Editing 622: Haiku Proof

Jump to: navigation, search

Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision Your text
Line 8: Line 8:
  
 
==Explanation==
 
==Explanation==
−
In this comic [[Cueball]] attends a math class after having been awake for two full days (48 hours). After that he begins to {{w|hallucinate}} and dreams that the teacher [[Miss Lenhart]] (a [http://xkcd.com/622/info.0.json professor] in this comic) answers [[Megan|Megan's]] question, about a proof that there are an infinite number of {{w|prime numbers}}, in {{w|haiku}}. After the first line she floats up and during the third and final line she flies over the students heads. Note also that when Cueball looks up at the flying teacher when she takes off, Megan never moves her head because it's not happening in her world, and Cueball only hallucinates the teachers flies.
 
−
 
 
{{w|Euclid's theorem}} states that there are an infinite number of primes, prime numbers being numbers that are only divisible by themselves and 1. The most notable proof of this theorem, and the one presented in this comic, was first given by Euclid himself in his ''{{w|Euclid's Elements|Elements}}''. A more traditional form of this proof follows:
 
{{w|Euclid's theorem}} states that there are an infinite number of primes, prime numbers being numbers that are only divisible by themselves and 1. The most notable proof of this theorem, and the one presented in this comic, was first given by Euclid himself in his ''{{w|Euclid's Elements|Elements}}''. A more traditional form of this proof follows:
  
 
:If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''<sub>1</sub>''p''<sub>2</sub>...''p''<sub>n</sub> = ''q''. Now consider ''q'' + 1. If this number is prime itself, then we have discovered a new prime number, contrary to the assumption that we had listed them all. If it is not prime, it must have a prime divisor. Since all of the ''p''<sub>k</sub> are a factor of ''q'', they cannot be a divisor of ''q'' + 1. So ''q'' + 1 is divisible by a prime not on the list, which again is a contradiction. Therefore, there must be infinitely many primes.
 
:If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''<sub>1</sub>''p''<sub>2</sub>...''p''<sub>n</sub> = ''q''. Now consider ''q'' + 1. If this number is prime itself, then we have discovered a new prime number, contrary to the assumption that we had listed them all. If it is not prime, it must have a prime divisor. Since all of the ''p''<sub>k</sub> are a factor of ''q'', they cannot be a divisor of ''q'' + 1. So ''q'' + 1 is divisible by a prime not on the list, which again is a contradiction. Therefore, there must be infinitely many primes.
  
−
At the last line of the haiku, [[Miss Lenhart]] says "Q.E.D., bitches!", Q.E.D. stands for "Quod Erat Demonstrandum", which means "Thus, it has been demonstrated." This is a Latin phrase which is used to show a proof is over. Ironically, the proof is not complete.
+
The comic essentially takes this proof and states it in the form of a {{w|haiku}}, which is a traditional form of Japanese poetry which is in Japanese broken up into patterns of {{w|morae}}, a unit that measures the length of sound. A haiku consists of three lines with 5, 7 and 5 morae respectively per line. This is less easy to do in English as English doesn't use the concept of syllable length, so we count haikus according to the syllables in each line.
  
−
The comic essentially takes this proof and states it in the form of a {{w|haiku}}, which is a traditional form of Japanese poetry, which is in Japanese broken up into patterns of {{w|morae}} (or {{w|syllables}}), a unit that measures the length of sound. A Japanese haiku consists of three lines with 5, 7 and 5 morae respectively per line. An English Haiku has 5, 7 and 5 syllables per line. The proof poem goes like this:
+
The haiku proof given is slightly off, as the first line talks about the "top prime's divisors," which makes no sense because the top prime doesn't have any divisors besides itself and one. You need to take the product of ''all'' primes, not just one. But, hey, it's a hallucination.
−
:Top prime's divisors'
 
−
:Product (plus one)'s factors are...?
 
−
:Q.E.D., bitches!
 
  
−
Which can be [http://www.syllablecount.com/ divided in syllables] like this:
+
The comic and title text conclude that going to class while sleep-deprived is an interesting, but entirely noneducational, experience.
−
:Top - prime's - di - vi - sors'
 
−
:Pro - duct - (plus - one)'s - fac - tors - are...?
 
−
:Q. - E.- D., - bit - ches!
 
−
 
 
−
The haiku proof given is slightly off, as the first line talks about the "top prime's divisors," which makes no sense because the top prime doesn't have any divisors besides itself and one. You need to take the product of ''all'' primes, not just one. But, hey, it's a hallucination. The haiku could be made to more closely resemble the actual argument while retaining haiku structure by replacing the first line with "Assume primes finite."
 
−
 
 
−
Haiku was also referred to before in [[554: Not Enough Work]].
 
−
 
 
−
The comic and title text conclude that going to class while sleep-deprived is an interesting, but entirely noneducational, experience. So, go for the sake of the hallucinations.
 
  
 
==Transcript==
 
==Transcript==
−
:[Miss Lenhart teaching a class gestures with both hands up as Megan, sitting at the first desk on a stool, raises a hand and asks a question. Cueball sits at the desks behind her supporting his head in both hands with the elbows on the desk.]
+
:[Students are sitting at desks.]
 
:Megan: How do you know there are an infinite number of primes?
 
:Megan: How do you know there are an infinite number of primes?
 
:Miss Lenhart: I'll answer in haiku!
 
:Miss Lenhart: I'll answer in haiku!
  
−
:[In a frame-less panel, Miss Lenhart lifts a hand up while answering. Both students sit upright on their stools.]
 
 
:Miss Lenhart: Top prime's divisors'
 
:Miss Lenhart: Top prime's divisors'
  
−
:[Miss Lenhart floats into the air with three lines beneath her legs. Cueball looks up. Megan does not change position.]
+
:[Miss Lenhart floats into the air.]
 
:Miss Lenhart: Product (plus one)'s factors are...?
 
:Miss Lenhart: Product (plus one)'s factors are...?
  
−
:[Miss Lenhart flies over the students heads with a curved line behind her. Neither student look up. The bottom frame of the panel is a curving thought/dream bobble that goes through the middle of the panel at a height just below the desk tops. Two thought circles goes from Cueball's head down to this frame, and Cueball's thoughts are shown below outside of the panel - without any frame around.]
+
:[Miss Lenhart wafts over the students.]
 
:Miss Lenhart: Q.E.D., bitches!
 
:Miss Lenhart: Q.E.D., bitches!
−
:Cueball (thinking): Wow, after the 48-hour sleep-dep mark, lectures get ''really'' interesting.
+
:Cuebal [in thought bubble]: Wow, after the 48-hour sleep-dep mark, lectures get ''really'' interesting.
  
 
{{comic discussion}}
 
{{comic discussion}}
−
 
 
[[Category:Comics featuring Miss Lenhart]]
 
[[Category:Comics featuring Miss Lenhart]]
 
[[Category:Comics featuring Megan]]
 
[[Category:Comics featuring Megan]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
−
[[Category:Analysis]]
+
[[Category:Math]]
−
[[Category:Dreams]]
 

Please note that all contributions to explain xkcd may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see explain xkcd:Copyrights for details). Do not submit copyrighted work without permission!

To protect the wiki against automated edit spam, we kindly ask you to solve the following CAPTCHA:

Cancel | Editing help (opens in new window)

Templates used on this page:

Retrieved from "https://www.explainxkcd.com/wiki/index.php/622:_Haiku_Proof"