You can extend the dot product to imaginary fields, there are a couple of standard extractions. If I remember correctly (but my quantum physics background is really poor, so I’m ready to be proven wrong) the one compatible with the bra-ket notation is

a dot b := sum_i conj(a)_i b_i

I don’t. It’s the sort of thing that is “evident” so no one talks about it much. Plus, professors don’t want to point out how much the whole system sucks and not a lot of people go into PhDs to become professors.

Where does this definition come from?

All the geometric definitions of tensors I have met always assumed a base, such that a change of coordinate or of parametrization would change the values of the tensor. Unless you define the tensor by its action instead of its values?

Also, but that is because math likes to reuse names like Donald Duck reuses his jacket…

I think, a lot. The shift during the pandemic of requesting uniquely online presence definitely sped up a trend that could already be detected. And because it was unprecedented, “adults” weren’t able to guide younger ones along the transition.

On the other hand, I see the lasting effects isolation did to social skills in kids and teenagers…

I throw ?? (that is also the default error code for LaTeX, so the last sweep of the pdf is always a search for ??)

To build up on it: think long term as well.

Nowadays, it’s a 20% pay reduction. How does it look for long term? Will you have growth options in the new position? Will it sabotage your resume? Will you be able to keep adding to your 401k? How likely it is that a rotten apple coming would spoil the mood in the new job?

And: are you really really absolutely sure that the new job would be more chill for you? Think about yourself and think about how you would feel in that job after 6 months to a year. Would you still appreciate it? Would you get resentful because you have little to do while you could do so much more? What would be your frame of mind after a while?

Not like that anymore >.<

I wish you the best… do vitamins appear? That seems so little for a full day…

Honestly, I have seen many classrooms in which no one was talking to anyone. There would be a break in the lecture, and the lecture hall would be absolutely silent for 10-15 minutes until the lecture resumed. Other classes were a bit more chattery, or even way more. As a teacher now, it seems anecdotally that the problem is getting worse, but that’s what every teacher always said (“these younger generations!! Mumble mumble”)

True, on the other hand US is often a canary indicator. Often, not always.

In general, I have heard many variations of “people don’t read anymore” soooo many times, I wonder why it’s still news. Yeah, people read less books, more blog posts, more stuff on the internet and so on. It has significant effects on long term information connection, creation and maintenance of neural patterns and so on. Either we restructure the internet or that’s how it’s going to go…

I am not in the know, but it made me think of Jean Giono’s Man who planted Trees. A very obscure reference if true

Considering how widespread of a situation it is, I am surprised I haven’t found yet a good LaTeX package that handles temporary sections

Me too! That wasn’t even the only time I got comments on my code. Since then, I make a point of doing at least a cursory check on codes when I review as well

Yes. Yes, everything works a-okay. Somehow I fixed the code but never removed the obnoxious, full cap comment…

Once, I got a reviewer stating “in the code, I doubt line 43 was supposed to be submitted”

Line 43: FUUUCK, DOES NOT WORK

Succeeded, thanks! That’s uncanny!

Somehow, the fact that it’s set in 1507 instead of 1500 really tickles me! Like, you wouldn’t believe how much changed in those 7 years!

Good safety standards are wildly different in EU and US. In many parts of EU some form of raw meat or other is common, raw milk is not too unusual. Consuming these items in US is a small step away from voluntary food poisoning. Not considering all the cases of unsafe foods delivered to the US supermarkets. Anecdotally, I would say some call back or other happens once a month in US (would love more precise data, too lazy to look)