The thing about math, is that when I put it into all those huge steps; each step should be clear and understandable; and you should be able to see how I got from each one to the next, and to each one from the one before. That if the thing I suppose at the beginning is true; then everything after would also be true; right up to the end.
Spoiler:
So, A+24 = 35
supposing that 24 = 24; that 10 + 25 = 35
and that if X = Y; than X-24 = Y-24
then A+24 = 35 means
that (A + 24) - 24 = (35) - 24
and supposing that 24 - 24 = 0
Then A +0 = (10 + 25)- 24; and supposing that 24 + 1 = 25
then A +0 = ( 10 + 1 + 24) -24; and supposing that A +0 = A
then A = (10 + 1)
So, 24-24 = 0; that is inarguable. A + 0 = A, also inarguable. if X = Y; than X-24 = Y-24; also inarguable. That 24 = 24 is inarguable.
Now, the problem here is that we have to establish the following two; which are not inarguable.
10 + 25 = 35
24 + 1 = 25
Let's start with the second one. Imagine that you don't know what 24 and 25 are.
Since if X = Y; than X-1 = Y-1
than if 24 + 1 = 25; but we haven't resolved that into an inarguable equation (like 24 = 24)
it means that (24 + 1) - 1 = (25) - 1
so 24 = 25 - 1
so if X = Y; than X-24 = Y-24
so (24) - 24 = (25 - 1) - 24
and since 24-24 = 0; than
0 = (25 - 1) - 24
and since where X - 24 = 0; X = 24 because 24 - 24 = 0
So, if 0 = (25 - 1) - 24; then it is inarguable that 25 - 1 = 24; because if 0 = X-Y, than X = Y
so, 24 - 24 = 0 = (25-1)-24
then 25 - 1 = 24;
so we get (24-24 = 24-24 = 0) which is inarguable.
and since if X=Y; than X+1 = Y+1
(25-1)+1 = (24)+1; and since X+1-1 = X
25 = 24 + 1; that is now inarguable.
All that remains is for us to prove that 10 + 1 = 11
so, by if X = Y than X-1 = Y-1
(10 + 1)-1 = 11-1
10 = 11 - 1; and since X-X = 0; and when X=Y; X-X=Y-X=0 so when X=Y, X-Y + 0
(10-10) = (11-1)-10
0 = (11-1)-10; and since if Y-X = 0; then Y must = X
11-1 inarguably equals 10; so by if X=Y than X+1 = Y+1
(11-1)+1 = (10) + 1; and by -1 + 1 + 0
11 + 0 = 10 + 1; and by the inarguable X+0 =X
11= 10+1; and this is inarguable.
So, with all the things we suppose being inarguable, and following the same logic throughout, we can conclude safely that when
A+24 = 35
then A=(10+1); and since we know inarguably that (10+1) = 11; and since we know that when X = Y and Y = G, then X = G
we know that A=11.
But nooo, the trick with math is that mathematicians go straight from A+24=35 and get to A=11; without any of the steps in between. The beginning, which is A+24=35; is like a cliff; and the end, which is A=11; is like another cliff.
When you use the proofs correctly, using the inarguable tenets (X=X, X-1=X-1, X-X=0, and so on); it is a bridge connecting the cliffs; a straight pathway on which you can walk and not fall. Even the people who aren't considering themselves to be very good at math can still walk your bridge and get from A+24=35 to A=11; without falling.They can follow you; and see why the answer is what it is. You could only show some of the inarguable proofs and condense others; but then following you requires more effort; and some people must be considered to be like snakes. A bridge where you have to jump to get past missing sections might be okay for most people, but not for snakes, who are not noted for jumping but are just as agile as anybody (even those not good at math can still be as smart as anybody).
But mathematicians go straight from one cliff to the other, without steps or bridges; and then laugh at the snakes for not being able to follow them.
It's not that the snakes are incapable of getting from one cliff to the other. And maybe the snakes don't want to go on your bridge, and that's okay.
Spoiler:
But for me to go all: when B = the square root of {(B*A*D)/C};
and B, C, A, and D are whole numbers
A^2+ B^2+ C^2 + D^2 can be written as the sum of two squares (but one of the squares will involve imaginary numbers)
and expect everyone to instantly understand why; and the logic involved, and the math involved; would be wrong.
