explain xkcd - User contributions [en]

Talk:2042: Rolle's Theorem

2018-09-06T07:48:55Z

162.158.92.40:

Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. [[Special:Contributions/172.69.54.165|172.69.54.165]] 15:51, 5 September 2018 (UTC)
:Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)

:Proposed ideas for Munroe's Law:
::- Any seemingly simple idea will be difficult to prove; the simpler it seems, the harder the proof.
::- Any proof which is discovered by a layperson will have been previously discovered by an expert (or an "expert") in the field.
:[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|talk]]) 17:57, 5 September 2018 (UTC)

I feel like Euclid beat Randall to the punch here, a couple millennia. [[Special:Contributions/162.158.155.146|162.158.155.146]] 16:54, 5 September 2018 (UTC)

I don't see that Thales has proven Randall's theorem. Do not to be confused with {{w|Thales's theorem}}, that's about right angles. Maybe I'm blind or just dumb, but if so it has to be explained with more traceable background. I just believe that this diagonal is so trivial that even the ancient Greeks weren't engaged on a proof. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:38, 5 September 2018 (UTC)
* From {{w|Thales|Wikipedia}}: Other quotes from Proclus list more of Thales' mathematical achievements: "They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre." [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:39, 6 September 2018 (UTC)
* On the other hand not all historian believe Proclus. But van der Waerden does: [https://books.google.com/books?id=HK3vCAAAQBAJ&pg=PA88#v=onepage&q&f=false]. [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:49, 6 September 2018 (UTC)

:''Rolle's Theorem counterexample?''
Isn't the TAN(x) function a counterexample to this? Starting at a given point, it rises to infinity, then returns from negative infinity to the same point without ever having a slope of zero. [[Special:Contributions/172.68.58.89|172.68.58.89]] 06:58, 6 September 2018 (UTC)
* TAN(x) isn't differentiable at pi/2, hence the theorem doesn't apply--[[Special:Contributions/162.158.92.40|162.158.92.40]] 07:48, 6 September 2018 (UTC)

1799: Bad Map Projection: Time Zones

2017-02-15T11:00:07Z

162.158.92.40: Removed Spelling Error

{{comic
| number = 1799
| date = February 15, 2017
| title = Bad Map Projection: Time Zones
| image = bad_map_projection_time_zones.png
| titletext = This is probably the first projection in cartographic history that can be criticized for its disproportionate focus on Finland, Mongolia, and the Democratic Republic of the Congo.
}}
*A [http://imgs.xkcd.com/comics/bad_map_projection_time_zones_2x.png double sized version] of this image can be found by clicking the image at xkcd.com - the comic's page can also be accessed by clicking on the comic number above.
**It is the first large drawing using ''_2x'' added to the file name to indicate a different size. See much more details on this under the expanded explanation for the [[:Category:Large drawings|large drawings category]].

==Explanation==
{{incomplete|[[#Table of countries and their timezones|Table]] needs to be filled out for each country, both named and unnamed that are shown in the map with explanation of its timezone and why it looks as it does on the map. (Especially Russia, China and Greenland as well as those from title text needs explanation like that.}}

This is the second comic in the series of [[:Category:Bad Map Projections|Bad Map Projections]]. The first was released just over a month before this one and was called [[1784: Bad Map Projection: Liquid Resize]].

Notably, "Liquid Resize" was #107, while this comic features #79, so either Randall has put them in a new arbitrary order or he is counting down from least to most terrible.

Conceptually, the series is a comment on the fact that there is no perfect way to draw a map of the world on a flat piece of paper. Each one will introduce a different type of distortion, and the best projection for a given situation is sometimes very disputed. [[Randall]] previously explored 12 different projections in [[977: Map Projections]], and expressed his disdain for some types he sees as less efficient but whose users feel superior. None of them are really good as any 2D map projection will always distort in a way the spherical reality, and a map projection that is useful for one aspect (like navigation, geographical shapes and masses visualization, etc.) will not be so for all the others. Local maps of smaller areas can be quite accurate, but the idea of both these map projection comics is to map the entire globe on a flat surface.

Randall, being Randall, runs with the idea. Has made another map projection that is not only inaccurate, but utterly unusable.

This comic shows a {{w|Map projection|map projection}} in which countries are placed according to the {{w|Time zone|time zones}} that they fall under. Based on the way the Sun shines on the Earth, these time zones, which are based on the sun's position in the sky, would best be divided by roughly longitudinal (North-to-South Pole) lines.

