via https://duckduckgo.com/?q=DuckDuckGo+AI+Chat&ia=chat&duckai=1 with GPT-4o mini

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”. Of course, people wouldn’t mind if they didn’t shove it in their faces all the time. Where have I heard that before?

https://www.youtube.com/watch?v=KHc-7tzUPnY

Ja. Gut so, Jaqueline. Lass alles raus, Jaqueline. Nicht durch die Nasen!

The noun doesn’t matter after an adjective like ‘multiple.’ Nothing good ever follows ‘multiple.’

-Terry Pratchett, Guards! Guards!

An individual can use the roads if the can afford a car. Amazon must be operating 1000s or 10.000s of vehicles in the US alone. Clearly, some benefit more than others. Some win at Monopoly.

Are we at least agreed that it is a conservative policy? If you carve up the roads and gift them to the people who own the land next to the roads, it’s still conservative. It will lead to greater inequality and poverty. It’s not left-wing redistribution.

we’re now going to charge anyone who wants to use them and keep 100%. Oh, and you have no ownership rights, so we can restrict access to these roads as we see fit."

I don’t know what this means. What is currently happening that is like that? Besides, you want data to be owned, and an owner can restrict access. Shouldn’t you be all for that?

I thought of something that maybe gets this across. Think about roads. We all pay for them with taxes. Companies use these roads for free to make a profit. EG Amazon runs delivery vehicles on public roads.

The (center-)left take on that is: “You didn’t build that.” It can be an argument for progressive taxation and even a wealth tax.

Then there’s people who say that we should privatize all the roads. Let Amazon pay a toll for using those roads. Is it clear that this is a conservative policy?

You want to force people (not just companies) to pay for use of a new kind of intellectual property. That is capital income. You want money to go to property owners.

If you think about this for a second, you should realize that this means lower wages. If a bigger share goes to property owners, then employees must have a smaller share. The money can’t come from anywhere else.