explain xkcd - User contributions [en]

2550: Webb

2021-12-05T22:32:52Z

108.162.250.106: /* it's summer solstice down here */

{{comic
| number = 2550
| date = December 3, 2021
| title = Webb
| image = webb.png
| titletext = Each one contains a chocolate shaped like a famous spacecraft and, for the later numbers, a pamphlet on managing anxiety.
}}

==Explanation==
{{incomplete|Created by the JAMES WEBB SPACE TELESCOPE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic depicts an {{w|advent calendar}} geared toward astronomers anticipating the launch of the {{w|James Webb Space Telescope}}.

The James Webb Space Telescope is (currently, but after [[2014: JWST Delays|many prior delays]]) scheduled to be launched on the 22nd of December. Christmas will indeed come early for astronomers should the launch be successful.

A normal advent calendar marks the days until Christmas by allowing 'doors' to be opened, or other means of revealing some treat/picture. This is often from the 1st of the month until the 'big reveal' on the 24th or 25th, though other schemes may exist for cultural reasons. This particular calendar features 18 hexagonal features, intended to be sequentially accessed over several days, deliberately similar to the 18 gold-beryllium mirror segments designed to fold out to form the JWST's primary mirror. The first door is on the 5th, two days after this comic's publication date, while the last is the 22nd, marking 'The Big Day'.

Cueball's question could be interpreted two ways: Cueball doesn't know about JWST, so he is asking why this advent calendar ends before Christmas (and possibly fearing this calendar is similar to the one in [[1245: 10-Day Forecast]]); or Cueball does know about JWST and its history of delays, so he is asking why the calendar ends on 22 when there is no certainty in that launch date (and also implying that he expects it to be delayed).

December 22 is also the day after the northern hemisphere winter solstice. The end of the world was famously predicted for the winter solstice in [[998: 2012|2012]].

The title text references the fact that chocolates in advent calendars are often molded into different shapes, and the fact that the later numbers have a "pamphlet on managing anxiety" is probably supposed to quell the impeding fear that the launch would be delayed (or go wrong). The telescope's launch was initially planned for 2007, but due to various redesigns, financial issues, accidents, flaws, and the {{w|COVID-19 pandemic}}, the launch date was pushed back to 2011, then 2013, 2018, 2020, May 2021, October 2021, and finally to the current launch date in December 2021. It may also allude to post-launch concerns; even if the launch goes well, there will still be nervousness about reaching its intended observation point, unfolding/deploying successfully, and passing its final calibrations without problems. There are effectively no means to rescue/repair this expensive piece of equipment should anything be discovered to be amiss, unlike the {{w|Hubble Space Telescope}}, which was visited a number of times by the Space Shuttles to remedy and enhance various features. (There exist issues with even the HST that cannot currently be considered repairable, without the Shuttles or any proven replacement, and the JWST is to be located far beyond Hubble's operational orbit in a place expensive to get to.)

The JWST has been referenced previously in [[1730: Starshade]], [[2014: JWST Delays]], and [[2447: Hammer Incident]], as well as indirectly in [[975: Occulting Telescope]] and [[1461: Payloads]].

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Cueball and Ponytail are looking at an advent calendar. The advent calendar is in a hexagon shape, with 18 smaller hexagons with numbers ranging from 5-22 written on them.]
:Cueball: The hexagons are nice.
:Cueball: But why does it end at 22?
:[Caption below the panel:]
:Astronomer Advent Calendar

{{comic discussion}}
[[Category:Space]]

2546: Fiction vs Nonfiction

2021-11-26T20:21:56Z

108.162.250.106: /* Movies and Books */ Move "citation needed" tags to places where citations really are (not) needed

{{comic
| number = 2546
| date = November 24, 2021
| title = Fiction vs Nonfiction
| image = fiction_vs_nonfiction.png
| titletext = The real challenge is how to file Boba Fett's biography of Doris Kearns Goodwin.
}}

==Explanation==
{{incomplete|Created by A FICTIONAL DORIS KEARNS GOODWIN WATCHING A REAL BOBA FETT ON A DURASTEEL-BESKAR TV- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

[[Cueball]] is asking [[Ponytail]] and [[White Hat]] to classify different ''{{w|Star Wars}}'' books and movies as fiction or nonfiction. (Perhaps he is working at a library or bookstore, or sorting a personal collection.) ''Star Wars'' as a whole is a multimedia franchise, which includes films, TV series, novels, etc, but often singularly refers to {{w|Star Wars (film)|the original 1977 film}} later more lengthily titled ''Star Wars: Episode IV – A New Hope''. The classifications get more complicated to determine as the conversation progresses while revealing a quite specific obsession with the character of {{w|Boba Fett}}. The complexity may even end up converting {{w|Lumpers and splitters|lumpers into splitters}}, a philosophical distinction that another [[2518: Lumpers and Splitters|recent comic]] touched upon.

Nonfiction (also spelled non-fiction) is any document or media content that intends, in good faith, to present only truth and accuracy regarding information, events, or people. In contrast, fiction offers information, events, or characters expected to be partly or largely imaginary, or else leaves open if and how the work refers to reality.

In the end, White Hat suggests that, since Cueball has so many works featuring Boba Fett, it would be more useful to group them together in a new category rather than sorting them into the fiction and nonfiction sections.