However, this is not the case in practice, as the defined time zones tend to have very jagged boundaries. Since [[Randall]] knows he cannot fix the boundaries of the time zones, he instead "fixes" the world by making a map appear to match up with the time zone system. This results in bizarre distortions such as the large, gum-like strands of Greenland and enormous gulfs in parts of northern Russia.

The effect of this map is "punish" large countries with a single time zone - for instance, China, which uses UTC+8 across the whole country - and countries that share large time zones - for instance, almost all of Europe is packed into the Central European UTC+1 zone - by shrinking these down. Conversely, countries that span multiple time zones are stretched out - for example, the Democratic Republic of the Congo, as pointed out in the alt-text - as are those that belong to very small time zones - Finland and the Baltic states look huge because they are the only countries using the UTC+2 Eastern Europe time.

Other map projections distort countries this way as well, but based on their actual physical location as opposed to their position on imaginary time zones. The [[wikipedia:Mercator projection|Mercator projection]] is infamous for distorting Greenland in this way, to the point that it appears to be larger than Africa despite being nowhere near the same size. The title text lampoons the fact that the same phenomenon occurs on Randall's bad map projection, but for countries that do not tend to experience this on typical projections. Several smaller countries such as Finland, Mongolia, and the DRC, appear much larger than their actual size due to being stretched across time zone boundaries.

Some countries look especially odd. Greenland gets some jutting out points - these are the towns of {{w|Danmarkshavn}} (UTC) and {{w|Ittoqqortoormiit}} (UTC-1), which use different time zones to the rest of the island - while Russia gets big holes in it in places where there is a 2 hour time zone difference between states. For instance, in reality {{w|Komi}} and {{w|Khanty-Mansi}} touch each other. However, Komi uses Moscow time (UTC+3) and Khanty-Mansi uses Yekaterinburg Time (UTC+5). There is no state between them using UTC+4, so Randall draws a big gap in northern Russia here.

The map is imperfect since it doesn't allow for half-hour time zones (India, for instance, is on UTC+5.5). Instead, countries that span time zones are shifted so they straddle the two time zones, and are then marked with an asterisk. There's also no mention of daylight savings - all countries shown are given the base winter time. Depending on the time of year, countries will shift around - around June, many northern hemisphere countries will move east, while some southern hemisphere countries will move east around December. Randall attempts to preserve adjacencies where possible - for instance, Chad and Sudan are neighbors even though Chad uses West Africa Time (UTC+1) and Sudan uses East Africa Time (UTC+3). Randall draws an extremely thin strand connecting the countries though Central/South Africa Time (UTC+2), even though no part of Chad or Sudan uses this time. Similarly, a thin strand of Kazakhstan and Turkmenistan is shown projecting into the UTC+4 time zone in order to separate Russia and Iran, which do not really share a border.

===Errors===
* Randall mixes up Morocco and Western Sahara (a disputed territory)
* {{w|East Thrace}}, the European portion of Turkey, is shown in Eastern European time (UTC+2). Actually, like the rest of Turkey, it uses UTC+3

==Table of countries and their timezones==
*This table should include all countries not just those labeled.
**Also continents should be mentioned as they are also more or less distorted not necessarily depending on the distortion of the countries within.
*The labels used should be noted first, and the full country name (with wiki link) should be mentioned if abbreviations has been used in a bracket after.
*Timezone(s) for the country should be listed.
*Clear distortion shown in the image should be described
*Explanation for that based on timezone as well as other interesting details can be noted.

{| class="wikitable"
! Country/Continent
! Timezone(s)
! Distortions
! Explanation
|-
| Add more - just two examples made so far: || || ||
|-
| {{w|Europe}} (not labeled) || UTC+0-UTC+2 (?) || Compressed with the countries of mainland Europe pressed closer from both sides || Most of Europe use UTC+1 but these countries spread over a much larger area than just one zone. This is what becomes clear in the distortion
|-
| UK ({{w|United Kingdom}}) || UTC+0 || None || The country is fully within the single time zone used for the country. UK defined the timezones so their time zone is by definition the one with UTC+0 (or GMT).
|-
| {{w|Russia}} || Many (expand and mention all) || Three deep troughs almost cutting Russia in pieces, but not quite, also much longer at the normal|| Russia covers several timezones but also uses several, and should thus stay as large as normal. However, there are regions where it is only the southern parts of Russia that used a specific time zone, and two other regions above have a border whit two hours difference. This seems to occur three times explaining the troughs. (More on this and the length to the east needed)
|-
| Copy this line and the line above and set in directly under another entry || || ||
|}

==Transcript==
{{incomplete transcript|All the names on the countries}}
:[This transcript will note everything readable from the 2x zoom version found by clicking the comic on xkcd.]

