explain xkcd - User contributions [en]

Talk:3157: Emperor Palpatine

2025-10-22T09:10:24Z

82.132.244.183:

What happens when he is five years old in canon Star Wars [[User:Mathmaster|Mathmaster]] ([[User talk:Mathmaster|talk]])
:As a Youngling, he would obviously get a funny hat and a 'not quite so dangerous' training-lightsaber. At least for Jedi training, can't speak for Sith training, which probably goes with the exact opposite (funny shoes and a lightsaber that has no hilt?)... ;) 22:13, 20 October 2025 (UTC)

I don't think the title text is sarcastic. Making Palpatine look older in Return of the Jedi allowed the actor's age to be very precise for the character in the 3 subsequent movies (while allowing the same actor playing the character). --[[Special:Contributions/181.236.188.58|181.236.188.58]] 22:22, 20 October 2025 (UTC)

My first thought when reading the alt-text was of the reincarnated leader of the History Monks in the Discworld, analogous to the Dalai Lama. The memories and personallity of an old man, in the body of a toddler. The wise old man is normally in control, but sometimes the toddler takes over, leading to him wanting a biccie. {{unsigned ip|92.239.132.210|15:34, 21 October 2025}}

If he actually included a data point at Ian=74, Emperor=119 for Rise of Skywalker instead of just claiming "undefined", the trendline would have a positive slope...regardless of whether or not 119 is accurate, he clearly appears older than he does in Return of the Jedi, and even adding a point at (74, 89) would still result in a positive slope. However, I can get behind the idea of pretending Rise of Skywalker doesn't exist. [[Special:Contributions/136.226.154.60|136.226.154.60]] 16:24, 21 October 2025 (UTC)

Just by film chronology (because the EU and extended-EU already dealt with it, but has been largely decanonised since then), the true age of any particular Palpatine clone (there still may have been other extant ones, as well as such dead failures as might remain) is probably not much older than Jango's initial contribution to the Clone Trooper project, the same process being used (though not also on Kamino), and so roughly as old as Bobba Fett would be at that point (if surviving the Sarlak, etc), having had little to no 'aging up' treatment. Though ''with'' the aging up, effective developmental age is accelerated, and with both the hit'n'miss nature of the emperor-cloning process and the need of Exegol's caretakers to always try to keep a not-too-decrepit clone at hand to become a ready vessel for Sheev's spirit to occupy, his body's true age is probably quite young even if his apparent age is far older. And, in terms of psychological age, he's probably ''exactly'' as old as if he had not jumped-bodies, or maybe that minus any 'gap time' that his Sithish force-ghost might have had to have spent in some form of stasis as the transplantation process was being put into effect. [[Special:Contributions/82.132.236.174|82.132.236.174]] 21:39, 21 October 2025 (UTC)

The current explanation reads like an AI response. [[User:Xseo|Xseo]] ([[User talk:Xseo|talk]]) 07:22, 22 October 2025 (UTC)
:Or maybe it's just that AI responses tend to read like a collaborative edit by various people each with their own particular obsession to obscure details...?
:I'm not saying you're wrong to (presumedly) dislike the style and content, even the bits that I thought were both informative and interesting, but I don't actually know what bit(s) you might want to be different. You're welcome to make your own edits to your own satisfaction, however, in turn to be edited by those who come after you (or return) with their own stylistic/informational needs to fulfil. [[Special:Contributions/82.132.244.183|82.132.244.183]] 09:10, 22 October 2025 (UTC)

1980: Turkish Delight

2025-10-22T08:52:10Z

82.132.244.183: /* Explanation */ General edit

{{comic
| number = 1980
| date = April 13, 2018
| title = Turkish Delight
| image = turkish_delight.png
| titletext = I take it Narnia doesn't have Cinnabons? Because if you can magic up a plate of those, I'll betray whoever.
}}

==Explanation==
''{{w|The Lion, the Witch and the Wardrobe}}'' is a fantasy novel by British novelist {{w|C. S. Lewis}}, the first published and best known of seven novels in ''{{w|The Chronicles of Narnia}}''. In it, a group of four sibling children discover another world called Narnia. At the beginning of the story, the land is in a perpetual winter caused by the {{w|White Witch}} (the antagonist of the story). One of the children, {{w|Edmund Pevensie}}, is approached by the White Witch and offered {{w|Turkish delight}}, a type of confection, in exchange for leading the other children to her. What the book says and what the movie leaves out is he doesn't know the sweets (which he specifically requests, as apparently his favourite treat, rather than having them randomly foisted upon him) are magically created by the White Witch, enchanted such that the eater increasingly desires them as more of them are eaten. Not a full mind control, but more of a disinhibitingly strong temptation to obtain more.

Turkish delight is very different from typical confections found in the modern Western world and isn't very popular in the United States. The primary flavoring agent of Turkish delights, rosewater, has a strong perfume-like taste and is generally considered an acquired taste for western palates. [[Randall]], who has made comics about [[388: Fuck Grapefruit|being unimpressed by food]] in the past, comments that he was very disappointed when he tried Turkish delight, especially after having read in the novel about how delicious the characters considered it. If he were in Edmund's shoes, he would not have been persuaded by (or asked for) the same treat.

[http://www.slate.com/articles/life/food/2005/12/the_lion_the_witch_and_the_really_foul_candy.html It is not uncommon for present-day Narnia fans to be disappointed when they try Turkish delight], as different as it is to modern confections. However, in the late Victorian era, when Lewis grew up, [https://www.tor.com/2016/08/08/why-was-turkish-delight-the-ultimate-temptation-in-c-s-lewis-narnia/ Turkish delight was very popular in England]. Because it was nearly impossible for local confectioners to make properly, it had to be imported from Turkey, at great expense, making it a status symbol for the wealthy and a rare treat for those with less money. When Lewis wanted to come up with the perfect temptation for Edmund, he drew on his own childhood memories of a favorite rare and expensive treat — which would have been even harder to come by because of [https://flashbak.com/sugar-rationing-in-world-war-2-photos-13598/ sugar rationing] and severe trade disruptions during World War II, when the story was set. It also serves to emphasize how powerful the White Witch is for her to be able to offer such an expensive and hard-to-obtain treat so easily, and especially with no direct knowledge of either Turkey or its 'delights' (beyond Edmund's own words and unspoken thoughts) to trigger the magical formation of the treat.

{{w|Cinnabon}} (referenced in the title text) is a popular chain restaurant in the USA which serves mostly {{w|cinnamon roll|cinnamon buns}} covered in a thick, sugary glaze. The chain is not well known in Britain, but has recently opened a [https://www.cinnabon.co.uk/store-locator/ few restaurants], mainly in the London area. (A more common UK equivalent of the cinnamon bun is the {{w|Chelsea bun}}.) There are presumably no branches of Cinnabon in Narnia.{{Citation needed}} Randall is saying that he finds cinnamon buns delicious, to the point where he would betray anyone for them. Thus, had it been Randall instead of Edmund, he might have requested Cinnabons.

==Transcript==
:[A person wearing a cap, a fur coat, and gloves sits in a sled handing over a plate with small cubic pieces on it to a small boy with dark hair standing beneath. The boy reaches one hand to the plate.]
:Person in the sled: Have some Turkish delight. If you betray your family, there's more where that came from.

