Americans may be seeing serious savings in that picture.

I am seeing serious evolutionary pressure on liver genetics.

Meh. As a german, it just doesn’t make me tingle quite like sending tanks to the east.

Why do you believe that?

I’m glad to hear you say that, cause after sending I worried that I didn’t make much sense.

I used that text as a little test for the AIs at DDG. Here’s from Claude 3 Haiku.

Here is the translation to English:

Complex Numbers and Polynomials

Something that hardly anyone knows is that complex numbers, in addition to their application in Complex AC Calculations (known to HTL students), also have a second, important use.

In mathematics, there is often the problem of finding a number x for a given function f(x) such that f(x) = 0 holds.

This is often the case for polynomials, as many important mathematical functions can be well approximated by polynomials.

The Fundamental Theorem of Algebra states that if we allow x to be a complex number, then there is always a solution to the problem such that f(x) = 0.

Restriction: but the polynomial must not consist of only a constant term, i.e., f(x) = 5 would be inadmissible. The x must appear at least once in the polynomial. Otherwise, there are really no restrictions :-)

PS: In the example given in the image (f(x) = x^2 + 2 = 0), a solution would be approximately x = √2 i ≈ 1.4 i.

Then I asked: “Please make it understandable to a general audience and phrase it like a pop-science author would.”

Here is the translation in a more accessible, pop-science style:

The Hidden Power of Complex Numbers

Most people think complex numbers are just some obscure math concept, useful only for electrical engineers. But these mysterious numbers actually have a hidden superpower - they can solve all sorts of important math problems.

You see, in math, we often want to find a number x that makes a function f(x) equal to zero. This comes up a lot when working with polynomials - those nice, smooth equations made up of powers of x.

The problem is, sometimes there just doesn’t seem to be any real number x that does the trick. That’s where complex numbers swoop in to save the day!

The Fundamental Theorem of Algebra proves that as long as we allow x to be a complex number (a number with both a real and imaginary part), then there will always be a solution that makes f(x) equal to zero. No exceptions!

So complex numbers unlock the ability to solve all kinds of polynomial equations that would be impossible with just regular old real numbers. It’s like they have a secret mathematical superpower.

Of course, there is one small catch - the polynomial can’t be a simple constant, like f(x) = 5. It has to actually contain the variable x somewhere. But other than that, complex numbers can tackle any polynomial problem you throw at them.

So the next time you see an imaginary number like √(-1), remember - it’s not just some weird math trick. It’s a powerful tool for solving important equations. Complex numbers may seem strange, but they’re secretly the heroes of the math world!

Electrical engineers use them for calculating AC-circuits. In a DC circuit, you only have to worry about how much volt and amperes are in each part of the circuit. In an AC circuit, you also have to worry about the phase, cause the voltage goes up and down. The phase means where in that up and down you are.

The complex number is interpreted as a point on a 2-dimensional plane; the complex plane. You have the “normal” number as 1 axis, and orthogonal to that the imaginary axis. The angle of the vector to that point gives the phase.

They can be generally used for such “wavy” (ie periodical) processes. But I think this particular field of electrical engineering is the main application.

Believing that animals are just like us s hardly and outlandish belief, on the facts. We’re evolutionarily closely related. We have basically the same skeleton. Skull, spine, rib cage, hips, 4 extremities. Arms and legs go: 1 big bone, 2 smaller bones, and lotsa little bones. It looks to be the same with the brain.

We expect vegans not to blow up slaughterhouses or such. Fair enough. But expecting them to shut up about their beliefs is a bit much, no? Expecting them not to tell people how they feel, not to kiss in public, or hold a pride para… Sorry, wrong prosecuted minority.

I’ve heard these takes about vegans for literal decades now, and not once has an actual vegan popped up to tell me that I’m a murderer.

Ok, so that’s why you’re not making any sense. You have no idea what’s going on.

Look, it’s very simple. Vegans are a small, harmless minority. So some people bully them. Of course, it’s their own fault. They wouldn’t mind them if they weren’t “out and proud”. It’s always the same story. There’s almost no variation.

