What blew my mind is this. What is the sum of the infinite series

1, -1, 1, -1, ...

One answer is to look at it like this:

(1 - 1) + (1 - 1) + ... = 0

Another answer is to look at it like this:

1 + (-1 + 1) + (-1 + 1) + ... = 1

But then it gets weirder. What if you add two of the series together like so:

1 + -1 + 1 + -1 + ...

____ 1 + -1 + 1 + ...

(Please ignore the underscores. They’re just there because otherwise Lemmy messes up the whitespace.)

All the terms cancel out except that first 1 again. But this time it’s the sum of two of these series, which means that the sum of one series is 0.5 and somehow not an integer.

The correct answer is that you’re not allowed to add up infinite series like this so that’s why you get contradictory results if you try.

Being able to actually do anything you understand well enough, the way that magic works in many settings. A brilliant engineer can design an airplane, but he still needs lots of workers and machines and materials to actually build one. A wizard who knows how to cast “fly” can just go ahead and cast it and fly around. If he has the right books, he doesn’t need other people for anything at all.

The sort of mystery only possible in a story where the author himself doesn’t have to know what the secret is. I love science but I was very disappointed when I was a kid and I realized that science meant that everything ultimately had a mundane explanation. A mysterious structure? Built by some Bronze Age dudes. Dinosaurs? Unusually large animals. Legendary heroes? Made-up stories. Even if elves or unicorns turned out to be real, they would have a mundane explanation too because the whole universe follows rules.

Men are only emotional about the important things.

I think this is just OpenAI marketing.

“Insane thing: We are currently losing money on OpenAI Pro subscriptions!” he wrote in a post.

The problem? Well according to @Sama, “people use it much more than we expected.”

Oh no, ChatGPT is too useful to customers! Altman isn’t going to be telling any real problems that OpenAI has to the whole world over Twitter.

I can appreciate a sunset or a flower without needing these things to have “a human behind it all”.

With that said, art is far from the most important potential application of AI. I am merely amused that right now I can ask a computer to draw a cow in the style of Monet and get a pretty good result. The amazing thing is not present-day capability (which is remarkable but not world-changing) but rather what the rate of progress implies about the near future. I think that a computer better than any human at everything (or at least at every intellectual task) is likely within my lifetime.

It’s the end of the world as we know it, and I feel fine.

I was worried that this would be like those cookies pop-ups, but the functionality is still present here in the land of the free…

I live in NYC to support (and have the support of) my relatives, not because I want to. I also never said that I was rich. Even without the toll, driving in Manhattan is at the edge of what I can reasonably spend. Just the parking costs several times more than all my other discretionary spending put together.

I grew up in a Texas suburb and it was pretty nice (except for the humidity) but I don’t have first-hand experience with driving in a place like Houston or LA. I know that there’s a lot of traffic, but I’m genuinely curious about whether it’s really slower than mass transit in NYC is.

I want to clarify that I thought that Cambridge and Somerville were pretty nice - nicer than where I lived at the time. I had friends in Cambridge and I enjoyed visiting them, but I didn’t know anyone in Boston so I never felt like I had any reason to go there. I actually saw more of Boston earlier this year when a friend invited me to go there with her as a tourist than I ever did during the six years that I lived in Massachusetts. The waterfront was pretty, there was an Italian bakery with really good cannoli, and overall the city was cleaner and less crowded than NYC. I don’t have any particular desire to visit again, but that’s not because of anything wrong with Boston in particular.

I do see the irony in the fact that I spend a lot of money to live in a place that tens of millions of tourists visit every year but I really don’t like it. I’m here because this is where my relatives are and they’re not going to leave. (I tried to persuade them to, but it really would be very difficult for them.) I admit that while I know that many people like being in big cities, I don’t really understand why. The tourist attractions presumably get boring quickly even if they were interesting at first, and after that what’s left?

I just want to leave and go somewhere more pleasant and they’re going to charge me $9 every time I do that.

