A mathematician, a physicist and a biologist are flying in a air balloon and are lost.
They encounter a man walking below:
The biologist asks him: "do you know, where we are?"
"..." the man looks up and says nothing
The physicist ask him: "can you please tell us, where we are!"
"..." after a while the man says: "in a balloon".
The mathematician remarks, ah, he must be a philosopher.
The others: "how do you know?"
"Well, for once he needed a lot of time to answer. Then his answer is correct with our objective reality. And lastly, his answer is completely useless to us."
(in eastern soviet republics, philosophy was not in high regards, because the peoples governments were supposed to be philosophical (a la Marx) government, with in theory, very high standards)
I'm reminded of a joke I heard from a talk by the philosopher Dan Dennett:
A philosopher takes his friend to a magic show. After the usual business of vanishing a few small mammals, the magician's assistant lies in a magic box, and the magician, with a dramatic flair, begins to saw through the box.
The philosopher's friend leans over and asks What do you think is really going on? The philosopher gives it a moment's thought and replies They're using illusionist skills to give us the impression that he's sawing someone in two, but really he isn't. The philosopher's friend, unsatisfied, asks Right, but how? The philosopher shrugs dismissively, That's really not my department.
B. I hate how applicable this joke is to my life. Except I'm the friend asking, then has to figure all the shit out because all the people around me with degrees cant tell the difference between their ass and a hole in the ground.
A Soviet engineer needs some plumbing done in his apartment, and calls for a plumber. The plumber arrives, does his thing, and hands over the bill.
The engineer is shocked. -'What, this is like a quarter of what I make in a month - for half an hour's work???'
Plumber shrugs. -'Well, why don't you come join us? Easy work, well paid, no responsibility - just remember to keep mum about your degree, as we're not supposed to hire academics.'
Our engineer contemplates this for a while, applies for a job as a plumber - and gets it.
All is well, good money, no responsibilites - until management requires that they take evening school classes to gain new skills and thus better build socialism. So, grudgingly, our engineer enrolls in a math class and, upon arriving, finds that the teacher wants to establish what the plumbers already know.
-'You over there - could you please come to the blackboard and show us the formula for the area of a circle?' he asks our engineer.
Standing at the blackboard, he suddenly realizes he can't for the life of him remember the formula; while a bit rusty, he soon figures out how to reason it out - furiously writing out integrals on the blackboard, only to find the area of a circle is -(pi)*r^2.
Minus? How did a negative enter into it, he thinks, going over his calculations once again. No, still gets the same result. Sweat building, he turns away from the blackboard for a moment, turning to the other plumbers watching.
As in one voice, they all whisper -'Comrade, you must switch the limits to the integral!'
The "you learn limits in like, 9th grade" comment reminds me of this one:
Two mathematicians are in a bar. The first one says to the second that the average person knows very little about basic mathematics. The second one disagrees, and claims that most people can cope with a reasonable amount of math. The first mathematician goes off to the washroom, and in his absence the second calls over the waitress. He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question. All she has to do is answer one third x cubed.
She repeats "one thir -- dex cue"?
He repeats "one third x cubed".
She says, "one thir dex cuebd"?
Yes, that's right, he says. So she agrees, and goes off mumbling to herself, "one thir dex cuebd...".
The first guy returns and the second proposes a bet to prove his point, that most people do know something about basic math. He says he will ask the blonde waitress an integral, and the first laughingly agrees. The second man calls over the waitress and asks "what is the integral of x squared?".
The waitress says "one third x cubed" and while walking away, turns back and says over her shoulder "plus a constant!"
I've heard a variation of that were the professor is at a bar with a couple of visiting professors. He tells them, in this town pretty much everyone is smart and he proves it by asking the waitress. (The rest of the joke is the same.)
You can arrive at the same by slicing in nearly any manner you wish: vertical dx strips, horizontal dy strips, radial dtheta strips, concentric rings treated as rectangles, diagonal strips, literally anything you wish.
If you've never set up and worked a few, try the dx version and the dy version, then maybe fiddle with a few others. They all work.
The concentric rings one is trivial to work out. Integrate over r from 0 to R. Each ring at radius r has thickness dr, and has length 2 pi r, treated simply as a rectangle, which is "close enough" since each is arbitrarily thin. Then the integral is
int_0^R 2 pi r dr = 2pi r^2/2 from 0 to R = pi R^2.
A really pretty one cuts the circle into wedges, then rearranges them by alternating direction to make a "rectangle" approx r high, approx pi * r wide, with bumpy top and bottom. In the limit this has area pi * r * r, and can be shown to kids without needing calculus.
And it's not magic or circular, since pi is defined (in this case...) as the ratio of circumference to diameter.
I heard this one but it's a mathematician and a physicist in the balloon, and the physicist says the person must be a mathematician. As told by a math professor...
I know it soviet style:
A mathematician, a physicist and a biologist are flying in a air balloon and are lost.
They encounter a man walking below:
The biologist asks him: "do you know, where we are?"
"..." the man looks up and says nothing
The physicist ask him: "can you please tell us, where we are!"
"..." after a while the man says: "in a balloon".
The mathematician remarks, ah, he must be a philosopher. The others: "how do you know?"
"Well, for once he needed a lot of time to answer. Then his answer is correct with our objective reality. And lastly, his answer is completely useless to us."
(in eastern soviet republics, philosophy was not in high regards, because the peoples governments were supposed to be philosophical (a la Marx) government, with in theory, very high standards)