:[The boy tastes one piece.]

:[The boy looks at that piece.]

:[The boy looks up, to the direction where the gift came from, the piece still in his hands.]
:Boy: Wow.
:Boy: This is ... not great.

:[Caption below:]
:The ''Narnia'' books gave me a really unrealistic impression of how good Turkish delight tastes.

==Trivia==
*The world of Narnia is a recurring theme in [[xkcd]], with previous prominent appearances in [[665: Prudence]], [[821: Five-Minute Comics: Part 3]], [[969: Delta-P]], and [[1786: Trash]]. The forests in [[442: xkcd Loves the Discovery Channel]] panel 21 and [[269: TCMP]] may also be references to Narnia, namely, the Wood Between the Worlds in {{w|The Magician's Nephew}}.
*Randall has previously expressed disappointment when the taste of a food item does not match a promise implicit in its name. If Turkish Delight is not a delight, likewise Red Delicious apples are not delicious, according to [[388: Fuck Grapefruit]] and [[1766: Apple Spectrum]] and a footnote on [https://books.google.com/books?id=tgZIBAAAQBAJ&lpg=PP1&pg=PA97#v=onepage&q&f=false this What If page].

{{comic discussion}}
[[Category:Chronicles of Narnia]]
[[Category:Food]]

Talk:130: Julia Stiles

2025-10-22T08:15:15Z

82.132.244.183:

Randall is right once again. [[User:Netherin5|Netherin5]] ([[User talk:Netherin5|talk]]) 13:30, 5 March 2019 (UTC)

I can't beleive it took over 16 years for this factoid about Stiles to be [https://en.wikipedia.org/w/index.php?title=Julia_Stiles&diff=1186988046&oldid=1186323176 included on her Wikipedia page]. [[User:IIVQ|IIVQ]] ([[User talk:IIVQ|talk]]) 23:14, 23 December 2023 (UTC)

Is there a category for actual recognisable people on explainxkcd.com, as said in the Trivia section? [[User:42.book.addict|42.book.addict]] ([[User talk:42.book.addict|talk]]) 23:13, 2 February 2024 (UTC)
:[[:Category:Real people]], do you mean? [[Special:Contributions/162.158.74.69|162.158.74.69]] 00:22, 3 February 2024 (UTC) (PS, Welcome. You're a very busy newcomer (at least via a username), catching up on everywhere you can. I hope you enjoy your time here, I'm sure you've got a useful contributions in you!)
::[[:Category:Real people]] includes ''all'' comics that depict real people, but in most cases they are drawn as stick figures with blank faces in the usual XKCD style. The depiction of Julia Stiles here is done in a more realistic style. --[[Special:Contributions/208.59.176.206|208.59.176.206]] 04:02, 22 October 2025 (UTC)
:::A number of "real people stick figures" are (at least somewhat, once the reader has the context, like the Firefly/Serenity actors) actually recognisable by facial features (even if still no-eyes/nose/mouth, far from 'blank'). Ditto "fictional people stick figures" (e.g. Darth Vader?).
:::Perhaps what was being asked here (though it looks ambiguous, 42 should probably clarify) is more something that would be encompassed under some "non-stick figure" ("non-stickfigure"? "figure, non-sticklike"?) ukbrella category, with the very few examples that start from Barrel Boy and head onwards towards this sort of 'quality'/style. But it's already a small group of comics. Far smaller if you exclude 'fictional' BB (and presumably you'd not additionally include the ferret), so I'm not sure there's enough examples having similar "Julia"-styles to warrant non-fictional-non-stick specificity. But I'm sure someone with a bit of time could list them all, for us, if there are. [[Special:Contributions/82.132.244.183|82.132.244.183]] 08:15, 22 October 2025 (UTC)

2606: Weird Unicode Math Symbols

2025-10-22T07:52:20Z

82.132.244.183: Nope.

{{comic
| number = 2606
| date = April 13, 2022
| title = Weird Unicode Math Symbols
| image = weird_unicode_math_symbols.png
| titletext = U+2A0B ⨋ Mathematicians need to calm down
}}

==Explanation==
This comic proposes joke explanations for various {{w|unicode symbols}} with obscure or no known uses, see the [[#Table of symbols|table]] below.

It may have been inspired by this blog post [https://ionathan.ch/2022/04/09/angzarr.html U+237C ⍼ RIGHT ANGLE WITH DOWNWARDS ZIGZAG ARROW]. It was posted four days prior to this comic's release. The blog post went viral (in a limited sense) the same day the comic was published, perhaps as a consequence of it mentioning one of the symbols of the comic, Larry Potter. This caused the blogger to update his post with a [[33: Self-reference|reference]] to both xkcd and explain xkcd:
:"XKCD #2606 mentions ⍼ and its Explain XKCD entry cites this post"

The title text includes yet another special symbol ⨋, and this symbol prompts [[Randall]] to ask Mathematicians to calm down. See more details in the table below, where the title text symbol is mentioned in the last entry.

