Not because it’s about curves, which is what it’s about, by the way. It was because of this sentence within the prompt: “In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object.”
I wondered why it would have such an odd assortment of bolded words, plus things that are not continuous are called curves all the time around the math department at my university. So I, being the genius I am, went back to the prompt and discovered that the word “Winkipedia” was in fact a link to the Wikipedia article on curves. Then for no reason I thought of L’Hospital stealing Bernoulli’s work on curves, but that’s irrelevant to this discussion.
So I clicked the link and was taken to the Wikipedia article and, because I’m one of those special people who actually went and got a math degree, I understood this article. I knew exactly what it meant, except it was saying this bullshit stuff about curves. It was calling paths curves! The horror! And then I got to the part in the article where it says, Terminology is also not uniform. Often, topologists use the term "path" for what we are calling a curve, and "curve" for what we are calling the image of a curve. Aha! It all makes sense now! The fact that the article author doesn’t mention that most times the “curves” referred to are actually called “continuous mappings” is niggling but then again, it was probably an unemployed math graduate writing the article during unfilled spare time in the first place. You can’t expect too much.
But anyway, reading through the article, I see that the author pops down to the subject of the length of curves. I again disagree with his notation, since it’s much easier just to introduce the notion of polygonal paths over partitions of the [a,b] interval and go from there, but in any case, I can’t imagine anyone who didn’t already know this shit understanding it. It’s like out of nowhere he starts using supremums and Epsilon notation and mentioning Lipschitz-continuous and stuff. I don’t believe that supremums are generally introduced in undergrad math until upper division, and even then there’s usually three or four prerequisite upper division courses before you get there.
And then we get to the Curves in Differential Geometry section, and the author pulls manifolds out of the ass of mathematics, neglecting that you have to go through the mouth and esophagus and stomach and the entire rest of the gastrointestinal system to get there, and says it’s basic. Kind of makes you feel stupid if you don’t get it, doesn’t it?
This is a basic notion.
Well, yeah! Sure, that’s a basic notion! If you’ve spent four years of high school chugging through the mathematics programs to AP calculus and then a further four years in college devoted to a mathematics major and you took a topology course and 1) remembered what was said, 2) had a good enough teacher or book that you understood what was meant, 3) applied yourself to internalising it and 4) planned to continue on and make mathematics a part of your daily life. Then yes, it’s a basic notation.
But if you don’t fit that profile, it might as well be magical runes to you, mightn’t it?
Then I read further and the author casually mentions Ck, a notation and concept that was introduced to me in a course that was about half last-year BS (not BA, mind, BS, more rigorous degree) math students and about half graduate students. Oh yes. Basic. Moving on to Algebraic curves, there’s another basic notion, C(K). You’ll get bonus points from me if you can tell me the core difference between Ck and C(K). The last paragraph of this part looks mightily suspicious, like it was ripped from a textbook somewhere.
And the history of curves… dude. This part is full of half-assed shit. But whatever.
Moving on to more interesting topics than the criticism of the supercilious writing of one author by another equally supercilious one, let’s talk about how the Marquis de L’Hospital stole Bernoulli’s work! The great betrayal of one mathematician by another, scintillating accounts of how all of integral calculus was… all right, fine, it was early intellectual theft and L’Hospital got away with it because he was an aristocrat, so it was also the rich taking advantage of the poor. What else is new?
What about the Witch of Agnesi? The Witch of Agnesi, the curve yx2 = a2(a – y). It looks witchy, doesn’t it? The name arises from an interesting and quite disturbing story of repressed homosexuality and horrific murder.
Maria Agnesi, a young, disaffected woman who was the only daughter of Baron Ludmillio Agnesi, had learned to speak Italian, Latin, Greek, Spanish, French, German, and Hebrew by the time she was eleven. This unnerving display of intelligence frightened her father, and he forbade her to learn anything else. Higher knowledge was restricted from her, and she was locked in her room when it was discovered that she was secretly visiting the family library at nights and learning mathematics and physics.
She escaped from the prison her family had caged her in and fled the Agnesi estate and Italy entirely, disguising herself as a man and travelling to England. Here she caught the eye of a beautiful young noblewoman, who did not know that Maria was cross-dressing, and the two began a whirlwind romance that ended in marriage and, that night, shock and horror on the part of the noblewoman when she discovered that Maria was not, in fact, a man. Maria persuaded her to keep quiet and try and give the marriage a go, but in the end, the noblewoman was not able to persuade herself that Maria was the one for her. She fell in love with a nobleman and began to have an affair with him.
Unable to catch the eye of the woman she loved, Agnesi’s life went down the drain, and she once again had to flee when her wife’s paramour found out about her, this time right ahead of the hangman’s noose and charges of homosexuality and impersonating a man. She fled to Prussia, and it was here she first killed. About to be raped, she stabbed a man in his neck and he died. She carved the last equation she had learned before she left home, yx2 = a2(a – y), into his chest. She then began a murderous killing spree that spread across Prussia and Flanders, always carving that equation into the bodies of her victims. This equation, which looked mystical to people not in the know about math, and the knowledge that she was a woman (and of course in those times any woman capable of killing so many fine, superior men must by definition be in league with the Devil) inspired people to start calling her a witch.
When she was finally captured, she gave her name as Maria Agnesi and her last words before she was burned to death were “yx2 = a2(a – y).” She was actually silenced by an arrow to the throat because people thought she was calling on the Devil, and thus was spared the pain of burning to death. Ever since, the equation has been called, “the Witch of Agnesi.” Interesting, ne?
Actually, that’s pretty much entirely bullshit, except that she was called Maria Agnesi and she did learn all those languages. But in fact it’s called the Witch of Agnesi because the book that Agnesi wrote, Instituzioni Analitiche, was mistranslated: versiera (the versed sine curve) was mistranslated as “wife of the devil”, or witch (avversiera being the actual word for wife of the devil).
My story was more interesting. Or at least more fun to write. Anyway, I don’t really have much to say on curves except this. Curves are pretty. I like curves. Curves are my friends. My thoughts meander around crookedly just like they do!
Oh, and how many of you peeps understood that Wikipedia article? Honestly?
