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		<updated>2026-06-24T09:30:09Z</updated>
		<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2067:_Challengers&amp;diff=165294</id>
		<title>2067: Challengers</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2067:_Challengers&amp;diff=165294"/>
				<updated>2018-11-02T14:17:56Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Ballot Measures */ Fixing a typo&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2067&lt;br /&gt;
| date      = November 2, 2018&lt;br /&gt;
| title     = Challengers&lt;br /&gt;
| image     = challengers.png&lt;br /&gt;
| titletext = Use your mouse or fingers to pan + zoom. To edit the map, submit your ballot on November 6.&lt;br /&gt;
}}&lt;br /&gt;
To see the full zoomable picture go to the [https://xkcd.com/2067/ original] comic page.&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{incomplete|Need more explanation of the subcomics. Do NOT delete this tag too soon.}}&lt;br /&gt;
&lt;br /&gt;
[[File:challengers_loading_screen.png|thumb|200px|Loading screen]]&lt;br /&gt;
This comic shows all challengers to the {{w|United States elections, 2018|midterm elections}} hold on November 6, 2018. Many larger names provide a link to the homepage of the specific person, or an article about the election that candidate is participating in. The landmarks are taken from this {{w|List of U.S. National Historic Landmarks by state|Wikipedia}} page. Since the map is large there's also a [https://imgs.xkcd.com/comics/challengers.png loading screen] present that can be seen while the map is loading.&lt;br /&gt;
&lt;br /&gt;
There are also a total of nine comics embedded into the map at various locations. They are all loaded when you zoom in enough into the map to the appropriate section. &lt;br /&gt;
&lt;br /&gt;
===House===&lt;br /&gt;
[[File:challengers_subcomic_washington_dc.png|thumb|200px|House]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Washington, DC'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see Cueball standing in the middle of Washington, DC]&lt;br /&gt;
: Cueball: I can see my house from here!&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: Subcomic probably referencing the White House.&lt;br /&gt;
&lt;br /&gt;
===Ballot Measures===&lt;br /&gt;
[[File:challengers_subcomic_weed_california.png|thumb|200px|Ballot Measures]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Weed, California'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see Cueball holding a piece of paper talking to Megan]&lt;br /&gt;
: Cueball: Question #1 voids all 2018 ballot measures except itself.&lt;br /&gt;
: Cueball: Question #2 retroactively lowers the threshold for passing ballot measures to 5%&lt;br /&gt;
: Cueball: Question #3 requires a re-vote on all failed ballot measures a day later&lt;br /&gt;
: Cueball: Question #4 requires a re-vote on all passed ballot measures a day later&lt;br /&gt;
: Cueball: Question #5 bans those annoying phone scammers, but also says that if an odd number of ballot measures pass, Christmas is canceled&lt;br /&gt;
: Cueball: Question #6 makes a &amp;quot;yes&amp;quot; count as a &amp;quot;no&amp;quot; on odd-numbered ballot measures&lt;br /&gt;
: Cueball: Question #7 does nothing but counts as a ballot measure passing&lt;br /&gt;
: Cueball: Question #8 says that-&lt;br /&gt;
: Megan: I'm leaving these all blank and voting against whoever approves ballot measures&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: This probably refers to a ballot which would change how ballots are counted in the future. Lot of the proposed ideas sound complex and self-referential as well, therefore Megan just says that she doesn't wish to vote to any of them. This might refer to a fact that some people believe none of the choices on a ballot are good, and instead vote to no-one or deface their ballot papers&lt;br /&gt;
&lt;br /&gt;
===Carlymandering===&lt;br /&gt;
[[File:challengers_subcomic_seattle_washington.png|thumb|200px|Carlymandering]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Seattle, Washington'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see a presentation by Cueball to a group of people including White Hat and Hairbun sitting at an office desk. The presentation shows a map of a district]&lt;br /&gt;
: Cueball: Under my new Carlymandering plan, we'll create five red districts, five blue districts, and one district which contains only Carly Rae Jepsen&lt;br /&gt;
: Hairbun: That seems fair.&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: This refers to a Gerrymandering, a tactic used to re-shape voting district boundaries to make sure one candidate prevails over the other. The name is conflated with Carly Rae Jepsen, who is a Canadian singer.&lt;br /&gt;
&lt;br /&gt;
===Attack Ads===&lt;br /&gt;
[[File:challengers_subcomic_abernathy_texas.png|thumb|200px|Attack Ads]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Abernathy, Texas'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see Black Hat and Cueball talking]&lt;br /&gt;
: Black Hat: Starting on November 7th, we're going to blanket the airwaves with attack ads&lt;br /&gt;
: Cueball: Isn't the election on November 6th?&lt;br /&gt;
: Black Hat: Yeah, the advertising rates go way down after that.&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: Attack ads are campaign advertising that usually attack the opponents' campaign instead of promoting one's own. The comic also refers to the fact that media outlets usually spike their advertising prices during the campaign, and it becomes cheaper afterwards. However there's usually no point in advertising afterwards for a campaign as the polling has already taken place.&lt;br /&gt;
&lt;br /&gt;
===Scholten===&lt;br /&gt;
[[File:challengers_subcomic_storm_lake_iowa.png|thumb|200px|Scholten]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Storm Lake, Iowa'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: Queball: The midterms are so stressful.&lt;br /&gt;
: Megan: I just hope J.D. Scholten wins.&lt;br /&gt;
: Cueball: Why?&lt;br /&gt;
: Megan: Google Steve King.&lt;br /&gt;
: [Cueball looking at his phone]&lt;br /&gt;
: Cueball: Yikes.&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
&lt;br /&gt;
===Polls===&lt;br /&gt;
[[File:challengers_subcomic_primm_nevada.png|thumb|200px|Polls]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Primm, Nevada'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see a group of people]&lt;br /&gt;
: Remember: The only poll that counts is the one on Election Day. And the ones that help campaigns allocate resources. And the ones that drive media coverage and the ones that inform us all about what our fellow members of the public believe. And the ones that...&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: During campaign there are usually polling done by survey companies to determine each candidate's changes. This comic refers to the fact that usually the candidate that is behind in the polls usually says that they don't matter, as it's just a survey and not the final result. This is usually to encourage their voter base that it's still worth voting for them.&lt;br /&gt;
&lt;br /&gt;
===Spanberger===&lt;br /&gt;
[[File:challengers_subcomic_richmond_virginia.png|thumb|200px|Spanberger]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Richmond, Virginia'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [Cueball is holding a sign that says: Abigail Spanberger for Congress]&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: Abigail Spanberger is a candidate running for Congress in Virginia's 7th district, which includes Richmond. &lt;br /&gt;
&lt;br /&gt;
===St Louis===&lt;br /&gt;
[[File:challengers_subcomic_saint_louis_missouri.png|thumb|200px|St Louis]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Saint Louis, Missouri'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [We can see two people near the Gateway Arch talking]&lt;br /&gt;
: Ah, Saint Louis. Home of America's largest... Whatever that thing is.&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: Saint Louis, Missouri is the location of the Gateway Arch, the largest arch in the United States. (It's also one of the most recognizable arches in Saint Louis, according to [[1368: One Of The]].) Since in this comic they are next to the side of the arch, it is possible its sheer size stops them from determining what it is, although they should probably know.&lt;br /&gt;
&lt;br /&gt;
===Punish===&lt;br /&gt;
[[File:challengers_subcomic_chadron_nebraska.png|thumb|200px|Punish]]&lt;br /&gt;
&lt;br /&gt;
; Location&lt;br /&gt;
: '''Chadron, Nebraska'''&lt;br /&gt;
&lt;br /&gt;
; Transcript&lt;br /&gt;
: [Woman standing at a podium]&lt;br /&gt;
: If elected, I vow to find and punish the voters responsible.&lt;br /&gt;
&lt;br /&gt;
; Explanation&lt;br /&gt;
: Often candidates make promises of things they will do when they are elected. Vowing to find and punishing people responsible for a certain action, oftentimes criminals, is also common. However, these two things are conflated here to ludicrous effect.&lt;br /&gt;
&lt;br /&gt;
===Title text===&lt;br /&gt;
The title text shows the hint that the reader can zoom in and move over all US-States revealing many details can't be seen at the overall view. Furthermore [[Randall]] does a call to vote: he requests people to take an active part in the elections to change that picture.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[A loading screen appears shortly before the large picture has rendered. We can see an American flag in an oval badge with the text:]&lt;br /&gt;
:&amp;quot;I voted&amp;quot;&lt;br /&gt;
:[And beneath a text saying:]&lt;br /&gt;
:Loading...&lt;br /&gt;
&lt;br /&gt;
:2018 Midterm&lt;br /&gt;
:'''Challengers'''&lt;br /&gt;
:The bigger the candidate's name, the higher the office and the better their chances of success.&lt;br /&gt;
&lt;br /&gt;
:[In a frame a zoomable map shows all US-States (Alaska and Hawaii are shown in the left lower corner.) The candidates are shown colored mainly in red and blue at different sizes. Each state has many landmarks shown in gray. There are also many comics embedded into the picture.]&lt;br /&gt;
&lt;br /&gt;
:By Randall Monroe, Kelsey Harris, and Max Goodman&lt;br /&gt;
&lt;br /&gt;
:Landmarks from Wikipedia. Success odds estimated from district voting history, special election&lt;br /&gt;
:results, and seat ratings. Thank you to Dailykos Elections for their spreadsheets, shaplefiles election&lt;br /&gt;
:ratings, and advice, and to @davidshor, @charlotteeffect, and @thedlcc for additional candidate data.&lt;br /&gt;
&lt;br /&gt;
==Trivia==&lt;br /&gt;
*The comic [[Design_of_xkcd.com#Header|header]] had changed to:&lt;br /&gt;
:''Find out where to vote: [https://www.vote.org/ Vote.org]''&lt;br /&gt;
:''See what's on your ballot: [https://www.ballotready.org/ BallotReady.org]''&lt;br /&gt;
:This happened on the day this comic came out, as it up till [http://web.archive.org/web/20181101081612/https://xkcd.com/ the day before], had been a different reminder of the election only with the vote.org link.&lt;br /&gt;
*The interactive picture does not work in many browsers when using the link ''[https://www.xkcd.com www.xkcd.com]'', only the short ''[https://xkcd.com xkcd.com]'' works properly because the page uses an absolute link to a file ''[https://xkcd.com/2067/asset/map-data.json map-data.json]'' at the domain ''&amp;lt;nowiki&amp;gt;xkcd.com&amp;lt;/nowiki&amp;gt;'' which is not allowed from ''&amp;lt;nowiki&amp;gt;www.xkcd.com&amp;lt;/nowiki&amp;gt;'' according to {{w|Cross-origin resource sharing}}.&lt;br /&gt;
* The internal comics have a kind of &amp;quot;comic&amp;quot; inside the [https://xkcd.com/2067/asset/map-data.json map-data.json] file that contains all of the details shown on the map. All other locations, including politicians and landmarks inside the map-data.json have a kind of &amp;quot;label&amp;quot;&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Large drawings]]&lt;br /&gt;
[[Category:Interactive comics]]&lt;br /&gt;
[[Category:Comics with color]]&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Politics]]&lt;br /&gt;
[[Category:Elections]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:2066:_Ballot_Selfies&amp;diff=165022</id>
		<title>Talk:2066: Ballot Selfies</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:2066:_Ballot_Selfies&amp;diff=165022"/>
				<updated>2018-10-31T16:22:39Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--&amp;gt;&lt;br /&gt;
What harm do laws banning ballot selfies do?  [[User:Ryanker|Ryanker]] ([[User talk:Ryanker|talk]]) 15:51, 31 October 2018 (UTC)ryanker&lt;br /&gt;
: I'm thinking the flavor text is talking as if from the point of view of someone who has grown used to sharing photos of themselves with others, to communicate, encourage, feel connected.  Depicting their own behavior so directly might even seem a valid way to sway someone's opinion to such a person.  I guess when thinking about it, it would support democracy better to share the act of voting rather than the actual vote made. Curious regarding other opinions.  [[Special:Contributions/162.158.91.83|162.158.91.83]] 16:09, 31 October 2018 (UTC)&lt;br /&gt;
:: yes, fully agree with this. Just take all the selfies you want on the way there, in front of the place where you vote, on the way back. Just not during that one minute you spend inside the booth, and not showing your actual ballot. If you absolutely want to disclose what you actually voted for, you can still do so by writing a caption. It's that simple, and probably legal in most places around the world.--[[Special:Contributions/141.101.77.140|141.101.77.140]] 16:22, 31 October 2018 (UTC)&lt;br /&gt;
: Thought of another reason: if the government were to hack or misrepresent the vote, the people could use proof of voting to prove the fraud. [[Special:Contributions/172.68.50.136|172.68.50.136]] 16:12, 31 October 2018 (UTC)&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=969:_Delta-P&amp;diff=164688</id>
		<title>969: Delta-P</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=969:_Delta-P&amp;diff=164688"/>
				<updated>2018-10-24T18:19:01Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Transcript */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 969&lt;br /&gt;
| date      = October 26, 2011&lt;br /&gt;
| title     = Delta-P&lt;br /&gt;
| image     = delta p.png&lt;br /&gt;
| titletext = If you fire a Portal gun through the door of the wardrobe, space and time knot together, which leads to a frustrated Aslan trying to impart Christian morality to the Space sphere.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
''{{w|The Lion, the Witch and the Wardrobe}}'' is a book in which four children accidentally wander into a world known as {{w|Narnia}} through a wardrobe that only allows passage through to Narnia when you aren't looking for it. In the comic, someone connects an anchor to the wardrobe and throws it into the ocean. The formula describes the flow of water through the open doors when the wardrobe sits at the bottom of the ocean in 2 km depth, which means that a steady stream of water at an approximate velocity of 200 meters per second will flow into Narnia.&lt;br /&gt;
&lt;br /&gt;
The evil {{w|White Witch}}, who has made it [http://www.goodreads.com/quotes/93155-always-winter-but-never-christmas &amp;quot;always winter, and never Christmas,&amp;quot;] could not have anticipated that a wardrobe portal would suddenly begin spewing approximately 400,000 liters of water per second into Narnia.{{Citation needed}}&lt;br /&gt;
&lt;br /&gt;
Sea water freezes at low temperatures and flowing water freezes at even lower temperatures, depending how fast it is going. Water jetting out from this portal would be flowing very quickly indeed, approximately 200 meters per second (450 mph or 720 km/h) as the comic says; this is over half the speed of sound. And the water flow is approximately 400,000 liters per second, again, provided in the image above. The force of this water jet would be incredible. If you can imagine the force of a tractor trailer truck careening down the highway, the force of this jet is much much larger than that.&lt;br /&gt;
&lt;br /&gt;
This water would not freeze. First it would decimate any forest trees or iron lamp posts in front of it until it eventually slowed down and fell to the ground. There it would create a rapidly expanding river of sea water. Narnia would not stay frozen for long. Snow would melt, ice would break apart and the valley would quickly flood.&lt;br /&gt;
&lt;br /&gt;
Delta-P is a mathematical term for the difference in pressure. The shown formula is based on the {{w|Hagen–Poiseuille equation}} which can be applied to a flowing liquid in a long cylindrical pipe; thus the equation here results in an unphysically high flow rate because the opening is rectangular and too short for a {{w|Laminar flow|laminar flow}}. Using the ''Hagen–Poiseuille equation'' the maximum flow rate is given by:&lt;br /&gt;
:&amp;lt;math&amp;gt;Q_\max{} = \pi R^2 \sqrt\frac{2 \Delta P}{\rho}&amp;lt;/math&amp;gt;&lt;br /&gt;
:&amp;lt;math&amp;gt;\pi R^2&amp;lt;/math&amp;gt; is the pipe cross-sectional area (m&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;) and &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; is the fluid density (kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;).&lt;br /&gt;
From the {{w|Hydrostatics|hydrostatics}} of water the pressure difference depends on gravity and the height:&lt;br /&gt;
:&amp;lt;math&amp;gt;\Delta P = \rho g h,&amp;lt;/math&amp;gt;&lt;br /&gt;
:&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; is the gravitational acceleration (m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;) and &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; is the height (m).&lt;br /&gt;
Putting this together and changing the cross-sectional area to a rectangular area &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; we get the formula used by Randall:&lt;br /&gt;