===Table of symbols===
{| class="wikitable sortable"
|+ Symbols
|-
! Codepoint !! Symbol !! Unicode Name !!class="unsortable" | Actual use !!class="unsortable" | Randall's meaning !!class="unsortable" | Explanation
|-
| U+29CD || ⧍ || Triangle with Serifs At Bottom || No known mathematics use, but resembles the {{w|National Park Service}} cartographic symbol for a campsite. ([https://github.com/nationalparkservice/symbol-library/ Usage]) || Shark || May look like a shark fin sticking out of the water.
|-
| U+23E7 || ⏧ || Electrical Intersection || Indicates where wires branch off. || Traffic circle || Looks like a diagram of a {{w|roundabout}} as might be shown on a minimap beside a routing direction.
|-
| U+2A33 || ⨳ || {{w|Smash product}} || The quotient of the product of the underlying spaces of two {{w|pointed space}}s, where points in the {{w|product space}} are identified if they contain either labeled point as an element. || Hashtag || Looks somewhat like the {{w|Number sign|hash}} symbol (#) – commonly used for indicating tags called {{w|hashtag}}s in social media – turned by 45 degrees.
|-
| U+2A7C || ⩼ || Greater-Than with Question Mark Above || Used in proofs to indicate a greater-than relation that should exist but hasn't been proven yet (non-rigorous). || Confused alligator || One metaphor used when teaching inequality signs in primary school is that the sign looks like an alligator mouth "eating" the larger number. Question marks are commonly used in cartoons to indicate confusion on the part of a character.
|-
| U+299E || ⦞ || Angle with S Inside || Plural for the angle symbol (∠) ([https://www.quora.com/Unicode-How-is-the-s-in-triangle-glyph-used-in-mathematics discussion], [https://www.birdvilleschools.net/cms/lib2/TX01000797/Centricity/Domain/1114/Homework%20Helper%20Unit%203%20ch%209-10.pdf example]), rarely used. || Snack || May look like a mouth eating an S, where the S symbolizes some snack food, or the word "snack".
|-
| U+2A04 || ⨄ || {{w|Arity|N-ary}} Union Operator with Plus || [https://books.google.com/books?id=531cAgAAQBAJ&pg=PA165&lpg=PA165&dq=%E2%A8%84&source=bl&ots=oYXkMNXP-T&sig=ACfU3U2QvMRBkD7uVG0OSumKI0JQtjTIKA&hl=en&sa=X&ved=2ahUKEwios862ypL3AhWXVTABHTnQALQQ6AF6BAgKEAM Disjoint union], i.e. joining a family of sets that have no elements in common. || Drink refill || Looks like a cup with a plus to indicate adding drink to the cup.
|-
| U+2B48 || ⭈ || Rightwards Arrow Above Reverse Almost Equal To || Pairs with ⭂ which could conceivably mean {{w|Assignment (computer science)|assignment}} of an {{w|Approximation|approximation}}, but neither seem to be in use. Possibly intended to describe ill-defined projections. || Snakes over there || Looks like two squiggles to represent snakes and an arrow indicating the direction where they may be found.
|-
| U+225D || ≝ || Equal To By Definition || Indicates an equation where the left side is to be [https://www.reddit.com/r/math/comments/1z1mty/can_someone_please_explain_the_equal_to_by/ defined as the right side], usually used in proofs to indicate a definition is being introduced.|| Definitely, for sure || "Def" is a contraction of "definitely" used in slang; the equal sign looks like a double underline, indicating heavy emphasis.
|-
| U+237C || ⍼ || Right Angle with Downwards Zigzag Arrow || Two sources from the 1950s and 1960s describe it as a symbol for the {{w|Angzarr#History|"Richtungswinkel", or azimuth}}. In recent times it seems not to be in use and [https://ionathan.ch/2022/04/09/angzarr.html lengthy discussion] had ensued. Speculation includes a diode with a gate, a "not-right" angle, a proofreaders' mark to split a word, and indication of polarization direction. || Larry Potter || Looks like the letter "L" and a lightning bolt. {{w|Harry Potter (character)|Harry Potter}} is known for having a lightning bolt-shaped scar on his forehead. The character {{w|Legal disputes over the Harry Potter series#Nancy Stouffer|Larry Potter}} figured in a fraudulent legal claim against J.K. Rowling.
|-
| U+2A50 || ⩐ || Closed Union with Serifs and Smash Product || Indicates that a collection of topological spaces is {{w|Union-closed sets conjecture|closed}} when taking arbitrary unions and smash products. That is, if you take the union of any collection of topological spaces in the collection (even uncountably many), or the smash product of them, the result will also be in that collection. This is apparently important because the sets can't be isomorphic: one cannot be rearranged to be exactly the other. ([https://mathoverflow.net/questions/196084/counterexample-for-associativity-of-smash-product Example)] || Spider caught with a cup and index card || Spiders or other bugs found within someone's house or workspace may be caught with a glass and something flat, often a card or a magazine, to be released outside. The projecting lines of the smash product symbol resemble the legs of a spider. Confusingly, some fonts display this symbol with different numbers of "legs": eight, as a 45°-rotated hash symbol, or six as an asterisk.
|-
| U+2A69 || ⩩ || Triple Horizontal Bar with Triple Vertical Stroke || Emblem of the Romanian {{w|Iron Guard}} fascist political movement; Loosely resembles part of the {{w|International Association for Cryptologic Research|IACR}} logo, as depicted in [[153: Cryptography]]; possibly a [https://pages.cs.wisc.edu/~sandlund/NumericalTicTacToe.pdf four-by-four] {{w|tic-tac-toe}} board. || ℍ𝕒𝕤𝕙𝕥𝕒𝕘 || Hash symbol with one extra vertical and horizontal line, or perhaps a hash symbol which has been accidentally double-struck or overprinted.
|-
| U+2368 || ⍨ || APL Functional Symbol Tilde Diaeresis || Used for a two-argument operation to [https://aplwiki.com/wiki/Commute commute] (swap) its arguments or allow it to use a single provided argument in both argument slots, and to convert a value into a [https://aplwiki.com/wiki/Constant constant] function. || :/ || Looks like a confused or disappointed face. Randall's use is in fact common among {{w|APL (programming language)|APL}} programmers in the comments, as documented [https://aplwiki.com/wiki/APL_Orchard#Emoticons here] and [https://aplwiki.com/wiki/Humour#Glyph_puns here].
|-
| U+2118 || ℘ || Script Capital P || A stylized {{w|round hand}} 'p' used by Weierstrass for his "{{w|Weierstrass elliptic function|p-function}}," with features of both capital 𝒫  and small 𝓅. Sometimes also used as the {{w|power set}} operator.
|| Snake || This symbol coils around like a long snake, with a tapering-off tail on one end and a small "head" on the other.
|-
| U+2AC1 || ⫁ || Subset with Multiplication Sign Below || Indicates that one set is subset of another by means of a product. || <div style="writing-mode: vertical-rl; text-align: center;">User experience</div> || Looks like the letters "Ux" sideways; UX is a common abbreviation for {{w|user experience}}.
|-
| U+232D || ⌭ || {{w|Cylindricity}} || A symbol used in geometric dimensioning and tolerancing (GD&T) to represent a parameter called "cylindricity" which describes the statistical deviation of an ensemble of surfaces from a reference cylinder. ([https://cimquest-inc.com/metrology-minute-cylindricity/ Example use]) || Rolling dough between your hands to shape it into a ball || Looks like two flat hands (perhaps like stick-figure arms) rolling a ball between them. Rolling dough between one's hands to make it into a ball is an important step in making many kinds of pastry and bread.
|-
| U+2A13 || ⨓ || Line Integration with Semicircular Path Around Pole || Very rare symbol for half of a closed {{w|Contour integration|contour}} or {{w|Line integral|line}} integral which contains the {{w|Origin (mathematics)|origin}} in its interior. Contour integrals which circle the origin are very important in complex analysis. If such an integral were split into two parts, each could be represented by this symbol. It can be mistaken for ⨔, the integral not including the {{w|Zeros and poles|pole}}, with a wider and more complete arc around an offset dot. ([https://math.stackexchange.com/questions/2299363/where-is-the-%E2%A8%93-integral-symbol-defined Discussion])
|| Integral that avoids a bee on the whiteboard || Looks like an {{w|integral}} symbol with a bump that goes around a dot, as if a professor was drawing an integral on a whiteboard but did not want to disturb a bee that had landed right in the path of their marker.
|-
| U+2A0B (title text)|| ⨋ || Summation with Integral || The sum of the sum of the discrete elements (∑) and the integrals (∫) over the connected pieces. This symbol requires context to be meaningful but could occur, for instance, when computing probabilities using mixed distributions.
([https://twitter.com/fermatslibrary/status/1308743505309822977 See also here])
|| Mathematicians need to calm down || Each of the two symbols is specifically used to represent a kind of summation that is calculated completely differently from the other. Combining them could produce frustration for people unfamiliar with the usage. The comment given may make fun of mathematicians' tendency to form increasingly complex expressions in their work. It may as well be a pun on the pronounciation of the letter {{w|Esh (letter)|Esh}} (Shhhh).
|-
|}

