barsoap

Nothing. And that's why people don't write equations like that: You either see

     4
6 +
***
     2

or

 6 + 4
-------
   2

If you wrote 6 + 4 / 2 in a paper you'd get reviewers complaining that it's ambiguous, if you want it to be on one line write (6+4) / 2 or 6 + (4/2) or 6 + ⁴⁄₂ or even ½(6 + 4) Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.

Those two things are memorisation tasks. Maths is not about memorisation.

You are not supposed to remember that the area of a triangle is a * h / 2, you're supposed to understand why it's the case. You're supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it's stuck in: Start with the trivial case (right-angled triangle), then move on to more complicated cases. If you've understood that once, there is no reason to remember anything because you can derive the formula at a moment's notice.

All maths can be understood and derived like that. The names of the colours, their ordering, the names of the planets and how they're ordered, they're arbitrary, they have no rhyme or reason, they need to be memorised if you want to recall them. Maths doesn't, instead it dies when you apply memorisation.

Ein Anfänger (der) Gitarre Hat Elan. There, that's the Guitar strings in German. Why do I know that? Because my music theory knowledge sucks. I can't apply it, music is all vibes to me but I still need a way to match the strings to what the tuner is displaying. You should never learn music theory from me, just as you shouldn't learn maths from a teacher who can't prove a * h / 2, or thinks it's unimportant whether you can prove it.

x/0 is the set {+inf,-inf}, fite me IRL.

You're trying to transmit power via magnetism so distance is an issue.

Aluminium is actually a better conductor than copper when you judge it by mass, not volume. I think also by tensile strength.

In any case there's a reason that large overland wires aren't copper, but steel-cladded aluminium. Copper will always have its applications but so does gold and yet we're not running out of gold to plate connections with.

In cases like windings requiring more volume is actually an issue, in the case of PCBs... no, despite Apple's insistence, it's actually fine to have a phone that's 0.2mm thicker.

Unlikely as many Germanic languages have it, with similar meanings. It's a variant of "ja", yes. Add a bit of laconicy and you can make "Well." a sentence in itself.

Gigaset produces in Germany.

Of course Germany won't extradite we don't extradite nationals to non-EU countries. It can even happen that we don't extradite Americans to the US because they can demonstrate that they're likely to face torture in the US, such as isolation cells.

Autistic coders are only slightly more rare that autistic rail fans. There's no shortage of you guys in the field.

what you are doing should have a clear connection with some goal, or be clearly a goal in itself, otherwise you’ll achieve nothing.

"Understanding the whole stack" would, necessarily, be the second kind of goal. And you'll never get there as the field is evolving under your feet.

Yes, then you have another problem - how do you choose what you want to do if you don’t yet understand the whole in any approximation.

How did you decide to write English using the Latin alphabet? You did not, I presume, study the whole ancestry of the alphabet back to Hieroglyphs to understand it in it's entirety (did you know that 'A' is an upside-down ox head?), nor did you study alternative spellings, nor did you study linguistics to make sure that English, Modern English in particular, truly, is the best choice of language.

You were able to ignore all that, why are you not able to ignore things elsewhere?

And selective ignorance, btw, is a key skill to aquire as a coder. Encapsulation, abstraction, action at a distance being the root of all evil, all those are key principles to understand and skills to acquire. Why? Because you're not as smart as you wish you were. Being good at ignoring things, being good at saying "if I build it like this, I can from now on ignore the details" is the only way to do anything of any complexity. I don't care how my pants are constructed, about the lubrication the loom uses, I care whether they fit, are comfortable, durable.

When figuring out what to pack for vacation, do you already tetris your shirts and pants? Nah, that comes later. Right now, worry about not forgetting your sunglasses, don't worry, they'll fit somehow.

There’s a barrier a person has to grind through with their teeth before they understand that they want to learn Haskell and what that is.

Nah. Just start somewhere. If you later on realise that your interests lie elsewhere, then switch, but don't fret: If it was interesting enough to look at, how could it have been a waste of time.