:&amp;lt;math&amp;gt;Q_\max{} = A \sqrt{2 g h}&amp;lt;/math&amp;gt;&lt;br /&gt;
Assuming the wardrobe is two meter high and one in width (''A = 2 m&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'') and using the gravitational constant ''g = 9.81 m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' the flow rate is 396 m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; per second, or roughly 400.000 liters per second.&lt;br /&gt;
The water jet velocity ''v'' is based on {{w|Torricelli's law}}:&lt;br /&gt;
:&amp;lt;math&amp;gt;v=\sqrt{{2 g}{h}}&amp;lt;/math&amp;gt;&lt;br /&gt;
It gives 198 &amp;lt;sup&amp;gt;m&amp;lt;/sup&amp;gt;/&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; in this scenario.&lt;br /&gt;
&lt;br /&gt;
The title text references the video game ''{{w|Portal (video game)|Portal}}'' in which you solve puzzles using a gun which projects portals onto certain surfaces. In the game you cannot shoot a portal through a portal, but [[Randall]] says that if you try to create a portal with the portal gun through the wardrobe, space and time knot together. {{w|Aslan}} is a lion and a main character in C. S. Lewis's ''{{w|The Chronicles of Narnia}}'' series and represents Jesus Christ. The Space Sphere is a minor character in the game ''{{w|Portal 2}}''; it is a barely-sentient AI whose only preoccupation is going to space, and it would not be receptive to Aslan's teachings.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[An open wardrobe, with a boat anchor attached to one corner, falling towards water.]&lt;br /&gt;
:[Below the water line a formula with its variables explained is shown:]&lt;br /&gt;
:&amp;lt;math&amp;gt;Q = A \sqrt{2 g d}&amp;lt;/math&amp;gt;&lt;br /&gt;
:Q = flow rate&lt;br /&gt;
:A = area of opening&lt;br /&gt;
:d = ocean depth (2&amp;amp;nbsp;km)&lt;br /&gt;
:g = Earth gravity&lt;br /&gt;
&lt;br /&gt;
:[And below the formula:]&lt;br /&gt;
:Flow: ~400,000 &amp;lt;sup&amp;gt;liters&amp;lt;/sup&amp;gt;/&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
:Water jet velocity: ~200 &amp;lt;sup&amp;gt;m&amp;lt;/sup&amp;gt;/&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:[Caption below the frame:]&lt;br /&gt;
:The White Witch didn't know what hit her.&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
[[Category:Comics with color]]&lt;br /&gt;
[[Category:Physics]]&lt;br /&gt;
[[Category:Video games]]&lt;br /&gt;
[[Category:Fiction]]&lt;br /&gt;
[[Category:Chronicles of Narnia]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=465:_Quantum_Teleportation&amp;diff=164682</id>
		<title>465: Quantum Teleportation</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=465:_Quantum_Teleportation&amp;diff=164682"/>
				<updated>2018-10-24T18:03:47Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 465&lt;br /&gt;
| date      = August 20, 2008&lt;br /&gt;
| title     = Quantum Teleportation&lt;br /&gt;
| image     = quantum teleportation.png&lt;br /&gt;
| titletext = Science should be exactly as cool as the headlines sound. Like the &amp;quot;RUSSIANS CUT APART AND REASSEMBLE DOGS&amp;quot; thing&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{w|Quantum teleportation}} is a method of effectively taking a quantum state that exists in one laboratory and destroying it in the current laboratory and later recreating exactly the same — still unmeasured — quantum state in another laboratory that could potentially be very far away.&lt;br /&gt;
&lt;br /&gt;
This is achieved by first creating an entangled quantum state in a laboratory and moving one part of the entangled quantum state to a faraway laboratory. Now let's say a scientist desires to teleport the quantum state |ψ⟩ to a faraway lab. The scientists does a specific measurement on the combination of |ψ⟩ and their half of the entangled quantum state and the outcome of their measurement will be two bits of classical information. They can then telephone over the results of their two bits of information to tell scientists at the faraway lab how to do a measurement on their half of the entangled quantum state, which will recreate the quantum state |ψ⟩ at the faraway lab, effectively teleporting it. This is an important result in quantum mechanics, especially in regards to quantum computing.&lt;br /&gt;
&lt;br /&gt;
The name is misleading in that it does not create an efficient means of transportation via teleportation — something like the {{w|Transporter (Star Trek)|teleporters}} from ''{{w|Star Trek}}'' i.e. a ''conventional teleporter'' — where macroscopic objects like humans (composed of [http://www.wolframalpha.com/input/?i=number+of+atoms+in+a+human&amp;amp;lk=4&amp;amp;num=3 7&amp;amp;nbsp;×&amp;amp;nbsp;10&amp;lt;sup&amp;gt;27&amp;lt;/sup&amp;gt; atoms]) could be teleported to an arbitrary place.&lt;br /&gt;
&lt;br /&gt;
The comic jokes with the fact that news reporters wish to get a story about Star Trek teleporters and the scientist is angry that there is no interest in his quantum version — the reporters are even disappointed when they write their story. The last panel appears to indicate this scientist not only has a quantum teleporter he also has a &amp;quot;regular&amp;quot; teleporter of the type the reporter is asking about, which would be a gigantic news item, as it is one of the biggest challenges of this century (and possibly future ones as well), to build one. He uses the conventional to escape to The Bahamas.&lt;br /&gt;
&lt;br /&gt;
The whole method of quantum teleportation is predicated on being able to first create entangled quantum states and then transport, by conventional means, one-half of the entangled state. Only after this step, could you then destroy the shared entangled quantum state, to &amp;quot;teleport&amp;quot; a different quantum state to the new location.&lt;br /&gt;
&lt;br /&gt;
Quantum teleportation is deeply related to {{w|Bell's theorem}} where it's shown that quantum mechanics is incompatible with the idea of local hidden variables and which has been experimentally demonstrated (though a few very small loopholes still have not been conclusively ruled out). Explaining &amp;quot;it's a particle statistics thing&amp;quot; is a great explanation of the related Bell's theorem experiments, which demonstrate quantum entanglement which is at the root of quantum teleportation. In these experiments, physicists take an entangled quantum state move it apart and then randomly decide which direction to measure each side of the quantum states. Through a statistical analysis of the results, you can demonstrate and measure each entangled particle in a randomly chosen direction. The statistical correlations between the particles are consistent with quantum mechanics and inconsistent with any local hidden variable theory; however this instantaneous wave-function collapse does not break special relativity as wave-function collapse {{w|No-communication theorem|does not allow communication of any information}}. Instead you can just analyze the correlations after the fact and compare the hypothesis of local hidden variables to the inconsistent hypothesis predicted by quantum mechanics, and verify the quantum mechanical prediction.&lt;br /&gt;
&lt;br /&gt;
In the comic, Cueball explains to the reporter that quantum teleportation isn't what reporters build it up to be, before Cueball successfully teleports by switching his teleportation machine from quantum teleportation to regular teleportation.&lt;br /&gt;
&lt;br /&gt;
The title text refers to the controversial 1940s Soviet {{w|Experiments in the Revival of Organisms}} video that depicts a dog's head being cut off and revived. The film is controversial in that the footage is often perceived as being staged, though the {{w|Sergei S. Bryukhonenko|Soviet scientist}} depicted in the video was attempting these sorts of experiments and this research eventually led to the first Soviet open heart operation in 1957. Another instance of crazy headlines that may not be as interesting to the public when first explained — but may be an important step on the way to some type of practical use.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[A Cueball-like reporter and Cueball are facing each other, sitting in chairs.]&lt;br /&gt;
:Reporter: So, Quantum Teleportation-&lt;br /&gt;
:Cueball: The name is misleading. It's a particle statistics thing.&lt;br /&gt;
&lt;br /&gt;
:[Zoom in on the reporter.]&lt;br /&gt;
:Reporter: So it's not like Star Trek? That's boring.&lt;br /&gt;
&lt;br /&gt;
:[Zoom out again to both. Cueball leaves seat and moves behind it.]&lt;br /&gt;
:Cueball: Okay, I'm sick of this. Every time there's a paper on quantum teleportation, you reporters write the same disappointed story.&lt;br /&gt;
&lt;br /&gt;
:[Cueball has gone to device that was behind him and was out of the scope of the three previous panels. He turns a knob that makes a sound in a zigzag sound buble.]&lt;br /&gt;
:Reporter (Off panel): But-&lt;br /&gt;
:Cueball: Talk to someone else. I'm going to the Bahamas. &lt;br /&gt;
:Knob: ''Click''&lt;br /&gt;
&lt;br /&gt;
:[Inserted panel with a zoom in on the device which is labeled and the knob is now turned to the right position. Both possible positions are labeled.]&lt;br /&gt;
:Label: Teleporter&lt;br /&gt;
:Left: Quantum&lt;br /&gt;
:Right: Regular&lt;br /&gt;
&lt;br /&gt;
:[Cueball is beamed up in classic Star Trek fashion.]&lt;br /&gt;
:''Vrmmm''&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Multiple Cueballs]]&lt;br /&gt;
[[Category:Physics]]&lt;br /&gt;
[[Category:Star Trek]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=401:_Large_Hadron_Collider&amp;diff=164681</id>
		<title>401: Large Hadron Collider</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=401:_Large_Hadron_Collider&amp;diff=164681"/>
				<updated>2018-10-24T18:02:40Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 401&lt;br /&gt;
| date      = March 26, 2008&lt;br /&gt;
| title     = Large Hadron Collider&lt;br /&gt;
| image     = large_hadron_collider.png&lt;br /&gt;
| titletext = When charged particles of more than 5 TeV pass through a bubble chamber, they leave a trail of candy.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
The {{w|Large Hadron Collider}} (LHC) is the world's largest particle accelerator, used in physics research, and particularly for finding the {{w|Higgs Boson}}. The Higgs Boson is one quantum excitation of the Higgs Field, in the same way as the photon is a quantum of the electromagnetic field. Interaction between particles and the Higgs field can explain why other particles have mass. The Higgs Boson was first detected in 2012, and confirmed to exist in March 2013. It was the last particle of the {{w|Standard Model}} of Physics to be experimentally confirmed.&lt;br /&gt;
&lt;br /&gt;
At the time of this comic's writing, the LHC was nearing completion, and the comic imagines experimental physicists starting up the LHC for the first time. It has taken many years to complete, and its purpose is mainly to prove the Higgs Boson exists - but in the comic it turns out the experiment does not show the boson. Since they can't see the Higgs Boson, they can only wait for the theorists to determine what actually happened - and maybe they would then come up with an even more expensive way to find it. In reality, experiments ran for many years and were analyzed for a very long time (4–5 years) before the scientists could conclude that the particle did exist. But imagine the opposite - and you have the scenario of this comic with a five-year delay between panel 3 and 4.&lt;br /&gt;
&lt;br /&gt;
After the experiment failed the bored physicists try frying pigeons with the proton stream and instead end up giving a helicopter cancer. Both of which are impossible. This is because the stream is contained within the LHC, and non-organic entities can't get cancer. However, the proton stream could cause considerable damage to pigeons or humans, if it could hit any, as the U-70 synchrotron did to {{w|Anatoli Bugorski}} in 1978.&lt;br /&gt;
&lt;br /&gt;
At that time there was also a big concern by some people that the LHC could produce {{w|Micro black hole|microscopic black holes}}. However, {{w|Cosmic ray|cosmic rays}} regularly strike Earth's atmosphere with particles at higher energies; thus, if the proposed doomsday scenario were possible it should have already happened. Many jokes were published like this video [http://www.youtube.com/watch?v=INodNZY5ytE &amp;quot;LHC End of The World Black Hole&amp;quot;].&lt;br /&gt;
&lt;br /&gt;
The title text makes another joke about the effects of highly energetic particles, claiming that when they pass through a {{w|bubble chamber}} (an older particle detection device) they leave a trail of candy. TeV means {{w|Tera-|tera}}{{w|Electronvolt|electronvolt}} and it equals 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt; eV. 5 TeV is {{w|Electronvolt#Energy comparisons|about the energy}} of the LHC. It is of the order of the energy of a flying mosquito and would never be able to convert a liquid to candy or anything macroscopic.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:The Large Hadron Collider, CERN...&lt;br /&gt;
:Megan: Okay, moment of truth. &amp;quot;click&amp;quot;&lt;br /&gt;
:Large Hadron Collider: &amp;quot;VVVVVRRMMMMMM&amp;quot;&lt;br /&gt;
:Cueball: Do you see the Higgs Boson?&lt;br /&gt;
:Megan: Nope.&lt;br /&gt;
:Cueball: Huh.&lt;br /&gt;
:Megan: Well, then.&lt;br /&gt;
:Cueball: Until the theorists get back to us, wanna try hitting pigeons with the proton stream?&lt;br /&gt;
:Megan: Already on it. Cool! I just gave a helicopter cancer.&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Comics featuring Megan]]&lt;br /&gt;
[[Category:Physics]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=54:_Science&amp;diff=164677</id>
		<title>54: Science</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=54:_Science&amp;diff=164677"/>
				<updated>2018-10-24T17:56:04Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 54&lt;br /&gt;
| date      = January 18, 2006&lt;br /&gt;
| title     = Science&lt;br /&gt;
| image     = science.jpg&lt;br /&gt;
| titletext = Bonus points if you can identify the science in question&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
The solid line represents the theoretical {{w|blackbody radiation|radiation for a blackbody}} at 2.73&amp;amp;nbsp;K according to {{w|Planck's Law}} (derived as early as 1900 by {{w|Max Planck}}). The formula, almost as written in the graph, can be found {{w|Black-body radiation#Planck's law of black-body radiation|here}}. The only changes are that on Wikipedia, the frequency ''f'' is represented by the Greek letter ''ν'' (nu) and the temperature ''T'' is included as an independent variable, so ''I''(''f'') becomes ''I''(''v'',''T''). However, ''I''(''v'',''T'') still represents the {{w|Radiance#Spectral radiance|spectral radiance}} (similar to energy density). In this formula, ''h'' is the Planck constant, ''c'' is the speed of light in a vacuum, and ''k'' is the Boltzmann constant. The frequency (''f'' or ''v'') along the ''x''-axis is measured in {{w|gigahertz}}. The curve peaks at 160.4&amp;amp;nbsp;GHz. There is no scale or unit on the {{w|energy density}} on the ''y''-axis.&lt;br /&gt;
&lt;br /&gt;
The theory is that the blackbody in question was the universe at the point when it had cooled down enough {{w|Decoupling (cosmology)|to allow photons to escape}}, {{w|Chronology of the universe|0.38 million years}} into its {{w|Big Bang|13.8 billion years}} history. The photons that reach us today are the ones that have been travelling to us at lightspeed since then. As the light from astronomical objects suffers from {{w|redshift}} due to the expansion of the universe, and this shift becomes more pronounced with distance from the observer, this light displays in the infrared range.&lt;br /&gt;
&lt;br /&gt;
The title text praises viewers who can identify where this equation and corresponding graph come from (without consulting this wiki, of course).&lt;br /&gt;
&lt;br /&gt;
===Official T-shirt explanation===&lt;br /&gt;
This comic was made into a T-shirt, but is no longer available.&lt;br /&gt;
&lt;br /&gt;
On the xkcd store, there was both an '''explanation for the title:'''&lt;br /&gt;
&amp;lt;!-- Begin Quote DO NOT CORRECT This is a copy paste from xkcd with errors.--&amp;gt;&lt;br /&gt;
 Science: We finally figured out that you could separate fact from superstition by a completely radical method: observation. You can try things, measure them, and see how they work! {{w|Bitch (insult)|Bitches}}. &lt;br /&gt;
&amp;lt;!-- End Quote DO NOT CORRECT --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
And specifically an '''explanation for the graph:''' &lt;br /&gt;
&amp;lt;!-- Begin Quote DO NOT CORRECT This is a copy paste from xkcd with errors.--&amp;gt;&lt;br /&gt;
 The graph on the back of the shirt is data from the {{w|COBE|COBE mission}} which looked at the background microwave glow of the universe and found that it fit perfectly with the idea that the universe used to be really hot everywhere. This strongly reinforced the Big Bang theory and was one of the most dramatic examples of an experiment agreeing with a theory in history -- the data points fit perfectly, with error bars too small to draw on the graph. It's one of the most triumphant scientific results in history.&lt;br /&gt;
&amp;lt;!-- End Quote DO NOT CORRECT --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above is a direct copy paste, with errors. The current wiki page of the COBE mission can be found at {{w|Cosmic Background Explorer|http://en.wikipedia.org/wiki/Cosmic_Background_Explorer}}&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[A graph with a curve that begins at zero, then peaks at a given frequency, indicated via a thin vertical line, and then fades down towards zero. It is possible to see the data points, which fit the curve perfectly. The y-axis is labelled. Along the x-axis the zero point and the frequency where the peak has its maximum are labelled and close to the arrow the unit of this axis is written.]&lt;br /&gt;
:y-axis: Energy Density&lt;br /&gt;