===Movies and Books===
{| class="wikitable"
!Media name
!Explanation
|-
| ''{{w|Star Wars (film)|Star Wars}}''
| ''Star Wars'' is a science-''fiction'' movie released in 1977 (re-released in 1981 as ''Star Wars: Episode IV – A New Hope'')
|-
| ''{{w|The Making of Star Wars}}''
| This was a television special about how ''Star Wars'' was made, which would make it nonfiction.
|-
| ''Star Wars: The Adventures of Boba Fett''
| This would be one of the ''Star Wars'' franchise's continuity of stories, making it fictional. Not a currently extant release, but something like this {{w|List_of_Star_Wars_films#Unproduced_films|has been long anticipated}}, and now possibly inspired by the imminent release (as of the comic's time of posting) of {{w|The Book of Boba Fett}}.
|-
| ''Star Wars: The Official Guide to Boba Fett's Armor and Weapons''
| While the content of this guidebook is entirely fictional, the book is factual. Boba Fett (a fictional character){{citation needed}} does in fact [https://scifi.stackexchange.com/a/253196 have durasteel]/[https://starwars.fandom.com/wiki/Boba_Fett%27s_armor Beskar] armor (a fictional material), so the book is technically non-fiction.
|-
| ''Boba Fett's Gadgets and How He Got Them''
| This could either be a non-fictional book or docuseries similar to the previous entry, or instead an in-universe adventure series or film. The rhythm of the words is similar to the in-universe guidebook "[https://en.wikipedia.org/wiki/Fantastic_Beasts_and_Where_to_Find_Them Fantastic Beasts and Where to Find Them]" from the {{w|Harry Potter}} universe - this is a non-fiction book used educationally for young wizards within the fictitious world and also a fiction book within the real world.
|-
| ''Boba Fett: A Life'' by Doris Kearns Goodwin
| {{w|Doris Kearns Goodwin}} is a historian and biographer who has written biographies of many influential people. Since Goodwin is a non-fiction writer, one would have to read this (not actually existent{{citation needed}}) book to determine whether the biography is a fictional account of the character, or a factual account of the fictional history of the character. If the book doesn't establish any new canon, and is instead citing only recorded (fictional) facts from the Star Wars Universe and, perhaps, the real-world influences on and by the character, it could legitimately be considered non-fiction. Doris Kearns Goodwin is also mentioned in [[2160: Ken Burns Theory]].
|-
| (title text) Boba Fett's biography of Doris Kearns Goodwin
| It is unclear how, or why, a fictional character would write a biography on a real life person,{{citation needed}} but there's always the possibly that there was already a fictional Doris, in-universe to Boba, whose own life and exploits would be natural for an actually fictional factual output.
|}

==Transcript==
:[Cueball is talking to Ponytail and White Hat.]
:Cueball: ''Star Wars''?
:Ponytail: Fiction.

:[Same setting.]
:Cueball: ''The Making of Star Wars''?
:White Hat: Nonfiction.

:[Closeup of Cueball.]
:Cueball: ''Star Wars: The Adventures of Boba Fett''?
:Off-panel voice: Fiction.

:[Closeup of Ponytail.]
:Cueball (off-panel): ''Star Wars: The Official Guide to Boba Fett's Armor and Weapons''?
:Ponytail: Nonfiction, technically.

:[Cueball has lifted a hand palm up as he talks to Ponytail and White Hat.]
:Cueball: ''Boba Fett's Gadgets and How He Got Them''?
:Ponytail: ...Fiction?
:Ponytail: It depends.

:[Cueball is talking to Ponytail and White Hat. Ponytail has turned towards White Hat and has taken a hand to her chin.]
:Cueball: ''Boba Fett: A Life'', by historian Doris Kearns Goodwin?
:Ponytail: Hm.
:White Hat: Maybe we should just have a Boba Fett section.

{{comic discussion}}

[[Category:Star Wars]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring real people]]

2532: Censored Vaccine Card

2021-10-25T08:42:43Z

108.162.250.106: /* Explanation */

{{comic
| number = 2532
| date = October 22, 2021
| title = Censored Vaccine Card
| image = censored_vaccine_card.png
| titletext = CVS's pharmacies are fine, but I much prefer their [censored]s.
}}

==Explanation==
{{incomplete|Created by a B[censored]T. Do NOT delete this tag too soon.}}
This comic is another entry in a [[:Category:COVID-19|series of comics]] related to the {{w|COVID-19 pandemic|2020-21 pandemic}} of the {{w|SARS-CoV-2}} virus, which causes {{w|COVID-19}}, specifically regarding the [[:Category:COVID-19 vaccine|COVID-19 vaccine]].

The comic hinges on the sharing of vaccination card photos on social media as proof that the user has been vaccinated against COVID-19 (in this case, gotten a {{w|Booster dose|booster shot}}, a third dose of the vaccine). When people in the United States first started receiving their vaccine shots, a large number of them shared photos of the CDC vaccination proof cards that they received alongside the vaccines; it was enough of a trend that the {{w|Federal Trade Commission|FTC}} released an official statement warning vaccine recipients [https://www.consumer.ftc.gov/blog/2021/02/social-media-no-place-covid-19-vaccination-cards not to share photos], due to the cards containing {{w|Personal data|personal identification}} that probably should not be made public.

The irony here is that [[Randall]] has {{w|Sanitization (classified information)|"censored"}} some impersonal lines, such as the instructions that are identical on all vaccination cards, and many easy-to-guess lines, while not censoring any of said personal information.
The fourth line, labelled "other" is probably completely blank (as the third dose was on the day immediately prior to the publication one), but is completely blacked out.

The caption indicates that his intention is to "seem more mysterious". This is best exemplified by blanking most of the word "clinician" to leave the acronym "{{w|Central Intelligence Agency|CIA}}", referring to a US government agency known for its frequently "mysterious" (classified) activity, as well as its liberal use of redaction like that in the comic.

[[File:CDC_COVID-19_Vaccination_Record_Card.jpg|thumb|300px|A real and appropriately censored CDC vaccination record.]]

The "19" in COVID-19 is systematically censored in the comic. This is humorous because currently COVID-19 is the only thing that could be meant by "COVID-[anything]", and so the redaction is pointless. This may also be intended, in the interest of mystery, to imply some future outbreak of a similar disease (given an identifier based on the year of its inception).

The sentence at the top of the card, which appears once in English and once in Spanish, has equivalent portions redacted in both languages:
* "medical information" and "the vaccines you have received" in the English version, and
* "información médica" and "las vacunas que ha recibido" in the Spanish.
This is the first comic including a sentence (or, given the censorship, at least a good portion of one) in Spanish.

Randall's patient number is the 2nd to 9th digits of the fractional part of the decimal expansion of {{w|pi}} inclusively: 41592653

The lot numbers of the first and second doses allude to two numbers that appear frequently in Star Wars and other works related to George Lucas: 1138, and 2187. The lot number of the third dose is the {{w|1729 (number)|Ramanujan-Hardy number}}.