:[Caption at the top of the panel:]
:Bad map projection #79:
:<big>Time Zones</big>
:Where each country '''''should''''' be, based on its time zone(<small>s</small>)

:[Below the caption there is a map of the world divided and colored by political boundaries, with outlines around each continent in black and around each country in dark gray. Antarctica is not included. Bodies of water are white, and countries in pale shades of red, orange, yellow, green, blue, and purple. The map is clearly distorted, with Europa and Africa in the center, but not all continents or countries looks wrong. Africa, Australia and North America seems least distorted. But the bottom part of of South America is very slim, Greenland has two chewing gum like blobs stretched away from it to the right, Iceland is over the UK, and most of Europe has been compressed. Finland though is too large. In Africa especially Dem. Rep. the Congo has been enlarged. The worst distortion is in Asia, where especially Russia looks weird with three deep troughs down the length of the country and the end to the right seems to be much longer than usually. But also China is completely wrong as it has been compressed, Mongolia taking up most of its usual position.]

:[Most countries over a certain size have their name listed in a gray font. Small countries like Ireland and Haiti has their name listed because it can be noted in the oceans around them. Most other countries have the name inside the country, but if there is not enough room abbreviation are used like Germany which has Ger. noted. There are though several small countries in the middle of Europa which has no name, as there are simply not enough space for even an abbreviation. This is countries like Belgium, The Netherlands and Denmark a long the coast towards England (with not enough Ocean space either for the name) and the small central countries like Austria, Switzerland and Luxembourg. There are also a few specialties mentioned when time zones are not divided in full hours, for instance a foot note regarding half hour time zones. Below all the mentioned countries will be listed starting from the left, going through each (political) continent from top left and down, and the same for each country in the continent:]

:[North America:]
:Canada
:United States
:Mexico
:Cuba
:Haiti
:Jam.
:D.R

:[Central America:]
:Gua.
:Hon.
:Nic.
:CR.
:Pan.

:[South America:]
:Columbia
:...
:
:Argentina

:[Europa:]
:Greenland
:Iceland
:Ireland
:UK
:Norway
:...
:
:
:Bulgaria

:[Africa:]
:W.S.
:Algeria
:Tunis
:...
:
:
:
:South Africa
:Madagascar

:[Asia:]
:Russia
:
:
:...
:Iran*
:Afghanistan*
:...
:
:...
:Russia
:...
:
:...
:India*
:Nepal*
:...
:Bur*
:...
:
:
:...
:China
:N.K*
:S.K.
:Japan

:[Oceania:]
:Malaysia
:Indonesia
:Philippines
:Papua New Guinea

:[Australia. In the country there is a star * in the middle of it above the name:]
:<nowiki>*</nowiki>
:Australia
:New Zealand

:[Below Australia there is an arrow pointing to a pointing the south cost and below that a foot note for the stars * used above:]
:UTC +8:45
:(One small area)
:<nowiki>*</nowiki>=Half-hour offset

==Trivia==
*It is the first time a [[:Category:Large drawings|large comic's]] large version is called ''2x'' rather than for instance ''large''

{{comic discussion}}

[[Category:Large drawings]]
[[Category:Comics with color]]
[[Category:Maps]]
[[Category:Bad Map Projections]]

1788: Barge

2017-01-25T14:56:49Z

162.158.92.40: /* Explanation */

{{comic
| number = 1788
| date = January 20, 2017
| title = Barge
| image = barge.png
| titletext = My life goal is to launch a barge into the air and have it land on one of Elon Musk's rockets.
}}

==Explanation==
This is another one of the "[[My Hobby]]" series, where [[Randall]] tells about a strange hobby. With three drawings he shows the concept of his hobby, which is explained in details in the caption.

