That’s fairly simple: we restrict the complex phase to the range (-pi, pi] and the principal square root halves the complex phase. -1 has the phase value pi, so the principal square root has the the complex phase pi/2, so it’s i, while -i has a phase of -pi/2

This is technically incorrect. While the square root is both the positive and the negative solution, the sqrt (√) operator results in the principal square root. For nonnegative numbers this is the nonnegative square root and more generalised for complex numbers it’s the square root that halves the complex phase.

Now I am confused. How is engineering disjunct from science? And even beyond that, there is astronomy involved (star map, eurion being based on Orion), which has something to do with science.

The eurion constellation is a security feature used on many banknotes. It’s made up from 5 circles and often integrated into larger patterns that make it less obvious. Printers identify it and reject to print money.

I’m not American so I hadn’t heard of Kristi Noem before the last episode. But seeing this post, they were spot on

Except they paid someone to make them look like this

E-fuels are specifically allowed by the EU law. This was added at the last second due to lobbying from Germany and the German car lobby. Another option would be hydrogen engines. So yes, it is absolutely possible to build and sell new ICE cars after 2035 but they’re unlikely to be successful because of the high expected fuel costs.

Right now, depending on where you live, a more or less significant part of the electricity you charge EVs with is not emission free, that’s true. But there are two major advantages: EVs work with emission free electricity just the same as with emissive electricity. So once more or eventually all of the electricity becomes emission free, which is actively being worked on, the car would automatically become emission free. And secondly, you can control where the emissions happen. Especially in cities carbon and nitrous emissions from ICE cars significantly affect the air quality. Even if the electricity for an EV was produced in the most polluting way possible, that pollution would be located at the power plant and could be controlled or mitigated there.

EVs are actually particularly attractive with a higher portion of renewables in the electricity mix. With renewables you can’t control when the peak power production happens. But if you have EVs and their battery capacity in the grid, you could use these peaks of power production to charge the EVs instead of letting it go to waste.

We should really start emphasising that there is no blanket ban on combustion engines planned but an emissions ban. If the car manufacturers wanted to and found it feasible, they’re free to build emission free combustion engines. Every time they call it a combustion engine ban is an admission that they can’t or at least won’t build better engines.

From that chart Qobuz seems to be the all round best deal. Is there any catch?

If lab grown meat becomes readily available and reasonably cheap, that may become a reasonable argument.

The limit was 140 characters which is also the reason why twitter originally had a 140 character limit: you were able to tweet by SMS

More than half of the car crash fatalities were pedestrians so when you are driving yourself you have good odds to kill someone else rather than yourself

It was already shown that SteamOS is way better in terms of battery performance than Windows. So if Windows uses power saving mode by default, these results are even more damning:

There might be some tweaks to mitigate some of the short comings of Windows, but that doesn’t changed that the script has flipped. Before it was Linux that required tweaking and Windows would have a decent out of the box experience. Now SteamOS works great out of the Box while Windows needs tweaks. And at that point there is no reason for sticking with Windows unless your software specifically demands it.

Yes, because just because you bought a book you don’t own its content. You’re not allowed to print and/or sell additional copies or publicly post the entire text. Generally it’s difficult to say where the limit is of what’s allowed. Citing a single sentence in a public posting is most likely fine, citing an entire paragraph is probably fine, too, but an entire chapter would probably be pushing it too far. And when in doubt a judge must decide how far you can go before infringing copyright. There are good arguments to be made that just buying a book doesn’t grant the right to train commercial AI models with it.

My best guess is Russia tries to make their death toll appear as small as possible. If they take the bodies back, those soldiers are confirmed dead but if they don’t take them back, they can pretend, for some time at least, that those soldiers are MiA or PoWs.

Yeah but 2012 is like 5 years ago, right? Right?

If all you know are walls, windows will feel like freedom

Mostly yes, but I take issue with the statement that it’s “correct in terms of messaging”. In short, I’d say that it’s technically correct but incorrect in terms of messaging as pretty much everyone would understand the wrong message.

But being misleading is very much in character for Trump.

It might be correct in a technical sense but it’s first and foremost misleading. If something costs $150 and the seller offers for the price to come down 50%, you’d rightfully expect the price to be $75, not $100. The seller could argue that it’s some 50% markup being removed but would you believe that to be a genuine explanation, or that the seller is trying to mislead or scam you?

If pre-orders ever made sense, it was when you still needed a physical cartridge or disc and the game wouldn’t get patches anyways. But those days are long gone.