Now, if you're writing for mathematicians, who can leap and skip along the bridge, you might only have to include one out of ten of the proofs.
But saying that people are dumb for not being able to get
"A^2+ B^2+ C^2 + D^2 can be written as the sum of two squares (but one of the squares will involve imaginary numbers)" from "when B = the square root of {(B*A*D)/C}; and B, C, A, and D are whole numbers"
would be like being saying that people who speak and read Swahili but don't understand Nahuatl are illiterate. Provide a translation when your audience doesn't read your language. When your audience understands your language, you can go on with the jargon and the skipped steps as you please.
If your audience understands Pig Latin but not Morse Code; it doesn't mean they are ignorant of cryptography. If your audience understands Morse, it is appropriate to tap in Morse and give them a message that way. If they, however, understand Pig Latin but not Morse, then you should use Pig Latin. If they understand neither, then use neither or teach them a code. Communication is a two way street, even for mathematicians. Don't be a Fermat. Don't treat people as slow and clumsy because they can't jump from cliff to cliff. Don't treat people as dumb because they can't get instantly to the answer from the problem.
Calculators and Savants are amazing, and I don't mean to disparage how useful they are; but a person who is slow but steady at math is still a smart kid; and a person who needs the huge, long, proofs to get from the question to the answer; can still get to the answer.
You would be acing my logic class.
Making sure the arguments proceed logically is the entire point of that class.
Do not just say that a Parallellogram has area determined by width times height, the same as a rectangle.
Show a Paralellogram, and show how you can cut off a triangle, move it, and create a rectangle. Nobody will be able to argue against Width times Length equals the area of a rectangle (if they do, use a grid to demonstrate); and since you just demonstrated that every Parallelogram is a rearranged rectangle; that finding the rectangle's area (the rectangle corresponding to that specific parallelogram) will give you the area of the Parallelogram.
Show the class that you can cut up and rearrange shapes, and still have the same area. Show that a right triangle is half a rectangle; and that a non-right triangle can be turned into two right triangles (sometimes you have to rotate it). Show that you can cut up more complicated shapes, like octagons and such; into rectangles and triangles and so on.
Rather than memorizing a formula; you'd be teaching a method for the students to derive the formula themselves.
Now, when you have to teach circles, then you're out of luck. Sorry, but you can't cut up a circle into other shapes without some left over, and no matter how you try to arrange it, you can't use that method to get the exact area; just an approximation.
And that's why circles are, in fact, abominations.
Teach your class to fear irrational numbers and ovals. That be bad juju; dark magic, no good very bad terrible awful I'm moving to australia so wait for me Alexander.
Making sure the arguments proceed logically is the entire point of that class.
Yeah, well, the problem there is dealing with things like ethics, "should or should not", does X justify Y, and all that; understanding the human condition, and understanding meaning.
Math is good because you can make it inarguable, to some extent; you can make it go down all the way to 1 = 1. 1 = 1; no argument about meaning or significance, it just is. An answer is either right or wrong.
Also, winning arguments and being subjectively compelling and rational about emotional topics. You'd have to understand thought processes, especially your own.
Math is essentially a giant, self-consistent pattern system with equations that can be simplified to some extent without losing meaning.
Reality is way, way, way more loaded with subtleties and shades of meaning; with contexts and content and interpretations and perceptions.
Also, in Math, you don't have to be convincing. You don't have to persuade that 1=1; it's self-evident and inarguable. It's like putting a jigsaw puzzle together, each piece has a place and in the end it all comes together. Logic class would be more like drawing a picture.
Reality has far too little that is inarguable and self-evident.
Making sure the arguments proceed logically is the entire point of that class.
Yeah, well, the problem there is dealing with things like ethics, "should or should not", does X justify Y, and all that; understanding the human condition, and understanding meaning.
Math is good because you can make it inarguable, to some extent; you can make it go down all the way to 1 = 1. 1 = 1; no argument about meaning or significance, it just is. An answer is either right or wrong.
Also, winning arguments and being subjectively compelling and rational about emotional topics. You'd have to understand thought processes, especially your own.
Math is essentially a giant, self-consistent pattern system with equations that can be simplified to some extent without losing meaning.