:Along the x-axis:&lt;br /&gt;
::0 &lt;br /&gt;
::160.4 &lt;br /&gt;
::GHz&lt;br /&gt;
:[Above the graph to the right is the following formula, with the last inner parentheses only included to make the formula clear, since in the drawing the fractions are written above and below horizontal lines:]&lt;br /&gt;
:&amp;lt;math&amp;gt;I(f)=\left(\frac{2hf^3}{c^2}\right)\left(\frac{1}{e^\frac{hf}{kT}-1}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
:[Below the graph is written the following:]&lt;br /&gt;
:'''Science.'''&lt;br /&gt;
:It works, bitches.&lt;br /&gt;
&lt;br /&gt;
==Trivia==&lt;br /&gt;
*This was the 48th comic originally posted to [[LiveJournal]].&lt;br /&gt;
**The previous was [[50: Penny Arcade]].&lt;br /&gt;
**The next was [[51: Malaria]].&lt;br /&gt;
*This comic kept its original title: &amp;quot;Science&amp;quot;&lt;br /&gt;
**It is part of the last six comics on LiveJournal that all had a title without the word &amp;quot;Drawing&amp;quot; in it. &lt;br /&gt;
**Five of these had exactly the same title on both sites.&lt;br /&gt;
**Only 11 comics have the same title on both sites.&lt;br /&gt;
**Apart from the [[:Category:First day on LiveJournal|thirteen first comics]] posted to LiveJournal, there were only three other comics without the word &amp;quot;Drawing&amp;quot; in the title before these last six.&lt;br /&gt;
*Original [[Randall]] quote: &amp;quot;Bonus points if you can identify the science in question.&amp;quot;&lt;br /&gt;
**Only difference between this and the title text on xkcd is the last period: &amp;quot;.&amp;quot;&lt;br /&gt;
**It is rare that these two texts are so similar.&lt;br /&gt;
*This comic was one of the last 11 comics posted on LiveJournal.&lt;br /&gt;
**These 11 comics were [[:Category:Posted on LiveJournal after xkcd|posted both on LiveJournal and xkcd]] after the [[xkcd]] site opened on the 1st of January 2006. &lt;br /&gt;
**The first six comics were posted on both sites on the same day. But not this one.&lt;br /&gt;
*For some reason, this comic was first posted a week later on xkcd (25 January 2006), on the day that [[53: Hobby]] was released on LiveJournal.&lt;br /&gt;
**On the day 54: Science was released on LiveJournal (18 January 2006), another comic ([[51: Malaria]]) was released on xkcd.&lt;br /&gt;
**[[51: Malaria]] also became the next comic released on LiveJournal, but this meant that three comics in a row were posted a release day earlier on xkcd than on LiveJournal.&lt;br /&gt;
**Only with the last comic released on LiveJournal, [[55: Useless]], did the two sites release the same comic on the same day again.&lt;br /&gt;
* &amp;quot;It works, bitches&amp;quot; has been quoted by Richard Dawklins in 2013, when questioned on the superiority of science. It is not sure whether he was quoting xkcd, though. See https://www.theverge.com/2013/4/2/4173576/richard-dawkins-on-science-it-works-bitches&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics posted on livejournal| 48]]&lt;br /&gt;
[[Category:Posted on LiveJournal after xkcd]]&lt;br /&gt;
[[Category:Line graphs]]&lt;br /&gt;
[[Category:Analysis]]&lt;br /&gt;
[[Category:Math]]&lt;br /&gt;
[[Category:Physics]]&lt;br /&gt;
[[Category:Science]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2059:_Modified_Bayes%27_Theorem&amp;diff=164293</id>
		<title>2059: Modified Bayes' Theorem</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2059:_Modified_Bayes%27_Theorem&amp;diff=164293"/>
				<updated>2018-10-17T09:43:03Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: grammar fix&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2059&lt;br /&gt;
| date      = October 15, 2018&lt;br /&gt;
| title     = Modified Bayes' Theorem&lt;br /&gt;
| image     = modified_bayes_theorem.png&lt;br /&gt;
| titletext = Don't forget to add another term for &amp;quot;probability that the Modified Bayes' Theorem is correct.&amp;quot;&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{incomplete|When using the Math-syntax please also care for a proper layout. Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}&lt;br /&gt;
{{w|Bayes' Theorem}} is an equation in statistics that gives the probability of a given hypothesis accounting not only for a single experiment or observation but also for your existing knowledge about the hypothesis, i.e. its prior probability. Randall's modified form of the equation also purports to account for the probability that you are indeed applying Bayes' Theorem itself correctly by including that as a term in the equation.&lt;br /&gt;
&lt;br /&gt;
Bayes' theorem is:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;P(H \mid X) = \frac{P(X \mid H) \, P(H)}{P(X)}&amp;lt;/math&amp;gt;,&lt;br /&gt;
where&lt;br /&gt;
*&amp;lt;math&amp;gt;P(H \mid X)&amp;lt;/math&amp;gt; is the probability that &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt;, the hypothesis, is true given observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt;. This is called the ''posterior probability''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(X \mid H)&amp;lt;/math&amp;gt; is the probability that observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; will appear given the truth of hypothesis &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt;. This term is often called the ''likelihood''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(H)&amp;lt;/math&amp;gt; is the probability that hypothesis &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is true before any observations. This is called the ''prior'', or ''belief''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(X)&amp;lt;/math&amp;gt; is the probability of the observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; regardless of any hypothesis might have produced it. This term is called the ''marginal likelihood''.&lt;br /&gt;
&lt;br /&gt;
The purpose of Bayesian inference is to discover something we want to know (how likely is it that our explanation is correct given the evidence we've seen) by mathematically expressing it in terms of things we can find out: how likely are our observations, how likely is our hypothesis ''a priori'', and how likely are we to see the observations we've seen assuming our hypothesis is true. A Bayesian learning system will iterate over available observations, each time using the likelihood of new observations to update its priors (beliefs) with the hope that, after seeing enough data points, the prior and posterior will converge to a single model.&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;P(C)=1&amp;lt;/math&amp;gt; the modified theorem reverts to the original Bayes' theorem (which makes sense, as a probability one would mean certainty that you are using Bayes' theorem correctly).&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;P(C)=0&amp;lt;/math&amp;gt; the modified theorem becomes &amp;lt;math&amp;gt;P(H \mid X) = P(H)&amp;lt;/math&amp;gt;, which says that the belief in your hypothesis is not affected by the result of the observation (which makes sense because you're certain you're misapplying the theorem so the outcome of the calculation shouldn't affect your belief.)&lt;br /&gt;
&lt;br /&gt;
This happens because the modified theorem can be rewritten as: &amp;lt;math&amp;gt;P(H \mid X) = (1-P(C))\,P(H) + P(C)\,\frac{P(X \mid H)\,P(H)}{P(X)}&amp;lt;/math&amp;gt;. This is the {{w|Linear interpolation|linear-interpolated}} weighted average of the belief you had before the calculation and the belief you would have if you applied the theorem correctly. This goes smoothly from not believing your calculation at all (keeping the same belief as before) if &amp;lt;math&amp;gt;P(C)=0&amp;lt;/math&amp;gt; to changing your belief exactly as Bayes' theorem suggests if &amp;lt;math&amp;gt;P(C)=1&amp;lt;/math&amp;gt;. (Note that &amp;lt;math&amp;gt;1-P(C)&amp;lt;/math&amp;gt; is the probability that you are using the theorem incorrectly.)&lt;br /&gt;
&lt;br /&gt;
The title text suggests that an additional term should be added for the probability that the Modified Bayes Theorem is correct. But that's ''this'' equation, so it would make the formula self-referential, unless we call the result the Modified Modified Bayes Theorem (or Modified&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;). It could also result in an infinite regress -- we'd need another term for the probability that the version with the probability added is correct, and another term for that version, and so on. If the modifications have a limit, then we can make that the Modified&amp;lt;sup&amp;gt;&amp;amp;omega;&amp;lt;/sup&amp;gt; Bayes Theorem, but then we need another term for whether we did ''that'' correctly, leading to the Modified&amp;lt;sup&amp;gt;&amp;amp;omega;+1&amp;lt;/sup&amp;gt; Bayes Theorem, and so on through every {{w|ordinal number}}. It's also unclear what the point of using an equation we're not sure of is (although sometimes we can: {{w|Newton's Laws}} are not as correct as Einstein's {{w|Theory of Relativity}} but they're a reasonable approximation in most circumstances. Alternatively, ask any student taking a difficult exam with a formula sheet.).&lt;br /&gt;
&lt;br /&gt;
If we denote the probability that the Modified&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; Bayes' Theorem is correct by &amp;lt;math&amp;gt;P(C_n)&amp;lt;/math&amp;gt;, then one way to define this sequence of modified Bayes' theorems is by the rule &amp;lt;math&amp;gt;P_n(H \mid X) := P_{n-1}(H \mid X) P(C_n) + (1-P(C_n))P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One can then show by induction that &amp;lt;math&amp;gt;P_n(H \mid X) = \prod_{i=1}^n P(C_i)\left(\frac{P(X \mid H)}{P(X)} - P(H) \right) + P(H).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If we assume that one doubts each step infinitely (that is, &amp;lt;math&amp;gt;P(C_i)&amp;lt;1&amp;lt;/math&amp;gt; for any &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt;), then we can calculate a limit.&lt;br /&gt;
&lt;br /&gt;
Without changing a limit, we can assume that &amp;lt;math&amp;gt;P(C_i) = p&amp;lt;/math&amp;gt; where &amp;lt;math&amp;gt;0&amp;lt;p&amp;lt;1&amp;lt;/math&amp;gt;. Then we can write a limit as:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\lim_{n \to \infty} P_n(H \mid X) =\lim_{n \to \infty} \prod_{i=1}^n p\left(\frac{P(X \mid H)}{P(X)} - P(H) \right) + P(H) =&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;=\lim_{n \to \infty} p^n\left(\frac{P(X \mid H)}{P(X)} - P(H)\right) ^n + P(H)=&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;=\lim_{n \to \infty} p^n q^n + P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where both &amp;lt;math&amp;gt;|p|&amp;lt;1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;|q|&amp;lt;1&amp;lt;/math&amp;gt;, so&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\lim_{n \to \infty} P_n(H \mid X) = 0 + P(H) = P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This may interpreted as an universal truth that we have to trust ''something'' eventually, otherwise everything boils down to an unconditional belief.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
{{incomplete transcript|Do NOT delete this tag too soon.}}&lt;br /&gt;
&lt;br /&gt;
:Modified Bayes' theorem:&lt;br /&gt;
&lt;br /&gt;
:P(H|X) = P(H) × (1 + P(C) × ( P(X|H)/P(X) - 1 ))&lt;br /&gt;
&lt;br /&gt;
:H: Hypothesis&lt;br /&gt;
:X: Observation&lt;br /&gt;
:P(H): Prior probability that H is true&lt;br /&gt;
:P(X): Prior probability of observing X&lt;br /&gt;
:P(C): Probability that you're using Bayesian statistics correctly&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Statistics]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2059:_Modified_Bayes%27_Theorem&amp;diff=164291</id>
		<title>2059: Modified Bayes' Theorem</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2059:_Modified_Bayes%27_Theorem&amp;diff=164291"/>
				<updated>2018-10-17T09:41:29Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: I've added a limit for n -&amp;gt; infty. Oh my god, am I a nerd...?&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2059&lt;br /&gt;
| date      = October 15, 2018&lt;br /&gt;
| title     = Modified Bayes' Theorem&lt;br /&gt;
| image     = modified_bayes_theorem.png&lt;br /&gt;
| titletext = Don't forget to add another term for &amp;quot;probability that the Modified Bayes' Theorem is correct.&amp;quot;&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{incomplete|When using the Math-syntax please also care for a proper layout. Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}&lt;br /&gt;
{{w|Bayes' Theorem}} is an equation in statistics that gives the probability of a given hypothesis accounting not only for a single experiment or observation but also for your existing knowledge about the hypothesis, i.e. its prior probability. Randall's modified form of the equation also purports to account for the probability that you are indeed applying Bayes' Theorem itself correctly by including that as a term in the equation.&lt;br /&gt;
&lt;br /&gt;
Bayes' theorem is:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;P(H \mid X) = \frac{P(X \mid H) \, P(H)}{P(X)}&amp;lt;/math&amp;gt;,&lt;br /&gt;
where&lt;br /&gt;
*&amp;lt;math&amp;gt;P(H \mid X)&amp;lt;/math&amp;gt; is the probability that &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt;, the hypothesis, is true given observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt;. This is called the ''posterior probability''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(X \mid H)&amp;lt;/math&amp;gt; is the probability that observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; will appear given the truth of hypothesis &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt;. This term is often called the ''likelihood''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(H)&amp;lt;/math&amp;gt; is the probability that hypothesis &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is true before any observations. This is called the ''prior'', or ''belief''.&lt;br /&gt;
*&amp;lt;math&amp;gt;P(X)&amp;lt;/math&amp;gt; is the probability of the observation &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; regardless of any hypothesis might have produced it. This term is called the ''marginal likelihood''.&lt;br /&gt;
&lt;br /&gt;
The purpose of Bayesian inference is to discover something we want to know (how likely is it that our explanation is correct given the evidence we've seen) by mathematically expressing it in terms of things we can find out: how likely are our observations, how likely is our hypothesis ''a priori'', and how likely are we to see the observations we've seen assuming our hypothesis is true. A Bayesian learning system will iterate over available observations, each time using the likelihood of new observations to update its priors (beliefs) with the hope that, after seeing enough data points, the prior and posterior will converge to a single model.&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;P(C)=1&amp;lt;/math&amp;gt; the modified theorem reverts to the original Bayes' theorem (which makes sense, as a probability one would mean certainty that you are using Bayes' theorem correctly).&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;P(C)=0&amp;lt;/math&amp;gt; the modified theorem becomes &amp;lt;math&amp;gt;P(H \mid X) = P(H)&amp;lt;/math&amp;gt;, which says that the belief in your hypothesis is not affected by the result of the observation (which makes sense because you're certain you're misapplying the theorem so the outcome of the calculation shouldn't affect your belief.)&lt;br /&gt;
&lt;br /&gt;
This happens because the modified theorem can be rewritten as: &amp;lt;math&amp;gt;P(H \mid X) = (1-P(C))\,P(H) + P(C)\,\frac{P(X \mid H)\,P(H)}{P(X)}&amp;lt;/math&amp;gt;. This is the {{w|Linear interpolation|linear-interpolated}} weighted average of the belief you had before the calculation and the belief you would have if you applied the theorem correctly. This goes smoothly from not believing your calculation at all (keeping the same belief as before) if &amp;lt;math&amp;gt;P(C)=0&amp;lt;/math&amp;gt; to changing your belief exactly as Bayes' theorem suggests if &amp;lt;math&amp;gt;P(C)=1&amp;lt;/math&amp;gt;. (Note that &amp;lt;math&amp;gt;1-P(C)&amp;lt;/math&amp;gt; is the probability that you are using the theorem incorrectly.)&lt;br /&gt;
&lt;br /&gt;
The title text suggests that an additional term should be added for the probability that the Modified Bayes Theorem is correct. But that's ''this'' equation, so it would make the formula self-referential, unless we call the result the Modified Modified Bayes Theorem (or Modified&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;). It could also result in an infinite regress -- we'd need another term for the probability that the version with the probability added is correct, and another term for that version, and so on. If the modifications have a limit, then we can make that the Modified&amp;lt;sup&amp;gt;&amp;amp;omega;&amp;lt;/sup&amp;gt; Bayes Theorem, but then we need another term for whether we did ''that'' correctly, leading to the Modified&amp;lt;sup&amp;gt;&amp;amp;omega;+1&amp;lt;/sup&amp;gt; Bayes Theorem, and so on through every {{w|ordinal number}}. It's also unclear what the point of using an equation we're not sure of is (although sometimes we can: {{w|Newton's Laws}} are not as correct as Einstein's {{w|Theory of Relativity}} but they're a reasonable approximation in most circumstances. Alternatively, ask any student taking a difficult exam with a formula sheet.).&lt;br /&gt;
&lt;br /&gt;
If we denote the probability that the Modified&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; Bayes' Theorem is correct by &amp;lt;math&amp;gt;P(C_n)&amp;lt;/math&amp;gt;, then one way to define this sequence of modified Bayes' theorems is by the rule &amp;lt;math&amp;gt;P_n(H \mid X) := P_{n-1}(H \mid X) P(C_n) + (1-P(C_n))P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One can then show by induction that &amp;lt;math&amp;gt;P_n(H \mid X) = \prod_{i=1}^n P(C_i)\left(\frac{P(X \mid H)}{P(X)} - P(H) \right) + P(H).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If we assume that one doubts each step infinitely (that is, &amp;lt;math&amp;gt;P(C_i)&amp;lt;1&amp;lt;/math&amp;gt; for any &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt;), then we can calculate a limit.&lt;br /&gt;
