> That part is fine. But why, then, does multiplying zzˉ give a “magnitude” that works in a reasonable way?
Because the product of all Galois conjugates is a norm and the determinant of the linear operator defined by general field multiplication of a primitive element when viewing the field extension as a vector space of the extension field over the base field.
Although the geometric interpretation of norms in Galois theory really only works for the complex numbers because only the complex numbers are a field. Quaternions are not a field.
Yes, I'm ignorant, because Heidegger isn't saying anything. He didn't teach me anything. Thus I remain ignorant, unknowing.
You can't even explain what he said, you just said, "go learn his words". That's not knowledge, that's not insight. That's just "the wordplay is great". But it's not content. It's merely form, it's sophistry, it's useless and meaningless.
I asked a very specific question originally. What does "time is the ripening of temporality" mean? That's one way to translate one of the things he says, using different words for time and ripening in German. He's playing word games because those words sound similar in German and people like you confuse it for profundity.
You actually read Being and Time? What the heck do you get out of it? Heidegger just seems to play word games with German words without actually saying anything. "Time is the ripening of temporality." tf do phrases like that mean??
An ad is never helpful because ads are designed to mislead me into buying something I didn't need or knew about before I saw the ad.
If nothing else, an ad cannot impartially compare a product with the competition (and sometimes the "competition" is buying nothing at all), therefore every ad lies.
If I already needed or knew about it, I didn't need the ad.
If I was happy with my life without the product advertised, I didn't need the ad.
Furthermore, ads are fueling our capitalist, consumerist economy that is destroying the planet. Ads are a literal existential threat to humans.
I don't use phones, so if I have to go somewhere, I have to memorise the route. I enjoy the exercise. I look up the directions on my laptop, mentally rehearse the points of interest that will indicate to me where I need to take particular turns, and then have to put into practice my memory with the actual physical landscape I tour as I follow this route. Sometimes I make mistakes, but correcting them is part of the exercise.
It seems very few people nowadays know how to follow a route, especially an unfamiliar one, without being tethered to their GPS.
The Japanese release of the game flips around the "soundless" sections with the music section, suggesting that listening to that rocking track for most of your flight is the intended experience.
The information to properly land the plane is in the manual. The required air speed and altitude have never been a secret, if you read the manual (which I guess most kids didn't).
The real difficulty, not explored in this disassembly, is that the game has semi-realistic physics! My older brother was in flight school at the time and was able to easily land the plane and taught me how to do it.
As the article states, "Altitude and speed are both controlled by throttle input and pitch angle". So you can't just hit the engines or air brakes button to change your speed. If you lower the nose of the plane, you'll speed up and vice versa! So you have to carefully juggle your speed and altitude by altering both your pitch and your engines/air brakes.
My brother taught me that my speed wouldn't reduce if I'm nosediving, so raise the nose a little while opening my air brakes for a quick reduction in speed and then level out to maintain altitude. The game actually models this somewhat accurately!
We did try it. We tried it for a couple of millenia. It was much harder to understand and our collective mathematical output as a human species was much slower than it is now.
> they can't be bothered to write more than 1 character
You try handwriting all of your code and let's see how long until you start abbreviating everything.
Mathematical notation is all abbreviations. We used to write mathematics without abbreviations. It was absolutely horrid. Try reading some 13th century mathematics, translated to your language (e.g. Fibonacci https://archive.org/details/laurence-sigler-fibonaccis-liber... ), and see how much of it you understand without the benefit of symbolic notation. We would even write aaa instead of a^3.
The point with mathematical notation is that it can all be sounded out and it's extremely general and abstract. Generally, x is not a measurement, a quantity with a unit, a meaningful anything. It's just a number, and x is a better name than front_server_count or whatever thing you're programming about.
Because the product of all Galois conjugates is a norm and the determinant of the linear operator defined by general field multiplication of a primitive element when viewing the field extension as a vector space of the extension field over the base field.
Although the geometric interpretation of norms in Galois theory really only works for the complex numbers because only the complex numbers are a field. Quaternions are not a field.