Given the reasonable assumption{{citation needed}} that the partially censored year relates to the twentieth century, the date of birth on the card corresponds to that given in the acknowledged [[Randall_Munroe#Timeline|timeline]] for Randall.

{{w|CVS Pharmacy}} is a pharmacy chain in the US which provides COVID-19 vaccinations. CVS #05309 is in Pineville, LA, while Randall lives in Massachusetts; it is not clear why he would have received his first vaccine dose in Louisiana.

The title text comments on the "Provider or clinic site" of the second dose on the card. Where the word "pharmacy" appears in the previous row (and would be on a real card), it is censored in the comic. The most reasonable assumption is that the word is still "pharmacy" and that Randall has simply chosen to redact that instance for some reason, but the title text humorously implies that it was in fact some ''other'' CVS-related venture where he got his second dose, for instance a "CVS Parking lot" or perhaps an {{w|anti-submarine warfare carrier}}.

CVS's parent company, {{w|CVS Health}}, does have other enterprises with compatible names: {{w|CVS Caremark}} and {{w|CVS Health#CVS Specialty|CVS Specialty}}. However, neither of these provide COVID-19 vaccinations.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Profile picture of a Cueball's head and shoulders, with unreadable lines of text to the right.]
:Check it out, I just got my booster!

:[Picture of the U.S. COVID-19 Vaccination Record Card attached on a media post. The card includes pre-printed information in black and handwritten information in blue, the latter indicated here by bold text. Some of the text has been blacked out, indicated here by "[censored]".]

:COVID-[censored] Vaccination record card
:[At the upper right of the card appears the logo of the U.S. Department of Health and Human Services, a stylized eagle surrounded by the words "Department of Health & Human Services USA", although those words are not legible in this drawing. Next to that appears the logo of the Centers for Disease Control and Prevention, a shaded box with the letters "CDC" and the words "Centers for Disease Control and [censored]" below it.]

:Please keep this record card, which includes [censored]
:about [censored]
:Por favor, guarde esta tarjeta de registro, que incluye [censored]
:[censored] sobre [censored]

:'''Munroe''' '''Randall'''
----
:Last Name First Name

:'''10-17-[censored]84''' '''41592653'''
----
:Date of birth Patient number

:[A table fills the remainder of the card. It has four columns and five rows. The first row gives the column names:]
:Vaccine. Manufacturer lot number. Date. Provider or clinic site.
:[The rest of the rows have been filled out. Each "date" cell also includes pre-printed "MM DD YY" below the line where the date is written.]
:1st dose COVID-[censored]. '''Pfizer ER1138'''. '''04'''/'''01'''/'''21'''. '''CVS Pharmacy Clinician #5309'''.
:2nd dose COVID-[censored]. '''Pfizer ES2187'''. '''04'''/'''22'''/'''21'''. '''CVS''' [censored] [censored].
:Other. '''3rd dose''' [censored] '''FH1729'''. '''10'''/'''21'''/'''21'''. [censored] [censored] [censored]'''CIA'''[censored].
:Other. [censored]. [censored]/[censored]/[censored]. [censored].

:[Caption below panel:]
:Security tip: To seem more mysterious, try censoring only ''non''-identifying information.

{{comic discussion}}

[[Category:Comics with color]]
[[Category:COVID-19]]
[[Category:COVID-19 vaccine]]
[[Category:Comics featuring Randall Munroe]]

Talk:2529: Unsolved Math Problems

2021-10-16T04:25:00Z

108.162.250.106:

Center panel possibly related to "The drunkards walk" and theories on randomised motion.
https://www.quantamagazine.org/random-walk-puzzle-solution-20160907/
More references https://mathworld.wolfram.com/RandomWalk.html

2498: Forest Walk

2021-10-08T03:10:28Z

108.162.250.106: /* Explanation */

{{comic
| number = 2498
| date = August 4, 2021
| title = Forest Walk
| image = forest_walk.png
| titletext = The only other person to walk by was a linguist back in the 80s, but she just spent a while dissecting the phrase 'help me down' before getting distracted by a squirrel and wandering off.
}}

==Explanation==
[[Megan]] is walking through a wide landscape with [[Beret Guy]] who owns a big part of it. Megan is surprised that he owns such a big property, however, Beret Guy is known for his inexplicable businesses such as in [[1493: Meeting]] and from [[1032: Networking]]; we know he probably has enough resources to be able to buy it. Alternatively, he might have simply inherited it from his mom [[502: Dark Flow]], or may not really understand the concept of actually owning it. Nevertheless he walks here everyday, and from the context of the comic it seems pretty much no one else comes here.

They meet a rather disheveled-looking bearded man hanging from a parachute caught in a tree. The man shakes a stick at them and demands to be helped down to the ground. Beret Guy simply addresses him as "Mister Cooper" and asks if he promises to return the money he took. The man angrily refuses, and Beret Guy casually says he'll see him again tomorrow, suggesting that this conversation has become a daily routine.

Megan asks if the man was D. B. Cooper, which Beret Guy immediately confirms. He then comments on an owl nest as another bit of "neat stuff" found on his land, suggesting that he finds Cooper's presence to be just another mildly interesting part of this land.

{{w|D. B. Cooper}} is the identity given to a man who hijacked a Boeing 727 aircraft in 1971. He collected a $200,000 ransom (equivalent to $1,250,000 in 2020) and famously donned a parachute and jumped from the plane over the state of Washington. He was never seen or heard from again. Despite lengthy FBI investigations and nation-wide publicity, the hijacker was never identified. A few thousand dollars of the ransom money was found in a river, nearly 10 years after the hijacking, but the remainder has never been recovered. The only things known about him are a police composite drawing and the name "Dan Cooper", under which he had purchased his airline ticket (he was called "D.B" as a result of a miscommunication with the media, and the name stuck).

The high-profile case, followed by the never-solved mystery has led to a massive amount of speculation as to his identity, background, and what became of him. Many consider the most likely scenario to be that he didn't survive the parachute jump, and simply crashed somewhere that his body was never found. Others imagine that he escaped with the money, and simply managed to evade capture.

The comic is insinuating that, after leaping from the plane, he got entangled in tree in Beret Guy's land, and has been there ever since.

