Could have just used fermi estimation and been done with it easy
1+1=1 because 2 rounds down.
48+54=110
48 rounds down to 10, 54 rounds up to 100. 100 plus 10 is 110.
TheNinthShader
Shit, I messed up on the second thing. Its supposed to equal 100 total.
DarkVeghetta
You know, fermi estimation is very much like religion. It’s not proper math, but damnit if it won’t try to pretend like it is!
TamiDOA
Quantum physics is virtually a religion. Most of it can’t really be proven or dis-proven, so you have to take on faith based on the teachings of its preachers that say it must be true because the math they created to explain it says so.
Oh, and by quantum physics, 1 is only probably equal to 1 … or not, and simultaneously. 🙂
thejeff
And yet it works. Quantum physics is actually pretty solid. We just don’t understand it. The world is stranger than we can imagine.
String theory, on the other hand…
Agemegos
Quantum mechanics is amazingly solid. It gives (mostly) probabilistic predictions rather that precise ones, but the probabilities it calculates are amazingly accurate. It explained a whole bunch of stuff that seemed bizarre and arbitrary (such as the bell-shaped thermal spectrum and the sharp lines in emission and absorption spectra), and it predicted a wide range of bizarre-sounding phenomena that turned out actually to occur and that we use to make transistors, microchips, diodes, LEDs, and lasers.
And it doesn’t say that 1 is only probably equal to 1.
TamiDOA
I never said it didn’t work, just that it has many characteristics of a religion.
And as Dina might say, I must must have said the JOKE (whence the 🙂 ) wrong. It’s another version of “How many cats does Schrödinger have? One and zero … probably.”
TamiDOA
Another characteristic of a religion is the reaction that occurs when perceived heresy is spoken/typed. Did I just witness quantum fundamentalists? 🙂
DarkVeghetta
Religions obfuscate reality rather then accurately predict its inner workings. Key word being accurate. It doesn’t matter if it’s bizarre as long as the end result lines up with objective, provable fact.
No, please.
I assume those people slip through the cracks from time to time and I just haven’t seen them, but they’re free to go elsewhere for entertainment.
Jason
Pretty sure they probably don’t slip through the comment moderation? I know first time commenters are moderated and I’m sure I remember Willis saying the comment section itself is read through and manually moderated. Which I gotta say, with comment threads of this size, is serious dedication to never leaving a computer.
Disloyal Subject
Yeah, but if someone’s first comment is fine but they later go off the deep end I imagine their comment would still be up at first.
Because math is more fundamental and it tends not to be completely disproven so easily. That’s why intelligent people tend to not like that everything they think they know is a lie (again), and that this time even math has broken.
Needfuldoer
Math. Math never changes.
Meamoi
The math isn’t broken, but our shortcuts for it are.
However, math IS incomplete, and NEVER can be complete. Godel proved that one. Although I don’t suggest reading his works, they have been shown to literally drive people insane. Like literally literally. Like, they read the book, brain goes “world does not compute,” they try to prove him wrong, fail, can’t accept it being right, spiral into a deranged madness, and get taken away by men in white coats. Literally insane.
On the flip side, if you want to learn what he taught without going insane, I suggest reading “Godel, Escher, Bach.” It does a good job of “slowly” preparing you for the Godel’s big reveal. (Every chapter is a paradigm shift). So when you finally get to the end, you can actually understand Godel without it shattering your brain, because you’ve already fixed a lot of the parts that you didn’t know were broken and so don’t go through the “everything I ever learned is a lie” mental breakdown.
Yet Another Laura H.
Oh, goodness, 1000000 points for Gödel. He was required reading at my college, where the only required math class did not involve numbers. You would think that would be easy, but the math for a course where Calvinball was also required reading… well, I was pretty good at the math of quantum physics, but I literally got a headache in “IS2” every day. It was the best kind of brainhurt.
Ana
Actually, nothing incomplete in the underlying math here, it’s just all the answers I’ve read here that are, in one way or another. At least in Portugal, this kind of exercise is pretty typical in 9th grade math – whenever you want to divide by a non constant expression, you have to branch out in order to handle the zero case.
This statement is always true regardless of the truth value of (2 = 1 && a²-ab != 0). All this tells you is that you’ve reached a dead end in your proof, at least if you want to prove something other than ‘all values of b in the value set satisfy the condition when you solve for a’ and other than ‘all values of a in the value set satisfy the condition when you solve for b’
Full disclosure: I was a mediocre student in university math.
Don’t worry, you’ll most likely not have to use any math higher than algebra in the real world. Unless you’re studying to become something that requires higher math like physics or whatever.