&lt;br /&gt;
Without changing a limit, we can assume that &amp;lt;math&amp;gt;P(C_i) = p&amp;lt;/math&amp;gt; where &amp;lt;math&amp;gt;0&amp;lt;p&amp;lt;1&amp;lt;/math&amp;gt;. Then we can write a limit as:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\lim_{n \to \infty} P_n(H \mid X) =\lim_{n \to \infty} \prod_{i=1}^n p\left(\frac{P(X \mid H)}{P(X)} - P(H) \right) + P(H) =&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;=\lim_{n \to \infty} p^n\left(\frac{P(X \mid H)}{P(X)} - P(H)\right) ^n + P(H)=&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;=\lim_{n \to \infty} p^n q^n + P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where both &amp;lt;math&amp;gt;|p|&amp;lt;1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;|q|&amp;lt;1&amp;lt;/math&amp;gt;, so&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\lim_{n \to \infty} P_n(H \mid X) = 0 + P(H) = P(H)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This may interpreted as an universal truth that we have to trust ''something'' eventually, otherwise everything boils down to a unconditional belief.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
{{incomplete transcript|Do NOT delete this tag too soon.}}&lt;br /&gt;
&lt;br /&gt;
:Modified Bayes' theorem:&lt;br /&gt;
&lt;br /&gt;
:P(H|X) = P(H) × (1 + P(C) × ( P(X|H)/P(X) - 1 ))&lt;br /&gt;
&lt;br /&gt;
:H: Hypothesis&lt;br /&gt;
:X: Observation&lt;br /&gt;
:P(H): Prior probability that H is true&lt;br /&gt;
:P(X): Prior probability of observing X&lt;br /&gt;
:P(C): Probability that you're using Bayesian statistics correctly&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Statistics]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1276:_Angular_Size&amp;diff=164135</id>
		<title>1276: Angular Size</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1276:_Angular_Size&amp;diff=164135"/>
				<updated>2018-10-13T02:11:27Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 1276&lt;br /&gt;
| date      = October 11, 2013&lt;br /&gt;
| title     = Angular Size&lt;br /&gt;
| image     = angular size.png&lt;br /&gt;
| titletext = If the celestial sphere were mapped to the Earth's surface, astronomy would get a LOT easier; you'd just need a magnifying glass.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
This comic is a comparison of the {{w|angular diameter|angular diameters}} (or apparent diameter) of various celestial objects at the surface of the earth relative to a vertex at the center of the Earth as diagrammed in the opening panel. The objects' scales are compared to actual objects on earth. Each size given is for the object at its closest approach to earth.&lt;br /&gt;
&lt;br /&gt;
London's {{w|M25 motorway}} is around 60&amp;amp;nbsp;km (35&amp;amp;nbsp;miles) across, a {{w|soccer field}} is about 100&amp;amp;nbsp;meters long (109&amp;amp;nbsp;yards), a {{w|Table tennis table|ping pong table}} is 274&amp;amp;nbsp;centimeters long (9&amp;amp;nbsp;feet), a {{w|laptop}} is about 35&amp;amp;nbsp;centimeters across (13.75&amp;amp;nbsp;inches), the {{w|tilde}} symbol on a keyboard is about 5&amp;amp;nbsp;millimeters long (197&amp;amp;nbsp;mils), and a cell of ''{{w|Escherichia coli|E. coli}}'' is about 2&amp;amp;nbsp;microns long (78.75&amp;amp;nbsp;millionths of an inch).&lt;br /&gt;
&lt;br /&gt;
A simple {{w|Intercept theorem|formula}} can be used to find the size on earth of a celestial object when the size of or distance to the object is known. This is done by taking the radius of the earth, multiplying by the diameter of the object, and dividing by the distance to the object from the center of the earth.&lt;br /&gt;
&lt;br /&gt;
The space objects referenced in the panels are:&lt;br /&gt;
&lt;br /&gt;
*The {{w|Sun}} and the {{w|Moon}}, and also the open cluster {{w|Messier 25}}, have approximately the same size (around 0.5&amp;amp;nbsp;degrees of arc) when seen from the Earth.&lt;br /&gt;
&lt;br /&gt;
*{{w|Mercury (planet)|Mercury}}, {{w|Venus}}, {{w|Mars}}, {{w|Jupiter}}, {{w|Saturn}}, {{w|Uranus}}, and {{w|Neptune}} are the other planets of the {{w|Solar System}}.&lt;br /&gt;
&lt;br /&gt;
*{{w|Io (moon)|Io}}, {{w|Europa (moon)|Europa}}, {{w|Ganymede (moon)|Ganymede}}, and {{w|Callisto (moon)|Callisto}} are the main moons of Jupiter; {{w|Titan (moon)|Titan}} is the largest moon of Saturn; and {{w|Triton (moon)|Triton}} is the largest moon of Neptune. {{w|Ceres (dwarf planet)|Ceres}} and {{w|Pluto}} are {{w|dwarf planet}}s.&lt;br /&gt;
&lt;br /&gt;
*{{w|Phobos (moon)|Phobos}} and {{w|Deimos (moon)|Deimos}} are the moons of Mars. {{w|Eris (dwarf planet)|Eris}} is another dwarf planet. {{w|R Doradus}} and {{w|Betelgeuse}} are giant stars, respectively around 180 and 640&amp;amp;nbsp;light-years away. R Doradus is the star with the largest apparent diameter (other than the sun, of course).&lt;br /&gt;
&lt;br /&gt;
*{{w|4942 Munroe}} is an asteroid [http://blog.xkcd.com/2013/09/30/asteroid-4942-munroe/ named] after xkcd author [[Randall]] Munroe. {{w|Proxima Centauri}}, {{W|Alpha Centauri|Alpha Centauri AB}}, {{w|Barnard's star}} and {{w|Sirius}} are nearby stars (all within 10&amp;amp;nbsp;light-years from the Sun).&lt;br /&gt;
&lt;br /&gt;
*{{w|HD 189733 b}}, {{w|Gliese 581 g}}, {{w|Gliese 667 Cc}}, {{w|82 G. Eridani#Planetary_system|HD 20794 c}}, {{w|Tau Ceti#Planets|Tau Ceti c}}, and {{w|KOI-1686.01}} are {{w|extrasolar planet}}s; the parenthetical names are references to the comic [[1253: Exoplanet Names]]. However, some of the planets' parenthetical names do not match the table in the previous comic. For example, HD 20794 c is called &amp;quot;Legoland&amp;quot; rather than &amp;quot;Moonchild&amp;quot; in [[1253: Exoplanet Names]]. The {{w|black hole}} at the center of our Galaxy is {{w|Sagittarius A*}}, a massive object containing a mass more than 4&amp;amp;nbsp;million times of our Sun.&lt;br /&gt;
&lt;br /&gt;
*{{w|Voyager 1}} and {{w|Voyager 2|2}} are space probes launched in 1977, and currently around 125 and 100&amp;amp;nbsp;{{w|astronomical unit}}s away, respectively.&lt;br /&gt;
&lt;br /&gt;
The title text states that astronomy would be much easier if the celestial sphere were mapped to the earth - like a giant {{w|globe}}. Due to the distance of the stars you would just need magnifying glass to see the areas representing distant stars instead of an expensive powerful telescope to see huge distances.&lt;br /&gt;
&lt;br /&gt;
Approximate values for the mappings to the Earth sphere (based on mean Earth radius at 6,371.0&amp;amp;nbsp;km or 3,958.8&amp;amp;nbsp;mi.):&lt;br /&gt;
{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Panel&lt;br /&gt;
! Object&lt;br /&gt;
! Distance&lt;br /&gt;
! Diameter&lt;br /&gt;
! Size at Earth sphere&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;4&amp;quot;| Panel 1&lt;br /&gt;
|| {{w|Sun}}&lt;br /&gt;
|| 149,600,000&amp;amp;nbsp;km (9.296×10&amp;lt;sup&amp;gt;7&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1,392,684&amp;amp;nbsp;km (865,373.7&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 59.3&amp;amp;nbsp;km (36.8&amp;amp;nbsp;mi.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Moon}} &amp;lt;small&amp;gt;Semi-major axis&amp;lt;/small&amp;gt;&lt;br /&gt;
|| 384,399&amp;amp;nbsp;km (238,854&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3,476.28&amp;amp;nbsp;km (2,160.06&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 57.6&amp;amp;nbsp;km (35.8&amp;amp;nbsp;mi.)&lt;br /&gt;
|-&lt;br /&gt;
|| Moon &amp;lt;small&amp;gt;Perigee&amp;lt;/small&amp;gt;&lt;br /&gt;
|| 363,295&amp;amp;nbsp;km (225,741&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3,476.28&amp;amp;nbsp;km (2160.06&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 60.9&amp;amp;nbsp;km (37.8&amp;amp;nbsp;mi.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Messier 25}}&lt;br /&gt;
|| 2,100 light-years &amp;lt;br/&amp;gt; 19.867 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (12.158 × 10&amp;lt;sup&amp;gt;15&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 19 light-years &amp;lt;br/&amp;gt; 179.753 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (111.693 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 57.6&amp;amp;nbsp;km (35.8&amp;amp;nbsp;mi.)&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;7&amp;quot;| Panel 2&lt;br /&gt;
|| {{w|Mercury (planet)|Mercury}} (closest approach}&lt;br /&gt;
|| 92 million km (57 million mi.)&lt;br /&gt;
|| 4,879.4&amp;amp;nbsp;km (3,031.9&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.34&amp;amp;nbsp;km (370&amp;amp;nbsp;yd.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Venus}} (closest approach)&lt;br /&gt;
|| 41 million km (25 million mi.)&lt;br /&gt;
|| 12,103.6&amp;amp;nbsp;km (7,520.83&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.9&amp;amp;nbsp;km (1.2&amp;amp;nbsp;mi.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Mars}} (closest approach)&lt;br /&gt;
|| 56 million km (35 million mi.)&lt;br /&gt;
|| 6,792.4&amp;amp;nbsp;km (4,220.6&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.77&amp;amp;nbsp;km (840&amp;amp;nbsp;yd.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Jupiter}}&lt;br /&gt;
|| 778,547,200&amp;amp;nbsp;km (4.8377 × 10&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 139,822&amp;amp;nbsp;km (86,881.4&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.14&amp;amp;nbsp;km (1,250&amp;amp;nbsp;yd.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Saturn}}&lt;br /&gt;
|| 1,433,449,370&amp;amp;nbsp;km (1.5676 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 120,536&amp;amp;nbsp;km (74,897.6&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.54&amp;amp;nbsp;km (590&amp;amp;nbsp;yd.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Uranus}}&lt;br /&gt;
|| 2,876,679,082&amp;amp;nbsp;km (1.7875 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 51,118&amp;amp;nbsp;km (31,763&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.11&amp;amp;nbsp;km (120&amp;amp;nbsp;yd.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Neptune}}&lt;br /&gt;
|| 4,503,443,661&amp;amp;nbsp;km (2.7983 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 49,528&amp;amp;nbsp;km (30,775&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.07&amp;amp;nbsp;km (230&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;8&amp;quot;| Panel 3&lt;br /&gt;
|| {{w|Io}}&lt;br /&gt;
|| 778,547,200&amp;amp;nbsp;km (483.77 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3,643&amp;amp;nbsp;km (2,264&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 29.8&amp;amp;nbsp;m (74.8&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Europa}}&lt;br /&gt;
|| 778,547,200&amp;amp;nbsp;km (483.77 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3,122&amp;amp;nbsp;km (1,940&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 25.5&amp;amp;nbsp;m (83.7&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Ganymede}}&lt;br /&gt;
|| 778,547,200&amp;amp;nbsp;km (483.77 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 5,262&amp;amp;nbsp;km (3,270&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 43.1&amp;amp;nbsp;m (141&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Callisto}}&lt;br /&gt;
|| 778,547,200&amp;amp;nbsp;km (483.77 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 4,821&amp;amp;nbsp;km (2,996&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 39.5&amp;amp;nbsp;m (130&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Titan (moon)|Titan}}&lt;br /&gt;
|| 1,433,449,370&amp;amp;nbsp;km (890.7 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 5,150&amp;amp;nbsp;km (3,200&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 22.9&amp;amp;nbsp;m (75.1&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Triton}}&lt;br /&gt;
|| 4,503,443,661&amp;amp;nbsp;km (2.7983 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2,705.2&amp;amp;nbsp;km (1,680.9&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3.8&amp;amp;nbsp;m (12&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Ceres}} (perihelion)&lt;br /&gt;
|| 380,995,855&amp;amp;nbsp;km (236.74 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 974.6&amp;amp;nbsp;km (605.6&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 16.3&amp;amp;nbsp;m (53.5&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Pluto}} (perihelion)&lt;br /&gt;
|| 4,437,000,000&amp;amp;nbsp;km (2.757 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2,306&amp;amp;nbsp;km (1,433&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3.3&amp;amp;nbsp;m (11&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;6&amp;quot;| Panel 4&lt;br /&gt;
|| {{w|Phobos}}&lt;br /&gt;
|| 56 million km (35 million mi.)&lt;br /&gt;
|| 26.8 × 22.4 × 18.4&amp;amp;nbsp;km (16.7 × 13.9 × 11.4&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3.05&amp;amp;nbsp;m (10.0&amp;amp;nbsp;ft.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Deimos}}&lt;br /&gt;
|| 56 million km (35 million mi.)&lt;br /&gt;
|| 15 × 12.2 × 10.4&amp;amp;nbsp;km (9.3 × 7.58 × 6.46&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.71 m (5&amp;amp;nbsp;ft. 7&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Eris}} (perihelion)&lt;br /&gt;
|| 5.723 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (3.556 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2,326&amp;amp;nbsp;km (1,445&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2.59 m (8&amp;amp;nbsp;ft. 6&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| Eris (aphelion)&lt;br /&gt;
|| 14.602 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (9.0733 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2,326&amp;amp;nbsp;km (1,445&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.01 m (3&amp;amp;nbsp;ft. 3.8&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Betelgeuse}}&lt;br /&gt;
|| 643 ± 146 light-years &amp;lt;br/&amp;gt;max. 7.464 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (4.638 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 950–1,200 solar radii &amp;lt;br/&amp;gt;max. 1.671 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (1.038 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.43 m (4&amp;amp;nbsp;ft. 8.3&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|R Doradus}}&lt;br /&gt;
|| 178 ± 10 light-years &amp;lt;br/&amp;gt;max. 1.778 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (1.105 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 370 ± 50 solar radii &amp;lt;br/&amp;gt;max. 0.515 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (320 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.85 m (6&amp;amp;nbsp;ft. 0.8&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;6&amp;quot;| Panel 5&lt;br /&gt;
|| {{w|4942 Munroe}}&lt;br /&gt;
|| 2.2 AU (1.2 AU closest to earth, 179.4 × 10&amp;lt;sup&amp;gt;6&amp;amp;nbsp;km or 111.5 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 9–10&amp;amp;nbsp;km (5.6-6.2&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 35.5&amp;amp;nbsp;cm (14.0&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Proxima Centauri}}&lt;br /&gt;
|| 4.243 light-years &amp;lt;br/&amp;gt; 40.142 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (24.943 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.141 solar radii &amp;lt;br/&amp;gt; 0.196 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (122 × 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3.11&amp;amp;nbsp;cm (1.22&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Barnard's Star}}&lt;br /&gt;
|| 5.980 light-years &amp;lt;br/&amp;gt; 56.574 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (32.668 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.196 solar radii &amp;lt;br/&amp;gt; 0.272 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (169×10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 3.06&amp;amp;nbsp;cm (1.20&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Alpha Centauri B}}&lt;br /&gt;
|| 4.366 light-years &amp;lt;br/&amp;gt; 41.305 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (25.666 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.865 solar radii &amp;lt;br/&amp;gt; 1.204 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (748 × 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 18.6&amp;amp;nbsp;cm (7.32&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Sirius}}&lt;br /&gt;
|| 8.6 light-years &amp;lt;br/&amp;gt; 81.362 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (50.556 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.711 solar radii &amp;lt;br/&amp;gt; 2.382 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (1.480 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 18.7&amp;amp;nbsp;cm (7.36&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Alpha Centauri A}}&lt;br /&gt;
|| 4.366 light-years &amp;lt;br/&amp;gt; 41.305 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (25.666 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.227 solar radii &amp;lt;br/&amp;gt; 1.708 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (1.061 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 26.3&amp;amp;nbsp;cm (10.4&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
| rowspan=&amp;quot;9&amp;quot;| Panel 6&lt;br /&gt;
|| {{w|HD 189733}} b&lt;br /&gt;
|| 63 light-years &amp;lt;br/&amp;gt; 596.024 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (370.352 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.138 Jupiter radii &amp;lt;br/&amp;gt; 159,117&amp;amp;nbsp;km (98,870.7&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.7&amp;amp;nbsp;mm (67 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| Gliese 581 g&lt;br /&gt;
|| 20.3 light-years &amp;lt;br/&amp;gt; 192.052 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (119.336 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.3 to 2.0 Earth radii &amp;lt;br/&amp;gt; max. 25,484&amp;amp;nbsp;km (15,835&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.85&amp;amp;nbsp;mm (33 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Gliese 581}} (Parent star)&lt;br /&gt;