Uncanny situations are nothing new to Beret Guy, since he himself possesses [[:Category:Strange_powers_of_Beret_Guy|many strange powers]]. Hence, the concept of a famous criminal hanging from a tree for nearly 50 years doesn't seem any more interesting to him than an owl's nest. In keeping with the typical bizarre-ness of Beret Guy's life, it isn't explained how a man could survive for half a century hanging from a tree, why he'd choose to remain trapped there for his entire life, rather than return money that he's in no position to spend, or why Beret Guy wouldn't simply report his whereabouts to the police. All of these are simply accepted as unremarkable realities of life, for him.

D. B. Cooper was already referenced by Randall in [[1400: D.B. Cooper]], [[1501: Mysteries]] and [[2452: Aviation Firsts]].

The title text may reference to the linguist from [[2390: Linguists]] who is more interested in the linguistic nuances that people use than in actually responding to their call for assistance. It is not known how many others have walked through Beret Guy's land, in the interim, or whether it is their own nature or the general aura from Beret Guy, but the linguist clearly did not much more than ponder the phrase "help me down". Megan also seems in no particular hurry to intervene.

==Transcript==
:[Megan and Beret Guy are walking through a landscape with spread out trees and grass and puddles on the ground.]
:Megan: Wow, this is all yours?
:Beret Guy: Yeah! All the way back to the river!
:Beret Guy: I walk here every day.

:[Megan still walks towards Beret Guy who has now stopped and is looking up while speaking to a man hanging in a tree in front of them. The man has long wild hair and a large beard. He hangs from his parachute which has been folded around a large branch sticking out from beneath the top of the tree. He is holding a long stick of some sort, seemingly attempting to threaten Beret Guy, as the stick and his legs are vibrating as indicated with small lines.]
:Beret Guy: Morning, Mister Cooper!
:Cooper: You help me down '''''this instant!'''''

:[Pan down to show only Beret Guy and nothing else. Cooper replies from off-panel from the top corner.]
:Beret Guy: Do you promise to give back all the money you took?
:Cooper [off-panel]: '''''Never!'''''
:Beret Guy: Okay! See you tomorrow!

:[Megan and Beret Guy continue walking through the landscape with three small trees behind them, as well as grass, rocks and a small puddle. Megan looks back over her shoulder towards where Cooper is hanging.]
:Megan: Was that D.B. Cooper?
:Beret Guy: Yeah, and up ahead there's an owl nest!
:Beret Guy: There's so much neat stuff here.

{{comic discussion}}

[[Category:Comics featuring Megan]]
[[Category:Comics featuring Beret Guy]]
[[Category:Comics featuring D. B. Cooper]]
[[Category:Animals]] 
[[Category:Squirrels]] 
[[Category:Language]] 
[[Category:Strange_powers_of_Beret_Guy]]

Talk:75: Curse Levels

2021-10-08T01:51:33Z

108.162.250.106: Possible explanation of perspective difference between Aus/UK and US re swearwords

I'm sorry that I don't know who to attribute this to, but I once heard a comedian refer to someone as a "mother-effin' fucker". - [[Special:Contributions/108.162.242.10|108.162.242.10]] 22:32, 26 July 2014 (UTC)

It should be noted (or I feel compelled to point out) that the word "cunt" is not seen as all that bad in Great Britain. It's something closer to damn or even just a term that's used in the U.S. like "douche" or others. "Stop being such a cunt, Gary." It's not really all that bad.[[Special:Contributions/108.162.246.108|108.162.246.108]] 00:23, 15 September 2016 (UTC)

: I'm British. The last comment is dead wrong. Far from being “not that bad” it’s basically the polar opposite: pretty much the most shocking and vulgar swear word there is, in a class of its own far beyond other swear words.

:: I think you're talking about Australians.

:: Not that either perspective is particularly relevant, since Randall is American. However, for what it's worth, every reference I've ever seen to British use of the word says that it's more mild than it is in America. Maybe you just live in a weird region where that's not the case. Or maybe all those other people are wrong and it's become a weird urban myth. I guess I'll never know, unless I do, at which point I will.[[Special:Contributions/162.158.126.28|162.158.126.28]] 02:17, 21 December 2017 (UTC)

::: It may be milder than it is in America, but it's still about as strong as it gets. Maybe Brits are just generally more tolerant of swearing in general. It also depends very much on context and inflection - the offense would usually be much greater if it was said in an aggressive manner, than it would be if used in the way that the first commenter did. It also depends on where in the country - in Northern Ireland, for example (which, granted, isn't actually GB, but still) it doesn't seem to be considered anywhere near as strong as it is in most of England.[[Special:Contributions/141.101.76.16|141.101.76.16]] 15:44, 12 January 2018 (UTC)

:Going to have to disagree here. 'Cunt' is a one of the most offensive swear words, although vulgar language is probably a little less offensive in Britain given the frequency of vulgar language. [[User:Beanie|Beanie]] ([[User talk:Beanie|talk]]) 14:13, 16 March 2021 (UTC)

:It is definitely different in Australia. While it's still the rudest swearword, it is ONLY a swearword, which is why it seems less rude. Australians (and presumably Britons) don't put as much emphasis on swearwords as some sort of terrible thing, compared to Americans. This difference has been expressed quite succinctly (by @thomas_violence on Twitter) thus: "I love little cultural differences, like how Americans are super offended by the word cunt but here in Australia we're super offended by school children being slaughtered with automatic weapons".