N0083rP00F
And even then most use advanced expert systems to do the math for them. Like why reinvent the quadratic every time you do a little bit of particle physics?
I have trouble wrapping my head around Physics.
But I know buzz words like “Quantum” and “Q-Bit”.
Meamoi
At least until you get to calculus and/or statistical analysis. Once you learn either one, you may not directly use them often, but you quickly begin to use shortcut versions of them *everywhere*.
“Wait… if I do that… it’s going to progress asymptotically, but if I do this, it’ll be exponential… at least until I hit this limit… OK! Now I know how I’m going to manage my calorie intake for the next two months!”
Agemegos
Yep. Very true.
It’s a box full of sharp and handy intellectual tools.
That’s not a fallacy, the math is just messed up.
a=b
a²=ab
a²+a²=a²+ab
2a²=a²+ab
2a²-2ab=a²+ab-2ab
2(a²-ab)=a²-ab <<<HERE
2(a^2 – ab) = 2(0) = 0
0 = 0
As MatthewTheLucky pointed out, this proof that 2 = 1 is accomplished by dividing by zero. You can prove anything that way. It’s the step in Ana Chronistic’s math right after the step you marked with HERE.
Dude, at “HERE” there are no errors. On the right he’s factorizing (by 2) and on the left he’s doing ab-2ab which is -ab. no problems there. The idea of the falacy is something you missed in your conclusion. You just skipped to the reason why it’s a falacy: You ended up with zeroes. The math is flawless, it just doesn’t work that way. To isolate 2=1, you’d have to divide by (a^2-ab) on both sides. But that is 0. Which is to say, you’d have to divide by zero, which you can’t.
I understand that it’s a fallacy, and I know that it can’t be a real proof. However, I’m missing where it messes up. Where the logic disappears. Is it at a specific point along your equation development, or is a=b doomed to cause fallacies from the start?
I find it helps to plug in some value — say, 5 — for a and b, and see how each equation works out. That makes it more visible when you’re dividing by 0.
The reason is that a + a != a unless a = 0. Take a look at this line:
2(a²-ab)=a²-ab
Now substitute a for b
2(a²-a²)=a²-a²
a² – a² = 0, therefore 2 * 0 = 1 * 0, i.e. this sequence of operations only holds true when a = b = 0.
It is not saying that 2 = 1 but that 2 * (something) = 1 * (the same thing) can be true, and it is only true when a = b = 0
Jaenus
Basically, in mathematics, ab = ac means b = c only holds true IF (and only IF) a is non-zero. Think about it. If a = 0 then b could be 9 and c could be 5000 and it would still be true that ab = ac since 0 * anything = 0. But b is definitely not equal to c.
That’s what is being done in the last step to get 2 = 1 from 2(a²-ab)=a²-ab what is really happening is a division on both sides by the factor a²-ab, but that’s a²-a², which is 0. The statement is that 2 * 0 = 1 * 0, which is true.
a snow ʍousɐ
b=c can hold true if a is zero. But ab=ac does not IMPLY b=c unless a is non-zero. In other words, reducing both sides by canceling will only be guaranteed to work when a is non-zero.
.
Nope, the equations Ana Chronistic has given are true for all numbers a and b which meet the condition a=b!
(Of course with the exception of the last one, as divison by zero).
The failure in logic comes from them not simplifying ab to a^2. math does tricksy things when you play with the names of variables. for example:
a^2=b
log(a)b=2
lnb/lna=2
lnb=2lna
lnb/2=lna
e^lnb/2=a
e=(lnb/2)root(a)
log(a)e=2/lnb
log(a)e*lnb=2
lne/lna*lnb=2
1/lna*lnb=2
now for the switcheroo
1/lna*2lna=2
2lna/lna=2
2=2
…i guess i failed to break logic.
Damnit ya’all, you guys try turn this place into a xkcd area? You seriously start sounding that way>_<"
DarkVeghetta
Ah, the ONLY time I get to feel like all those hours of math in school had any point to them – comic comment sections.
Deanatay
Dude, you gots no problems when someone fills a page with a rant about child abuse or sexism, but get upset when it’s about math?
It’s just math, dude. Nothin’ but numbers. Don’t be afraid.
DarkVeghetta
I don’t think he’s upset. Somehow I doubt anyone familiar enough with xkcd to recognize such would frown upon math. It’s probably more of a ‘Seriously? xD’
Ah HA! 2a²=a²+ab and they’re both having 2ab subtracted from them. Therefore it’s 0 = 0! So a=0! So it works out fine! I get to keep my sanity for another day! ^^
It breaks because the square root function isn’t well-defined and continuous on the entirety of the complex plane, you have to cut a slit down the negative x axis to make a proper “function”. So it’s not a real proof, but disproving it is just a matter of knowing that sqrt(ab) = sqrt(a)sqrt(b) when a and b are positive.