(Full disclosure: right now I want to save some money so I park my car in a Brooklyn neighborhood that doesn’t have street cleaning and then when I want to go somewhere, I take the subway to my car first. I won’t have to pay this toll if I keep doing that, but it isn’t fun and I really want to go back to having my car near me. I’m actually blowing off a dinner invitation as I write this post, because seeing those people would be nice but not nice enough that I actually want to get on the subway.)

Edit: Also I don’t really mind the downvoting. I know most people around here either like urban areas, dislike cars, or both so I wasn’t expecting sympathy from everyone. I do wonder whether the people talking about how wonderful taking mass transit is have ever actually taken mass transit.

I used to live in the Boston area, but out by I95. That’s actually where I learned how to drive. The Boston subway is a lot less gross than the New York subway, but I still only went to Boston about once a year. There wasn’t anything in Boston that was worth getting on the subway for me. However, Cambridge and Somerville weren’t too bad to drive to, as long as I had a plan for where to park.

I’m not saying Boston is a bad place. I just don’t like most of the things that people go into a city to do. The funny thing is that I live in Manhattan because I work around here, driving to work is entirely unrealistic, and I’d rather walk than take the subway.

Those people who can’t afford groceries shouldn’t be complaining either. After all, they’re not literally starving and there are starving children in Africa…

Even in NYC (where driving is particularly slow and mass transit is particularly well developed) it’s still usually significantly faster to drive than it is to take mass transit unless you’re traveling within Manhattan or between two stops of the same express train. The trips I frequently take are about twice as fast by car as by mass transit, so from my point of view I am forced to take mass transit (when I have nowhere to park at my destination) while people outside the city have the luxury of quickly driving directly from where they are to where they want to be.

I’m not going to get into my opinion of how pleasant (or not) taking mass transit is compared to driving, because that’s subjective. However, I will note that according to the MTA’s own survey, a little over half of the people who do take mass transit are dissatisfied by it.

Mass transit is necessary here because the city has an old layout not designed for cars and so it wouldn’t be able to function if everyone had to drive. That doesn’t imply that mass transit is pleasant or convenient. It’s just often the only option.

Yeah, I live inside the congestion pricing zone.

My intuition is that it is a hardware failure. GPUs can develop issues that show up intermittently. You can try running GPU stress-testing software to check if that’s the case.

However, did you recently update your graphics drivers? If you did, try rolling back to an older version.

I think it’s a big deal for me because English isn’t my native language. I have something to prove in a way that native speakers don’t.

I do. I proofread everything to make sure that swipe typing got it right, and I judge people who get it wrong.

It does bug me that the possessive form (fundamental to the language) rather than the informal contraction is the non-standard one, but I suppose it matches “his” and “hers”.

I have no problem communicating with people through verbal means, but I don’t get body language beyond the obvious (e.g. smiling). I mean, I get why people do it but I don’t get how people do it. Generally this isn’t a big deal but it does make dating really frustrating. I can communicate my own interest indirectly through verbal innuendo, but if the other person is doing anything non-verbal then I’ll miss it.

Here are two that I thought were particularly striking visually.

Brothers a Tale of Two Sons: The site of a battle between giants, where you had to navigate among bodies fifty feet tall.

Alice Madness Returns: The ice level, where you could see sea monsters frozen in the ice. (Ignore the text; I couldn’t find a better screenshot.)

wage slave

I think a lot of the people working that much make more money than they actually want to spend. The few that I know do. (They invest most of it.) They still want to have even more, but in the way that an athlete wants to set a new record.

I have been consistently surprised by how good each of the Toy Story films was. I can’t think of a way to make 5 after the way 4 ended (unless it has new protagonists) but I expect the folks making the movie to surprise me again.

Trade (facilitated by money) doesn’t require humans. It just requires multiple agents and positive-sum interactions. Imagine a company, run by an AI, which makes robots. It sells those robots to another company, also run by an AI, which mines metal (the robots do the mining). The robots are made from metal the first company buys from the second one. The first AI gets to make more robots than it otherwise would, the second AI gets to mine more metal than it otherwise would, and so both are better off.

They don’t care that they’re stuck in a loop, the same way humans keep creating new humans to create new humans to create new humans and so forth.