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

could not be me in the second frame

i hope i don’t end up with the -4000 mAh battery if i buy the phone

if you learn how to solve zeno’s problem in the first book, it may be possible to solve 100% of your problems in the second book

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

this would include all the 210 drugs that got FDA approved from 2010-2016 (source).

the system is so fucked.

i just go crazy on the tabs and close them all at the end of the day. if an important tab got lost, then i can just find it through my browser history

this seems like the only proper way to do anything in C++. it’s a language where there’s 5 ways to do 1 thing and 1 way to do 5 things.

yep, this is a lemmy.ml post alright

and then they had the audacity to put that picture on the cover of the textbooks

a couple always means two.

every time anyone says “a couple”, i ask them if they mean two. it’s not pleasant exchange for either of us, but it must be done

i also hate how hotels will now call people “guests” instead of customers. some restaurants do this too. it just makes things feel more gross and corporate. like it’s trying to force the whole “we’re all a family here” mentality on the customers

i think it depends on what you mean by “accurately”.

from the perspective of someone living on the sphere, a geodesic looks like a straight line, in the sense that if you walk along a geodesic you’ll always be facing the “same direction”. (e.g., if you walk across the equator you’ll end up where you started, facing the exact same direction.)

but you’re right that from the perspective of euclidean geometry, (i.e. if you’re looking at the earth from a satellite), then it’s not a straight line.

one other thing to note is that you can make the “perspective of someone living on the sphere” thing into a rigorous argument. it’s possible to use some advanced tricks to cook up a definition of something that’s basically like “what someone living on the sphere thinks the derivative is”. and from the perspective of someone on the sphere, the “derivative” of a geodesic is 0. so in this sense, the geodesics do have “constant slope”. but there is a ton of hand waving here since the details are super complicated and messy.

this definition of the “derivative” that i mentioned is something that turns out to be very important in things like the theory of general relativity, so it’s not entirely just an arbitrary construction. the relevant concepts are “affine connection” and “parallel transport”, and they’re discussed a little bit on the wikipedia page for geodesics.

it’s a bit of a “spirit of the law vs letter of the law” kind of thing.

technically speaking, you can’t have a straight line on a sphere. but, a very important property of straight lines is that they serve as the shortest paths between two points. (i.e., the shortest path between A and B is given by the line from A to B.) while it doesn’t make sense to talk about “straight lines” on a sphere, it does make sense to talk about “shortest paths” on a sphere, and that’s the “spirit of the law” approach.

the “shortest paths” are called geodesics, and on the sphere, these correspond to the largest circles that can be drawn on the surface of the sphere. (e.g., the equator is a geodesic.)

i’m not really sure if the line in question is a geodesic, though

they’re also taller than cars

they made a very influential isEven algorithm