I think this paper is refuting Conway (and others') proof of the claim that a set can be divided into 3+ parts without relying on the Axiom of Choice. It does so by observing that the proof only applies to sets that have an ordering, which is to say that there is an algorithm for picking an element from the set, which am extra constraint beyond having only a test for determining whether a known object is an element is in the set. It then goes on to prove that it is not possible to evenly divide a set that lacks such a selection algorithm.
> I think this paper is refuting Conway (and others') proof of the claim that a set can be divided into 3+ parts without relying on the Axiom of Choice.
This paper is not refuting Conway's, and Conway's paper does not prove the claim that a set can be divided in 3+ parts without relying on AC.
What the Conway's paper proves is that, without assuming AC, if there is a bijection between A×n and B×n for some finite n, then there is a bijection between A and B. Axn can be equivalently written as the union of a×n, as a ranges over the elements of A, similarly B×n can be written as the union over b×n. This paper shows that if instead you take the union over a×N_a, where the sets N_a are pairwise disjoint and have n elements, and similarly instead of considering B×n you consider the union of b×N_b, where the sets N_b are pairwise disjoint and have n elements, then the existence of a bijection between those two unions is not sufficient to construct a bijection between A and B if we're not assuming AC. The main point here is that without choice we cannot order all of the N_a's and N_b's at the same time, while in Conway's paper, since N_a=N_b=n={0,1,...,n-1}, they are already uniformly ordered and no such issue arises.
To be fair, I think some people just quickly and intuitively "get" what's expected from them when doing proofs, without any formal introduction. But for others (like me) it is very much helpful to at least list the basic natural deduction inference rules, and to do a bunch of exercises where they have to use these rules explicitly. Otherwise they are floating in thin air, with only a hazy idea of what a "valid logical step" even is.
You can build those and then pick if you want them even or odd, which are regular-number concepts. That is exactly what they did, and what I described. You go and re-read it.
Your China article is from 2004. China's regime's ability to control media and its residents is stronger now than then, and the people in charge are more insecure and defensive. That may be enough to explain the change in PR strategy.
Alternatively, past leaks simply weren't bad enough to embarrass the State and could be blamed on local officials. This one got so big so fast that a more defensive posture was required.
> Editors’ note, March 2020: We are aware that this story is being used as the basis for unverified theories that the novel coronavirus causing COVID-19 was engineered. There is no evidence that this is true; scientists believe that an animal is the most likely source of the coronavirus.
which seems to be unscientific editorializing. There is some evidence, as presented in the OP for example, and there is "no evidence" for any other origin theory either.
And the Chinese government in Wuhan showed from the start with Li Wenliang's experience, that any evidence that pointed to imperfect competence in Wuhan would be destroyed by the totalitarian government.
There is one for $70 on amazon that might be a contender. I'm sure if I searched aliexpress or something I could find something better for even cheaper.
Look at how hard it is to make people pay 0.99 on the app store for an app. It's not the price, it's the fact that you have to pay.
Deciding to buy Netflix is a one-time decision, and then you have access to the full catalog, without any friction. I added "for free", meaning that I don't have to decide whether or not I want it enough to pay, and then enter my payment details, manage an account & password, etc.
When Netflix was the only game in town, it actually made a measurable dent in pirate traffic; a fact which was widely reported at the time. Now that content owners want to have their own Netflix (thus draining its catalogue), piracy rises again [1].
It's true that there's a certain limit the "it's not a price problem" statement. I'm perfectly willing to pay up to a certain amount per month on entertainment services (and I do), but at some point, enough is enough. That certain amount will vary from person to person, the industry just needs to find that sweet spot and stop trying to turn potential clients into criminals.
I think that piracy overall isn't a simple issue: trying to put every pirates in the same bag isn't going to work, because not everyone has the same set of motivations: some have issues with packaging, some with price, and perhaps there are other kinds of issues?
What can be done on the other hand, is to figure out what are the main reasons for piracy (ie, on average, what are the driving factors), and what can be done to remove them.
Packaging in the music industry took a while to adjust: they first fought really hard against Napster and the like, when the customers were quite ready to accept digital content, but the DRM solutions were mostly in the way, or the network technology wasn't quite ready. Nowadays, everyone takes for granted that music is bandwidth cheap, and content owners realized that removing the packaging issue did remove a large part of the piracy, because those who pirated for lack of good delivery didn't have to anymore, and with this market share acquired, the revenues increased, which meant that prices could go down, and thus another chunk of the piracy crowd became customers as well.
I guess that my point is that price isn't a completely solvable problem, but it's not entirely orthogonal to the other issues.
Clearly, price cannot be reduced down to zero, there will always be people finding this or that to be too expensive for what it is. Note that ads do not reduce cost to zero for the consumer in the case of digital streaming: they still have to pay in ad view time, which leads to ad blockers, yet another form of piracy.
> If Netflix was working so well, all those other services wouldn't exist, because they'd have no customers.
Even if Netflix is working perfectly well, they can't have the monopoly of creativity. They might produce good content (something you seem to disagree with, I personally don't have an opinion on that), but they cannot prevent other distributors to do the same. The main reasons for this are that:
- again people cannot be put all in the same bag: what one will be interested in might bore the next,
- "topics" can be exclusive (GP alluded to that): For instance, Disney owns "Star Wars", and if you want to watch some of that stuff, you'll have to go to them.
You're right on price, there's definitely a certain nuance to be had there. I tried adding it to my original post, but it only diluted my point, so I kept it about convenience.
You won't ever get rid of piracy, but you can reduce it to negligible levels by offering what people want: a reasonable price & a good user experience. Music offers this currently, and piracy is pretty much a solved problem for them: only 2.9% of piracy is music [1]. I'd argue most people prefer having access to all the music they want on the device they want just a click away, for 10-15$ per month, than tracking down & downloading a good-quality torrent that won't give you a virus. Ad-sponsored versions are also an option here, and broadcast TV & radio's rich histories would indicate that's a pretty good business model. Just don't get greedy & do both (looking at you, Cable TV).
Or something like that.