|| 20.3 light-years &amp;lt;br/&amp;gt; 192.052 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (119.336 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.29 solar radii &amp;lt;br/&amp;gt; 201,695&amp;amp;nbsp;km (125,411&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.34&amp;amp;nbsp;cm (528 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Sagittarius A*|Black hole at the center of our Galaxy}}&lt;br /&gt;
|| 25,900 light-years &amp;lt;br/&amp;gt; 245.032 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (152,260 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| Mass 4.31 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;lt;br/&amp;gt;12.684 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (7.8815 × 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.33&amp;amp;nbsp;mm (13 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Gliese 667}} Cc&lt;br /&gt;
|| 22.7 light-years &amp;lt;br/&amp;gt; 214.757 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (133.444 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 2.0 Earth radii &amp;lt;br/&amp;gt; 25,484&amp;amp;nbsp;km (15,835&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.76&amp;amp;nbsp;mm (30 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| Gliese 667 (Parent star)&lt;br /&gt;
|| 22.7 light-years &amp;lt;br/&amp;gt; 214.757 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (133.444 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.42 solar radii &amp;lt;br/&amp;gt; 584,927&amp;amp;nbsp;km (363,457&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 1.74&amp;amp;nbsp;cm (685 mils)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|HD 20794}} c (Parent star)&lt;br /&gt;
|| 20 light-years &amp;lt;br/&amp;gt; 189.214 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (117.572 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.92 solar radii &amp;lt;br/&amp;gt; 1,281,269&amp;amp;nbsp;km (796,143.6&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 4.31&amp;amp;nbsp;cm (1.70&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Tau Ceti}} C (Parent star)&lt;br /&gt;
|| 11.905 light-years &amp;lt;br/&amp;gt; 112.629 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (69.9844 × 10&amp;lt;sup&amp;gt;12&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.793 solar radii &amp;lt;br/&amp;gt; 1,104,398&amp;amp;nbsp;km (686,241.1&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 6.25&amp;amp;nbsp;cm (2.46&amp;amp;nbsp;in.)&lt;br /&gt;
|-&lt;br /&gt;
|| {{w|Koi-1686.01}} (Parent star)&lt;br /&gt;
|| 1033.8 light-years &amp;lt;br/&amp;gt; 9.780 × 10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (6.077×10&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.52 solar radii &amp;lt;br/&amp;gt; 724,195&amp;amp;nbsp;km (449,994&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 0.47&amp;amp;nbsp;mm (19 mils)&lt;br /&gt;
|-&lt;br /&gt;
| Panel 7&lt;br /&gt;
|| Voyager probes&lt;br /&gt;
|| ({{w|Voyager 1}} at 126.10 AU) 18.86 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;km (11.72 × 10&amp;lt;sup&amp;gt;9&amp;lt;/sup&amp;gt;&amp;amp;nbsp;mi.)&lt;br /&gt;
|| 20 meters (66&amp;amp;nbsp;ft.) (with antennas)&lt;br /&gt;
|| 6.76&amp;amp;nbsp;µm (266 × 10&amp;lt;sup&amp;gt;&amp;amp;minus;6&amp;lt;/sup&amp;gt;&amp;amp;nbsp;in.)&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===Remarks===&lt;br /&gt;
A {{w|Football_pitch#Pitch_boundary|professional soccer field}} is 105 × 68 meters, but the depicted soccer field is about 93 × 61 meters (based on the size of the center circle which has a diameter of 20 yards). However, according to the angular diameter of the referenced celestial objects, Randall did his calculations using the 105 × 68 meter dimensions.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:The size of the part of Earth's surface directly under various space objects&lt;br /&gt;
:[Several images are shown, of space objects of differing size and at different distances from Earth, illustrating the differing sizes of their &amp;quot;shadows&amp;quot; as mapped onto Earth's surface viewed from the center of the Earth.]&lt;br /&gt;
&lt;br /&gt;
:[The first image merely sets the stage: Earth is a full circle, with two figures — Cueball and Megan — standing on it; a small space object casts a &amp;quot;shadow&amp;quot; on Megan, while a slightly larger object, though proportionally farther away, casts just about the same size shadow next to Cueball.]&lt;br /&gt;
&lt;br /&gt;
:[The second image is a map showing London, with the Thames running through it, and a ring highway running around it labeled &amp;quot;London's M25 Orbital Freeway&amp;quot;. A grey circle is overlaid, just about the diameter of the M25; it is labeled &amp;quot;The Sun and The Moon (about the same size)&amp;quot;.]&lt;br /&gt;
&lt;br /&gt;
:[The third image has a small grey rectangle in one corner labeled &amp;quot;Soccer field&amp;quot; for comparison. The image is dominated by four large, grey circles, considerably larger than the soccer field, labeled &amp;quot;Saturn&amp;quot;, &amp;quot;Mars&amp;quot;, &amp;quot;Jupiter&amp;quot;, and &amp;quot;Venus&amp;quot;, with Mars slightly larger than Saturn, Jupiter approximately twice the diameter of Saturn, and Venus approximately three times the diameter of Saturn. Smaller circles are labeled &amp;quot;Mercury&amp;quot;, &amp;quot;Uranus&amp;quot;, and &amp;quot;Neptune&amp;quot;, with Mercury still somewhat larger than the soccer field, Uranus about its size, and Neptune slightly smaller.]&lt;br /&gt;
&lt;br /&gt;
:[The fourth image has the soccer field blown up to take up much of the view; its center circle, goal areas, and corner kick areas are visible. Labeled grey circles of various circles are again overlain: Callisto and Ganymede are about as large as one half of the field; Io, Titan, and Europa are somewhat smaller than half the field; and Ceres, Triton, and Pluto are much smaller (all three together would probably fit into the soccer field's center circle).]&lt;br /&gt;
&lt;br /&gt;
:[In the fifth image, there is a different grey rectangle, this one labeled &amp;quot;Ping Pong table&amp;quot;, with a few balls and paddles visible. An irregular ovoid labeled &amp;quot;Phobos&amp;quot; is about the size of the table, as is a circle labeled &amp;quot;R. Doradus&amp;quot;. An irregular circular shape labeled &amp;quot;Deimos&amp;quot; is about the size of half the table; a circle labeled &amp;quot;Betelgeuse&amp;quot; is a little smaller, and a circle labeled &amp;quot;Eris&amp;quot; is a little smaller, though still comfortably filling most of half of the table.]&lt;br /&gt;
&lt;br /&gt;
:[In the sixth image, a light grey image of laptop computer keyboard and screen is shown, viewed from directly above. An irregular shape labeled &amp;quot;4942 Munroe&amp;quot; is slightly larger than the laptop, while circles labeled &amp;quot;Alpha Centauri A&amp;quot;, &amp;quot;Sirius&amp;quot;, and &amp;quot;Alpha Centauri B&amp;quot; form a descending series somewhat smaller than it. Circles labeled &amp;quot;Proxima Centauri&amp;quot; and &amp;quot;Barnard's Star&amp;quot; are considerably smaller than the laptop: Proxima Centauri would fit on the trackpad, while Barnard's Star covers perhaps four keys on the keyboard.]&lt;br /&gt;
&lt;br /&gt;
:[In the seventh image we see a greatly zoomed-in shape which is identified as the &amp;quot;Tilde on laptop keyboard&amp;quot;. A circle labeled &amp;quot;HD 189733 b (permadeath)&amp;quot; is almost as large as the tilde is wide; a circle labeled &amp;quot;Tau Ceti C (giant dog planet)&amp;quot; is somewhat smaller. Circles labeled &amp;quot;Gleise 581 g (jelly-filled planet)&amp;quot;, &amp;quot;Gleise 667 C c (PILF)&amp;quot;, and &amp;quot;HD 20794 c (moonchild)&amp;quot; are all 1/2 to 1/3 as wide as the tilde is wide. A smaller circle labeled &amp;quot;Event horizon of the black hole at the center of our galaxy&amp;quot; fits comfortably within the tilde's stroke width. A very small dot off in one corner (much smaller than the tilde or anything else in the image) is labeled &amp;quot;KOI-1686.01 (emergency backup earth)&amp;quot;.]&lt;br /&gt;
&lt;br /&gt;
:[Finally, in the eighth image, the size comparison is to the grey outlines of four bacilliform bacteria labeled &amp;quot;E. coli&amp;quot;. The outlines of two interstellar probes are shown, with circular main housings and protruding instruments and antennae. They are labeled &amp;quot;Voyager 1&amp;quot; and &amp;quot;Voyager 2&amp;quot;.]&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
[[Category:Math]]&lt;br /&gt;
[[Category:Astronomy]]&lt;br /&gt;
[[Category:Exoplanets]]&lt;br /&gt;
[[Category:Soccer]]&lt;br /&gt;
[[Category:Space probes]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:2057:_Internal_Monologues&amp;diff=163948</id>
		<title>Talk:2057: Internal Monologues</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:2057:_Internal_Monologues&amp;diff=163948"/>
				<updated>2018-10-10T15:17:17Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: mathematicians&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--&amp;gt;&lt;br /&gt;
&lt;br /&gt;
No maths? Too bad...&lt;br /&gt;
&lt;br /&gt;
[[Special:Contributions/141.101.77.116|141.101.77.116]] 14:39, 10 October 2018 (UTC)Some Nerd&lt;br /&gt;
&lt;br /&gt;
:Mathematicians don't need to wonder why, they can show their working. [[Special:Contributions/141.101.77.140|141.101.77.140]] 15:17, 10 October 2018 (UTC)&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2056:_Horror_Movies&amp;diff=163891</id>
		<title>2056: Horror Movies</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2056:_Horror_Movies&amp;diff=163891"/>
				<updated>2018-10-09T09:36:10Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */ editing to make more concise&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2056&lt;br /&gt;
| date      = October 8, 2018&lt;br /&gt;
| title     = Horror Movies&lt;br /&gt;
| image     = horror_movies.png&lt;br /&gt;
| titletext = &amp;quot;Isn't the original Jurassic Park your favorite movie of all time?&amp;quot; &amp;quot;Yes, but that's because I like dinosaurs and I WANT there to be an island full of them. If John Hammond's lab had been breeding serial killers in creepy masks, I wouldn't have watched!&amp;quot; &amp;quot;Wait, are you sure? That could actually be good.&amp;quot; &amp;quot;Ok, I WOULD watch the scenes where Jeff Goldblum tries to convince a bunch of executives that the park is a bad idea.&amp;quot;&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{incomplete|Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}&lt;br /&gt;
&lt;br /&gt;
{{w|Horror_film|Horror movies}} are a {{w|Film_genre|genre}} of {{w|movie|movie or film}} which attempts to elicit the emotional response of {{w|fear}} in the viewer.  Some enjoy that type of movie because it allows them to experience and release that emotion, perhaps as a form of {{w|catharsis}} or release.  Others take a more detached view and enjoy watching bad things happen to other people, perhaps deriving humor or enjoyment out of a situation that they are glad not to be in themselves.&lt;br /&gt;
&lt;br /&gt;
[[Randall]], represented by [[Cueball]], states that he simply does not understand why people would want to watch a movie whose themes and intended emotions are steeped in such negativity. While he fully admits he is criticizing from a position of ignorance (and tries his best not to think less of horror movie fans) he still cannot wrap his head around them.&lt;br /&gt;
&lt;br /&gt;
The title text refers to the ''{{w|Jurassic Park (film)|Jurassic Park film}}'', which could be considered a &amp;quot;horror&amp;quot; film as there are elements of fear and terror, especially when the dinosaurs Randall loves so much are chasing and eating humans. However, it is usually placed in the adventure or science fiction genre. Randall, instead of claiming that ''Jurassic Park'' isn't a horror film, replies by saying that he likes dinosaurs and would be pleased to visit an amusement park about dinosaurs. An amusement park about &amp;quot;Serial killers in creepy masks&amp;quot; refers to a horror movie trope from the ''{{w|Halloween (franchise)|Halloween}}'' and the ''{{w|Friday the 13th (franchise)|Friday the 13th}}'' series of films, among others. Randall's final comment indicates that though he does not like horror films, he does like {{w|Jeff Goldblum}} (who portrays {{w|Ian Malcolm (Jurassic Park character)|Ian Malcolm}} in the film), and would watch his attempts to prevent the brilliant idea of breeding serial killers.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[White Hat and Cueball are standing together and talking. White Hat points at Cueball who has raised his arms.]&lt;br /&gt;
:White Hat: Wanna see a horror movie?&lt;br /&gt;
:Cueball: Sure! I love watching terrible things happen to people and feeling afraid!&lt;br /&gt;
&lt;br /&gt;
:[Caption below the frame:]&lt;br /&gt;
:I know everyone's into what they're into, but I have never understood horror movies.&lt;br /&gt;
&lt;br /&gt;
== Trivia ==&lt;br /&gt;
In early issues, [[Randall]] frequently referenced his fear of [[:Category:Velociraptors|velociraptors]].&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Comics featuring White Hat]]&lt;br /&gt;
[[Category:Jurassic Park]]&lt;br /&gt;
[[Category:Dinosaurs]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1047:_Approximations&amp;diff=163868</id>
		<title>1047: Approximations</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1047:_Approximations&amp;diff=163868"/>
				<updated>2018-10-08T23:35:44Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 1047&lt;br /&gt;
| date      = April 25, 2012&lt;br /&gt;
| title     = Approximations&lt;br /&gt;
| image     = approximations.png&lt;br /&gt;
| titletext = Two tips: 1) 8675309 is not just prime, it's a twin prime, and 2) if you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
This comic lists some approximations for numbers, most of them mathematical and physical constants, but some of them jokes and cultural references.&lt;br /&gt;
&lt;br /&gt;
Approximations like these are sometimes used as {{w|mnemonic}}s by mathematicians and physicists, though most of Randall's approximations are too convoluted to be useful as mnemonics.  Perhaps the best known mnemonic approximation (though not used here by Randall) is that &amp;quot;π is approximately equal to 22/7&amp;quot;.  Randall does mention (and mock) the common mnemonic among physicists that the {{w|fine structure constant}} is approximately 1/137.  Although Randall gives approximations for the number of seconds in a year, he does not mention the common physicists' mnemonic that it is &amp;quot;π × 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt;&amp;quot;, though he later added a statement to the top of the comic page addressing this point. &lt;br /&gt;
&lt;br /&gt;
At the bottom of the comic are expressions involving {{w|transcendental numbers}} (namely π and e) that are tantalizingly close to being exactly true but are not (indeed, they cannot be, due to the nature of transcendental numbers).  Such near-equations were previously discussed in [[217: e to the pi Minus pi]].  One of the entries, though, is a &amp;quot;red herring&amp;quot; that is exactly true.  &lt;br /&gt;
&lt;br /&gt;
Randall says he compiled this table through &amp;quot;a mix of trial-and-error, ''{{w|Mathematica}}'', and Robert Munafo's [http://mrob.com/pub/ries/ Ries] tool.&amp;quot;  &amp;quot;Ries&amp;quot; is a &amp;quot;{{w|Closed-form expression#Conversion from numerical forms|reverse calculator}}&amp;quot; that forms equations matching a given number.&lt;br /&gt;
&lt;br /&gt;
The {{w|world population}} estimate for 2017 is still accurate. The estimate is 7.4 billion, and the population listed at the website census.gov is roughly the same. The current value can be found here: [https://www.census.gov/popclock/ United States Census Bureau - U.S. and World Population Clock]. Nevertheless there are other numbers listed by different sources.&lt;br /&gt;
&lt;br /&gt;
The first part of the title text notes that &amp;quot;Jenny's constant,&amp;quot; which is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}, is not only prime but a {{w|twin prime}} because 8675311 is also a prime. Twin primes have always been a subject of interest, because they are comparatively rare, and because it is not yet known whether there are infinitely many of them.  Twin primes were also referenced in [[1310: Goldbach Conjectures]]. &lt;br /&gt;
&lt;br /&gt;
