yeah it sucks

people can’t be in two places at once

the name seems to be an unfortunate choice that stems from their historical usage as “a means to an end”. i.e, they were first used as part of a method to find some solutions to cubic equations. this method would require algebraic manipulations of complex numbers, but the ultimate goal was to discover a real root. the complex roots would be discarded once a real root was found (if it existed).

the wikipedia article attributes the name to Descartes:

… sometimes only imaginary, that is one can imagine as many as I said in each equation, but sometimes there exists no quantity that matches that which we imagine.

which i think helps to highlight how skeptical the people at that time were about the existence of the “imaginary” numbers.

source: memories of my first complex analysis class, and https://en.wikipedia.org/wiki/Complex_number#History

i’d strongly recommend reading the history section of that wikipedia page to anyone interested in the topic, it has some pretty fun history

you also can’t drive it on the roads too much or else the tires will go bad

it’s rough when the math gets so complicated that you have to break your finger in order to be able to visualize things

There is also the hilariously misguided belief that good coders do not produce bugs so there’s no need for debugging.

i’m terrified of people who think this way. my experience has been that they are much less inclined to check for bugs in their code and tend to produce much buggier code

could not be me in the second frame

i wish they would do this in math instead of the boring system where it’s always alphabetical

that’s an extremely rare sighting but it’s so satisfying to read

what are your thoughts on “whence”?

ask and ye shall receive.

http://web.archive.org/web/20240912024402/https://www.theatlantic.com/politics/archive/2024/09/kamala-harris-broke-donald-trump/679780/

that would be a lot clearer. i’ve just been burned in the past by notation in analysis.

my two most painful memories are:

• in the (baby) rudin textbook, he uses f(x+) to denote the limit of _f _from the right, and f(x-) to denote the limit of f from the left.
• in friedman analysis textbook, he writes the direct sum of vector spaces as M + N instead of using the standard notation M ⊕ N. to make matters worse, he uses M ⊕ N to mean M is orthogonal to N.

there’s the usual “null spaces” instead of “kernel” nonsense. ive also seen lots of analysis books use the → symbol to define functions when they really should have been using the ↦ symbol.

at this point, i wouldn’t put anything past them.

unless f(x₀ ± δ) is some kind of funky shorthand for the set f(x) : x ∈ ℝ, x - x₀ | < δ . in that case, the definition would be “correct”.

it’s much more likely that it’s a typo, but analysts have been known to cook up some pretty bizarre notation from time to time, so it’s not totally out of the question.

i think the ε-δ approach leads to way more cumbersome and long proofs, and it leads to a good amount of separation between the “idea being proved” and the proof itself.

it’s especially rough when you’re chasing around multiple “limit variables” that depend on different things. i still have flashbacks to my second measure theory course where we would spend an entire two hour lecture on one theorem, chasing around ε and η throughout different parts of the proof.

best to nip it in the bud id say

i still feel like this whole ε-δ thing could have been avoided if we had just put more effort into the “infinitesimals” approach, which is a bit more intuitive anyways.

but on the other hand, you need a lot of heavy tools to make infinitesimals work in a rigorous setting, and shortcuts can be nice sometimes

🤐

they chose to hide it in plain sight

you’d likely need to go somewhere a bit more extreme to wait for silksong

it also bothers me when people say “my algorithm” to refer to the thing that recommends posts to them. people shouldn’t ever say “my algorithm” unless they personally own a copy of the kick-ass prog-metal band

well, according to the congressional budget office,

In 2023, federal subsidies for health insurance are estimated to be $1.8 trillion

and this report by research america shows that the private sector spent around $150 billion on “research and development” in 2019.

it’s no secret that the private healthcare industry jacks up the prices of things to increase profits. so, some napkin math makes me think it’s not that far-fetched to think that we can save more than $150 billion in healthcare subsidies if we stop privatized healthcare and dramatically lower the costs of medical care. we could then put that $150 billion back into research, without needing to appease the private sector at all.