==Transcript==
<big>Weird Unicode Math Symbols</big>
And their meanings

{|
| U+29CD || ⧍ || Shark
|-
| U+23E7 || ⏧ || Traffic circle
|-
| U+2A33 || ⨳ || Hashtag
|-
| U+299E || ⦞ || Snack
|-
| U+2A04 || ⨄ || Drink refill
|-
| U+2B48 || ⭈ || Snakes over there
|-
| U+225D || ≝ || Definitely, for sure
|-
| U+237C || ⍼ || Larry Potter
|-
| U+2A50 || ⩐ || Spider caught with a cup and index card
|-
| U+2A69 || ⩩ || ℍ𝕒𝕤𝕙𝕥𝕒𝕘
|-
| U+2368 || ⍨ || :/
|-
| U+2118 || ℘ || Snake
|-
| U+2AC1 || ⫁ || <div style="writing-mode: vertical-rl; text-align: center;">User experience</div>
|-
| U+232D || ⌭ || Rolling dough between your hands to shape it into a ball
|-
| U+2A13 || ⨓ || Integral that avoids a bee on the whiteboard
|}

{{comic discussion}}
[[Category:Unicode]]
[[Category:Math]]
[[Category:Harry Potter]]

1991: Research Areas by Size and Countedness

2025-10-22T07:50:32Z

82.132.244.183: /* Explanation */ Minor grammatical changes ("between A and B"/”from A to B" choice, and clausal comma shifted to the more apt side of the conjunction to the post-clause continuation).

{{comic
| number = 1991
| date = May 9, 2018
| title = Research Areas by Size and Countedness
| image = research_areas_by_size_and_countedness.png
| titletext = Mathematicians give a third answer on the vertical axis, "That question is poorly defined, but we have a sub-field devoted to every plausible version of it."
}}

==Explanation==

This comic is a [[:Category:Scatter plots|scatter plot]] that ranks different research fields according to the precision of the knowledge of the number of the studied object (vertical axis) vs. how large (the size of) the studied object is on the horizontal axis.

For instance, the facts pertaining to the number of United States presidents are well known (although the exact number can be disputed, in that Grover Cleveland's non-consecutive terms are usually counted seperately, so the official count exceeds the number of individuals who have become President; Donald Trump repeating this feat), so the study of their history is at the top of the Y-axis. This study is placed close to the Y-axis as the size of a president is about midway in size between the two extremes of the X-axis, elementary particles to the left (small) and the entire cosmos (cosmology) to the right (big).

On the X-axis, Presidents are close to the middle. Both presidents and other larger life forms (as a research area) including extinct animals (paleontology) and exobiology are all close to the same central position just right of the Y-axis, with smaller animals like birds and insects just to the left of the Y-axis. But where the number of presidents is well known (aside from the handling of split-terms), then the number of exoplanet life forms (exobiology) is completely unknown (and would likely be affected by other disputes, such as whether something the size of Pluto counts as a planet) and thus it will be found at the very bottom of the Y-axis, since we have no idea if there is life elsewhere and if so how many places will it be and how varied.

The 19 research areas are listed and explained in the [[#Tables of research areas|tables]] below.

In the title text, mathematicians may give a third answer that the concept of counting the things being studied is not reasonable, because the things are abstract or otherwise not discrete. There are many different types of math that blend into each other, and many have turned into separate sub-disciplines based on different interpretations of fundamental rules. As a specific example in geometry, different interpretations of how many lines you may draw parallel to another line through a given point has lead to {{w|hyperbolic geometry|hyperbolic}} (infinite parallel lines) and {{w|spherical geometry|spherical}} (0 parallel lines) geometric systems that are just as valid (and valuable, in some contexts) as the more commonly known {{w|Euclidean geometry|Euclidean}} (1 parallel line) geometry. As a specific example of the blending, {{w|number theory}}, {{w|set theory}}, and {{w|topology}} all interrelate and it is difficult to concretely say whether many theorems belong to one branch of math or another.

Another way to interpret this is that mathematicians do not know exactly how many mathematical objects there are. For example, under one interpretation of contingent, mathematicians do not know whether there are any infinities between {{w|beth zero}} and {{w|beth one}} (and analogously for {{w|Large cardinal axiom#Hierarchy of consistency strength|large cardinal axioms}}, so mathematicians do not know how many types of infinity there are but, based on set theorists investigating how the existence of certain types of infinity implies the existence of certain other types of infinity, one can say that set theory is a field devoted to studying every plausible version.

For a table with the coordinates given in percentage for each research field, see the table in the [[#Trivia|trivia]] section

===Upper left quadrant===
This is the section with the small items with count known.

{| class = "wikitable sortable"
! Research field
! Size of the thing
! Knowledge of #
! Explanation
|-
|{{w|Elementary particle physics}}
| The smallest subjects that we have actually detected are the {{w|elementary particles}}. In the {{w|Standard Model}} of particle physics, they are considered point masses (i.e. to have zero width). They may be made of smaller {{w|String theory|strings}} but if so these have still not been detected.
| We think we have a fairly good estimate of how many elementary particles that are known. There could be some uncertainty though, so it is not at the very top.
|Elementary particle physics is concerned with the study of subatomic particles (the smallest things that we know of), of which there are 17, not including antimatter. Most notably, until recently it was uncertain whether the {{w|Higgs boson}} was one of the elementary particles, but scientists have a "pretty good estimate" because the mathematical models don't predict the existence of many other particles.
|-
|{{w|Dentistry}}
|Several mm to several centimeters
|Most teeth are visible to the naked eye, and dentists have x-ray technology to see what's not visible, so counting them is pretty straightforward.
|Dentistry is the study of teeth (pretty small, both in size as well as in quantity). Humans adults grow 32 teeth, which is a "pretty good estimate" since it is very rare for {{w|Hyperdontia|more than 32 teeth to grow}} and it is rather common for {{w|wisdom teeth}} to be surgically extracted or in some cases never to develop. Children may only have 20 teeth before they start falling out, but each tooth that falls out is because another tooth is growing underneath, so a child might have as many as 52 teeth, counting the child teeth that haven't fallen out yet plus the adult teeth that are starting to form. So while a dentist will usually have a good idea how many teeth will be in a patient's mouth, they won't know for sure until they look or consult dental records.
|-
|{{w|Shakespeare}} studies
|Most are the size of typical book. In printed form, they would be in the range of tens of centimeters in height and width and ~1 centimeter in depth. Although, if stored in digital form, they could be much smaller than a tooth, so it seems to refer to print or handwritten originals.
|Generally, 36 plays are attributed to him, but between 1 and 3 additional plays are considered "lost" (i.e. at some point between being first published or performed and scholars seriously studying Shakespeare, all known copies, references, and fragments were destroyed, making it impossible to determine whether Shakespeare actually wrote them or whether they actually existed as separate plays), and {{w|Shakespeare apocrypha|some 20 more}} are believed to have been written by him, but not signed. To make matters worse, some plays that ''were'' published or performed under Shakespeare's name are believed to have been written as collaborations (not fully by him) or mis-attributed (we don't know who wrote them but most people say it was him).
There are also {{w|Shakespeare authorship question|various fringe theories}} that say very few, or even none, of the 'Shakespeare' works are actually by that man from Stratford. None of the alternative origins are widely accepted, however, and "Shakespeare studies" could still be considered the best umbrella term for the same group creative works that all the different Anti-Stratfordians are wanting to reattribute to numerous other people.
|Shakespeare studies is concerned with the works ascribed to William Shakespeare. These works are studied fairly commonly, so the position in about the middle makes sense. We also have a "pretty good" estimate of how many works are 'by Shakespeare'. Although the exact number is unknown, relative to other items on this list, we have a good estimate.
|-
|{{w|Ornithology}}
|Birds tend to be small, with most species able to be held comfortably in hand; even the largest known flying bird, the {{w|Condor}}, stands smaller than the average human, with a handful of non-flying avians such as the {{w|ostrich}} being larger, but still weighing less than 2-3 humans.
|The number of known bird species is [https://en.wikipedia.org/wiki/Bird#Diversification_of_modern_birds estimated at about 10,000], though [https://www.amnh.org/about-the-museum/press-center/new-study-doubles-the-estimate-of-bird-species-in-the-world a 2016 research result] suggested a near-doubling of this figure. As for the number of individual birds, a paper aptly titled [https://link.springer.com/article/10.1023/A:1018341530497 "How many birds are there?"] examines a number of ways of counting them; the results are "surprisingly consistent", with counts of approximately 200-400 billion individual birds.
|We do have a "pretty good estimate", to within perhaps a factor of two.
|-
|Ancient {{w|literature}}
|As above, with Shakespeare plays, original or print reproductions would be the size of a book, typically. Although ancient {{w|scrolls}} may have different dimensions with similar total volume.
|Because of the high number of {{w|lost works}}, it is hard to have a solid estimate of the number, although rough lists have been made (e.g. {{w|Ancient literature#List of ancient texts}}).
|While it is fairly straightforward to look up how many books [http://www.proquest.com/products-services/Books-in-Print.html are currently in print], or how many books [https://mashable.com/2010/08/05/number-of-books-in-the-world/ all currently printed information would fit into if bound into equal-length volumes], and then limiting those estimates to those that date before a specific year, counting how many books from the period of interest haven't survived to the present day (books that were "{{w|lost work|lost}}" either by deliberate discontinuation, or accidental destruction such as in the {{w|Destruction of the Library of Alexandria|Library of Alexandria}}) is a bit more difficult. However, because we know the work existed (it is mentioned by name in some other text), we have "pretty good estimate" that the number of lost works is "only" in the tens of thousands, as is the number of surviving works.
|}