876 thoughts on “Original Sin”
Ana Chronistic
“uh well, at least 1+1=2? THAT’S NOT A LIE”
a=b
a²=ab
a²+a²=a²+ab
2a²=a²+ab
2a²-2ab=a²+ab-2ab
2(a²-ab)=a²-ab
2=1
“SHIT“
MatthewTheLucky
Hey! Stop dividing by zero!
Inkblot
But it is such a beautiful lie.
TheNinthShader
Could have just used fermi estimation and been done with it easy
1+1=1 because 2 rounds down.
48+54=110
48 rounds down to 10, 54 rounds up to 100. 100 plus 10 is 110.
TheNinthShader
Shit, I messed up on the second thing. Its supposed to equal 100 total.
DarkVeghetta
You know, fermi estimation is very much like religion. It’s not proper math, but damnit if it won’t try to pretend like it is!
TamiDOA
Quantum physics is virtually a religion. Most of it can’t really be proven or dis-proven, so you have to take on faith based on the teachings of its preachers that say it must be true because the math they created to explain it says so.
Oh, and by quantum physics, 1 is only probably equal to 1 … or not, and simultaneously. 🙂
thejeff
And yet it works. Quantum physics is actually pretty solid. We just don’t understand it. The world is stranger than we can imagine.
String theory, on the other hand…
Agemegos
Quantum mechanics is amazingly solid. It gives (mostly) probabilistic predictions rather that precise ones, but the probabilities it calculates are amazingly accurate. It explained a whole bunch of stuff that seemed bizarre and arbitrary (such as the bell-shaped thermal spectrum and the sharp lines in emission and absorption spectra), and it predicted a wide range of bizarre-sounding phenomena that turned out actually to occur and that we use to make transistors, microchips, diodes, LEDs, and lasers.
And it doesn’t say that 1 is only probably equal to 1.
TamiDOA
I never said it didn’t work, just that it has many characteristics of a religion.
And as Dina might say, I must must have said the JOKE (whence the 🙂 ) wrong. It’s another version of “How many cats does Schrödinger have? One and zero … probably.”
TamiDOA
Another characteristic of a religion is the reaction that occurs when perceived heresy is spoken/typed. Did I just witness quantum fundamentalists? 🙂
DarkVeghetta
Religions obfuscate reality rather then accurately predict its inner workings. Key word being accurate. It doesn’t matter if it’s bizarre as long as the end result lines up with objective, provable fact.
Agemegos
For those following along at home, here is the wikipedia article on Fermi estimates.
TheGrammarLegionary
Neat, but I’ve got a trick to make 2+2=whatever the fuck I decide it is.
Ana Chronistic
2+2=5
for extremely large values of 2
Reflex76
“There . . . are . . . *four* lights!”
Matthew Chapdelaine
Ugh. Naked Picard. You made me remember. Goddamn you.
Zabl-Fahr
the ballad of jean-luc and the four lights
https://www.youtube.com/watch?v=0NFITME0zI8
TamiDOA
If we’re not careful, someone here is going to prove black is white and Joyce is going to get run over at a zebra crossing!
Meamoi
White is the absence of color on paper. Black is the absence of color in light.
White is light’s black.
Black is solid’s white.
Black is white, just seen from a difference perspective.
By the way, Darth Vader killed your father.
Falling Star
Pink is just the abscense of green pigment.
Lurlock
Unless it’s also invisible. And a unicorn.
a snow ʍousɐ
White pigment is the absorption of nothing. Black is nothing. Black pigment is the absorption of everything.
Mr. Random
Fish? FAIRY GOD PARENTS!
Sudden Clarity Clarence
Is it a gun?
Matthew Chapdelaine
Is it safe?
thejeff
Oh it’s perfectly safe. It’s us who are in trouble.
Ana Chronistic
[inb4 UR OPPRESSING MAH CHRISTIAN FREEDUMS not reading the alt-text]
[[or the FAQ]]
Disloyal Subject
No, please.
I assume those people slip through the cracks from time to time and I just haven’t seen them, but they’re free to go elsewhere for entertainment.
Jason
Pretty sure they probably don’t slip through the comment moderation? I know first time commenters are moderated and I’m sure I remember Willis saying the comment section itself is read through and manually moderated. Which I gotta say, with comment threads of this size, is serious dedication to never leaving a computer.