The launch company {{w|SpaceX}} is currently testing a reusable rocket system, where the {{w|multi-stage rocket|first rocket stage}} is capable of landing back on either the launch pad or an {{w|autonomous spaceport drone ship}} after launch (See [https://www.youtube.com/watch?v=lEr9cPpuAx8 this video] displaying both types of landing, from when the sea landing was successful the first time). The rockets guide themselves in to land by aiming towards a giant launch pad with the "X" from the SpaceX logo painted on it. Randall imagines creating a similar-looking barge and placing it near the intended landing site, except his barge's platform would be hollow in the middle with only a sheet of paper supporting the part where the rocket would land.

Since the paper is painted to look just like the real SpaceX it is presumably the goal of this setup to trick a returning first stage rocket into falling into the sea, similar to the old {{w|trapping pit}}. If a rocket attempts to land on Randall's barge, it will quickly burn through the paper and fall into the sea and explode (see example in video above).

However just leaving the barges adrift in the ocean won't help. Because it was indicated, that the rocket is not aiming using its camera, but in fact targeting the same GPS coordinates the barge is aiming at. So it is unlikely Randall would catch any rockets using this trick.

Also traversing the ocean near the rockets flightpath is being temporarily disallowed, due to dangers for those ships. So his ship would probably be removed by the authorities, or at least cause a scrub of the launch that day.

This "my hobby" is probably the most destructive one so far, as it would result in the loss of the nine space rocket engines at the bottom of the first rocket stage. It would also likely be the most expensive even disregarding the costs to others, due to the costs associated with buying and damaging a barge specifically for a prank (though it could potentially be reused if it did not get destroyed by the exploding rocket).

This hobby seems more appropriate for [[Black Hat]], considering that he is a real [[classhole]], showing that Black Hat is as much part of Randall as [[Cueball]].

The title text plays on the incredible difficulty of successfully landing a rocket on a barge, which {{w|Elon Musk}} was the first (and so far only) to do successfully with his SpaceX company (Note that other companies has done something similar at least on land, like {{w|Blue Origin}} who managed to [https://www.youtube.com/watch?v=nNRs2gMyLLk return ther first sate] before SpaceX did, but see this video about [https://www.youtube.com/watch?v=b8c7RUjNFDo Why Blue Origin’s rocket landing shouldn’t be compared to SpaceX]).

Reusing rockets like this is a feat that has only recently become possible, some 60 years after the launch of the first satellite {{w|Sputnik 1}}. In the title text Randall thus imagines an even more implausible idea of reversing Elon Musk's idea by launching an entire ''barge'' into the air and then have it land on one of Elon Musk's rockets. Launching a barge in the first place would be tremendously difficult - they are big, heavy and not very {{w|aerodynamic}}. Maneuvering it through the air precisely enough to one come down on top of a rocket would be much more difficult, but if it worked it would certainly destroy the rocket. Randall though thinks the irony of reversing the feat of landing a rocket on a barge is so funny he has made it into one of his life goals.

This comic was published on the week following SpaceX's {{w|List_of_Falcon_9_and_Falcon_Heavy_launches#2017|Iridium 1 mission}}, where the first stage of the rocket which delivered 10 satellites into orbit successfully landed on a barge near California. This was [https://www.youtube.com/watch?v=GLz-M7pki7U filmed from the returning stage 1] and also [https://www.youtube.com/watch?v=78AxtAyW4Vo from further away] (See more details of the launch [https://www.youtube.com/watch?v=c8wy5sQ2JDE here]). It marked the seventh time SpaceX successfully landed and recovered its booster on a commercial mission.

==Transcript==
:[There is one panel in this comic with the main drawing at the bottom. Two smaller drawings are inserted above this drawing to explain the idea.]

:[The first insert shows a barge with no center and a large piece of paper with the SpaceX logo above the barge.]

:[The second insert shows the paper stretched over the hole.]

:[The main drawing at the bottom shows a cross-section of the barge in water, showing there is only water below the paper. Above the paper the large first stage, without the top part with the payload, of a reusable rocket is attempting to land on the paper on the SapceX logo (not visible in this view). It is still so high above the fake barge that the exhaust fire below the rocket is nowhere near the paper.]

:[Caption below the panels:]
:My hobby: Hollowing out the center of a barge, stretching paper over the hole painted with the SpaceX logo, and leaving it floating offshore near launch sites.

{{comic discussion}}

[[Category:My Hobby]]
[[Category:Space]]
[[Category:Comics featuring Elon Musk]]