The second part of the title text makes fun of the unusual mathematical operations contained in the comic.  {{w|Pi|π}} is a useful number in many contexts, but it doesn't usually occur anywhere in an exponent. Even when it does, such as with complex numbers, taking the πth root is rarely helpful.  Similarly, {{w|e (mathematical constant)|e}} typically appears in the basis of a power (forming the {{w|exponential function}}), not in the exponent. (This is later referenced in [http://what-if.xkcd.com/73/ Lethal Neutrinos]).&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Thing to be approximated:&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Formula proposed&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Resulting approximate value&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Correct value&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Discussion&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|One {{w|light year}} (meters)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|99&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|9,227,446,944,279,201&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|9,460,730,472,580,800 (exact)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Based on 365.25 days per year (see below). 99&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt; and 69&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt; are sexual references. &lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Earth's surface (m&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|69&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|513,798,374,428,641&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|5.10072 × 10&amp;lt;sup&amp;gt;14&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|99&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt; and 69&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt; are sexual references.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Oceans' volume (m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|9&amp;lt;sup&amp;gt;19&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1,350,851,717,672,992,089&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.332 × 10&amp;lt;sup&amp;gt;18&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Seconds in a year&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|75&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|31,640,625&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|31,557,600 (Julian calendar), 31,556,952 (Gregorian calendar)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|After this comic was released [[Randall]] got many responses by viewers. So he did add this statement to the top of the comic page:&lt;br /&gt;
&amp;quot;Lots of emails mention the physicist favorite, 1 year = pi × 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; seconds. 75&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; is a hair more accurate, but it's hard to top 3,141,592's elegance.&amp;quot; π × 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; is nearly equal to 31,415,926.536, and 75&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; is exactly 31,640,625. Randall's elegance belongs to the number π, but it should be multiplied by the factor of ten.&lt;br /&gt;
&lt;br /&gt;
Using the traditional definitions that a second is 1/60 of a minute, a minute is 1/60 of an hour, and an hour is 1/24 of a day, a 365-day common year is exactly 31,536,000 seconds (the &amp;quot;''Rent'' method&amp;quot; approximation) and the 366-day leap year is 31,622,400 seconds. Until the calendar was reformed by Pope Gregory, there was one leap year in every four years, making the average year 365.25 days, or 31,557,600 seconds. On the current calendar system, there are only 97 leap years in every 400 years, making the average year 365.2425 days, or 31,556,952 seconds. In technical usage, a &amp;quot;second&amp;quot; is now defined based on physical constants, even though the length of a day varies inversely with the changing angular velocity of the earth.  To keep the official time synchronized with the rotation of the earth, a &amp;quot;leap second&amp;quot; is occasionally added, resulting in a slightly longer year.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Seconds in a year (''Rent'' method)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|525,600 × 60&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|31,536,000&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|31,557,600 (Julian calendar), 31,556,952 (Gregorian calendar)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&amp;quot;''Rent'' Method&amp;quot; refers to the song &amp;quot;{{w|Seasons of Love}}&amp;quot; from the musical ''{{w|Rent (musical)|Rent}}''. The song asks, &amp;quot;How do you measure a year?&amp;quot; One line says &amp;quot;525,600 minutes&amp;quot; while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Age of the universe (seconds)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|15&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|437,893,890,380,859,375&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|4.354 ± 0.012 × 10&amp;lt;sup&amp;gt;17&amp;lt;/sup&amp;gt; (best estimate; exact value unknown)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|This one will slowly get more accurate as the universe ages.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Planck's constant&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {1} {30^{\pi^e}}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.6849901410 × 10&amp;lt;sup&amp;gt;−34&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.62606957 × 10&amp;lt;sup&amp;gt;−34&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Informally, the {{w|Planck constant}} is the smallest action possible in quantum mechanics.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Fine structure constant&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{1}{140}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.00&amp;lt;span style=&amp;quot;text-decoration: overline;&amp;quot;&amp;gt;714285&amp;lt;/span&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.0072973525664 (accepted value as of 2014), close to 1/137&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|fine structure constant}} indicates the strength of electromagnetism. It is unitless and around 0.007297, close to 1/137. At one point it was believed to be exactly the reciprocal of 137, and many people have tried to find a simple formula explaining this (with a pinch of {{w|numerology}} thrown in at times), including the infamous {{w|Arthur Eddington|Sir Arthur Adding-One}}.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Fundamental charge&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {3} {14 \pi^{\pi^\pi}}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.59895121062716 × 10&amp;lt;sup&amp;gt;−19&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.602176565 × 10&amp;lt;sup&amp;gt;−19&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|This is the charge of the proton, symbolized ''e'' for electron (whose charge is actually −''e''. You can blame Benjamin Franklin [[567|for that]].)&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Telephone number for the {{w|White House}} switchboard&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {1} {e^ {\sqrt[\pi] {1 + \sqrt[e-1] 8}} }&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.2024561414&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|202-456-1414&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Jenny's constant&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\left( 7^ {\frac{e}{1} - \frac{1}{e}} - 9 \right) \pi^2&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|867.5309019&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|867-5309&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|A telephone number referenced in {{w|Tommy Tutone}}'s 1982 song {{w|867-5309/Jenny}}. As mentioned in the title text, the number not only prime but a {{w|twin prime}} because 8675311 is also a prime. &lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|World population estimate (billions)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Equivalent to &amp;lt;math&amp;gt;6 + \frac {\frac34 y + \frac14 (y \operatorname{mod} 4) - 1499} {10}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2005 — 6.5&amp;lt;br&amp;gt;&lt;br /&gt;
2006 — 6.6&amp;lt;br&amp;gt;&lt;br /&gt;
2007 — 6.7&amp;lt;br&amp;gt;&lt;br /&gt;
2008 — 6.7&amp;lt;br&amp;gt;&lt;br /&gt;
2009 — 6.8&amp;lt;br&amp;gt;&lt;br /&gt;
2010 — 6.9&amp;lt;br&amp;gt;&lt;br /&gt;
2011 — 7.0&amp;lt;br&amp;gt;&lt;br /&gt;
2012 — 7.0&amp;lt;br&amp;gt;&lt;br /&gt;
2013 — 7.1&amp;lt;br&amp;gt;&lt;br /&gt;
2014 — 7.2&amp;lt;br&amp;gt;&lt;br /&gt;
2015 — 7.3&amp;lt;br&amp;gt;&lt;br /&gt;
2016 — 7.3&amp;lt;br&amp;gt;&lt;br /&gt;
2017 — 7.4&amp;lt;br&amp;gt;&lt;br /&gt;
2018 — 7.5&amp;lt;br&amp;gt;&lt;br /&gt;
2019 — 7.6&amp;lt;br&amp;gt;&lt;br /&gt;
2020 — 7.6&amp;lt;br&amp;gt;&lt;br /&gt;
2021 — 7.7&amp;lt;br&amp;gt;&lt;br /&gt;
2022 — 7.8&amp;lt;br&amp;gt;&lt;br /&gt;
2023 — 7.9&amp;lt;br&amp;gt;&lt;br /&gt;
2024 — 7.9&amp;lt;br&amp;gt;&lt;br /&gt;
2025 — 8.0&amp;lt;br&amp;gt;&lt;br /&gt;
2026 — 8.1&amp;lt;br&amp;gt;&lt;br /&gt;
2027 — 8.2&amp;lt;br&amp;gt;&lt;br /&gt;
2028 — 8.2&amp;lt;br&amp;gt;&lt;br /&gt;
2029 — 8.3&amp;lt;br&amp;gt;&lt;br /&gt;
2030 — 8.4&amp;lt;br&amp;gt;&lt;br /&gt;
2031 — 8.5&amp;lt;br&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Grows by 75 million every year on average.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|U.S. population estimate (millions)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Equivalent to &amp;lt;math&amp;gt;310 + 3(y - 2010)&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2000 — 280&amp;lt;br&amp;gt;&lt;br /&gt;
2001 — 283&amp;lt;br&amp;gt;&lt;br /&gt;
2002 — 286&amp;lt;br&amp;gt;&lt;br /&gt;
2003 — 289&amp;lt;br&amp;gt;&lt;br /&gt;
2004 — 292&amp;lt;br&amp;gt;&lt;br /&gt;
2005 — 295&amp;lt;br&amp;gt;&lt;br /&gt;
2006 — 298&amp;lt;br&amp;gt;&lt;br /&gt;
2007 — 301&amp;lt;br&amp;gt;&lt;br /&gt;
2008 — 304&amp;lt;br&amp;gt;&lt;br /&gt;
2009 — 307&amp;lt;br&amp;gt;&lt;br /&gt;
2010 — 310&amp;lt;br&amp;gt;&lt;br /&gt;
2011 — 313&amp;lt;br&amp;gt;&lt;br /&gt;
2012 — 316&amp;lt;br&amp;gt;&lt;br /&gt;
2013 — 319&amp;lt;br&amp;gt;&lt;br /&gt;
2014 — 322&amp;lt;br&amp;gt;&lt;br /&gt;
2015 — 325&amp;lt;br&amp;gt;&lt;br /&gt;
2016 — 328&amp;lt;br&amp;gt;&lt;br /&gt;
2017 — 331&amp;lt;br&amp;gt;&lt;br /&gt;
2018 — 334&amp;lt;br&amp;gt;&lt;br /&gt;
2019 — 337&amp;lt;br&amp;gt;&lt;br /&gt;
2020 — 340&amp;lt;br&amp;gt;&lt;br /&gt;
2021 — 343&amp;lt;br&amp;gt;&lt;br /&gt;
2022 — 346&amp;lt;br&amp;gt;&lt;br /&gt;
2023 — 349&amp;lt;br&amp;gt;&lt;br /&gt;
2024 — 352&amp;lt;br&amp;gt;&lt;br /&gt;
2025 — 355&amp;lt;br&amp;gt;&lt;br /&gt;
2026 — 358&amp;lt;br&amp;gt;&lt;br /&gt;
2027 — 361&amp;lt;br&amp;gt;&lt;br /&gt;
2028 — 364&amp;lt;br&amp;gt;&lt;br /&gt;
2029 — 367&amp;lt;br&amp;gt;&lt;br /&gt;
2030 — 370&amp;lt;br&amp;gt;&lt;br /&gt;
2031 — 373&amp;lt;br&amp;gt;&lt;br /&gt;
2032 — 376&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Grows by 3 million each year.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Electron rest energy (joules)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {e} {7^{16}}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|8.17948276564429 × 10&amp;lt;sup&amp;gt;−14&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|8.18710438 × 10&amp;lt;sup&amp;gt;−14&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Light year (miles)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2&amp;lt;sup&amp;gt;42.42&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|5,884,267,614,436.97&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|5,878,625,373,183.61 = 9,460,730,472,580,800 (meters in a light-year, by definition) / 1609.344 (meters in a mile)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|{{w|42 (number)|42}} is, according to {{w|Douglas Adams}}' ''{{w|The Hitchhiker's Guide to the Galaxy}}'', the answer to the Ultimate Question of Life, the Universe, and Everything.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sin\left(60^\circ\right) = \frac {\sqrt 3} {2}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{e}{\pi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.8652559794&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.8660254038&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sqrt 3&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{2e}{\pi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.7305119589&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.7320508076&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Same as the above&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|γ (Euler's gamma constant)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {1} {\sqrt 3}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5773502692&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5772156649&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|Euler–Mascheroni constant}} (denoted γ) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Feet in a meter&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {5} {\sqrt[e]\pi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|3.2815481951&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|3.280839895&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Exactly 1/0.3048, as the {{w|international foot}} is defined as 0.3048 meters.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sqrt 5&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{2}{e} + \frac32&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2.2357588823&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2.2360679775&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Avogadro's number&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;69^{\pi^\sqrt{5}}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.02191201246329 × 10&amp;lt;sup&amp;gt;23&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.02214129 × 10&amp;lt;sup&amp;gt;23&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Also called a mole for shorthand, {{w|Avogadro's number}} is (roughly) the number of individual atoms in 12 grams of pure carbon. Used in basically every application of chemistry.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Gravitational constant ''G''&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {1} {e ^ {(\pi-1)^{(\pi+1)}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.6736110685 × 10&amp;lt;sup&amp;gt;−11&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.67385 × 10&amp;lt;sup&amp;gt;−11&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The universal {{w|gravitational constant}} G is equal to ''Fr''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/''Mm'', where ''F'' is the gravitational force between two objects, ''r'' is the distance between them, and ''M'' and ''m'' are their masses.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|''R'' (gas constant)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;(e + 1) \sqrt 5&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|8.3143309279&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|8.3144622&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|gas constant}} relates energy to temperature in physics, as well as a gas's volume, pressure, temperature and {{w|mole (unit)|molar amount}} (hence the name).&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Proton–electron mass ratio&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;6 \pi^5&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1836.1181087117&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1836.15267246&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Liters in a {{w|gallon}}&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;3 + \frac{\pi}{4}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|3.7853981634&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|3.785411784 (exact)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|A U.S. liquid gallon is defined by law as 231 cubic inches&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|''g''&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt; or ''g''&amp;lt;sub&amp;gt;n&amp;lt;/sub&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6 + ln(45)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|9.8066624898&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|9.80665&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|Standard gravity, or standard acceleration due to free fall is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665&amp;amp;nbsp;m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, which is exactly 35.30394&amp;amp;nbsp;km/h/s (about 32.174&amp;amp;nbsp;ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, or 21.937&amp;amp;nbsp;mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5 percent greater at the poles than at the equator.&lt;br /&gt;
&lt;br /&gt;
Randall used a letter ''g'' without a suffix, which can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Proton–electron mass ratio&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {e^8 - 10} {\phi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1836.1530151398&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1836.15267246&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|φ is the {{w|golden ratio}}, or &amp;lt;math&amp;gt;\textstyle{ \frac{1+\sqrt 5}{2} }&amp;lt;/math&amp;gt;. It has many interesting geometrical properties.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Ruby laser wavelength (meters)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{1}{1200^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6.9&amp;lt;span style=&amp;quot;text-decoration: overline;&amp;quot;&amp;gt;444&amp;lt;/span&amp;gt; × 10&amp;lt;sup&amp;gt;−7&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|~6.943&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|ruby laser}} wavelength varies because &amp;quot;ruby&amp;quot; is not clearly defined.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Mean Earth radius (meters)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;5^8 6e&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6,370,973.035&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6,371,008.7 (IUGG definition)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|Earth radius#mean radii|mean earth radius}} varies because there is not one single way to make a sphere out of the earth. Randall's value lies within the actual variation of Earth's radius. The International Union of Geodesy and Geophysics (IUGG) defines the mean radius as 2/3 of the equatorial radius (6,378,137.0&amp;amp;nbsp;m) plus 1/3 of the polar radius (6,356,752.3&amp;amp;nbsp;m).&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sqrt 2&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac35 + \frac{\pi}{7-\pi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.4142200581&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.4142135624&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|There are recurring math jokes along the lines of, &amp;quot;&amp;lt;math&amp;gt;\textstyle{ \frac35 + \frac{\pi}{7-\pi} - \sqrt{2} = 0}&amp;lt;/math&amp;gt;, but your calculator is probably not good enough to compute this correctly&amp;quot;. See also [[217: e to the pi Minus pi]].&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac12&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5 (exact)&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|This is the exactly correct equation referred to in the note, &amp;quot;Pro tip – Not all of these are wrong&amp;quot;, as shown below and also [http://math.stackexchange.com/questions/140388/how-can-one-prove-cos-pi-7-cos3-pi-7-cos5-pi-7-1-2 here]. If you're still confused, the functions use {{w|radians}}, not {{w|degrees (angle)|degrees}}.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|γ (Euler's gamma constant)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac{e}{3^4} + \frac{e}{5}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5772154006&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|0.5772156649&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|The {{w|Euler–Mascheroni constant}} (denoted γ) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sqrt 5&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\frac {13+4\pi} {24-4\pi}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2.2360678094&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2.2360679775&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\sum_{n=1}^{\infty} \frac{1}{n^n}&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|&amp;lt;math&amp;gt;\ln(3)^e&amp;lt;/math&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.2912987577&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1.2912859971&lt;br /&gt;
