2193: Well-Ordering Principle - Revision history

162.218.182.23: /* Explanation */ Chronology

2025-10-21T19:15:24Z

‎Explanation: Chronology

FaviFake: /* Explanation */

2025-04-19T08:33:30Z

‎Explanation

FaviFake at 08:32, 19 April 2025

2025-04-19T08:32:48Z

172.68.205.93: Adding links to other genie comics

2025-04-01T17:57:59Z

Adding links to other genie comics

Sollyucko: mention the axiom of choice

2023-06-12T05:54:11Z

mention the axiom of choice

Natg19: /* Transcript */ genie

2023-02-23T05:38:35Z

‎Transcript: genie

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 ==Explanation==
-This is one of five other comics relating to genies ([[152: Hamster Ball]], [[879: Lamp]], [[1391: Darkness]], [[532: Piano]], and [[2741: Wish Interpretation]]).
+This is one of five other comics relating to genies ([[152: Hamster Ball]], [[532: Piano]], [[879: Lamp]], [[1391: Darkness]], and [[2741: Wish Interpretation]]).
 In the comic, [[Megan]] has found a genie lamp. A genie (or {{w|Jinn}}) in a lamp is a supernatural, immortal being from many fairy tales, the most well known that from {{w|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.

@@ Line 8: / Line 8: @@
 ==Explanation==
-This is one of five other comics relating to genies:
+This is one of five other comics relating to genies ([[152: Hamster Ball]], [[879: Lamp]], [[1391: Darkness]], [[532: Piano]], and [[2741: Wish Interpretation]]).
 In the comic, [[Megan]] has found a genie lamp. A genie (or {{w|Jinn}}) in a lamp is a supernatural, immortal being from many fairy tales, the most well known that from {{w|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.

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 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" -- which usually is just a figure of speech, but may actually be ''literally'' true in this case given the ''Back to the Future'' series' central theme of time travel). 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.  Such a wish fulfillment might even require actual time travel to the time and location where the costume existed. The title text can also be interpreted as [[Randall|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, {{w|Wishing_well|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 [[:Category:Well|Well series]]).
+An additional, subtle pun plays on the word "well". In European folklore, {{w|Wishing well|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 [[561: Well]] and [[568: Well 2]].)
 ==Transcript==

← Older revision		Revision as of 17:57, 1 April 2025
Line 8:		Line 8:

	==Explanation==		==Explanation==
		+	This is one of five other comics relating to genies:
		+
		+	*[[152: Hamster Ball]]
		+	*[[879: Lamp]]
		+	*[[1391: Darkness]]
		+	*[[532: Piano]]
		+	*[[2741: Wish Interpretation]]
		+
	In the comic, [[Megan]] has found a genie lamp. A genie (or {{w\|Jinn}}) in a lamp is a supernatural, immortal being from many fairy tales, the most well known that from {{w\|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.		In the comic, [[Megan]] has found a genie lamp. A genie (or {{w\|Jinn}}) in a lamp is a supernatural, immortal being from many fairy tales, the most well known that from {{w\|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.

@@ Line 14: / Line 14: @@
 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 {{tvtropes|JackassGenie|twist a mortal's desire into their own personal hell}}. Even when the wish-granting entity isn't malicious, they're often portrayed as carrying unintended consequences, such that extremely consequential wishes become extremely dangerous. So Megan tries to play it safe by wishing for something innocuous and with little room for harmful side-effects.  Unfortunately, Megan appears to have forgotten the overarching trope: all wishes can be twisted against the wisher.
-The genie may also be reluctant to fulfill the wish due to the insurmountable practical difficulties of fulfilling such subjective, ill-defined request. The {{w|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 {{w|preference}}, while {{w|Reflexive relation|reflexive}} and {{w|Transitive relation|transitive}}, is not {{w|Well-founded relation|well-founded}} (or {{w|Symmetric relation|symmetric}} or necessarily {{w|Antisymmetric relation|antisymmetric}} or {{w|Connex relation|(semi-)connex}} for that matter) and is therefore considered to be a {{w|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.
+The genie may also be reluctant to fulfill the wish due to the insurmountable practical difficulties of fulfilling such subjective, ill-defined request. The {{w|well-ordering principle}} is a mathematical fact stating that every non-empty set of positive integers contains a least element; a generalization of this is the {{w|well-ordering theorem}} which is equivalent (given {{w|Zermelo–Fraenkel set theory}}) to the {{w|axiom of choice}}, the subject of [[982: Set Theory]]. This principle would apply to Megan's request if there was guaranteed to be an absolute worst costume of Marty McFly. However, subjective {{w|preference}}, while {{w|Reflexive relation|reflexive}} and {{w|Transitive relation|transitive}}, is not {{w|Well-founded relation|well-founded}} (or {{w|Symmetric relation|symmetric}} or necessarily {{w|Antisymmetric relation|antisymmetric}} or {{w|Connex relation|(semi-)connex}} for that matter) and is therefore considered to be a {{w|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 {{w|Public opinion|common or widely-shared opinion}}, the title text contemplates organizing a "nationwide" search. People's preferences can be combined, such as with a {{w|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 [https://www.docdroid.net/bcKvZmM/preference-aggregation.pdf many other ways to combine preferences] (e.g. voting) but none of them meet all of the criteria considered desirable, as demonstrated by {{w|Arrow's impossibility theorem}}. There is no way to exclude the possibility that even an omniscient and omnipotent genie might be {{w|Omnipotence paradox|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. The genie could fulfill the wish by showing Megan every McFly costume ever worn, which would necessarily show her the worst by any possible definition, but could be the trap she was hoping to avoid because viewing all the "hundreds of thousands" would take an inordinately long time.

← Older revision		Revision as of 05:38, 23 February 2023
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	[[Category:Math]]		[[Category:Math]]
	[[Category:Back to the Future]]		[[Category:Back to the Future]]
		+	[[Category:Genie]]