Reality is way, way, way more loaded with subtleties and shades of meaning; with contexts and content and interpretations and perceptions.
Also, in Math, you don't have to be convincing. You don't have to persuade that 1=1; it's self-evident and inarguable. It's like putting a jigsaw puzzle together, each piece has a place and in the end it all comes together. Logic class would be more like drawing a picture.
Reality has far too little that is inarguable and self-evident.
But, but, but, aren't many hats circular or oval-like in form?
The universe is an aberration. If matter and antimatter were equally distributed life probably wouldn't exist. If the universe wasn't an abomination, we wouldn't have paradoxes like the Barnach-Taski. Also, we'd be able to know the position and velocity of an electron if reality worked right. Reality is filled with glitches and paradoxes like that.
Hats exist in at least three dimensions, Circles and ovals exist in two.
Also, for enclosing the largest space with a shape of the least perimeter, circles are good.
But in terms of finding exact area, tessellating, or finding two whole numbers with a ratio of pi; or of having a finite number of sides and a finite number of angles; it's a monster.
When it comes to geometry and deriving area, circles are awful. No matter how fine and how small you make the grid, the circle never becomes a series of straight lines. I hate things that cannot be resolved or simplified into exactness.
No matter how far you go, you cannot find a pattern in Pi, you cannot simplify it into n/k, where n and k are whole numbers. You cannot tesselate circles, no matter how small you go; it goes into infinity. For a nice, simple math class based in being able to make things rational and understandable; circles are a problem. You can't cut up a circle into nice shapes without leaving something extra, it's basically a thing where you have to memorize the formula and go "it is because that's the way it is". It's an inexplicable, unresolvable thing on which a lot of geometry is based. You can't make a square with the exact area of a certain circle.
I'd rather have my students believe that circles are bad juju then have then think that there are things that I can't explain (note: I am not a teacher. These are hypothetical students_.
When it comes for finding the one point that is equidistant from given three points not on a straight line; circles are amazing.
^^ There is no better way to be served one's morning coffee. We can confirm this fact. Many methods have been looked into. There is no superior alternative.
You are the end result of a “would you push the button” prompt where the prompt was “you have unlimited godlike powers but you appear to all and sundry to be an impetuous child” – Zero, 2022
Princess Leia was seen by reliable witnesses to be in the control room of the Death Star just before Alderaan was destroyed!
The controls for the great laser that destroyed the planet are in the same room, not far from her.
Additionally, it turns out that Darth Vader is, in fact, her father; and he was also in that room at the time.
Clearly, they were working together; and Princess Leia is simply trying to hide her involvement in the destruction of her home planet.
Also, one of the two droids with the death star blueprints that Leia sent to Tatooine, those droids so instrumental in relaying the information for destroying the death star; was, in fact, built by Darth Vader himself; on Tatooine. The other was owned by Darth Vader's late wife.
So, clearly, we have Leia in league with her father and his evil droids; destroying Alderaan and then blowing up the death star to kill all the innocent stormtroopers aboard.
got back from taking my brothers to trick-or-treat.
Pros this year:
increased witch costume count the guy following around the police car who was wearing a pigman costume getting the secretly good candies that kids don't like
Cons this year:
the lady who shouted "look he's dressed as a rapper" when I was carrying the fake ninja knife from my little brother's costume
I would do the same thing, but I would go around murdering both orphans and non-orphans because NOPE HUMANITY NO LEONARDO DA VINCI FOR YOU I MURDERED HIM AS A CHILD SO I COULD GET A SWEDISH FISH.
Comments
Assassin poems, Poems that shoot
guns. Poems that wrestle cops into alleys
and take their weapons leaving them dead
Assassin poems, Poems that shoot
guns. Poems that wrestle cops into alleys
and take their weapons leaving them dead
Do not just say that a Parallellogram has area determined by width times height, the same as a rectangle.
Show a Paralellogram, and show how you can cut off a triangle, move it, and create a rectangle. Nobody will be able to argue against Width times Length equals the area of a rectangle (if they do, use a grid to demonstrate); and since you just demonstrated that every Parallelogram is a rearranged rectangle; that finding the rectangle's area (the rectangle corresponding to that specific parallelogram) will give you the area of the Parallelogram.