Disloyal Subject
Yeah, but if someone’s first comment is fine but they later go off the deep end I imagine their comment would still be up at first.
inqntrol
Math, why is it always math?
Noah
Because math is more fundamental and it tends not to be completely disproven so easily. That’s why intelligent people tend to not like that everything they think they know is a lie (again), and that this time even math has broken.
Needfuldoer
Math. Math never changes.
Meamoi
The math isn’t broken, but our shortcuts for it are.
However, math IS incomplete, and NEVER can be complete. Godel proved that one. Although I don’t suggest reading his works, they have been shown to literally drive people insane. Like literally literally. Like, they read the book, brain goes “world does not compute,” they try to prove him wrong, fail, can’t accept it being right, spiral into a deranged madness, and get taken away by men in white coats. Literally insane.
On the flip side, if you want to learn what he taught without going insane, I suggest reading “Godel, Escher, Bach.” It does a good job of “slowly” preparing you for the Godel’s big reveal. (Every chapter is a paradigm shift). So when you finally get to the end, you can actually understand Godel without it shattering your brain, because you’ve already fixed a lot of the parts that you didn’t know were broken and so don’t go through the “everything I ever learned is a lie” mental breakdown.
Yet Another Laura H.
Oh, goodness, 1000000 points for Gödel. He was required reading at my college, where the only required math class did not involve numbers. You would think that would be easy, but the math for a course where Calvinball was also required reading… well, I was pretty good at the math of quantum physics, but I literally got a headache in “IS2” every day. It was the best kind of brainhurt.
Ana
Actually, nothing incomplete in the underlying math here, it’s just all the answers I’ve read here that are, in one way or another. At least in Portugal, this kind of exercise is pretty typical in 9th grade math – whenever you want to divide by a non constant expression, you have to branch out in order to handle the zero case.
a = b
( … )
2(a²-ab) = a²-ab
(2(a²-ab) = a²-ab && a²-ab != 0) || (2(a²-ab) = a²-ab && a²-ab = 0)
(2 = 1 && a²-ab != 0) || (2*0 = 0)
(2 = 1 && a²-ab != 0) || (0 = 0)
(2 = 1 && a²-ab != 0) || true
This statement is always true regardless of the truth value of (2 = 1 && a²-ab != 0). All this tells you is that you’ve reached a dead end in your proof, at least if you want to prove something other than ‘all values of b in the value set satisfy the condition when you solve for a’ and other than ‘all values of a in the value set satisfy the condition when you solve for b’
Full disclosure: I was a mediocre student in university math.
Tacos
Don’t worry, you’ll most likely not have to use any math higher than algebra in the real world. Unless you’re studying to become something that requires higher math like physics or whatever.
N0083rP00F
And even then most use advanced expert systems to do the math for them. Like why reinvent the quadratic every time you do a little bit of particle physics?
Matthew Chapdelaine
I have trouble wrapping my head around Physics.
But I know buzz words like “Quantum” and “Q-Bit”.
Meamoi
At least until you get to calculus and/or statistical analysis. Once you learn either one, you may not directly use them often, but you quickly begin to use shortcut versions of them *everywhere*.
“Wait… if I do that… it’s going to progress asymptotically, but if I do this, it’ll be exponential… at least until I hit this limit… OK! Now I know how I’m going to manage my calorie intake for the next two months!”
Agemegos
Yep. Very true.
It’s a box full of sharp and handy intellectual tools.
0kami
Integers… Very dangerous.
You go first.
Creaks
I got this reference.
Willoughby Chase
Maths.
Numbers are shiny.
DarkVeghetta
So. Very. SHINY!
TamiDOA
So are tin-foil hats! And those who find security in tin-foil hats OR shiny math are a few steps further removed from reality.
greenergrassgrowing
That’s not a fallacy, the math is just messed up.
a=b
a²=ab
a²+a²=a²+ab
2a²=a²+ab
2a²-2ab=a²+ab-2ab
2(a²-ab)=a²-ab <<<HERE
2(a^2 – ab) = 2(0) = 0
0 = 0
Or am I missing a joke somewhere?
Peduncle
As MatthewTheLucky pointed out, this proof that 2 = 1 is accomplished by dividing by zero. You can prove anything that way. It’s the step in Ana Chronistic’s math right after the step you marked with HERE.
It’s very handy to be able to prove anything.
Znayx
Dude, at “HERE” there are no errors. On the right he’s factorizing (by 2) and on the left he’s doing ab-2ab which is -ab. no problems there. The idea of the falacy is something you missed in your conclusion. You just skipped to the reason why it’s a falacy: You ended up with zeroes. The math is flawless, it just doesn’t work that way. To isolate 2=1, you’d have to divide by (a^2-ab) on both sides. But that is 0. Which is to say, you’d have to divide by zero, which you can’t.