I thought you were saying that it’s ok to bully them because they believe the wrong thing. That’s what @redisdead is saying. He compares them to “right wing cunts” when they speak their beliefs. Fascis get bashis. Just like vegans, I guess.

Watch the company you keep.

Vegans believe that animals have the same rights to live as humans. A nazi believes that the “others” do not have the same right to live as “his people”.

I don’t think you’ll be able to convince me that these are morally or ethically equivalent positions. But I see the point. They both believe the wrong thing. The out-group sucks. Yes, I know how humans tick.

Ok, I understand. You don’t like them because of their beliefs.

At first, I was confused. Isn’t the fact that you believe something the only justification for saying something? I mean, otherwise you’d be lying. But you’re saying you disagree with the belief in the first place, right?

Well, it’s what they believe. What exactly is the problem there? I have never been called a murderer. There just aren’t that many vegans around. I don’t know in what kind of circles this would be a common occurrence.

They are a small, harmless minority. Isn’t that enough? Maybe it’s made worse by the fact that they are perceived as non-violent and effeminate, because of their strong opposition to suffering, even when the victims are helpless, like animals. There is no personal risk in bullying them. It’s like the hate for environmental activists, trans-women, or liberals in general. I wouldn’t know that vegans aggressively proselytize their life-style if people didn’t aggressively tell me so; something that they share with “the gays”.

Come to think of it. That DMCA argument would really wreck fair use.

It’s illegal to remove “copyright management information” (CMI). In this case meaning the FOSS license. The argument was, that when copilot spits out verbatim snippets of source code without the license, this constitutes removal of the CMI. The point of the argument was that fair use is not a defense under the DMCA. These verbatim snippets are pretty obvious fair use to me, so countering that defense is important if they hope to get anywhere with their suit.

By the same argument, any meme image is illegal. They are taken from somewhere without the original license or attribution. Yikes.

Do Americans know the history of Arlington? I was quite amazed to learn how it became a military cemetery. Not hanging Robert Lee and the other high-ranking traitors is perhaps the biggest single mistake in US history. He is still the highest ranking US soldier to ever betray his country, no?

Don’t listen to me on that. I have no idea how the community feels on copyright or fair use. Whenever AI comes up, the most dogmatic copyright maximalism dominates. On other subjects, the debate is more nuanced. I don’t know how that fits together at all. But I guarantee you, if Alsup ruled on a case like this/OP, they would… Well, most comments would not like the ruling or him.

Yes, I know what you mean. But looking at the comments here, Fair Use is not a popular concept. I remember that Alsup specifically quoted the copyright clause in his ruling. I can’t imagine any argument that would make him rule, on the whole, for the plaintiffs in a case such as this.

Judge William Alsup.

Now I remember that guy. He decided oracle vs google. I can’t imagine he has many fans here.

Wow, long take. I didn’t want “much the same” to bear a lot of meaning. In the german inquisitorial system, in a criminal case, the judge takes over the (police) investigation from the prosecution. When the police become aware of a possible crime, they inform the bureau of the state attorney. A state attorney is responsible for the investigation and for uncovering the truth. But once the case goes to court, the responsibility goes to the judge.

In a civil suit, the parties are basically in charge and not the judge. It’s true that the judge has a more active role in German civil procedure. While the court is not supposed to run its own investigation, it can request additional evidence if it’s necessary to judge the arguments of either side. I am not clear on the details. Where matters of fact must be determined by an expert, either party can request the court to provide one. But they can also make their own arrangements. The court can also solicit an expert opinion on its own, if necessary. Typically, the expert’s opinion is given as a written statement. An oral disposition may happen when questions remain. Afaik, it’s unusual to depose an expert without having first requested a written statement. Either party or the court may question the witness.

Hmm. In what way is the German system more effective? I know of some hair-raising cases. Me, I blame the law-makers and not the judges, but others see it differently. I can’t think of a single related case, where I’d say that the judgement served everyone’s interests.

ETA: Bad question. You explained how the German system is more effective. I’m wondering about cases where I can see this in action. IE: “well-informed and incisive decisions on anything in the computer hardware / EE or computer science fields.”