===Upper right quadrant===
This is the section with the big items with count known.

{| class = "wikitable"
! Research field
! Size
! Knowledge of #
! Explanation
|-
|{{w|Marine mammal|Marine}} {{w|Mammalogy|Mammology}}''[sic]''
|They range in size from the {{w|Marine Otter}} (about 1m) to the {{w|Blue Whale}} (up to 30m).
|About 125 non-extinct species.
|Marine mammals are the largest extant animals. The US Government [http://www.nmfs.noaa.gov/pr/species/mammals/ recognizes] 119 marine mammals. However, what constitutes each species is [https://www.marinemammalscience.org/species-information/list-marine-mammal-species-subspecies/ constantly being revised], with new studies indicating either that what used to be considered a subspecies is actually a separate species, or that what used to be considered a separate species is actually a subspecies. As the depths of the ocean are further explored, species that were outright unknown are spotted and need to be classified. However, since marine mammals breathe air and thus must surface, it's likely that all species have been observed by scientists.
|-
|{{w|List_of_Presidents_of_the_United_States|Presidential History}}
|All presidents are {{w|Heights of presidents and presidential candidates of the United States|human-sized}}, with the tallest being {{w|Abraham Lincoln}} at 6 ft 4 in and the shortest being {{w|James Madison}} at 5 ft 4 in.
|As of 2021, 46 people (only 45 are unique; Grover Cleveland is counted twice because his terms were not consecutive) have served or are serving as President of the United States.
|Presidents are generally considered "big" men in history. Therefore, each one is fairly well known and documented. There is, however, some discussion on how many presidents there have been in the history of the United States, since prior to the {{w|Twenty-fifth Amendment to the United States Constitution|25th amendment}}, it was unspecified whether vice presidents counted as presidents during the President's absence. Most notably, this ambiguity is the reason {{w|David Rice Atchison}}'s tombstone is inscribed with the words "President of the United States for one day" (he was not eligible and did not accept the duties even if he was).
|-
|{{w|Railway engineering}}
|Railways can span across countries, and therefore are fairly large
|As railroads are built by humans, we know pretty well how many there are. However small systems (parks, mines) may make this number uncertain.
|A railway can span anywhere from a few hundred feet, to thousands of miles, so they're pretty big. The type of a railway is generally given by its {{w|track gauge}}, which is defined as "standard" (the usual gauge for a region or country), "narrow" (rails closer together than that standard) and "broad" (rails farther apart than that standard). Since what is standard varies from country to country, and indeed from line to line, how many kinds of "narrow" gauge and "broad" gauge exist depend on who you ask. However, whereas every region has ''a'' standard gauge, "{{w|standard-gauge railway}}" has a specific meaning used by rail technicians and enthusiasts worldwide, of a track with rails 1435 mm (4 ft 8.5 in) apart. Anything narrower than that is often described as a narrow-gauge line, even if it is the standard gauge for a particular rail network.
|-
|{{w|Geology}}
|The {{w|Earth}} is larger, by far, than everything else on the chart except the universe (Cosmology), black holes, and God (at least under some conceptions, see "Theology" below).
|There is only one Earth (at least if you set aside the possibility of multiverses, see below in Cosmology).
|Geology is generally considered the study of rocks (small rocks being considered fragments of mountain layers, so what counts as a "rock" for a geologist can be pretty big). There is no universally agreed upon number to how many {{w|List of rock types|types of rock}} there are, but all geologists agree they can be grouped into igneous, metamorphic, and sedimentary rock. Alternatively, geology can be construed as the study of the planet Earth's composition ( *geo*- meaning "Earth" ), and geologists are confident that the planet Earth is big and there is only one of it.
|-
|{{w|Cosmology}}
| As this encompasses (at least) all of the visible parts of the {{w|universe}} we live in, there can be no other "items" to study that would be larger.
| There is only one visible universe, but there could be multiverses/parallel universes, and also an infinite universe beyond the borders of our own part of this universe's event horizon. So it depends on who you ask if they say there is one of and infinite number of universes to study, thus it is placed close to the middle of the two extremes.
|Cosmology is the study of the universe. There is an asterisk with the note "Depends on who you ask", relating to the estimate of how many universes there are. While it might seem obvious that there is only one universe, some branches of physics believe that our universe is part of a {{w|multiverse}}, and this remains an open and contested subject in the field.
|}

===Lower left quadrant===
This is the section with the small items with count unknown.

