Why are these posts always shitting on teachers? I don't know what teachers you're seeing, but I've never seen any teacher of any subject / age-group ever discourage anyone for thinking about something a different way. Quite the contrary, different ways of approaching problems are always encouraged.

And this is why it is ludicrous to believe that ultra-rich people earn their fortune with hard work or good ideas. Being rich generates its own money. Being poor is expensive. There should be no billionaires, for any reason. Such concentrated wealth is very bad.

While I disagree that "billions is beyond being halved", there is some truth to the idea that numbers can get so big that halving doesn't make much difference. That seems very very counter-intuitive, so I'll try to briefly explain.

Consider (10^10 + 2). That's 10000000000+2. I think it's fair to say that the +2 doesn't make a lot of difference. It's still approximately 10^10.

So then, consider 10^(10^10)×100. That's a huge number, too big to type here, then multiplied by 100. So the result is 100 times bigger than the huge number. But... writing it down we see this:

10^(10^10)×100 = 10^(10^10+2) ≈ 10^(10^10).

So although ×100 does make it one hundred times bigger... that just doesn't really make a lot of difference to a number as big as that one. As numbers get bigger and bigger, they start to take on properties a bit like 'infinity'. Addition stops being important, then multiplication, then for even bigger numbers exponentiation doesn't huge much of an impact either.

Mathematically, I think this is really cool and interesting. But I don't think 1 billion is that big. 10^9 is big enough that +2 doesn't matter much, but not so big that ×2 doesn't matter.

[edit] (I'm struggling to get the nested powers to look right... So hopefully my meaning is clear enough anyway.)

To this very day, I know nobody - NOBODY - who even comes close to Gmail’s spam filtering capability.

I disagree. Perhaps you need hard evidence for a claim like that.

I have a gmail account, and a proton mail account. My gmail account is packed with spam. It has so much spam its crazy. The account is basically unusable. Which is fine, because I no longer trust google. It's been years since I've told anyone to use this account.

On the other hand, I can count on one hand the number of times I've got a spam message in my inbox on protonmail. In fact, I remember. It's 2. The account isn't as old, but I've used it to sign up for at least as many things. It's my main account now - partially because I've turned anti-google, but also because its not choked by mountains of junk.

(To be fair, I suspect the main reason that my gmail account is so bad is that it has a popular username, and other people have accidentally signed up for things with my email accidentally instead of their own. Nevertheless, the fact is that the gmail is spam-central, and the protonmail account is clean.)

Cascading Style

I think modern AI would know that though, since it follows almost immediately from Fermat's Little Theorem.

You should know, it is possible that other people find this comic funny even though you don't. And no matter how much you 'explain' why it isn't humorous, you can't undo the fact that other some people have found it funny. So then, what do you think people learn from your explanation?; Probably something about you rather than something about the comic.

At the same time as Pink Floyd singing the same line?

Yeah, especially given that so many popular vegetables are members of the brassica genus

Nar. A statement and its converse are not equivalent.

If you just start talking to some random person about it, then you're unlikely to get a high-quality conversation; because most of the stuff people will say about it is inane or obvious or obviously wrong, etc. But there are definitely interesting discussions and thoughts that can be had about it. I've had countless garbage conversations about, and a handful of good ones. Probably my favoutite take is from Daniel Dennett's book "Freedom Evolves". He is very careful to build up a strong picture of what is it that we're talking about and what the 'obvious' problems are, before then carefully and systematically showing those things aren't really problems with what we were talking about anyway. Before reading that book, I was hard line in the camp of "obviously free will doesn't exist; that's a scientific fact"; but after reading it... well, I'd now say "it depends exactly what you mean, but probably the free will you're talking about does exist.".

I'd say this comic is more relevant:

The meaning of free will is exactly what people are discussing when they talk about whether or not it exists. What does and what doesn't count as free will is what's up for discussion.

And it is a license. I'm just responding to the comment about the law.

My understanding is that GOG is an exception to this. Here is a quote that I got from an Ars Technica article

California's AB2426 law, signed by Gov. Gavin Newsom Sept. 26, excludes subscription-only services, free games, and digital goods that offer "permanent offline download to an external storage source to be used without a connection to the internet." Otherwise, sellers of digital goods cannot use the terms "buy, purchase," or related terms that would "confer an unrestricted ownership interest in the digital good." And they must explain, conspicuously, in plain language, that "the digital good is a license" and link to terms and conditions.

Since GOG does offer permanent offline installers that can be used without an internet connection, GOG's sales are exempt from this new law.

If we're talking about DRM as in a measure to prevent copying, or require online security check, or anything like that, then no GOG game has DRM. One of GOG's core policies is that all of their games are DRM free. However, some people have stretched the definition a little to include other stuff. For example, if an online multiplayer game requires GOG Galaxy to connect to its online servers, some people consider that to be DRM.

There are some posts on GOG's official forums where people try to list all the games that have "DRM" of any kind. So if you're interested, that's where you could look. But if you just want to have confidence that you'll be able to install and run the game in the future, then don't worry about it. No GOG game has anything that would prevent that.

Partially so, but a lot of adult pain is due to bad posture, and weak muscles from lack of exercise. (Weak muscles don't directly result in pain, but it does mean that stuff like "looking in the mailbox weird", or sneezing, or lifting something off the floor can result in stuff going wrong.)

I find it amusing that they "use cookies to give you the best possible experience", but then ask you to pay to not have them.

It's a geometry puzzle. Of course they aren't going to get out a protractor to carefully get the 80° drawn to scale. The point of these puzzles isn't that we actually want to know what the angle is. The point is to navigate a maze of logic. (A very short maze in this particular case.)