I'm pretty sure that line of the article didn't mean to imply that we don't know, or aren't sure, only that it goes beyond the scope of the article and isn't directly relevant to the topic at hand.
It's really the last thing that keeps any trustworthy source from recommending switching to linux for gaming without reservation. As soon as you want to play any competitive online multiplayer games, which to my understanding is the vast majority of people, you're going to have problems with some anti-cheat not working on Linux sooner or later.
I'm not saying it's the only thing that stops mass adoption of Linux for gaming, but I think we'd see a massive uptick very quickly, if this problem went away.
According to Wikipedia, there are countably many algebraic numbers, and that makes intuitive sense to me as well. Do you have a source that the set of algebraic numbers is uncountable?
An interesting thing about the quote you highlighted is that it's already true about the set of real numbers itself. The set of real numbers that can be precisely, individually identified is a countable subset of all real numbers. That means the vast majority of real numbers, an uncountable amount of them, can not be individually defined and thought about.
> Maybe it's the idea of a completed infinity that's my problem; maybe it's the fact I don't understand how to define (or forgot cauchy sequences in detail) an arbitrary real.
As someone who also has never fully made his peace with the diagonality argument, but just chosen to accept it as true, as a given, this kind of bumps up against an interesting implication of different cardinalities of infinity.
To precisely define an arbitrary real you'd need some kind of finite string that uniquely identifies that real number. Finite strings can be mapped, 1 to 1, to natural numbers. Therefore there can't be a finite string for any real number that uniquely identifies it. Otherwise we'd have a mapping between natural numbers and real numbers.
In fact, the set of uniquely identifiable real numbers is a countable subset of real numbers. [1]
Somehow, this realization has helped me make peace with the uncountability of real numbers.
[1] Sorry if use words like "unique", "identify", "define" in not quite the right way. I hope the meaning I'm going for comes across.
If they provide something of value to their audience, they can take money from their audience, in exchange for that value. If they do not provide value for their audience, them ceasing to exist is not a loss for society.
> I hope the next time there is a pandemic like Covid that we do more sensible things like not ban access to outdoor activities, shutdown beaches, shutdown everything for months, destroy the economy, etc..
At the time we didn't have enough information to know locking down outdoor activities was unnecessary. All we knew is it is more contagious than other infectious diseases, like the flu. Given what we knew, it was a reasonable policy, even if in hindsight we know it wasn't necessary.
It's funny how the same people who kept saying we don't have enough information about if masks work, because we didn't test them enough specifically with covid, are now the ones who say we should have known that outdoor activities could have been left open.
> Also ironically WFH is great unless you are the poor soul who still needs to work on the “front line” every day like warehouse workers, delivery drivers, etc.
"Front line" workers like warehouse workers and delivery drivers also profit from limiting vectors of infection by office workers staying home. Nothing "ironic" about it.
I don't have a strong opinion in the matter, but the argument is that banning things don't automatically make them go away. Banning things that people want to do will make organized crime spring up around it, which is often worse. The idea is, by allowing it in some limited legal way, you make it unprofitable for the organized criminals.
If the point of this exercise is to create a game that removes first move advantage, while keeping the game as unchanged as possible, this is an utter failure.
Turning a game of perfect information into a bluffing and anticipation game is not a minor change. It's a fundamental change of the essence of what the game is.
I admit that while I do regularly play chess, I'm not super well versed in either FEN nor Chess960. That said, I've been trying to figure out why you would need a different notation for Chess960 for half an hour now, and I just can't figure it out. All explanations I'm seeing just make some vague mention about ambiguity in the regular notation for Chess960, but I, personally, can't think of a situation in which the regular notation is insufficient.
The KQkq still unambiguously mark which player can castle to which side, and once either a rook or King move for the first time, you just remove the corresponding letter(s). What am I missing?
You're correct. In fact I'm not seeing any two probe words that will give you a definite piece of positive information, without taking into account a third word.
I made my own mistake when trying to figure out this puzzle, that I didn't notice until your comment prompted me to go back and check through it again. I thought after the three even words, the solution had to BAY or all three even words had to be zeroes. But without using any of the odd probe words, words starting with BU- are also still a possibility.
I understand this, but the person who responded said Passkeys are exactly the same as SSH and used the same, when asked what they are. If that was true, then we would just teach non-technical users to use SSH Keys.