The dunk already happened as you can see but here's the link if you wanna go marvel at the real thing: https://twitter.com/renatokara/status/1412484734949675013?s=19
Math has given us bombs. Math has given us cars. Math has given us video games, which have given us gamers. It's time that we all admit that math is more dangerous than it's worth and we never do it again.
Here's programming math that will blow non-programmer math people's minds:
x = x + 1
because it's not even a math expression, it's an assignment statement invented by someone who doesn't do math lol
I don't trust anyone that understands what this dumb science nerd stuff is.
remembering a day in high school in 2008 (:curious-marx:) i saw a cover for The Economist magazine or w/e depicting a bunch of revolutionaries holding a flag that said "DEATH TO DERIVATIVES"
that was my mood throughout high school calculus
I think the additional rules isn't the hard part for most people, it's the problems that come on exams that require you to actually understand the theory and apply it to a word problem.
Edit: thinking more about this, on my Calc 1 final I had a problem I'm sure a lot of students saw and immediately moved on.
Let f(x) = e^x. If F(x) is an antiderivative of f(x) and g(x) is a derivative of (f), then find the derivative of the function F(x)-g(x)
It's obviously a really really easy problem and the math on it is nothing but d/dx[(e^x + C) - e^x] = d/dx( C ) = 0. But the fact you need to know what all those words mean together is IMO what makes calc a hurdle for most people.
Isn't the whole point of Liebnitz notation to be able to do that?
math is cool. y'all should watch the turning a sphere inside out video
It's been so long since I took calculus. Can you just cancel the diagonal dx, or is the whole point of the joke that you can't?
For literally every conceivable situation that anyone who isn't a professional mathematician or physicist would ever encounter, yes you absolutely can treat dy/dx as a fraction.
Because it basically is a fraction, either the limit of a fraction as both parts go to zero, or a fraction of two infinitesimals (numbers between 0 and the smallest or positive or negative real number). A lot of mathematicians get sad when you use infinitesimals but it's fine.
For literally every conceivable situation that anyone who isn’t a professional mathematician or physicist would ever encounter, yes you absolutely can treat dy/dx as a fraction.
Not really.
df/dx=df/dt.
If you pretend they're fractions you will find dx/dt=1 which is wrong in general. For instance, let's say f(x)=3, x(t)=sint+t.
There is a lot of confusion that can be caused in instances like that.
EDIT: I suppose in this case you could say df is 0 so you can't do that, but there is other confusing stuff that can happen if you don't pay attention to what the derivatives represent. For instance, you may have df/dx(0)=df/dt(0) in which case it is a really bad idea to treat them as fractions.
The df terms in df/dx and df/dt represent fundamentally different things tho, so you couldn't just cancel them like that even if you're thinking of it as a fraction. The df term in df/dt is some function of t (say g(t)dt, if you think of dt as an arbitrarily small incriment in t) and in df/dx it's some function of x (say h(x)dx)).
This turns df/dx =df/dt into (g(t)dt)/dt) = (h(x)dx)/dx, which reduces to g(t)=h(x), which is fine and doesn't cause any contradictions.
The df terms in df/dx and df/dt represent fundamentally different things tho
That is why you shouldn't think of them as fractions lol
EDIT: What I mean is that when you look at the notation and treat it as a simple fraction, the dfs look like they're the same thing.
You typically can't do that if you want to be rigorous in math. It's more complicated.
It's not a fraction, it is a derivative, which is a limit of a fraction. Often you can treat it as a fraction but you have to know what you're doing because otherwise you may mess up.
My father has such a massive hard on for Newton and for some reason it just pisses me off and feels very Euro centric.
I mean Newton did discover some amazing stuff, but much of the ground work was done in prior centuries by Arabic Mathematicians (and arguably Kepler founded integral calculus).
But to troll your father I suggest always referring to Calculus as the "Science of Fluxions" and demanding Newton's shitty notation be used. Any attempt to use sane calculus should trigger an accusation of Leibniz worship.
I hate these "I wish to be a derivative so I can lie tangent to your curves" high school calculus low-effort meme shit so much. It sucks ass, that's why everyone forgets how to do calculus the second they walk out of the final exam.
that’s why everyone forgets how to do calculus the second they walk out of the final exam.
Yes, people didn't forget math until the memes came.
An American Science Fiction author named Ted Chiang wrote a lauded series of short stories that were collected as Stories of Your Life and Others. His most notable story is "Story of Your Life" that was adapted into the film Arrival.
So after seeing and loving Arrival and seeing praise for Chiang's writing from authors I like I decided to pick up his short story collection. And I was unimpressed. Most of the stories struck me as oddly detached and cold. The stories are largely about weird logic puzzles. There's at least two where the protagonist becomes a super genius but grows so logical that he loses his human capacity for empathy. Not that the stories were bad, they're just not what I want from short stories. I read for drama, and melodrama, and pathos. And in a short story I tend to like lush, evocative prose.
Anyway, there were two that I really liked. In one an Elamite laborer is called to Babylon, for the Babylonians had built their tower all the way to the vault of Heaven, but need a special crew to tunnel through to Heaven. He tunnels through and climbs the last steps to Heaven only to find himself on Earth, several hundred miles from Babylon, having come up in a lake. He concludes that the Earth is not a sphere or flat sheet but actually a curved cylinder.
More relevant to the discussion at hand my favorite story of the bunch was about a Mathematics professor. In the story she discovers that, beyond a certain point, mathematics breaks down and has no relationship to material reality. And this revelation severely depresses her, because she thought that through mathematics she could, essentially, "solve" the universe. But the story is also about her strained marriage and also grieving a lost dream. I thought it was the least detached, the most emotional, of all the stories in the collection.
In conclusion, I hate that math is taught backwards. It wasn't until I took Trig and Calc II in college that they started to explain more about what all that algebra and lower-level calculus was actually about. And that was so many years ago that I forgot anyway. Why wasn't I ever taught mathematics theory? They made me memorize proofs at some point, but I didn't really understand what they meant so I forgot them. I don't know, maybe it's on me. Maybe if I'd been curious and actually just read the math textbooks on my own I would've learned theory. I did that for other subjects, sometimes. I guess I feel like my entire math education from grade school onwards, even my high school calc course, was all about rote memorization, which isn't a path to either curiosity or true understanding. Or it wasn't for me.
