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*[[List of all comics]] contains a table of most recent xkcd comics and links to the rest, and the corresponding explanations. There are incomplete explanations listed [[:Category:Incomplete explanations|here]]. Feel free to help out by expanding them!
 
*[[List of all comics]] contains a table of most recent xkcd comics and links to the rest, and the corresponding explanations. There are incomplete explanations listed [[:Category:Incomplete explanations|here]]. Feel free to help out by expanding them!
 
*If you see that a new comic hasn't been explained yet, you can create it: '''[[Help:How to add a new comic explanation|Here's how]]'''.
 
  
 
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Revision as of 23:48, 8 December 2013

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Well-Ordering Principle
We could organize a nationwide old-photo-album search, but the real Worst McFly is probably lost to time.
Title text: We could organize a nationwide old-photo-album search, but the real Worst McFly is probably lost to time.

Explanation

Ambox notice.png This explanation may be incomplete or incorrect: Created by a BAD MARTY MCFLY COSTUME. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.

In the comic, Megan has found a genie lamp. A genie (or Jinn) in a lamp is a supernatural, immortal being from many fairy tales, beginning with Aladdin, who grants one or more wishes to the person who frees it, such as by polishing or opening the lamp. Instead of wishing for multiple wishes, flight, money, or other "traditional" wishes, Megan instead wishes to see the worst Marty McFly Halloween costume.

Marty McFly, played by actor Michael J. Fox, is a main character of the science fiction film about time travel Back to the Future, which was released, we are reminded, over thirty years ago, starting a series of sequels. The films are popular, so many people dress up as McFly or Doc Brown, the other main character, on Halloween, a holiday on October 31 when it is traditional in the USA to wear different costumes. McFly's outfit in the original film consists of little more than an orange vest, jean jacket, checkered shirt, jeans, and sneakers. It would seem difficult to get this wrong.

In the final panel, the genie questions why she would wish for something so mundane, when he has the power to grant wishes beyond her wildest dreams. Megan, being savvy of tropes, used in fiction since biblical times, points out that encounters with wish-granting entities often turn out to be traps; genies in fiction will often interpret wishes in ways the wisher did not intend, and particularly mean-spirited ones will twist a mortal's desire into their own personal hell. So Megan tries to play it safe by wishing for something innocuous and with little room for harmful side-effects.

The well-ordering principle is a mathematical fact stating that every non-empty set of positive integers contains a least element. This principle would apply to Megan's request if there was guaranteed to be an absolute worst costume of Marty McFly. However, subjective preference, while reflexive and transitive, is not well-founded (or symmetric or necessarily antisymmetric or (semi-)connex for that matter) and is therefore considered to be a preorder, also called a quasiorder. This means that the genie may not be able to fulfill Megan's wish if the selection is based on the preferences of any one person. For example, the genie may have no opinion on the quality of any McFly costume, or might judge them on criteria completely different from Megan's. Her own criteria might apply to some pairs of costumes but not others, leading to ambiguity as to which is the worst, and no way to say whether any of the candidate possibilities are as bad as the others.

While Megan isn't explicitly wishing for a common or widely-shared opinion, the title text contemplates organizing a "nationwide" search. People's preferences can be combined, such as with a mean opinion score which, while not strictly well-ordered, is usually able to identify a single worst costume, or at least a set of costumes tied for worst place according to aggregate subjective preferences. There are many other ways to combine preferences (e.g. voting) but none of them meet all of the criteria considered desirable, as demonstrated by Arrow's impossibility theorem. There is no way to exclude the possibility that even an omniscient and omnipotent genie might be technically unable to fulfill the wish, at least without, for example, changing one or more persons' preferences or modifying the space-time continuum to retroactively change the quality of some costumes of the past.

Depending on how wish-fulfilling works, the genie needs to find out, how to fulfill it. Just stating a wish which is proven to have a solution may be quite complicated for the genie. It could be more complex if the wish is about processing real existing information instead of making a fantasy real. The genie has to think and do research work instead of making a small change. In mathematical expressions of sets one can just formulate 'a wish' with only few limits.

The title text may explain why Megan is interested in this wish: any means available to her would be restricted to a geographic area's (nationwide) photographs or drawings from memory. It is likely the worst costume was either never photographed, or isn't remembered accurately by those who saw it (it is lost to time). By asking the genie to show her, she might be able to see the truly worst costume without being restricted to only those for which evidence remains.

The title text can also be interpreted as Randall's wish to know about the worst costume. So this is not Megan but Randall who has the wish to see this costume. The best we can do today is to look through all the available photos of McFly costumes. But even if one of those could be agreed upon to be the worst, there is no guarantee that there is not even worse versions that is not documented for posterity. In this interpretation, what Randall really would like is to use a dangerous genie wish to get around these difficulties.

An additional, subtle pun plays on the word "well". In European folklore, water wells are often associated with spirits which may grant wishes, similar to genies. Thus, Megan's explanation of why she made a simple request of the genie is a statement of her "well-ordering principle"; her principle for ordering wishes from wells. (See also the Well series).

Transcript

Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.
[Megan rubs a lamp held in her hands. A genie appears from the end of the lamp. The genie resembles the top half of Cueball's body, with a head, torso, and crossed arms, but with a squiggle representing a puff of smoke in place of his legs.]
Genie: Greetings, mortal. You have freed me. I will grant you one wish.
Megan: Hmm.
[Megan holding the lamp to her side. The genie is off-panel.]
Megan: It's been over 30 years since Back to the Future came out. Since then, probably hundreds of thousands of people have tried to dress as Marty McFly for Halloween.
Genie: OK, and?
[Megan, holding the lamp to her side, talking to the genie, who is floating in the air.]
Megan: Of those people, one of them must have done the worst job.
Megan: My wish is to see their costume.
[Megan still holding the lamp and talking to the genie. The genie is exasperated, and has his hands raised.]
Genie: Not a billion dollars? Flight? Infinite wishes?
Megan: These wish things are always traps.
Megan: Just show me the worst McFly and we'll call it even.


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