|align=&amp;quot;left&amp;quot;|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===Proof===&lt;br /&gt;
&lt;br /&gt;
One of the &amp;quot;approximations&amp;quot; actually is precisely correct: &amp;lt;math&amp;gt;\textstyle{ \cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7} = \frac12 }&amp;lt;/math&amp;gt;.  Here is a proof:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Multiplying by 1 (or by a number divided by itself) leaves the equation unchanged: &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;= \left( \cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7} \right) \frac{2 \sin\frac{\pi}{7}}{2 \sin\frac{\pi}{7}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The &amp;lt;math&amp;gt;\textstyle{ 2 \sin\frac{\pi}{7} }&amp;lt;/math&amp;gt; on the top of the fraction is multiplied through the original equation:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;= \frac {2 \cos \frac{\pi}{7} \sin\frac{\pi}{7} + 2 \cos \frac{3\pi}{7} \sin\frac{\pi}{7} + 2 \cos \frac{5\pi}{7} \sin\frac{\pi}{7}} {2 \sin\frac{\pi}{7}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Use the trigonometric identity &amp;lt;math&amp;gt;\textstyle{ 2 \cos A \sin B = \sin (A+B) - \sin(A-B)}&amp;lt;/math&amp;gt; on the second and third terms in the numerator:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\begin{align}&lt;br /&gt;
&amp;amp;= \frac {2 \cos \frac{\pi}{7} \sin \frac{\pi}{7} + \left[\sin \left(\frac{3\pi}{7} + \frac{\pi}{7}\right) - \sin \left(\frac{3\pi}{7} - \frac{\pi}{7}\right) \right] + \left[\sin \left(\frac{5\pi}{7} + \frac{\pi}{7}\right) - \sin \left(\frac{5\pi}{7} - \frac{\pi}{7}\right) \right]} {2 \sin\frac{\pi}{7}} \\&lt;br /&gt;
&amp;amp;= \frac {2 \cos \frac{\pi}{7} \sin \frac{\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{2\pi}{7} \right] + \left[\sin \frac{6\pi}{7} - \sin \frac{4\pi}{7} \right]} {2 \sin\frac{\pi}{7}}&lt;br /&gt;
\end{align}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Use the trigonometric identity &amp;lt;math&amp;gt;\textstyle{ 2 \cos A \sin A = \sin 2A }&amp;lt;/math&amp;gt; on the first term in the numerator:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\begin{align}&lt;br /&gt;
&amp;amp;= \frac {\sin \frac{2\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{2\pi}{7} \right] + \left[\sin \frac{6\pi}{7} - \sin \frac{4\pi}{7} \right]} {2 \sin\frac{\pi}{7}} \\&lt;br /&gt;
&amp;amp;= \frac {\sin \frac{6\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{4\pi}{7} \right] + \left[\sin \frac{2\pi}{7} - \sin \frac{2\pi}{7} \right]} {2 \sin\frac{\pi}{7}} \\&lt;br /&gt;
&amp;amp;= \frac {\sin \frac{6\pi}{7} } {2 \sin\frac{\pi}{7}}&lt;br /&gt;
\end{align}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Noting that &amp;lt;math&amp;gt;\textstyle{\frac{6\pi}{7} + \frac{\pi}{7} = \pi}&amp;lt;/math&amp;gt; and that the sines of supplementary angles (angles that sum to π) are equal:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\begin{align}&lt;br /&gt;
&amp;amp;= \frac {\sin \frac{\pi}{7} } {2 \sin\frac{\pi}{7}} \\&lt;br /&gt;
&amp;amp;= \frac12 \quad \quad \quad \text{Q.E.D.}&lt;br /&gt;
\end{align}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:'''A table of slightly wrong equations and identities useful for approximations and/or trolling teachers.'''&lt;br /&gt;
:(Found using a mix of trial-and-error, ''Mathematica'', and Robert Munafo's ''Ries'' tool.)&lt;br /&gt;
: All units are SI MKS unless otherwise noted.&lt;br /&gt;
&lt;br /&gt;
:{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot; | Relation:&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Accurate to within:&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | One light-year(m)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 99&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 40&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Earth Surface(m&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 69&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 130&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Oceans' volume(m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 9&amp;lt;sup&amp;gt;19&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 70&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Seconds in a year&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 75&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 400&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Seconds in a year (''Rent'' method)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 525,600 x 60&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 1400&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Age of the universe (seconds)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 15&amp;lt;sup&amp;gt;15&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 70&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Planck's constant&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 1/(30&amp;lt;sup&amp;gt;π&amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 110&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Fine structure constant&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 1/140&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | [I've had enough of this 137 crap]&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | Fundamental charge&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | 3/(14 * π&amp;lt;sup&amp;gt;π&amp;lt;sup&amp;gt;π&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot; | one part in 500&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|White House Switchboard&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|1/&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;sup&amp;gt;π&amp;lt;/sup&amp;gt;√(e&amp;lt;sup&amp;gt;(1 + &amp;lt;sup&amp;gt;(e-1)&amp;lt;/sup&amp;gt;√8)&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Jenny's Constant&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|(7&amp;lt;sup&amp;gt;(e/1 - 1/e)&amp;lt;/sup&amp;gt; - 9) * π&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;3&amp;quot; align=&amp;quot;center&amp;quot;|Intermission:&amp;lt;br /&amp;gt; World Population Estimate&amp;lt;br /&amp;gt; which should stay current&amp;lt;br /&amp;gt; for a decade or two:&amp;lt;br /&amp;gt;&lt;br /&gt;
Take the last two digits of the current year&lt;br /&gt;
&lt;br /&gt;
Example: 20[14] &lt;br /&gt;
&lt;br /&gt;
Subtract the number of leap years since hurricane Katrina&lt;br /&gt;
&lt;br /&gt;
Example: 14 (minus 2008 and 2012) is 12&lt;br /&gt;
&lt;br /&gt;
Add a decimal point&lt;br /&gt;
&lt;br /&gt;
Example: 1.2&lt;br /&gt;
&lt;br /&gt;
Add 6&lt;br /&gt;
&lt;br /&gt;
Example: 6 + 1.2&lt;br /&gt;
&lt;br /&gt;
7.2 = World population in billions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Version for US population:&lt;br /&gt;
&lt;br /&gt;
Example: 20[14]&lt;br /&gt;
&lt;br /&gt;
Subtract 10&lt;br /&gt;
&lt;br /&gt;
Example: 4&lt;br /&gt;
&lt;br /&gt;
Multiply by 3&lt;br /&gt;
&lt;br /&gt;
Example: 12&lt;br /&gt;
&lt;br /&gt;
Add 10&lt;br /&gt;
&lt;br /&gt;
Example: 3[22] million&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Electron rest energy&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|e/7&amp;lt;sup&amp;gt;16&amp;lt;/sup&amp;gt; J&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 1000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Light-year(miles)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|2&amp;lt;sup&amp;gt;(42.42)&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 1000&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|sin(60°) = √3/2 = e/π&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 1000&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|√3 = 2e/π&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 1000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|γ(Euler's gamma constant)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1/√3&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 4000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Feet in a meter&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|5/(&amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;√π)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 4000&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|√5 = 2/e + 3/2&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 7000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Avogadro's number&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|69&amp;lt;sup&amp;gt;π&amp;lt;sup&amp;gt;√5&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 25,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Gravitational constant G&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1 / e&amp;lt;sup&amp;gt;(π - 1)&amp;lt;sup&amp;gt;(π + 1)&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 25,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|R (gas constant)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|(e+1) √5&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 50,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Proton-electron mass ratio&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6*π&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 50,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Liters in a gallon&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|3 + π/4&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 500,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|g&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|6 + ln(45)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 750,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Proton-electron mass ratio&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|(e&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt; - 10) / ϕ&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|one part in 5,000,000&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Ruby laser wavelength&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|1 / (1200&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|[within actual variation]&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Mean Earth Radius&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|(5&amp;lt;sup&amp;gt;8&amp;lt;/sup&amp;gt;)*6e&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|[within actual variation]&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;3&amp;quot; align=&amp;quot;center&amp;quot;|Protip - not all of these are wrong:&lt;br /&gt;
|-&lt;br /&gt;
|colspan=&amp;quot;2&amp;quot; align=&amp;quot;center&amp;quot;|√2 = 3/5 + π/(7-π)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2&lt;br /&gt;
|-&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|γ(Euler's gamma constant) = e/3&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; + e/5&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|√5 = (13 + 4π) / (24 - 4π)&lt;br /&gt;
|align=&amp;quot;center&amp;quot;|Σ 1/n&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; = ln(3)&amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
[[Category:Charts]]&lt;br /&gt;
[[Category:Math]]&lt;br /&gt;
[[Category:Physics]]&lt;br /&gt;
[[Category:Protip]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1984:_Misinterpretation&amp;diff=156216</id>
		<title>1984: Misinterpretation</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1984:_Misinterpretation&amp;diff=156216"/>
				<updated>2018-04-24T06:10:07Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: Added possible explanation.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 1984&lt;br /&gt;
| date      = April 23, 2018&lt;br /&gt;
| title     = Misinterpretation&lt;br /&gt;
| image     = misinterpretation.png&lt;br /&gt;
| titletext = &amp;quot;But there are seven billion people in the world! I can't possibly stop to consider how ALL of them might interpret something!&amp;quot; &amp;quot;Ah, yes, there's no middle ground between 'taking personal responsibility for the thoughts and feelings of every single person on Earth' and 'covering your eyes and ears and yelling logically correct statements into the void.' That's a very insightful point and not at all inane.&amp;quot;&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
[[Cueball]] is complaining that people are mad at him ''again'' because of misinterpretation. And since he is being perfectly clear it cannot be his fault that '''everyone'' is misinterprets him (hence the title). &lt;br /&gt;
&lt;br /&gt;
However, the off-screen voice sarcastically points out that communication is an activity that only involves one person. Hence the speaker makes it clear that &amp;quot;real&amp;quot; communication involves work on behalf of both the speaker as well as the listener. Cueball claims that he is being “perfectly clear”, but if there is room for misinterpretation on behalf of almost everyone that reads his comments, then he is not.&lt;br /&gt;
&lt;br /&gt;
In the title text, Cueball then answers that with seven billon people in the world he cannot possibly consider how ALL of them interprets his comments. Today his messages could potentially reach the whole world, and his claim that there will always be someone that would (intentionally) misunderstand something. The reply comes once again sarcastically, deriding his point and saying that a middle ground between taking up such an effort and entirely avoiding it must be reached.&lt;br /&gt;
&lt;br /&gt;
This avoidance is phrased using a [[762: Analogies|simile]] as “covering your eyes and ears and yelling logically correct statements into the void”, implying that no one would understand the logical sentences (thus the void), and would instead read them more naturally – and also that ignoring the appalled reaction of listeners to their own interpretation of the sentences is similar to covering your eyes and years. This action makes communication more difficult through the popular{{Citation needed}} means of speech, text and sign language. If the hands are occupied with covering either part, then Braille communication is also impossible. Therefore, the action of “covering your eyes and ears” is a metaphor for deliberately making it more difficult to communicate with oneself. Another likely explanation is, communication is a difficult task for Cueball to begin with, thus he subconsciously rejects criticism as it would hurt his impeccable logic.&lt;br /&gt;
&lt;br /&gt;
It is clear that Cueball is acting as a straw man to further Randall's point, and the off-panel character is portrayed as the (sarcastic) voice of reason.&lt;br /&gt;
&lt;br /&gt;
Randall returns to a recurring theme in his comics, regarding, in contexts of communication, the responsibility of the speaker for how they are interpreted, which again is a part of the larger category of comics about problems with [[:Category:Social interactions|social interactions]]. Having gradually gotten less subtle, this theme is now laid bare, there being no joke other than the sarcasm. What follows is a chronological history of this theme.&lt;br /&gt;
&lt;br /&gt;
*Much earlier than the other comics below, but related, [[169: Words that End in GRY]] is a surreal reprimand upon people who act smug when their bad communication is misunderstood.&lt;br /&gt;
*The title text of [[1028: Communication]] notes that “Anyone who says that they're great at communicating but 'people are bad at listening' is confused about how communication works.”&lt;br /&gt;
*The title text of [[1860: Communicating]] also asserts that the responsibility of a misunderstanding lies with the speaker, not the listener — a theme explored in the comic via the character Humpty Dumpty.&lt;br /&gt;
*The comic [[1911: Defensive Profile]] implies that a person who boasts of having “no filter” in their (social media) speech is actually merely insecure about making people mad with their statements.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
:[Cueball is sitting in an office chair at a desk in front of a laptop with his hands raised above the keyboard. An off-panel person replies to his remarks.]&lt;br /&gt;
:Cueball: Ugh, people are mad at me again because they don't read carefully.&lt;br /&gt;
:Cueball: I'm being perfectly clear. It's not '''''my''''' fault if everyone misinterprets what I say.&lt;br /&gt;
:Off-panel person: Wow, sounds like you're great at communicating, an activity that famously involves just one person.&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Social interactions]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1937:_IATA_Airport_Abbreviations&amp;diff=150376</id>
		<title>1937: IATA Airport Abbreviations</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1937:_IATA_Airport_Abbreviations&amp;diff=150376"/>
