Difference between revisions of "622: Haiku Proof"

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==Explanation==
 
==Explanation==
{{w|Euclid's theorem}} states that there are an infinite number of primes. (In case it's been a while, remember that prime numbers are 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:
+
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. Basically it is a dream, as also indicated with Cueball's thought that are "outside" this {{w|lucid dream}} where it could be seen as it was the entire comic, except Cueball's thoughts, that are inside the dream bubble. (Dreams being a [[:Category:Dreams|recurring theme]] in xkcd). Note also that where Cueball looks up after the flying teacher when she takes off, Megan never moves her head to watch her teacher fly, because it's not happening in her world, and Cueball only dream the teachers moves.
  
: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. Since each ''p''<sub>k</sub> is a factor of ''q'', they cannot be a factor of ''q'' + 1. So ''q'' + 1 has no prime factors, which means it must be prime itself; however, we assumed we had listed every prime number, which means a contradiction has occurred. Then our supposition is false, so there must be an infinite number of primes.
+
{{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:
  
The comic essentially takes this proof and states it in the form of a {{w|haiku}}, which is a traditional form of Japanese poetry where the three lines must have 5, 7, and 5 syllables, respectively. Actually, the 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.
+
: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.
  
The comic and title text conclude that going to class while sleep-deprived is an interesting, but entirely noneducational, experience.
+
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 haiku consists of three lines with 5, 7 and 5 syllables respectively per line. An English Haiku has 5, 7 and 5 syllables per line. And the proof poem goes like this:
 +
: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:
 +
: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.
 +
 
 +
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 do go for the sake of the hallucinations.
  
 
==Transcript==
 
==Transcript==
:[Students are sitting at desks.]
+
:[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.]
:Student #1: How do you know there are an infinite number of primes?
+
:Megan: How do you know there are an infinite number of primes?
:Professor: I'll answer in haiku!
+
:Miss Lenhart: I'll answer in haiku!
  
:Professor: Top prime's divisors'
+
:[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'
  
:[The professor floats into the air.]
+
:[Miss Lenhart floats into the air with three lines beneath her legs. Cueball looks up. Megan does not change position.]
:Professor: Product (plus one)'s factors are...?
+
:Miss Lenhart: Product (plus one)'s factors are...?
  
:[The professor wafts over the students.]
+
:[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.]
:Professor: Q.E.D., bitches!
+
:Miss Lenhart: Q.E.D., bitches!
:Student #2 [in thought bubble]: Wow, after the 48-hour sleep-dep mark, lectures get ''really'' interesting.
+
:Cueball (thinking): 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:Math]]
 
[[Category:Math]]
 +
[[Category:Dreams]]

Latest revision as of 21:33, 25 April 2018

Haiku Proof
After somewhere around 40 hours, there's no academic reason to go to the class. Only go for the hallucinations.
Title text: After somewhere around 40 hours, there's no academic reason to go to the class. Only go for the hallucinations.

Explanation[edit]

In this comic Cueball attends a math class after having been awake for two full days (48 hours). After that he begins to hallucinate and dreams that the teacher Miss Lenhart (a professor in this comic) answers Megan's question, about a proof that there are an infinite number of prime numbers, in haiku. After the first line she floats up and during the third and final line she flies over the students heads. Basically it is a dream, as also indicated with Cueball's thought that are "outside" this lucid dream where it could be seen as it was the entire comic, except Cueball's thoughts, that are inside the dream bubble. (Dreams being a recurring theme in xkcd). Note also that where Cueball looks up after the flying teacher when she takes off, Megan never moves her head to watch her teacher fly, because it's not happening in her world, and Cueball only dream the teachers moves.

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 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. p1p2...pn = 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 pk 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.

The comic essentially takes this proof and states it in the form of a haiku, which is a traditional form of Japanese poetry which is in Japanese broken up into patterns of morae (or syllables), a unit that measures the length of sound. A haiku consists of three lines with 5, 7 and 5 syllables respectively per line. An English Haiku has 5, 7 and 5 syllables per line. And the proof poem goes like this:

Top prime's divisors'
Product (plus one)'s factors are...?
Q.E.D., bitches!

Which can be divided in syllables like this:

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.

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 do go for the sake of the hallucinations.

Transcript[edit]

[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.]
Megan: How do you know there are an infinite number of primes?
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 floats into the air with three lines beneath her legs. Cueball looks up. Megan does not change position.]
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: Q.E.D., bitches!
Cueball (thinking): Wow, after the 48-hour sleep-dep mark, lectures get really interesting.


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Discussion

A prime number must also be a natural number greater that one. -- ‎204.8.8.13 (talk) (please sign your comments with ~~~~)

I removed the paragraph about the haiku being off, as it is not "top prime's divisors," but "top prime's divisors' " (notice the second apostrophe). So the question is actually what the (prime) factors of the product of all prime divisors plus one are. KillaBilla (talk) 21:57, 12 June 2014 (UTC)

I've put it back, since the paragraph is correct - the proof is incorrect. That second apostrophe just means it is the product belonging to the top prime's divisors. The product of the top prime's divisors is just the top prime. --141.101.98.234 14:40, 5 April 2015 (UTC)
"All primes' divisors'" would've been correct (although the "divisors" is still unnecessary). --108.162.254.185 10:16, 16 July 2015 (UTC)

I made a new poem: The product of all- Primes, plus one, divisors are?- Q.E.D., ******s! 108.162.216.148 23:56, 10 January 2017 (UTC)