It's relatively easy to see that you can't take a product of groups where that factorization arises if it doesn't already factorize in the individual factors
Turns out Abelian factors spoil the mechanism of anomaly cancellation you got these constraints in the first place from, so they're out (this is a relatively recent insight, 2010 I think)
@0celo7 It comes from the explicit computation of the anomaly polynomial
@0celo7 Sure - the simple Lie groups are completely classified by their Lie algebras/Dynkin diagrams and getting the dimension of a vector space isn't hard.
apparently you take the 120 generators of SO(16) and throw in a Majorana-Weyl spinor of Spin(16) (128 components) and write down some surprisingly simple commutators between them
Also, promising that I am asking this entirely out of technical interest, would you mind telling me what needs you have not been able to serve on a Linux system?
I am genuinely interested and will not try to "convert" you.
My laptop runs a flavor of Ubuntu. I love it in many ways, but the battery life is terrible and I think it's because the Linux drivers just aren't optimized.
I want to make my C++ project cross platform, and I'm considering using Cygwin/MinGW.
But what is the difference between them ?
Another question is whether I will be able to run the binary on a system without Cygwin/MinGW ?
Erik Verlinde has proposed a emergent structure of Gravity in a recent paper Emergent Gravity and the Dark Universe
Abstract from paper cited above
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic...
@BenNiehoff welcome to the chat. have been reading about Verlinde myself lately, citing him in here & am attracted to his ideas esp wrt "emergent properties". plz consider this :) physics.meta.stackexchange.com/questions/7783/…
a ha! I found a resource with some concrete information about exceptional Lie algebras in the e-series (including the higher ones that don't have finite-dimensional representations)
@BenNiehoff it seems to be relatively new/ somewhat radical wrt est theory, yhave a bunch of links on it, am planning to blog on it soon, Hossenfelder has some blogs on it, also Quanta mag profiled it recently
@BenNiehoff have you looked at her paper? am a fan, coincidentally was just reading her blog today wrt simulation hypothesis as refd by aaronson, have blogged on that a bit )( also
@BenNiehoff Personally, I don't think that's a legit question type, but I'm not going to mod-close that question. If people don't want those questions they're gonna have to step up and close them.
@BenNiehoff you debated simulation hypothesis on facebook? bummer its not linkable. are you pro/ anti? full disclosure, have leaned pro myself for many yrs & am in good company :P
I find the question of whether or not we live in a simulation entirely pointless - how could we ever tell either way? It's just Descartes' demon in a modern disguise.
@ACuriousMind to some degree think thats a very valid objection, to another degree there are some proposed, even beginning-to-implement experiments that attempt to isolate "very subtle" anomalies in spacetime fabric so to speak
@ACuriousMind the copenhagen concept comes into play. but if there is any "granularity" to spacetime that would seem to be more consistent with a simulation idea that involves discreteness at very infinitesmal levels
@ACuriousMind (admittedly/ concede) there is a lot of (popsci) hype over the simulation hypothesis, in this way its much like AI lately. it didnt "entirely" help that recently elon musk has endorsed it... o_O
@vzn "More consistent" in what sense? Why can't the world be "granular" without being a simulation? You can't make any sort of likelihood arguments here because our sample size of universes is exactly 1.
to me the only physical thing that could falsify the "simulation" hypothesis is the existence of an oracle: a physical system or process that produces results that are intrinsically incomputable
@ACuriousMind the analogy is analog vs digital computing. agreed its a very abstract concept. it would take a long time for physics to come to investigate it seriously. but it seems many of the concepts are already present in QM & other areas of physics. & lets not disregard all the high profile proponents incl nobel prize winner 't Hooft
@BalarkaSen Let $(f_n)\subset L^p(\Bbb R^d)$ with $f_n\to f$ pointwise a.e. and $||f_n||\to ||f||$. It's known that $f\in L^p(\Bbb R^d)$. For $\epsilon>0$ can one find $K\subset\Bbb R^d$ compact and $n_0\in\Bbb N$ such that for $n\ge n_0$: $$\int_{K^c}|f_n|^p \, dx<\epsilon?$$
It's clear this can be done for each $n$, but why can one choose $K$ uniformly?
The idea here being that if $f_n$'s norms converge and it converges pointwise, then the masses of $f_n$ get concentrated in some compact set $K$ for large $n$.
OK. Today's xkcd is pretty funny. But you have to sing to get the full effect. With your best fake Eye-talian accent. Unless you really are Italian of course, in which case you should use a real accent.
@yuggib There was a while when the scary immigrants who were ruining our great country (that is the USA) were those dirty, Catholic, Italians who were living in groups int he slums and not learning our language and taking our jobs and all those other things that worry certain people so very much.
One the ways that "regular" Americans (meaning the Scots and Irish and Poles and other immigrants who'd been here a little longer) had of pointing out the difference was by intentionally mispronouncing the adjective: Eye-talian.
@yuggib Rubbish. Anyone who finds themselves shamed by a catchy but essentially throwaway song urgently needs (a) a sense of proportion and (b) a sense of humour!
I want to make my C++ project cross platform, and I'm considering using Cygwin/MinGW.
But what is the difference between them ?
Another question is whether I will be able to run the binary on a system without Cygwin/MinGW ?
Erik Verlinde has proposed a emergent structure of Gravity in a recent paper Emergent Gravity and the Dark Universe
Abstract from paper cited above
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic...
