622: Haiku Proof

2022-07-17T07:19:53Z

Ddoubledog: Included a proposal to improve the haiku.

{{comic
| number = 622
| date = August 12, 2009
| title = Haiku Proof
| image = haiku_proof.png
| titletext = After somewhere around 40 hours, there's no academic reason to go to the class. Only go for the hallucinations.
}}

==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:

:If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''1''p''2...''p''n = ''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''k 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}} (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:
: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. 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==
:[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.

{{comic discussion}}

[[Category:Comics featuring Miss Lenhart]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Cueball]]
[[Category:Analysis]]
[[Category:Dreams]]

2549: Edge Cake

2021-12-02T10:11:01Z

Ddoubledog: /* Explanation */

{{comic
| number = 2549
| date = December 1, 2021
| title = Edge Cake
| image = edge_cake.png
| titletext = Every time IERS adds or removes a leap second, they send me a birthday cake out of superstition.
}}

==Explanation==
{{incomplete|Created by AN EDGY CAKE- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

[[Megan]] wishes Emily, represented as [[Hairbun]], Happy Birthday, prompting a confused [[Cueball]], as someone, probably Emily, told him that her birthday was sometime last month. Emily explains that she was born over the North Pole in a plane, meaning that she was born in every timezone at once. Technically though this is false, as there are some timezones (such as {{w|Nepal Standard Time|UTC+5:45}}) that are not represented at the north pole. Except for the one hour before it's midnight at the International Date Line, the date in eastern time zones is one day ahead of western time zones. She also says that it was February 29th (presumably it was also February 28 or March 1 in some time zones). February 29th only happens once every four years in the Gregorian calendar, adding to the confusion - people born on February 29th often celebrate their non-leap-year birthdays on arbitrary days (or {{w|The_Pirates_of_Penzance#Synopsis|not at all}}). Also, the airplane was changing ownership from one country to another at the time, so any attempt to use the airplane owner's timezone would not work - even if it's {{w|Birth aboard aircraft and ships|normally not so complicated}}.

The punchline is that rather than try to identify the correct birthday for Emily, the {{w|BIPM}} has decided to let her have birthdays whenever she wants.

Cueball's final line is a pun on "{{w|edge case}}", an engineering term referring to situations or conditions that are unusual in a way likely to cause problems unless specifically accounted for. Edge pieces are generally only important with sheet goods (brownies sheet cakes, etc), which are typically cut into pieces creating a difference between pieces originating on the edge and pieces originating from the center. Since the sides of a cake are often frosted, an edge piece has two faces covered in frosting and a corner piece has three, while a center piece only has one.

The title text states that the {{w|IERS}} sends Emily a cake every time they add or remove a leap second, out of superstition. The International Earth Rotation and Reference Systems Service is in charge of global time standards. It occasionally adds one leap-second to {{w|Coordinated Universal Time}} to adjust for changes in the rotation speed of the Earth.

==Transcript==
:[Megan is walking towards Cueball and Emily (who resembles Hairbun), holding a cake.]
:Megan: Happy birthday, Emily!
:Cueball: Wait, wasn't that last month? When's your birthday, anyways?
:Emily: It's complicated.

:[A diagram of a flight path over the North Pole, with meridian lines radiating out from the center. Emily's dialogue appears above the diagram, but she herself does not appear in this panel.]
:Emily: My mom went into labor on an arctic international flight that diverted directly over the North Pole.
:Emily: I was born in every time zone at once.

:[With Megan standing behind her, Emily holds out a plate of cake to Cueball.]
:Emily: It was also February 29th, and the airline was just changing ownership between countries.
:Emily: The International Bureau of Weights and Measures finally issued a declaration that it's my birthday whenever I want.
:Emily: Cake?
:Cueball: Nice, it's all edge pieces.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Hairbun]]
[[Category:Time]]

explain xkcd - User contributions [en]

622: Haiku Proof

2549: Edge Cake