Talk:2435: Geothmetic Meandian

2021-03-12T21:48:43Z

108.162.250.106: /* Why is this funny? */

Oh, this one's good. Just checked in (no, I wasn't hovering over the refresh button, my first visit today!) and one glance had me in paroxysms of laughter. But how to explain it? Gonna have to think about that. [[Special:Contributions/141.101.98.96|141.101.98.96]] 01:12, 11 March 2021 (UTC)

I made a really bad spreadsheet to understand better how it works: https://docs.google.com/spreadsheets/d/1fqmHwDmirJrsKPdf94PutFDw31DMAYxNeR7jef1jneE/edit?usp=sharing

Someone fix my ''awful'' transcript edits please. --[[User:Char Latte49|Char Latte49]] ([[User talk:Char Latte49|talk]]) 02:31, 11 March 2021 (UTC)

Seeing the Python added to the Explanation, try this Perl (typed straight here, so not tested)...
## Your prefered variations of "#!/usr/bin/perl", "use strict;" and "use warnings;" here! ##
sub F { my (@vals)=@_; my $invVals=1/int(@vals);
my ($geo,$arith,$med)=(1); # Only defining $geo, so first *= works correctly!
while (@vals) { my($lo,$hi)=(shift @vals,pop @vals); # $hi may be undef - this is intended!
$arith+=$lo; $geo*=$lo; unless (defined $hi) { $med = $lo; last }
$arith+=$hi; $geo*=$hi; unless (@vals) { ($med)=F($lo,$hi) }
}
return ($arith*$invVals, $geo**$invVals, $med);
}
sub GMDN { my (@vals)=sort @_; my $lim=10**(-5); # Adjust $lim to taste...
return "Error: No vals!" unless @vals; # Catch!
return $vals[0] unless ($vals[$#vals]-$vals[0]) > $lim;
return GMDM(F(@vals));
}
my @test=(1,1,2,3,5);
print "Values: @test\nGeothmetic Meandian: ".GMDN(@test)."\n";
...debugged in my head, so probably fatally flawed but easily fixed/adapted anyway. [[Special:Contributions/141.101.99.109|141.101.99.109]] 03:04, 11 March 2021 (UTC)

Why so complicated?
perl -e 'use strict; use warnings; sub F { my ($s,$p) = (0,1); my @srt = sort {$a<=>$b} @_; for (@_) { $s += $_; $p *= $_; } return ($s/@_,$p**(1/@_),$srt[$#_/2]); } sub Gmdn { print join(", ",@_=F(@_)),"\n" for 0..20; return @_; } print join(", ",Gmdn(1,1,2,3,5)),"\n";'
(With interim results) SCNR -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 03:18, 11 March 2021 (UTC)
:''I'' can read your version (and I see you do explicit {$a<=>$b}, which indeed ''may'' be necessary in mine for real use, along with additional sanity checks, I will check later) but I wanted to make mine neat, and ''slightly'' tricksy in implementation, but still not quite so entirely obfuscated to the more uninitiated. TIMTOWTDI, etc, so I like your (almost) bare-bones version too. ;)
:(Is 20 cycles enough to converge in sufficiently extreme cases? Won't give "Too deep" error, though, even if it takes at least that long. There's a definite risk that mine might, as written.) [[Special:Contributions/141.101.99.229|141.101.99.229]] 03:45, 11 March 2021 (UTC)
::Given the lack of precision in Randall's example usage, I think 20 cycles ought to be enough for everyone ;-P. I'm trying to prove that the interval's size has to shrink by somewhat close to a factor of 1/2 every cycle, but it's tricky and it's late. If I can assume a factor of 1/2 in the long run, 64 iterations should pin down a 64-bit float.
::I actually didn't try to obfuscate, I was just too lazy to type more ;-). Otherwise I might have left out the "return"s and passing parameters at all. -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 04:21, 11 March 2021 (UTC)
:::I find the one-liner more readable: it's straightforward and pretty minimal. For what its worth, here's my version: <pre>perl -MList::Util=sum,product -E 'sub F { (sum @_)/@_, (product @_)**(1/@_), (sort { $a <=> $b } @_)[$#_/2] } $, = " "; say @v = @ARGV; say @v = F(@v) for 1..30' 1 1 2 3 5</pre> 30 iterations is enough for the numbers to display identically on this system (to 14 decimal places). I think it's even cleaner in Raku (formerly Perl 6): <pre>raku -e 'sub F(@d) { @d.sum/@d, [*](@d)**(1/@d), @d.sort[@d/2] }; say my @v = +«@*ARGS; say @v = F(@v) for 1..33' 1 1 2 3 5</pre> On this system, Rakudo yields an additional decimal place, which takes another 3 iterations to converge. [[User:Smylers|Smylers]] ([[User talk:Smylers|talk]]) 06:53, 11 March 2021 (UTC)

Side-thought: is GMDN (nowhere near as logical an ETLA contraction of the title term as, say, 'GMMD' or 'GTMD') actually an oblique reference to the GNDNs as popularised/coined by Trek canon? Worth a citation/Trivia? [[Special:Contributions/162.158.158.97|162.158.158.97]] 04:12, 11 March 2021 (UTC)

Besides of nerdgasm is there some reason why the program code is relevant for the explanation? [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 08:55, 11 March 2021 (UTC)
:Apparently not. I moved it to the trivia section. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 07:51, 12 March 2021 (UTC)

I do not agree with the statement that "The title text may also be a sly reference to an actual mathematical theorem, namely that if one performs this procedure only using the arithmetic mean and the harmonic mean, the result will converge to the geometric mean." Could one produce a reference to this result? A simple computer experiment does not show this "theorem" to be true, i.e. for the procedure to return the geometric mean of the original entry. [[User:Pointfivegully|Pointfivegully]] ([[User talk:Pointfivegully|talk]]) 15:04, 12 March 2021 (UTC)

== Proof of convergence ==

Can any of you come up with a mathematical proof that repeated application of F on a set of (say) positive real numbers is guaranteed to converge toward a single real number, i.e. that the GMDN of a set of positive real numbers is well-defined?

One observation I've made is that if you consider that maximum and minimum numbers in the original set to be x1 and xn (without loss of generality), something we know for sure is that AM(x1, ..., xn), GM(x1, ..., xn) and Median(x1, ..., xn) are all at least x1 and at most xn that is to say...

x1 <= AM(x1, ..., xn), GM(x1, ..., xn), Median(x1, ..., xn) <= xn

So range(AM(x1, ..., xn), GM(x1, ..., xn), Median(x1, ..., xn)) is necessarily <= range(x1, ..., xn).

And given that we know that unless x1, ..., xn are all equal, that x1 < AM(x1, ..., xn) < xn, we have an even stricter result (unless x1, ..., xn are all equal) that is
range(AM(x1, ..., xn), GM(x1, ..., xn), Median(x1, ..., xn)) < range(x1, ..., xn).