Show the class that you can cut up and rearrange shapes, and still have the same area. Show that a right triangle is half a rectangle; and that a non-right triangle can be turned into two right triangles (sometimes you have to rotate it). Show that you can cut up more complicated shapes, like octagons and such; into rectangles and triangles and so on.
Rather than memorizing a formula; you'd be teaching a method for the students to derive the formula themselves.
Now, when you have to teach circles, then you're out of luck. Sorry, but you can't cut up a circle into other shapes without some left over, and no matter how you try to arrange it, you can't use that method to get the exact area; just an approximation.
And that's why circles are, in fact, abominations.
Teach your class to fear irrational numbers and ovals. That be bad juju; dark magic, no good very bad terrible awful I'm moving to australia so wait for me Alexander.
Assassin poems, Poems that shoot
guns. Poems that wrestle cops into alleys
and take their weapons leaving them dead
Math is good because you can make it inarguable, to some extent; you can make it go down all the way to 1 = 1. 1 = 1; no argument about meaning or significance, it just is. An answer is either right or wrong.
Also, winning arguments and being subjectively compelling and rational about emotional topics. You'd have to understand thought processes, especially your own.
Math is essentially a giant, self-consistent pattern system with equations that can be simplified to some extent without losing meaning.
Reality is way, way, way more loaded with subtleties and shades of meaning; with contexts and content and interpretations and perceptions.
Also, in Math, you don't have to be convincing. You don't have to persuade that 1=1; it's self-evident and inarguable. It's like putting a jigsaw puzzle together, each piece has a place and in the end it all comes together. Logic class would be more like drawing a picture.
Reality has far too little that is inarguable and self-evident.
Assassin poems, Poems that shoot
guns. Poems that wrestle cops into alleys
and take their weapons leaving them dead
Hats exist in at least three dimensions, Circles and ovals exist in two.
Also, for enclosing the largest space with a shape of the least perimeter, circles are good.
But in terms of finding exact area, tessellating, or finding two whole numbers with a ratio of pi; or of having a finite number of sides and a finite number of angles; it's a monster.
When it comes to geometry and deriving area, circles are awful. No matter how fine and how small you make the grid, the circle never becomes a series of straight lines. I hate things that cannot be resolved or simplified into exactness.
No matter how far you go, you cannot find a pattern in Pi, you cannot simplify it into n/k, where n and k are whole numbers. You cannot tesselate circles, no matter how small you go; it goes into infinity. For a nice, simple math class based in being able to make things rational and understandable; circles are a problem. You can't cut up a circle into nice shapes without leaving something extra, it's basically a thing where you have to memorize the formula and go "it is because that's the way it is". It's an inexplicable, unresolvable thing on which a lot of geometry is based. You can't make a square with the exact area of a certain circle.
I'd rather have my students believe that circles are bad juju then have then think that there are things that I can't explain (note: I am not a teacher. These are hypothetical students_.
When it comes for finding the one point that is equidistant from given three points not on a straight line; circles are amazing.
Princess Leia was seen by reliable witnesses to be in the control room of the Death Star just before Alderaan was destroyed!
The controls for the great laser that destroyed the planet are in the same room, not far from her.
Additionally, it turns out that Darth Vader is, in fact, her father; and he was also in that room at the time.
Clearly, they were working together; and Princess Leia is simply trying to hide her involvement in the destruction of her home planet.
Also, one of the two droids with the death star blueprints that Leia sent to Tatooine, those droids so instrumental in relaying the information for destroying the death star; was, in fact, built by Darth Vader himself; on Tatooine. The other was owned by Darth Vader's late wife.
So, clearly, we have Leia in league with her father and his evil droids; destroying Alderaan and then blowing up the death star to kill all the innocent stormtroopers aboard.
It's a funny thing said by people on the internet before me.
Pros this year:
increased witch costume count
the guy following around the police car who was wearing a pigman costume
getting the secretly good candies that kids don't like
Cons this year:
the lady who shouted "look he's dressed as a rapper" when I was carrying the fake ninja knife from my little brother's costume
I really hope not.
I hope it's more like this
So they did try to do something with Angela Anaconda
The line "You're tearing me apart" in The Room is meant to be an homage to the same line in Rebel Without a Cause.
you're tearing me apart
death on two legs
you never had a heart
of your own