				<updated>2018-01-04T11:37:37Z</updated>
		
		<summary type="html">&lt;p&gt;141.101.77.140: /* Explanation */ Dartford has no airport&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 1937&lt;br /&gt;
| date      = January 3, 2018&lt;br /&gt;
| title     = IATA Airport Abbreviations&lt;br /&gt;
| image     = iata_airport_abbreviations.png&lt;br /&gt;
| titletext = IATA stands for International AirporT Abbreviation.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{incomplete|Expansion needed. Do NOT delete this tag too soon.}}&lt;br /&gt;
This comic is making fun of the three-letter codes assigned to mostly all {{w|IATA airport code|airports}} in the world. These codes are overseen by the {{w|International Air Transport Association|IATA (International Air Transport Association)}}. Some airport codes are very intuitive, taking letters from the city name (e.g., DEN for Denver). Other codes are somewhat intuitive, taking a letter or two from the nearby city name but adding an additional letter (e.g., LAX for Los Angeles). Other codes make seemingly no sense at all (e.g., ORD for Chicago's O'Hare International, due to it formerly being named Orchard Field). In many cases, the airport codes appear to have been chosen (or invented) because they are also common abbreviations and acronyms. &lt;br /&gt;
&lt;br /&gt;
If we use the table provided, Randall's friend is flying into Edwards Air Force Base and then down to whatever. This is not a typical flight. In actuality, the friend is flying into Newark tonight and Detroit tomorrow.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
 |'''IATA Code''' || '''Actual Assigned City/Airport''' || '''Description in the comic''' || '''Explanation'''&lt;br /&gt;
 |-&lt;br /&gt;
 | AMD || {{w|Sardar Vallabhbhai Patel International Airport|Ahmedabad}} || {{w|Amsterdam }}|| Amsterdam is the capital of the Netherlands. Its airport (called {{w|Amsterdam Airport Schiphol|Schiphol}}) has the IATA code AMS. &amp;quot;AMD&amp;quot; may also refer to &amp;quot;{{w|Advanced Micro Devices}}&amp;quot;, a brand of computer processors.&lt;br /&gt;
 |-&lt;br /&gt;
 | ANC || {{w|Ted Stevens Anchorage International Airport|Anchorage}} || {{w|Ankh-Morpork}} || Ankh-Morpork is a fictional city-state featured in ''{{w|Discworld}}''.  ANC is also an abbreviated name for the {{w|African National Congress}}.&lt;br /&gt;
 |-&lt;br /&gt;
 | ATL || {{w|Hartsfield–Jackson Atlanta International Airport|Atlanta}} || Atalantë || Another name for J.R.R. Tolkien's fictional island of {{w|Númenor}} (which is in turn a reference to the sinking of {{w|Atlantis}}). This may also be an intentional misspelling of &amp;quot;Atlanta&amp;quot;. ATL may also be an abbreviation for &amp;quot;above the line&amp;quot; - the area in an internet article or post containing the main content; as contrasted with BTL (&amp;quot;below the line&amp;quot;) where readers' comments appear.&lt;br /&gt;
 |-&lt;br /&gt;
 | BAE || {{w|Barcelonnette – Saint-Pons Airfield|Barcelonnette}} || {{w|Beijing}} || Beijing is the capital of China. {{w|Beijing Capital International Airport|Its airport}} has the IATA code PEK (possibly from Peking, alternate former spelling of its name). &amp;quot;{{w|Bae (word)|Bae}}&amp;quot; is a slang term meaning girlfriend,  boyfriend, or significant other. Randall has presumably assigned this to Beijing as, when pronounced as a word, rather than an abbreviation, it resembles the first syllable.&lt;br /&gt;
 |-&lt;br /&gt;
 | BLT || {{w|Blackwater Airport|Blackwater}} || {{w|Baltimore}} || A &amp;quot;{{w|BLT}}&amp;quot; is a bacon, lettuce, and tomato sandwich.&lt;br /&gt;
 |-&lt;br /&gt;
 | BUF || {{w|Buffalo Niagara International Airport|Buffalo}} || {{w|Sunnydale}} || Sunnydale is a fictional California city that serves as the primary setting for ''{{w|Buffy the Vampire Slayer|'''Buf'''fy the Vampire Slayer}}''.&lt;br /&gt;
 |-&lt;br /&gt;
 | CLT || {{w|Charlotte Douglas International Airport|Charlotte}} || [CENSORED] || The censored word may be &amp;quot;{{w|clitoris}}&amp;quot;. [[Randall]] has used this word in the comic before ([[243: Appropriate Term]]), but it is censored here for comic effect.&lt;br /&gt;
 |-&lt;br /&gt;
 | DFW || {{w|Dallas/Fort Worth International Airport|Dallas/Fort Worth}} || Down For Whatever || &amp;quot;Down for Whatever&amp;quot; is an expression used to indicate that one is okay with doing whatever his or her friends are doing in a social situation, or whatever comes up during a social situation.&lt;br /&gt;
 |-&lt;br /&gt;
 |DTF || ''not assigned'' || {{w|Dartford}} || &amp;quot;DTF&amp;quot; is an abbreviation used to indicate &amp;quot;Down To Fuck&amp;quot;. Dartford is a town in Kent, UK, about 10 miles SE of London. It does not have an airport. The nearest is probably {{w|London City Airport}}, LCY.&lt;br /&gt;
 |-&lt;br /&gt;
 | DTW || {{w|Detroit Metropolitan Airport|Detroit}} || Down To Whatever || See &amp;quot;DFW&amp;quot;.  &amp;quot;Down to Whatever&amp;quot; could indicate that one is getting on a plane with the intention of being fine with whatever the plane's destination turns out to be.&lt;br /&gt;
 |-&lt;br /&gt;
 | DWI || ''not assigned'' || Delaware International || &amp;quot;DWI&amp;quot; is an abbreviation for &amp;quot;Driving While Intoxicated&amp;quot; or &amp;quot;Driving While Impaired.&amp;quot; Randall notes in the ''what if?'' book that Delaware has no airports.&lt;br /&gt;
 |-&lt;br /&gt;
 | EWR || {{w|Newark Liberty International Airport|Newark}} || {{w|Edwards Air Force Base}} || Edwards Air Force Base (which has the IATA code EDW) is a United States Air Force installation in southern California, about 22 miles (35 km) northeast of Lancaster and 15 miles (24 km) east of Rosamond. It is notable for its pivotal role in NASA spaceflight development.&lt;br /&gt;
 |-&lt;br /&gt;
 | FFS || ''not assigned'' || Flagstaff Station || &amp;quot;FFS&amp;quot; is an abbreviation for &amp;quot;For Fuck's Sake.&amp;quot;&lt;br /&gt;
 |-&lt;br /&gt;
 | FHQ || ''not assigned'' || FHQWHGADS || The string &amp;quot;fhqwhgads&amp;quot; appeared as the first part of the sender name in the email &amp;quot;[http://www.youtube.com/watch?v=Lml_AKkhCVY i love you]&amp;quot; sent to Strong Bad in the {{w|Homestar Runner}} cartoons; Strong Bad ended up [http://www.youtube.com/watch?v=votBDwhTu1E writing a song] dedicated to the &amp;quot;character&amp;quot;, and, after this comic's release, Strong Bad's official Twitter account [https://twitter.com/StrongBadActual/status/948696499885694976 posted about the reference].&lt;br /&gt;
 |-&lt;br /&gt;
 | FYI || {{w|Fresno Yosemite International Airport}} || Fayetteville || &amp;quot;FYI&amp;quot; often stands for &amp;quot;For Your Information&amp;quot;. Fresno Yosemite International also has the code FAT for Fresno Air Terminal. Fayetteville is the name of many cities in the United States.&lt;br /&gt;
 |-&lt;br /&gt;
 | HGM || ''not assigned'' || Hogsmeade || {{w|Places_in_Harry_Potter#Hogsmeade|Hogsmeade}} is a fictional location in the ''{{w|Harry Potter}}'' series.&lt;br /&gt;
 |-&lt;br /&gt;
 | HSV || {{w|Huntsville International Airport|Huntsville}} || {{w|Huntsville, Alabama|Huntsville}} || This is one where Randall and the IATA agree. HSV is better known as the Hue-Saturation-Value color space or German soccer club Hamburger SV.  It is also Herpes Simplex Virus, a venereal disease.&lt;br /&gt;
 |-&lt;br /&gt;
 | IAD || {{w|Washington Dulles International Airport|Washington (Dulles)}} || {{w|Boise Airport|Idaho (Boise)}} || IAD is the symbol for Dulles International Airport (which was originally &amp;quot;DIA&amp;quot; but it was felt that could be confused when hand-written with &amp;quot;DCA&amp;quot;, the sign for nearby {{w|Ronald Reagan Washington National Airport}}). The Idaho Falls airport is IDA, while Idaho (Boise) is BOI, so it is unclear why BOI was chosen instead of IDA.&lt;br /&gt;
 |-&lt;br /&gt;
 | IUD || Doha || Washington (Dulles) || An &amp;quot;IUD&amp;quot; is an &amp;quot;IntraUterine Device,&amp;quot; or form of birth control.  Doha is the capital of Qatar in the Middle East and Persian Gulf. The Actual IATA code for Dulles is IAD (see above).&lt;br /&gt;
 |-&lt;br /&gt;
 | JFC || ''not assigned'' || {{w|Jefferson City}} || &amp;quot;JFC&amp;quot; is an abbreviation for &amp;quot;Jesus Fucking Christ.&amp;quot; JFK is John F. Kennedy International Airport, New York's main airport and one of the most famous in the world. Jefferson City is the state capital of Missouri, and also the name of several other cities.&lt;br /&gt;
 |-&lt;br /&gt;
 | KUL || {{w|Kuala Lumpur International Airport|Kuala Lumpur}} || {{w|Kingdom of Loathing}} || Kingdom of Loathing is an online, browser-based RPG. It contains an [http://kol.coldfront.net/thekolwiki/index.php/Elemental_International_Airport International Airport], previously lacking a three digit code. Kuala Lumpur is the capital city of Malaysia.&lt;br /&gt;
 |-&lt;br /&gt;
 | LAX || {{w|Los Angeles International Airport|Los Angeles}} || Las Angalas || &amp;quot;Las Angalas&amp;quot; is a &amp;quot;Los Angeles&amp;quot; with every vowel replaced with an &amp;quot;a&amp;quot; character. It's sometimes used as a joking nickname for &amp;quot;Los Angeles.&amp;quot; The Frank Black song &amp;quot;Los Angeles&amp;quot; uses this pronunciation.&lt;br /&gt;
 |-&lt;br /&gt;
 | LOL || {{w|Derby Field|Lovelock}} || {{w|Louisville}} || &amp;quot;LOL&amp;quot; often stands for &amp;quot;Laughing Out Loud&amp;quot;. Lovelock is a city in the state of Nevada. Louisville is the largest city in the state of Kentucky.&lt;br /&gt;
 |-&lt;br /&gt;
 | MDW || {{w|Midway International Airport|Chicago, IL (Midway)}} || {{w|Midway Atoll}} || Midway Atoll was the site of one of the most significant World War II Pacific naval battles and is the namesake of the Chicago airport. Its actual IATA code is MDY.&lt;br /&gt;
 |-&lt;br /&gt;
 | MIA || {{w|Miami International Airport|Miami}} || {{w|Colombo, Sri Lanka}} || MIA stands for &amp;quot;Missing In Action&amp;quot;. It is also the stage name of a {{w|M.I.A. (rapper)|rapper of Sri Lankan heritage}}.&lt;br /&gt;
 |-&lt;br /&gt;
 | OMW || ''not assigned'' || {{w|Omaha}} || Eppley Airfield in East Omaha, Nebraska, has an IATA code of OMA. &amp;quot;OMW&amp;quot; is an abbreviation for &amp;quot;On My Way.&amp;quot;&lt;br /&gt;
 |-&lt;br /&gt;
 | ORD || {{w|O'Hare International Airport|Chicago, IL (O'Hare)}} || {{w|Orlando}} || O'Hare was once known as Orchard Place/Douglas Field, hence ORD.&lt;br /&gt;
 |-&lt;br /&gt;
 | PDX || {{w|Portland International Airport|Portland}} || Pordlanx || Consider how LAX has a random &amp;quot;X&amp;quot; at the end. And &amp;quot;ORD&amp;quot; is an actual IATA code. Randall messes with &amp;quot;Portland&amp;quot; here in much the same way.&lt;br /&gt;
 |-&lt;br /&gt;
 | PHL || {{w|Philadelphia International Airport|Philadelphia, PA}} || {{w|Pittsburgh}} || Pittsburgh International Airport has a IATA code of PIT. Philadelphia and Pittsburgh are the two largest cities in Pennsylvania and are at opposite ends of the state.&lt;br /&gt;
 |-&lt;br /&gt;
 | SAN || {{w|San Diego International Airport|San Diego}} || San Diego&amp;lt;br&amp;gt;San Juan&amp;lt;br&amp;gt;San Jose&amp;lt;br&amp;gt;San Francisco&amp;lt;br&amp;gt;San Antonio || San Diego International Airport has SAN; nearby airports include Montgomery Field (MYF), MCAS Miramar (NKX), NAS North Island (NZY), Brown Field (SDM), and Gillespie Field (SEE).&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;There are several cities named San Juan or San Jose. Their airport codes are as follows: San Juan, Puerto Rico: SJU and SIG.  &amp;lt;br&amp;gt;San Juan, Argentina: UAQ.&amp;lt;br&amp;gt;San Jose, California, USA: SJC.&amp;lt;br&amp;gt; San Jose, Costa Rica: SJO. &amp;lt;br&amp;gt;San Jose, Mexico: SJD. &amp;lt;br&amp;gt;San Jose, Philippines: SJI&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;San Francisco, CA has the airport  code of SFO.&amp;lt;br&amp;gt;San Antonio, TX has the airport code of SAT.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Randall's plan to assign the code SAN to every place name beginning &amp;quot;San&amp;quot; would likely cause chaos for travellers.&lt;br /&gt;
 |-&lt;br /&gt;
 | SEA || {{w|Seattle–Tacoma International Airport|Seattle/Tacoma or SeaTac}} || [Indicates Water Landing] || This is presumably a reference to the fact that &amp;quot;SEA&amp;quot; could be interpreted as &amp;quot;Sea&amp;quot;. Like some other major airports (e.g., {{w|San Francisco International Airport}} and {{w|LaGuardia Airport}}), SEA is very close to a large body of water (in SeaTac's case {{w|Puget Sound}}), so missing the airport may end up in a water landing. The SeaTac airport is located between Seattle and Tacoma, two cities in WA.&lt;br /&gt;
 |-&lt;br /&gt;
 | SMH || Sapmanga || Smithfield || &amp;quot;SMH&amp;quot; often stands for &amp;quot;Shaking My Head&amp;quot;. Sapmanga is a location in Papua New Guinea. There are various cities named Smithfield in the United States and around the world.&lt;br /&gt;
 |-&lt;br /&gt;
 | STL || {{w|St. Louis}} || {{w|Silent Hill}} || Silent Hill is a fictional city appearing in the series of video games and movies with the same name. &lt;br /&gt;
 |-&lt;br /&gt;
 | SWF || {{w|Stewart International Airport|Newburgh, New York}} || Sherwood Forest || .swf is the file extension for ShockWave Flash files. &amp;quot;SWF&amp;quot; can also stand for &amp;quot;Single White Female&amp;quot; in personal ads. In legend, {{w|Sherwood Forest}} was the location of Robin Hood's hideout.&lt;br /&gt;
 |-&lt;br /&gt;
 | TBA || Tabibuga || {{w|Tribeca}} || &amp;quot;TBA&amp;quot; often stands for &amp;quot;To Be Announced&amp;quot;. Tabibuga is a location in Papua New Guinea. Tribeca (original styled TriBeCa) is an area in New York City. ''{{w|Angie Tribeca}}'' is an American comedy television series.&lt;br /&gt;
 |-&lt;br /&gt;
 | TMI || {{w|Tumlingtar Airport| Tumlingtar}} || {{w|Turkmenistan}} International || &amp;quot;TMI&amp;quot; often stands for &amp;quot;Too Much Information&amp;quot;. Tumlingtar is a city in Nepal. Turkmenistan is a country in Central Asia.&lt;br /&gt;
 |-&lt;br /&gt;
 | YYY || {{w|Mont-Joli Airport|Mont-Joli}} || {{w|Toronto}} Downtown || Mont-Joli is a city in Quebec,  Canada. The small airport in downtown Toronto is {{w|Billy Bishop Toronto City Airport}}, which has an actual IATA code of YTZ. This may be a play on the below designation for the larger Toronto airport, YYZ. It could also be Randall asking &amp;quot;why why why&amp;quot; some of these codes are so odd.&lt;br /&gt;
 |-&lt;br /&gt;
 | YYZ || {{w|Toronto Pearson International Airport|Toronto}} || {{w|Toronto Pearson International Airport|Toronto Pearson}} || This one is correct. The band Rush is from Toronto and named an instrumental song after the airport call sign. See {{w|YYZ (instrumental)}}&lt;br /&gt;
 |-&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The title text is a pun about the acronym ''IATA'', stating it stands for '''I'''nternational '''A'''irpor'''T''' '''A'''bbreviation. This is as wrong as everything else here, because the real ''International Air Transport Association'' is not an organization only responsible for abbreviations in aviation.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
{{incomplete transcript|Do NOT delete this tag too soon.}}&lt;br /&gt;
:[A list with abbreviations and their meaning is shown in two columns.]&lt;br /&gt;
&lt;br /&gt;
:[On top left the header reads:]&lt;br /&gt;
:Confused by those airport abbreviations used by your friends who fly a lot?&lt;br /&gt;
&lt;br /&gt;
:Just memorize this list!&lt;br /&gt;
&lt;br /&gt;
:[On top right some social media conversation is shown:]&lt;br /&gt;
:I'm flying into EWR tonight, then DTW tomorrow.&lt;br /&gt;
:[Answer (in blue, two message bubbles):]&lt;br /&gt;
:Ok, cool&lt;br /&gt;
:I definitely know what those mean without Googling&lt;br /&gt;
&lt;br /&gt;
:[The list:]&lt;br /&gt;
:{| class=&amp;quot;wikitable style=border:none;&amp;quot;| &lt;br /&gt;
|-&lt;br /&gt;
| AMD || Amsterdam&lt;br /&gt;
| TMI || Turkmenistan International&lt;br /&gt;
|-&lt;br /&gt;
| BAE || Beijing&lt;br /&gt;
| LAX || Las Angalas&lt;br /&gt;
|-&lt;br /&gt;
| ORD || Orlando&lt;br /&gt;
| EWR || Edwards Air Force Base&lt;br /&gt;
|-&lt;br /&gt;
| IAD || Idaho (Boise)&lt;br /&gt;
| PHL || Pittsburgh&lt;br /&gt;
|-&lt;br /&gt;
| JFC || Jefferson City&lt;br /&gt;
| SWF || Sherwood Forest&lt;br /&gt;
|-&lt;br /&gt;
| IUD || Washington Dulles&lt;br /&gt;
| KUL || Kingdom of Loathing&lt;br /&gt;
|-&lt;br /&gt;
| FYI || Fayetteville&lt;br /&gt;
| STL || Silent Hill&lt;br /&gt;
|-&lt;br /&gt;
| LOL || Louisville&lt;br /&gt;
| BUF || Sunnydale&lt;br /&gt;
|-&lt;br /&gt;
| ATL || Atalante&lt;br /&gt;
| TBA || Tribeca&lt;br /&gt;
|-&lt;br /&gt;
| HGM || Hogsmeade&lt;br /&gt;
| SMH || Smithfield&lt;br /&gt;
|-&lt;br /&gt;
| OMW || Omaha&lt;br /&gt;
| BLT || Baltimore&lt;br /&gt;
|-&lt;br /&gt;
| ANC || Ankh-Morpork&lt;br /&gt;
| YYY || Toronto Downtown&lt;br /&gt;
|-&lt;br /&gt;
| HSV || Hunstville&lt;br /&gt;
| YYZ || Toronto Pearson&lt;br /&gt;
|-&lt;br /&gt;
| SAN || San Diego&lt;br /&gt;
| MIA || Colombo, Sri Lanka&lt;br /&gt;
|-&lt;br /&gt;
| SAN || San Juan&lt;br /&gt;
| CLT || [Censored]&lt;br /&gt;
|-&lt;br /&gt;
| SAN || San Jose&lt;br /&gt;
| FHQ || Fhqwhgads&lt;br /&gt;
|-&lt;br /&gt;
| SAN || San Francisco&lt;br /&gt;
| FFS || Flagstaff Station&lt;br /&gt;
|-&lt;br /&gt;
| SAN || San Antonio&lt;br /&gt;
| DTF || Dartford&lt;br /&gt;
|-&lt;br /&gt;
| DWI || Delaware International&lt;br /&gt;
| MDW || Midway Atoll&lt;br /&gt;
|-&lt;br /&gt;
| DFW || Down for Whatever&lt;br /&gt;
| PDX || Pordlanx&lt;br /&gt;
|-&lt;br /&gt;
| DTW || Down to Whatever&lt;br /&gt;
| SEA || [Indicates Water Landing]&lt;br /&gt;
|-&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics with color]]&lt;br /&gt;
[[Category:Puns]]&lt;/div&gt;</summary>
		<author><name>141.101.77.140</name></author>	</entry>

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