So, it's clear that range(x1, ..., xn) > range(F(x1, ..., xn)) > range(F(F(x1, ..., xn))) > range(F(F(F(x1, ..., xn)))) > ... and it's also clear that all of these ranges are >= 0. There is a result in number theory that says that any infinite sequence of real numbers which monotonically decreases and is bounded from below converges.

So we know for sure that range(F(F(...F(x1, ..., xn)...))) converges but we still have to show that it converges to 0 to show that the GMDN converges to a single real number.

I'm not sure how to proceed. Does anyone have any ideas?

EDIT:
I just noticed that unless x1, ..., xn are all equal, AM(x1, ..., xn) is at least ((n-1)/n) * range(x1, ..., xn) away from both x1 and xn. So not only do we have that range(x1, ..., xn) > range(F(x1, ..., xn)) from before, but we also have that ((n-1)/n) * range(x1, ..., xn) >= range(F(x1, ..., xn)). This guarantees that that the range falls exponentially on repeated applications of F. So it's certain that the the range ultimately converges to 0, and hence that the GMDN is well-defined.

It might be a good idea for someone to concretely present this idea as a proof on Page.

See my additional notes below. -Ramakarl

[[Special:Contributions/172.69.135.44|172.69.135.44]] 05:07, 11 March 2021 (UTC) Anirudh Ajith

:That doesn't quite work as it stands, since proving AM is that distance away does not say anything about the other two averages. I think it's true, but a little more rigour is required. [[Special:Contributions/141.101.98.120|141.101.98.120]] 09:17, 11 March 2021 (UTC)

When trying this myself I first arrived at 2.082, not 2.089. What threw me off was the incomplete formula for the median, which only works with sorted lists. The three values returned by F(...) aren't necessarily sorted.
[[Special:Contributions/141.101.76.194|141.101.76.194]] 09:49, 11 March 2021 (UTC)

<pre>
First: almost all invocations are with exactly 3 arguments (The output of the previous invocation), so we don't have to deal with N inputs at all.
Notation: In iteration n we have the values min[n] <= mid[n] <= max[n] (in any order) and can compute AM[n], GM[n] (and median[n] = mid[n]).
Let Q[n] := max[n]/min[n] >= 1, R[n] := max[n]-min[n] = (Q[n]-1)*min[n].
We already established that R is decreasing and min is increasing, so Q is decreasing.

Theorem: There is an n0 with R[n+1] <= R[n]*2/3 for all n > n0.

Proof (by case discrimination for each n):
case 1: mid[n+1] != AM[n]:
R[n+1] <= Max(max[n]-AM[n],AM[n]-min[n])
= Max(max[n]*3-(max[n]+mid[n]+min[n]),(max[n]+mid[n]+min[n])-min[n]*3)/3
= Max(max[n]*2-(mid[n]+min[n]),(max[n]+mid[n])-min[n]*2)/3
<= (max[n]-min[n])*2/3
= R[n]*2/3
Hence: R[n+1] <= R[n]*2/3

case 2: mid[n+1] == AM[n]:
because GM <= AM: min[n+1] = GM[n], max[n+1] = mid[n]
Q[n+1] = mid[n]/GM[n]
= (mid[n]^3/(max[n]*mid[n]*min[n]))^(1/3)
= (mid[n]^2/(max[n]*min[n]))^(1/3)
<= (mid[n]/min[n])^(1/3)
<= Q[n]^(1/3)
R[n+1] = (Q[n+1]-1)*min[n+1]
<= (Q[n]^(1/3)-1)*GM[n]
<= (Q[n]^(1/3)-1)*(max[n]^2*min[n])^(1/3)
= (Q[n]^(1/3)-1)*Q[n]^(2/3)*min[n]
= (Q[n]-Q[n]^(2/3))*min[n]
= R[n]-(Q[n]^(2/3)-1)*min[n]
<= R[n]-(Q[n]-1)*min[n]/(Q[n]^(1/3)+1))
= R[n]-R[n]/(Q[n]^(1/3)+1)
= R[n]*(1-1/(Q[n]^(1/3)+1))
Now we can pick a q1 = Q(n1) with q1 > Q[n] >= 1 for n > n1 because Q is decreasing:
R[n+1] <= R[n]*(1-1/(q1^(1/3)+1))

Together with case 1, this gives R -> 0 and thus Q -> 1. So we can pick another q0 = Q(n0) with q0 <= 8:
R[n+1] <= R[n]*(1-1/(q0^(1/3)+1)) <= R[n]*2/3
</pre>
-- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 17:34, 11 March 2021 (UTC)

== Better Python implementations ==

I'd like to add a somewhat more compact Python implementation based on the numpy module.
import numpy as np

def F(x):
return np.mean(x), np.exp(np.log(x).mean()), np.median(x)

def GMDN(x, tolerance=1e-6):
while np.std(x) > tolerance:
x = F(x)
return x[0]

gmdn = GMDN([1, 1, 2, 3, 5])
print(gmdn)
--[[User:Lvdgraaff|Lvdgraaff]] ([[User talk:Lvdgraaff|talk]]) 10:42, 11 March 2021 (UTC)

No need for numpy, there's the statistics module in the stdlib

import math
import statistics

def F(*nums):
return (
statistics.mean(nums),
statistics.geometric_mean(nums),
statistics.median(nums),
)

def GMDN(*nums):
while not math.isclose(max(nums), min(nums)):
nums = F(*nums)
return nums[0]

gmdn = GMDN(1, 1, 2, 3, 5)
print(gmdn)

:For something as simple as this, I always find it cheating to use a package to abstract away the few actually necessary calculations. You might as well use a DWIM module and do 'result = DWIM(input)' as the sole command. But that's me for you. I'd write my own direct-to-memory screen RAM accesses, if silly things like OS HALs and GPU acceleration (once you find a way to message them as directly as possible) hadn't long since made that pretty much moot, if not actually verboten... [[Special:Contributions/141.101.99.109|141.101.99.109]] 17:53, 11 March 2021 (UTC)

