> That thinking of them as anything other than directions with magnitudes is wrong.
Mathematicians like to think of just about everything as vectors, so that sentence seems a bit off.
Anyway, yeah, starting from abstract definitions is a great way to make a student's life hell. After all, there's a reason universities teach linear algebra twice.
It does not. Quantum effects are a smokescreen for clinging onto the idea that "only humans can be human". BQP is quite easily contained in PSPACE, and more generally adding quantum operations does not move one beyond Turing machines (realistically - only something like a halting problem oracle does).
I think you missed the point of my comment. BQP (i.e. "stuff that is efficiently solvable by a quantum computer") is almost certainly bigger than P (i.e. "stuff that is efficiently solvable by classical computers"). There was not even remotely anything in my argument that was claiming "only humans can be human" or "only humans can be intelligent" or anything like that (that would have been a silly claim). And nothing remotely related to claiming quantum effects have anything to do with human brains.
It affects complexity. Sure, it is fascinating to learn there is a separation between computable and not computable tasks, but there is an important separation among the computable tasks as well. There are "practically computable" tasks (computable with a reasonable complexity) and "computable tasks that are still infeasible in the real universe" (e.g. tasks with exponential complexity). Amusingly, it seems that there are also tasks on the border between between practical and infeasible, that can be practically solved on a quantum computer, but can not be solved in a reasonable time on a classical computer (even one as big as the whole universe).
P.S. There was some abuse of naming conventions and nomenclature above.
P.P.S. While computability is a well proven concept, claims about complexity (i.e. practical vs infeasible "computable" tasks) are frequently only conjectures (although they have some supporting empirical observations).
P.P.P.S. The proper terms to google for as a starting point would be (really, this barely scratches the surface):
- complexity class P: computable tasks that can be efficiently solved by a classical computer
- complexity class BQP: computable tasks that can be efficiently solved by a quantum computer (and includes tasks that are conjectured to not be efficiently solvable by a classical computer)
- complexity class NP-hard: computable tasks that are conjectured to not be solvable by a classical or a quantum computer efficiently (i.e. a medium sized problem would take a computer bigger than the universe to solve)
For me, it was Chrome's peerless DevTools (although Firefox has been catching up recently) and the fact that entering full screen on Firefox freezes up the entire UI for me (it's probably some bad interaction with BSPWM).
Out of curiosity, who are the people who want DRM? I understand that big media producers want them, in some misguided attempt at protecting their IP, but is that it?
I guess people would even pay for Spotify, if it's DRM free (which means the stuff on it can be copied), but that is still considered "radical" (in the Overton window) for shareholders of media distributors.
That "Save your music offline" is a feature in 2019 is ridiculous.
Fuck yes I'd pay for a drm free audio service. Any competitor of Spotify's that offers this would instantly get me as a customer - assuming, of course, they have a similar offering to Spotify. Spotify is already mediocre compared to Grooveshark and YouTube, it really shouldn't get worse than that.
Yes but protecting their IP is futile, therefore DRM primarily targets legitimate users. The idea is to have complete control over the user experience. You can only watch movies on approved device X in approved app Y. The media companies can then use DRM to put hardware manufacturers and software developers under pressure and order them to do whatever they want.
Honestly, it's not that big a deal, in my opinion. Firstly, it looks much better, since the operators, i e. the ideas I'm most familiar with, take up the least space. Secondly (and more stupidly), millions of programmers don't even know English and they've managed to get by with ifs and elses, so I'm sure we'll manage.
It's because the std::ops::RangeInclusive struct is meant to be much more generic than just ranges over machine-sized integers. I think a generic range struct in C++ would similarly take references.
Isn't this letting Facebook and Comcast have their cake and eat it, too? Giving them full authority to censor whatever they want, but still not holding them liable for what they host?
Mathematicians like to think of just about everything as vectors, so that sentence seems a bit off.
Anyway, yeah, starting from abstract definitions is a great way to make a student's life hell. After all, there's a reason universities teach linear algebra twice.