{| class = "wikitable"
! Research field
! Size
! Knowledge of #
! Explanation
|-
|{{w|Mycology}}
|microscopic to a few miles
|Estimated at 2.2 million to 3.8 million species.(Though of these only about 120,000 have been described.)
|Mycology is the study of fungi (since fungi tend to grow flat -- excepting for mushrooms, which are their sexual organs, and do not exceed a foot in height (see [http://www.isciencetimes.com/articles/5740/20130729/giant-fungus-china-mushroom-world-s-largest-size.htm World's Largest mushrooms] -- mushrooms are generally considered small). Many fungi are microscopic, but some get to be a few miles in diameter.[http://www.nationalgeographic.com.au/nature/the-worlds-largest-living-organism.aspx The World's largest living organism.] It is a lot harder to discern which species a fungus is, and therefore classify it, so we "have no idea" how many kinds of fungi there are. Studies [https://www.ncbi.nlm.nih.gov/pubmed/21613136 vary wildly] between about 70,000 to over 5,000,000. There is a comic named after this study: [[1664: Mycology]].
|-
|[[1012: Wrong Superhero|Entymology]]
| For insects, from a fraction of a mm to several 100.
| Estimated from 1,000,000 to 3,000,000
|It is unclear whether [[Randall]] means {{w|entomology}} or {{w|etymology}} (probably neither; it's likely that this wasn't a mistake and it is possibly a direct reference to [[1012: Wrong Superhero]]). He may be referring to both fields as insects and words overlap in size. In either case, [https://www.ncbi.nlm.nih.gov/pubmed/28938083 estimates for insects] (entomology) vary from less than 1,000,000 to 30,000,000; and [https://www.quora.com/How-many-root-words-are-there-in-the-English-language estimates for root words] (etymology) reaching hundreds of thousands. Entomology was mentioned in the title text of [[1610: Fire Ants]].
|-
|-
|{{w|Microbiology}}
|The {{w|Smallest organisms|smallest viruses}} are around 30nm long. The largest bacterium may reach almost 1mm.[https://curiosity.com/topics/the-worlds-largest-bacterium-is-visible-to-the-naked-eye-curiosity/].
|120,000 to 10,000,000+.
|Microbiology studies microscopic (too small to see) organisms, of which some 1,400 are known and "estimates for the total number of microbial species vary wildly, from as low as 120,000 to tens of millions and higher", according to [https://www.quora.com/How-many-root-words-are-there-in-the-English-language Nature magazine].
|-
|{{w|Pharmacology}}
|{{w|Drugs}}, including {{w|medications}} and {{w|recreational drug use|illegal and recreational drugs}} are molecules which are sub-microscopic (in the range of nanometers).
|Although it is possible to tally all the known drugs, this is at the extreme low end of the pile because the number of possible organic compounds is nearly infinite and the fraction of those are bioactive is completely unknown.
|The number of drugs (pharmaceuticals) discovered and synthesized is not tallied, according to [https://www.raps.org/regulatory-focus%E2%84%A2/news-articles/2014/10/how-many-drugs-has-fda-approved-in-its-entire-history-new-paper-explains recent studies], but an estimate can be obtained by seeing how many have passed through the {{w|Food and Drug Administration|U.S. FDA}} (1,453). Many home remedies, which might technically qualify as drugs, have not been approved because {{w|Novelty (patent)|"everybody knows that"}}, as well as many solely recreational drugs since regulation might result in outlawing. Because of this, "we have no idea" how many drugs truly exist. Since drugs are extremely powerful molecules that are only administered in choice amounts, they are generally perceived as small.
|}

===Lower right quadrant===
This is the section with the big items with count unknown.

{| class = "wikitable"
! Research field
! Size
! Knowledge of #
! Explanation
|-
|{{w|Botany}}
|Plants tend to range from few centimeters to hundreds of meters. Therefore, on average plants are about the same size as human beings.
|Plants estimated from 295,000 to 305,000 in total.
|Botany studies plants, which can reach {{w|List of superlative trees|hundreds of feet by any measure}}. Some {{w|Pando (tree)|clonal colonies of trees}} spread for miles. However, plant tend to clump together in forests and jungles, which makes it hard to get to them and document them. Every year, thousands of new plants are discovered, with the best estimate being that there are [https://news.mongabay.com/2016/05/many-plants-world-scientists-may-now-answer/ nearly 400,000 vascular plants] and an additional [https://www.britannica.com/topic-browse/Plants/Nonvascular-Plants 12,000 non-vascular plants]. However, the rate of discovery doesn't appear to be slowing down significantly, so we truly "have no idea."
|-
|{{w|Paleontology}}
|Paleontologists study fossils, which range in size from very small to very large. When most people think of paleontologists though, they tend to think of them as studying large animals such as dinosaurs.
|Estimated at around 5 billion species.
|Paleontology studies fossils, particularly those of extinct animals, which can reach {{w|Largest prehistoric animals|huge sizes}}. However, since fossils form under very special circumstances, if the animal did not die under those special circumstances, there will be no record of their existence. Therefore, the number of extinct animals can never truly be known, but we've found [http://scienceblogs.com/authority/2010/01/12/how-do-we-know-that-most-of-th/ around 250,000]
|-
|{{w|Black Hole}} {{w|Astronomy}}
|Compared to most astronomical objects, black holes are fairly small. However, most of them (that we are able to detect) are still larger than the Earth, so they would still fall on the "big" end of this chart. Alternatively, Randall may be referring to their mass, which is on the scale of stars.
|It has been estimated that the number of black holes in the {{w|Milky Way}} is around 100 million ([http://hubblesite.org/explore_astronomy/black_holes/encyc_mod3_q7.html]), although there is uncertainty in that estimate and the total number in the universe depends on the size of the universe (see "cosmology", above).
|"Most stellar black holes [...] are impossible to detect. Judging from the number of stars large enough to produce such black holes, however, scientists estimate that there are as many as ten million to a billion such black holes in the Milky Way alone." ([https://science.nasa.gov/astrophysics/focus-areas/black-holes NASA Black Hole information page])
|-
|{{w|Exobiology}}
|The comic puts this in the size range of paleontology, which can include many sizes (see above), and also marine mammalogy, which tends to have individuals that are in the range of tens of centimeters to several tens of meters. However, {{w|life|life as we know it}} is dominated in numbers by {{w|microbes}}, and {{w|Evolutionary history of life|life on Earth}} began {{w|Abiogenesis|microscopic}}, leading most {{w|Astrobiology|Astrobiologists}} to hypothesize that life on other planets would necessarily include microbes and [https://en.wikipedia.org/wiki/Fermi_paradox#No_other_intelligent_species_have_arisen only possibly include macroscopic life].
|The estimate of {{w|List of potentially habitable exoplanets|how many planets with life there are}} varies from 16 to 40,000,000,000; additionally, [https://en.wikipedia.org/wiki/Habitability_of_natural_satellites#In_the_Solar_System multiple moons] are believed to be potentially habitable for some forms of life in our own solar system. However, the number of bodies apart from Earth confirmed to have life is currently zero. Even more uncertain than the number of potentially habitable exoplanets is the {{w|Rare Earth Hypothesis|huge uncertainty}} in the likelihood of life arising on a habitable planet.
|Exobiology refers to the study of life outside Earth, which requires {{w|SETI|scanning the entire universe for life}}. Currently, exobiology seeks to find a planet or similar body with life (and, {{w|definition of planet|to qualify as a planet}}, bodies capable of sustaining life are big). The uncertainty about how many planets have life in the Milky Way relates to the {{w|Fermi Paradox}}. For life, of the type we know, to exist outside of the Solar system there need to be planets around other stars. Such planets are called Exoplanets, and they have been a [[:Category:Exoplanets|recurrent subject]] on xkcd.
|-
|{{w|Theology}}
|Presumably, any god transcends the bounds of spacetime, making this the largest.
|Depends on who you ask.
|Theology is not a strict science, but as presented here it is the field concerned with the study of one or more {{w|deity|deities}} which is a sacred supernatural being. In particular, theologians study the question of whether {{w|theism|one or more gods exist}} {{w|atheism|or not}}, and, in the former case, whether there are {{w|polytheism|multiple gods}} or {{w|monotheism|just one}} or indeed whether there is literally only {{w|pantheism|one god}}. Although the existence of any supernatural being(s) is unfalsifiable by any known means, the entire human race has very strong opinions on the subject, so this field probably deserves the “depends on who you ask” disclaimer as well. Quantitative uncertainty is also mentioned in [[900: Religions]].
|}