== Sloppy notation? ==

As a mathematician, I immediately noticed a couple of annoying niggles. Firstly, it is only implied, but never clearly stated, that the input list is ordered - which means the median is wrong unless ordered. Now F outputs an ordered triple of real numbers, and in calculating G, this is fed in to F again directly. This will frequently give inputs that are not in order, and in subsequent iterations the "median" will always be the middle number - i.e. the geometric mean - regardless of the actual median. Secondly, Randall's final line gives the output of G as a single number, but as it is just the result of a repeated application of F, the output of G should be an ordered triple. I'm sure Randall is aware of both, and chose to cut out the implied ordering of the inputs and choosing one of the three values as the output of G as they aren't necessary for the joke, but maybe we should note something about this in the explanation.[[Special:Contributions/141.101.99.109|141.101.99.109]] 13:07, 11 March 2021 (UTC)
:First, I've never seen a definition of median which doesn't account for ordering itself, although I am a little annoyed at his definition for a different reason— that it doesn't account for even-length lists. Second, what I got from the comic initially is that GMDN is supposed to be a single number, specifically that value for which all three of its elements would become equal if implemented infinitely many times (and it ''will'' converge, because if the three elements are all the same it already has converged, and if at least two are different, both means will necessarily become greater than the least value and smaller than the greatest value due to the definition of 'mean'). Another annoyance I noted is that GMDN is real iff there are an even number of negative numbers and/or the length of the initial list is odd, but I suppose that can't be helped. Ooh, complex meandianing! [[User:BlackHat|BlackHat]] ([[User talk:BlackHat|talk]]) 15:15, 11 March 2021 (UTC)

== Is the arithmetic-geometric mean connected to geometry? ==

In the case that only the arithmetic and geometric mean are used the combined arithmetic-geometric mean can be interpreted as the radius R of a circle which has the same circumference as an ellipse with half axes a and b.

R = M(a,b)

Can the Geothmetic Meandian be interpreted are the radius R of a 3D sphere which has the same surface as an elliptic cylinder with half-axes a and b and length c ?

R = GMDN(a,b,c)

=== The RandallMunroe Set ===

Here is some MATLAB code (sorry) to generate an image showing the number of cycles required to converge, a' la' the Mandelbrot Set.
Not sure how to post an image here, but it is really cool.

% RandallMunroeSet.m
% From a suggestion by Randall Munroe in XKCD #2435 Mar 10 2021
% new statistic GMDN(x) = [mean(x), geomean(x), median(x)]
% calculation is recursive, ending when converged
% here we count the cycles required to converge and plot a' la' Madelbrot Set
% the initial X input can be any length vector, but we restrict to 3 space
% here for visualization, and fix Z so we get a 2D image
% so far, for positive values, it converges in less than 40 or not at all
% for negative x, set max cycles to something larger like 60
% I haven't plotted it, but there is logically another set that plots the
% resulting converged value.
% Explore!
% (c)2021 CC BY-NC 2.5 SBStevenson@uh.edu peace, love, trees

% here we answer the question, how many cycles does it take for GMDN to
% converge?
maxcycles = 40; stepsize = .0025;
z = 1; % pick a Z, any Z
x = stepsize:stepsize:(4-stepsize); % explore a range of x and y
y = x;
wbh = waitbar(0);
RMS = zeros(numel(x),numel(y),numel(z)); % no, not root mean square, this is the Randall Munro Set!

for idx = 1: numel(x)
waitbar(idx ./ numel(x)); % feedback on progress
for jdx = idx:numel(y) % result is symmetric across the diagonal, so we save time by computing above the diagonal

for kdx = 1:numel(z)
RMS(idx, jdx, kdx) = gmdn([x(idx),y(jdx),z(kdx)], maxcycles);
RMS(jdx, idx, kdx) = RMS(idx, jdx, kdx); % copy across the diagonal
end
end
end
close(wbh)
RMS = min(maxcycles,RMS);

if numel(z) == 1;
figure(420);
image(255*RMS./maxcycles);truesize; colormap(jet(256));
end
if numel(z) == 3; % allow for true color, but in practice it is so sensitive to initial z value it just gives three different sets unless the Zs are VERY CLOSE
figure(420);image(RMS./maxcycles);truesize;
end
title(['RandallMunro Set Z = ' num2str(z)]);

figure(3);hist(RMS(:),0:maxcycles);
%% How many cycles to converge?
function ncycles = gmdn(x, maxcycles)
ncycles = 0;
while ncycles < maxcycles
ncycles = ncycles + 1;
x = [mean(x), geomean(x), median3(x)];
if all(x(1) == x(2:3))
break
end
end

end

%% Geometric Mean
function result = geomean(x)
result = prod(x) .^ (1/numel(x));
end

%% Slightly faster median than builtin MATLAB function
function result = median3(x)
y = sort(x);
result = y(2);
end

== Proof - Possibly by Induction ==

Earlier question:
> Can any of you come up with a mathematical proof that repeated application of F on a set of (say) positive real numbers is guaranteed to converge toward a single real number

Define: 
F(n) = {An,Bn,Cn} 
F(n+1) = {An+1, Bn+1, Cn+1} = {ave(An,Bn,Cn), geomean(An,Bn,Cn), median(An,Bn,Cn)} 
R(n) = range of F = max(An,Bn,Cn)-min(An,Bn,Cn), for iteration n 
We want to show that the range R(n) converges to 0. 
With the following notation: max(n) == max(An,Bn,Cn), ave(n)==ave(An,Bn,Cn), .. 
We observe the following emperically for many different inputs: 
R(n) = max(n)-min(n) 
CASE 1: max(n)=ave(n), THEN max(n+1)=median(n+1)=geomean(n) AND min(n+1)=geomean(n+1) 
In this case max(n+1) is fixed to a previous value, the geomean(n), and min(n+1) takes on the new geomean(n+1) which is guaranteed to reduce the range R(n) as min(n) < geomean(n+1) < max(n). It also implies case 2 must be invoked because min(n+1)=geomean(n+1) at n+1. 
CASE 2: min(n)=geomean(n), THEN max(n+1)=ave(n+1) AND min(n+1)=median(n+1)=ave(n) 
In this case min(n+1) is fixed to a previous value, the ave(n), and max(n+1) takes on the new ave(n+1) which is guaranteed to reduce the range R(n) as min(n) < ave(n+1) < max(n). It also implies case 1 must be invoked because max(n+1)=ave(n+1) at n+1. 
 
