'And pity poor PhD students whose entire programs seem designed to make their life one enormous Ugh Field.'
This is uncomfortably on point for me. I'm mildly dyslexic and suffer with mild anxiety issues. Currently I'm trying to write up my PhD thesis and the whole process has got to the point where it is fairly unbearable. The problem is I'm the person that will probably be let down the most if I don't complete. I'm a part time student, requesting my third extension, and have now accumulated 10 years worth of 'ugh'. It's embarrassing.
Can't you just set up an alternative two factor authentication method? How about a Yubikey? I think that maybe if 2FA is not explicitly enabled on the account, Google try and enforce this 2FA 'light' method using SMS
Because with a Fourier series/transform you only get to play with the amplitude of the sine and cosine functions, not the offset. If you only had cosine functions in your sum you'd only be able to represent symmetric functions (and antisymmetric if only sine). Except actually I lied; if you sum both sine and cosine functions you do get to specify offsets. Think of this trig identity: sin(x + offset) = [cos(offset)] sin(x) + [sin(offset)] cos(x). Think about the terms in brackets as just being amplitudes. By having both sine and cosine in the sum you can represent any arbitrary offset by just changing their relative amplitude. This is one of those things which is nicer when you think about it in terms of complex numbers.