==Transcript==
:[An X-Y scatter plot of research areas, written in gray font, where both axes have arrows in both ends. At the end of each arrow is a label. Above the left part of the X-axis there is a line which goes to a text about the meaning of the X-axis. Similarly there is a line to from the top of the Y-axis to a questions “asked” to those that study the given subject, their answers being somewhere between the two labels on the Y axis.]

:[The X-axis from left to right, text first and then labels:]
:Size of the thing you study
:Small
:Big

:[The Y-axis from top to bottom, question first and then labels:]
:"That thing you study - how many of them are there?"
:"We have a pretty good estimate."
:"We have no idea"

:[The research areas names are listed here below by sorting them into the four quadrants from top left to bottom right. In each quadrant the areas are listed after most left first, and then top to bottom for those at the same x position.]

:[Upper left quadrant (Small & count known):]
:Elementary particle physics
:Dentistry
:Shakespeare studies
:Ornithology
:Ancient Literature

:[Upper right quadrant (Big & count known):]
:Presidential History
:Marine Mammology
:Railway Engineering
:Geology
:Cosmology*
:(*Depends who you ask)

:[Lower left quadrant (Small & count unknown):]
:Pharmacology
:Microbiology
:Entymology
:Mycology

:[Upper right quadrant (Big & count unknown):]
:Botany
:Paleontology
:Exobiology
:Black Hole Astronomy
:Theology

==Trivia==
Sortable table with the coordinates in percent:
{|class="wikitable sortable"
! Research area
! Size (%)
! Estimate (%)
|-
|Elementary Particle Physics ||7 ||72
|-
|Pharmacology ||12 ||6
|-
|Microbiology ||15 ||13
|-
|Dentistry ||21 ||84
|-
|Entymology ||24 ||25
|-
|Mycology ||29 ||38
|-
|Ornithology ||34 ||62
|-
|Shakespeare Studies ||37 ||88
|-
|Ancient Literature ||38 ||53
|-
|Botany ||60 ||40
|-
|Presidential History ||62 ||89
|-
|Marine Mammology ||66 ||68
|-
|Paleontology ||68 ||31
|-
|Exobiology ||68 ||5
|-
|Railway Engineering ||79 ||81
|-
|Geology ||90 ||90
|-
|Theology ||91 ||5
|-
|Black Hole Astronomy ||92 ||26
|-
|Cosmology ||94 ||62
|}

{{comic discussion}}

[[Category:Scatter plots]]
[[Category:Rankings]]
[[Category:Science]]
[[Category:Physics]]
[[Category:Astronomy]]
[[Category:Math]] 
[[Category:Fiction]] 
[[Category:Religion]] 
[[Category:Animals]] 
[[Category:Exoplanets]] 
[[Category:Politics]] 
[[Category:Geology]]
[[Category:Scientific research]]
[[Category:Mycology]]

Talk:2435: Geothmetic Meandian

2025-10-22T07:41:20Z

82.132.244.183:

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)

= Here is a reference https://math.stackexchange.com/questions/1734978/computing-square-roots-with-arithmetic-harmonic-mean. You must have made a mistake in your computer experiment. As an example, see the details I posted about Cueball and Megan exchanging dollars and euros. This is actually a handy way to compute square roots by hand.

== 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)

I'd like to add my own implementation:

from math import *
def getMeans(n=list):
n.sort()
mean=sum(n)/len(n)
if len(n)%2==1:
median=n[len(n)//2]
else:
median=(n[1+floor(len(n)/2)]-n[floor(len(n)/2)])/2
prod=1
for i in n:
prod*=i
gmean=prod**(1/len(n))
return [mean,median,gmean]
def gmdn(tol,n=list):
mList=n
mList=getMeans(mList)
while not (isclose(mList[0],mList[1],rel_tol=tol) and isclose(mList[1],mList[2],rel_tol=tol) and
isclose(mList[0],mList[2],rel_tol=tol) ) :
mList = getMeans(mList)
return (mList[0]+mList[1]+mList[2])/3
print(gmdn(1e-15,[1,1,2,3,5]))

which gives me 2.089057949736859

== 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)
::I guess it depends on whether we take x_{(n+1)/2} literally or not. If taken literally, the elements need to be sorted, and even-length lists don't work. If we assume the "median" is the literal part, and the notation is just a simplified sketch, then both are okay (median of even list is average of the two "middle" elements). [[Special:Contributions/172.68.143.160|172.68.143.160]] 22:00, 12 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)

: Here is a geometric interpretation of the inequality between them: {{w|Inequality_of_arithmetic_and_geometric_means#Geometric_interpretation}}. [[User:Danloeb|DanLoeb]] ([[User talk:Danloeb|talk]]) 19:31, 14 March 2021 (UTC) D--[[User:Danloeb|DanLoeb]] ([[User talk:Danloeb|talk]]) 19:31, 14 March 2021 (UTC)

=== 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

My python program:
from math import *
def getMeans(n=list):
n.sort()
mean=sum(n)/len(n)
if len(n)%2==1:
median=n[len(n)//2]
else:
median=(n[1+floor(len(n)/2)]-n[floor(len(n)/2)])/2
prod=1
for i in n:
prod*=i
gmean=prod**(1/len(n))
return [mean,median,gmean]
def gmdn(tol,n=list):
mList=n
mList=getMeans(mList)
while not (isclose(mList[0],mList[1],rel_tol=tol) and isclose(mList[1],mList[2],rel_tol=tol) and
isclose(mList[0],mList[2],rel_tol=tol) ) :
mList = getMeans(mList)
return mList[0]
print(gmdn(1e-15,[1,1,2,3,5]))

It gave me 2.0890579497368584

== 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]]

I believe we can produce a simpler, rigorous proof. Assuming a set of three is given, we can show that after every 2 iterations, the range is reduced by at least 1/3 of its original value, and therefore it converges exponentially to 0. We use the fact that each iteration, none of the three values will lie outside the range of the previous iteration. In addition, it can be shown that the arithmean lies at least 1/3 of the previous range away from the highest and lowest values of the previous iteration.

If the arithmean is the highest or lowest value on the first iteration, then the range will therefore already be small enough (and won't get bigger in the second iteration.) Otherwise, the only remaining option is that it is the middle (median) value. So on the second iteration, both the median and the arithmean are within the reduced 1/3 range, and at least one of them must be the highest or lowest value. The range will always be the required size.