Znayx
I understand that it’s a fallacy, and I know that it can’t be a real proof. However, I’m missing where it messes up. Where the logic disappears. Is it at a specific point along your equation development, or is a=b doomed to cause fallacies from the start?
DinaWho
It’s because you divide by zero (a^2-ab is 0), which doesn’t work.
Inkblot
You get problems when you try to say that (X•0)/0 = X.
Shay Guy
I find it helps to plug in some value — say, 5 — for a and b, and see how each equation works out. That makes it more visible when you’re dividing by 0.
Jaenus
The reason is that a + a != a unless a = 0. Take a look at this line:
2(a²-ab)=a²-ab
Now substitute a for b
2(a²-a²)=a²-a²
a² – a² = 0, therefore 2 * 0 = 1 * 0, i.e. this sequence of operations only holds true when a = b = 0.
It is not saying that 2 = 1 but that 2 * (something) = 1 * (the same thing) can be true, and it is only true when a = b = 0
Jaenus
Basically, in mathematics, ab = ac means b = c only holds true IF (and only IF) a is non-zero. Think about it. If a = 0 then b could be 9 and c could be 5000 and it would still be true that ab = ac since 0 * anything = 0. But b is definitely not equal to c.
That’s what is being done in the last step to get 2 = 1 from 2(a²-ab)=a²-ab what is really happening is a division on both sides by the factor a²-ab, but that’s a²-a², which is 0. The statement is that 2 * 0 = 1 * 0, which is true.
a snow ʍousɐ
b=c can hold true if a is zero. But ab=ac does not IMPLY b=c unless a is non-zero. In other words, reducing both sides by canceling will only be guaranteed to work when a is non-zero.
Amazi-Stool
.
Nope, the equations Ana Chronistic has given are true for all numbers a and b which meet the condition a=b!
(Of course with the exception of the last one, as divison by zero).
Evely
The failure in logic comes from them not simplifying ab to a^2. math does tricksy things when you play with the names of variables. for example:
a^2=b
log(a)b=2
lnb/lna=2
lnb=2lna
lnb/2=lna
e^lnb/2=a
e=(lnb/2)root(a)
log(a)e=2/lnb
log(a)e*lnb=2
lne/lna*lnb=2
1/lna*lnb=2
now for the switcheroo
1/lna*2lna=2
2lna/lna=2
2=2
…i guess i failed to break logic.
dmaxx
Damnit ya’all, you guys try turn this place into a xkcd area? You seriously start sounding that way>_<"
DarkVeghetta
Ah, the ONLY time I get to feel like all those hours of math in school had any point to them – comic comment sections.
Deanatay
Dude, you gots no problems when someone fills a page with a rant about child abuse or sexism, but get upset when it’s about math?
It’s just math, dude. Nothin’ but numbers. Don’t be afraid.
DarkVeghetta
I don’t think he’s upset. Somehow I doubt anyone familiar enough with xkcd to recognize such would frown upon math. It’s probably more of a ‘Seriously? xD’
Matthew Chapdelaine
You guys should read Lewis Carrol’s “A Game of Logic”. I’m
pretty sure you can find it for free in multiple places if you
Google it.
a snow ʍousɐ
Oh, cool! I love Dodgson!
Matthew Chapdelaine
These New Cakes are Not Nice. Some Old Cakes are Nice.
Therefore, No New Cakes are Nice.
Noah
Ah HA! 2a²=a²+ab and they’re both having 2ab subtracted from them. Therefore it’s 0 = 0! So a=0! So it works out fine! I get to keep my sanity for another day! ^^
Shay Guy
1 = sqrt(1) = sqrt(-1*-1) = sqrt(-1) * sqrt(-1) = i * i = -1
Therefore, 1 = -1.
Znayx
Interesting. Haven’t seen that one before either.
Stephanie
It breaks because the square root function isn’t well-defined and continuous on the entirety of the complex plane, you have to cut a slit down the negative x axis to make a proper “function”. So it’s not a real proof, but disproving it is just a matter of knowing that sqrt(ab) = sqrt(a)sqrt(b) when a and b are positive.
It’s… confusing ya.
a snow ʍousɐ
Definitely more complicated than division by 0.
Kenny
sqrt(1) = -1
Teach the Controversy
Reltzik
Add one pile of sand to one pile of sand. You get one pile of sand. 1 + 1 = 1.
*mindsplosion*
JA