Each case forces the range to be reduced while also forcing the alternate case on the next iteration. 

In other words, the maximum at each iteration alternates between the average and the median, and the minimum alternates between the geomean and the median. Thus either the minimum or the maximum at n+1 are always converging away from the minimum and maximum at previous n. 
While this is not a formal proof, since the initial observations are emperical, I believe that a proof-by-induction can be built based on the oscillating convergence (without the need for F to be differentiable). 

[[User:Ramakarl|Ramakarl]] ([[User talk:Ramakarl|talk]]) 00:00, 12 March 2021 (UTC)

:How can this be formulated as a PDE when F isn't even differentiable?
:Besides, R(Fn+1) < R(Fn) does not imply limit R(Fn) = 0 (Think R(n) := 1+1/n). -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 02:50, 12 March 2021 (UTC)
Agreed. F is not differentiable due to median. For arbitrary R(n) such as R(n)=1+1/n then limit R(Fn) != 0, however I do not define R(n) arbitrarily but define it as R(n)=max(An,Bn,Cn)-min(An,Bn,Cn) [[User:Ramakarl|Ramakarl]] 

[[User:snark]]
This has nothing to do with a PDE or the heat equation. It is an iterative map from R^3 to R^3 (after the first application of F). In
order to prove it converges you need to show that there is a fixed point and that the mapping takes you closer to it. The fixed points
are easy since F((x,x,x))=(x,x,x) so there is a line of fixed points. You can then calculate the perpendicular distance between the
starting point (x1,x2,x3) and the line given by (x(t),x(t),x(t)). Next you calculate the distance between f((x1,x2,x3)) and the line
and show that is is less than the first distance.

Agreed. I've removed reference to PDE or Heat equation except for the indirect similarity. The new suggestion for proof, which is incomplete, is inductive based on the observed alternation of the min/max between the geomean and arithmean. I believe it can be shown that for some N, there exists F(N)=k, where k=min(N)=max(N)=arithmean(N)=geomean(N)=median(N) within some epsilon, and k is the fixed point. This is because the min(n+1), median(n+1) and max(n+1) alternate between arithmean(n) and geomean(n), which are strictly inside the open interval ( min(n), max(n) ). [[User:Ramakarl|Ramakarl]]

== Why is this funny? ==
Wow, paragraphs and paragraphs of explanation, and calculations, and computer code describing everything about the XKCD comic.
I am impressed with how much people know. After all that explanation, can anyone tell me if there is anything comical about this comic?
Aside from the fact that Randal is combining formulas that don't usually get combined, is there anything here that strikes anyone as funny? The previous one about people asking absurd questions about what they could do after they are vaccinated had me laughing out loud. Can anyone tell me that they laughed at this comic and what was funny? Thanks. [[User:Rtanenbaum|Rtanenbaum]] ([[User talk:Rtanenbaum|talk]]) 01:56, 12 March 2021 (UTC)
:YMMV, but I found it funny because I just spent the last fortnight teaching how to find mean (and median, and quartiles for that matter) to 15/16yrolds. And they found that hard enough. I did not inform them of Geometric mean. I guess it's funny to me because it's such a long reach. [[User:Thisfox|Thisfox]] ([[User talk:Thisfox|talk]]) 02:48, 12 March 2021 (UTC)
::No, the joke is quite clearly explained in the text below the formula: "Pro Tip: If in doubt just mash them together". [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 07:53, 12 March 2021 (UTC)
::As I'm currently supposed to be working someone else should please add this with a proper formulation. I just re-added the incomplete tag. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 08:00, 12 March 2021 (UTC)
:: @Rtanenbaum funny you should give previous comic as example, as it is funny for exactly the same reason: using absurdity. The only difference is *most* people will get it why it is absurd to ride bicycle down the stairs in someones house (while it is OK to use bike outside, and it is OK to visit if you're vaccinated and thus use the stairs in someones house, BUT it is combining those unrelated activities that is absurd). Same thing here, only it requires some math background: using median has its uses, as does using geometric and arithmetic means, but it is combining them in this fashion that is absurd. And especially the recommendation to "mash mathematical functions you obviously don't understand as substitute to choosing correct one" is absurd. It is like you don't know you have to ADD prices of items on your receipt to calculate the total, so someone recommended you to use some random combination of mathematical operations to calculate the total. (with a added twist that suggested combination would return some result which is not far off the calculation). In addition, the fact that some people do not understand why it is funny (so might take such absurd recommendation seriously) makes it even more funny.--[[Special:Contributions/172.68.221.46|172.68.221.46]] 09:49, 12 March 2021 (UTC)
::Apparantly someone deleted the tag again without giving a further explanation... I will undo this change. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 09:58, 12 March 2021 (UTC)
:::'Twas not I, but note that this is 'explainxkcd' not 'explainwhyxkcdisfunny'. I think we both recognise that a cornucopia of details have been explained. It is even funnier to see someone insisting we continue to dissect the frog, but I'm not sure I need to fully explain that. ;) [[Special:Contributions/162.158.159.108|162.158.159.108]] 15:16, 12 March 2021 (UTC)
:Yes, here's a bit more on that.. I agree with [[User:Elektrizikekswerk|Elektrizikekswerk]] the joke is explained. The stat tip: "If you aren't sure whether to use the mean, median or geometric mean, just calculate all three, then repeat until it converges." is funny because there are many situations in the physical sciences where the arthmean, geometric mean and median for some data are different values. It is perhaps common that scientists not well versed in statistics are unsure which to use. The funny bit is imagining this less-statistically-versed-scientist throwing up their hands and just accepting the fixed constant given by iterating GMDN as the 'answer' irrelevant of any physical meaning. Also the name "geothmetic meandian" is funny because the word meandian is similar to both median, which it uses, and to ''meander'' which is indicated by the alternate assignment of the median on each iteration -- informally, this function meanders. [[User:Ramakarl|Ramakarl]]