precisely, why more as a manifold than as a square [O,2π[²? I also expected more talk about atlases. In simple cases, it's easy to think of a surface as a deformation of a flat shape, so a natural idea is to think of having a map from the plan to the surface. But, even for a simple sphere, most surfaces can't map to a single flat part of the plan, and you need several maps. But how do you handle the parts where the maps overlap? What Riemmann did was defining properties on this relationship between manifold points and maps (which can be countless). BTW, I know just enough about relativity to deny that "space-time [is] a four-dimensional manifold", at least a Riemmannian manifold. IIRC, the usual term is Minkowski-spacetime.
- gowld 1y ago> Precisely, why more as a manifold than as a square [O,2π[²? Because, as the article explains, it's a torus (loop crossed with a loop), not a square (segment crossed with a segment).
- griffzhowl 1y agoSpacetime is a four-dimensional manifold (at least theoretically - who knows what it is in reality). Technically it's a pseudo-Riemannian manifold since the metric is not positive definite: it can be negative or zero for non-zero vectors. A Riemannian manifold proper has a positive definite metric, but in popularizations like this I wouldn't really expect them to get into these kinds of distinctions.
- mr_mitm 1y agoMinkowski spacetime is the term in special relativity, i.e. the flat case, or zero curvature. In general relativity, spacetime is a pseudo Riemannian manifold, like the sibling comment says. Unlike Minkowski spacetime, it can be curved.
- doctoboggan 1y ago