my bike doesn’t have a central pedal. how does it stay up right?
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gone but not forgotten….
is this where ketchup comes from?
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
these are not arguments. they are beliefs/opinions
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
you could put “AI is making things worse.” after just about any sentence and it would probably be true.
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
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this is especially true in math. everybody’s chilling when it’s just calculus and linear algebra. but then it becomes about manifolds, orbifolds, presheaves, adjoints, limits, modules, homology, etc.