Edit: Note that this proof holds only assuming the values are nonnegative. Some sets of values including negative ones, such as gmdn(-4,-4,1), do not converge.
[[Special:Contributions/141.101.98.16|141.101.98.16]]

:This is not true. Convergence also holds for negative values, see discussion below. Adapting the code as mentioned there you'll be able to verify that gmdn(-4,-4,1) does in fact converge to 0 as predicted by the theory. --[[User:Jukamala|Jukamala]] ([[User talk:Jukamala|talk]]) 18:30, 10 February 2025 (UTC)

== 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]]
:Thanks to all who shared the absurdity so I could also enjoy the joke, and the joke is on me for needing to have a joke "explained". Now where is the button for me to give credit to the best answer? I want to be sure you get points toward your next-level badge. ;-) [[User:Rtanenbaum|Rtanenbaum]] ([[User talk:Rtanenbaum|talk]]) 16:23, 13 March 2021 (UTC)
:This is actually one of my favorite xkcd comics. Even before seeing this comic, one thing I would always do was take the AM(AM,GM) instead of using either average on it's own. [[User:nullcline|nullcline]] ([[User talk:nullcline|talk]]) 17:33, 20 July 2021 (UTC)

== PyPi-package ==
I made a PyPi-package, if anyone (for some God-forsaken reason) want to use this without implementing it (ya lazy gits): https://pypi.org/project/GMDN/ [[User:BollaBerg|BollaBerg]] ([[User talk:BollaBerg|talk]]) 15:03, 15 March 2021 (UTC)

== Proof - extension to negative values ==

As others have proven, the geothmetic meandian converges for <code>a,b,c > 0</code>.

Case <code>a==0, b,c>=0</code> (and permutations):
: then the geometric mean will always be 0. All derivations for <code>a,b,c > 0</code> still apply, thus the set always converges to 0.

Case <code>a,b,c <= 0</code>:
: <code>arithmean(a,b,c) == -arithmean(-a,-b,-c)</code>; the same holds for the median and the geometric mean. Thus convergence is given, with the absolute value of the result the same as for positive inputs.

Case <code>a<0, b,c>0</code>, Case <code>a,b<0, c>0</code>
: the geometric mean is negative iff 1 or 3 inputs are negative.
: the median is negative iff 2 or 3 inputs are negative.
: thus, any mixed sign input will yield a mixed sign output.
: thus, '''if''' the geothmetic meandian converges for mixed-sign inputs, the limit has to be +-0.
: unfortunately, the proof by 141.101.98.16 does not hold here unmodified: it relies on the next set always being within the range of the previous set. This is not true for the geometric mean with mixed-sign inputs. E.g. <code>geommean(-1,2,4)=-4</code>.
: However, what does hold is that geometric mean is always within the extended range of <code>+- max(abs(inputs))</code>.
: this is not yet sufficient proof.
[[User:Xlf|Xlf]] ([[User talk:Xlf|talk]]) 18:05, 15 March 2021 (UTC)

Given <code>Mn := max(abs(inputsn))</code> and <code>minn < 0 < maxn</code>, we still have <code>abs(AMn) ≤ Mn*2/3</code> (by dropping a summand with different sign from AMn), <code>abs(AMn+1) ≤ Mn+1*2/3 ≤ Mn*2/3</code> and <code>abs(midn+1) ≤ abs(AMn) ≤ Mn*2/3</code>, because AMn shares a sign with one of the others. <code>abs(GMn+1) = abs(GMn*midn*AMn)(1/3) ≤ Mn*(1*1*2/3)(1/3) ≤ Mn*(2/3)(1/3)</code>.
Consequently <code>Mn+2/Mn ≤ (2/3)(1/3)</code>, which shows convergence to 0. □ -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 16:43, 31 March 2021 (UTC)

:Talking about negative numbers, both code snippets in trivia do not work for negative numbers. In the first case due to how the latest python version handles fractional exponents. Check for example <code>a = -1; print(a ** (1/3))</code> which prints a complex number even though -1 is one of the cube-roots. I contemplated about adapting the code, e.g. using <code>numpy.cbrt</code> or inserting <code>prod = reduce(lambda x, y: x * y, args); gmean = abs(prod) ** (1 / len(args)); gmean *= -1 if prod < 0 else 1</code> but decided against it because a) the geometric mean is usually only defined for positive numbers and b) for lists of even lengths extension to negative numbers is not trivial as the desired behavior is unclear. --[[User:Jukamala|Jukamala]] ([[User talk:Jukamala|talk]]) 18:27, 10 February 2025 (UTC)

Edit: Deleted comment. Sorry for the accidental spam. [[User talk:Quillathe Siannodel|{)|(}]][[User:Quillathe_Siannodel|Quill]][[User talk:Quillathe Siannodel|{)|(}]] 14:54, 25 March 2021 (UTC)
:The joke is still not explained, as far as I can tell. Maybe it's too obvious but since people asked (see three sections above in the comments) I think the explanation of the actual joke shoudl be added. As I too find it quite obvious what the joke is I find it hard to really explain it which is the reason why I didn't. Besides of that, the incomplete tag actually says why it's incomplete (in this case). AND there is already a comment section (again, three sections above) about this problem. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 07:41, 26 March 2021 (UTC)
::Sorry. That wasn't a thing when I added this section.

can someone help me with my python code of this? i dont get why this isnt working! https://replit.com/@Bumpf/geothmetic for my code. if you want i can paste my code here. i also commented in the code the error and why i dont understand it. thank you in advance! (also the geometric formula thing in the table on the page is showing a big red error. Maybe fix that?) [[Special:Contributions/172.70.38.56|172.70.38.56]] 13:35, 26 March 2021 (UTC)Bumpf

Since it uses F(F(F...)) someone should write a Hascal version that actually uses the fixedpoint function. [[Special:Contributions/172.69.35.175|172.69.35.175]] 22:56, 30 March 2021 (UTC)

Short proof that the thing converges. Basically there are three cases, one is that the median is larger than both one is that it is smaller than both and one is that it is in between. If it is in between, both he max must decrease and the min must increase. If it is greater, then the minimum must increase. If it is less, the maximum must decrease. In all three cases max(F(n+1))-min(F(n+1))<max(F(n))-min(F(n)) so by monotonic convergence theorem it must converge.
[[Special:Contributions/172.70.206.163|172.70.206.163]] 02:40, 1 April 2022 (UTC)

== Example table formatting ==
Just seen (and slightly adjusted the edit of) the edit that gives the minima numbers in the table italics, to go with the maxima numbers being bold. But normal-weight italics is relatively indistinct from normal-weight unsloped, next to strongly-weighted bold. Contemplated changing it to underline, instead. Then wondered if that means we could overline the values that are maximum, and reassign bold (or maybe italics; but, no, not strikethough... similarly symbolic though that might be!) to median. So minimum, '''median''' and maximum, in whatever order they might appear. Just an idea for another editor, though... [[Special:Contributions/82.132.244.183|82.132.244.183]] 07:41, 22 October 2025 (UTC)