http://www.explainxkcd.com/wiki/index.php?title=Special:RecentChangesLinked/Category:Comics_featuring_Cueball&feed=atom&target=Category%3AComics_featuring_Cueballexplain xkcd - Changes related to "Category:Comics featuring Cueball" [en]2016-08-28T06:54:55ZRelated changesMediaWiki 1.19.17//www.explainxkcd.com/wiki/index.php?title=564:_Crossbows&diff=125841&oldid=113620564: Crossbows2016-08-28T00:17:26Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#Since the experimental confirmation or denial of the {{w|Higgs mechanism}} was widely recognized as important to the development of physics, the experimenters involved were likely to receive Nobel Prizes. Nobel Prizes, however, are only given to living people and groups of up to three in size. The experimenters, therefore, are preparing to fight to the death when the discovery comes. Peter Higgs had [http://www.reuters.com/article/2008/04/07/us-science-particle-idUSL0765287220080407 made a statement] in 2008 hinting that the confirmation would come within one year, and that statement was made one year before the Tuesday mentioned in the comic. Tentative experimental confirmation of the Higgs boson was made in July 2013.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#Since the experimental confirmation or denial of the {{w|Higgs mechanism}} was widely recognized as important to the development of physics, the experimenters involved were likely to receive Nobel Prizes. Nobel Prizes, however, are only given to living people and groups of up to three in size. The experimenters, therefore, are preparing to fight to the death when the discovery comes. Peter Higgs had [http://www.reuters.com/article/2008/04/07/us-science-particle-idUSL0765287220080407 made a statement] in 2008 hinting that the confirmation would come within one year, and that statement was made one year before the Tuesday mentioned in the comic. Tentative experimental confirmation of the Higgs boson was made in July 2013.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#At the time this was written, there was much hype about the Higgs mechanism, as it was a theory explaining how particles got their masses. Experimental confirmation of the Higgs mechanism and its signature particle (the {{w|Higgs boson}}) was seen with such importance that the boson was dubbed the "God particle". Detecting it, however, required accelerating particles to energies higher than ever before. Since this was at the cutting edge of physics, it was unknown what would actually happen. There were [http://www.theregister.co.uk/2008/09/05/lhc_to_leave_fabric_of_spacetime_continuum_unripped/ fears] that the experiment would create a micro black hole or worse. This comic could be seen as applying those fears to a common trope in horror movies and video games where a mutant infestation is created by unknowing scientists. The scientists here, apart from poor [[Cueball]], have done their research and armed themselves for any upcoming dangers. It is unknown whether these dangers are specific or not. Some argue that [[:Category:Velociraptors|velociraptors]] are a common enough theme in xkcd that the experimenters are preparing for a velociraptor attack. Others point out that the crossbow is a weapon in the game series {{w|Half-Life (video game)|Half-Life}}, whose plot has a similar infestation following failed physical experiment ripping dimensional seams. They mention that someone at the particle accelerator [http://img144.imageshack.us/img144/2131/freemanae8.jpg closely resembled] one of the main characters of Half-Life. Of course, the crossbows may just be a general preparation for danger.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#At the time this was written, there was much hype about the Higgs mechanism, as it was a theory explaining how particles got their masses. Experimental confirmation of the Higgs mechanism and its signature particle (the {{w|Higgs boson}}) was seen with such importance that the boson was dubbed the "God particle". Detecting it, however, required accelerating particles to energies higher than ever before. Since this was at the cutting edge of physics, it was unknown what would actually happen. There were [http://www.theregister.co.uk/2008/09/05/lhc_to_leave_fabric_of_spacetime_continuum_unripped/ fears] that the experiment would create a micro black hole or worse. This comic could be seen as applying those fears to a common trope in horror movies and video games where a mutant infestation is created by unknowing scientists. The scientists here, apart from poor [[Cueball]], have done their research and armed themselves for any upcoming dangers. It is unknown whether these dangers are specific or not. Some argue that [[:Category:Velociraptors|velociraptors]] are a common enough theme in xkcd that the experimenters are preparing for a velociraptor attack. Others point out that the crossbow is a weapon in the game series {{w|Half-Life (video game)|Half-Life}}, whose plot has a similar infestation following failed physical experiment ripping dimensional seams. They mention that someone at the particle accelerator [http://img144.imageshack.us/img144/2131/freemanae8.jpg closely resembled] one of the main characters of Half-Life. Of course, the crossbows may just be a general preparation for danger.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>#Finally, this comic may simply be general sympathy for those late to catch on to something. Substituting different things for "crossbow" and "Higgs excitation" would give a similar situation for Cueball. [[Randall]] apparently hates these situations. A layer of {{w|metahumor}} <del class="diffchange diffchange-inline">may </del>be present here, as Cueball may represent the clueless readers of xkcd who have to go to the [http://forums.xkcd.com/index.php forum] or [[Main Page|this wiki]] to understand its comics.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>#Finally, this comic may simply be general sympathy for those late to catch on to something. Substituting different things for "crossbow" and "Higgs excitation" would give a similar situation for Cueball. [[Randall]] apparently hates these situations. A layer of {{w|metahumor}} <ins class="diffchange diffchange-inline">could </ins>be present here, as Cueball may represent the clueless readers of xkcd who have to go to the [http://forums.xkcd.com/index.php forum] or [[Main Page|this wiki]] to understand its comics.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The proper interpretation of this comic, or whether there even is one, remains an open question.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The proper interpretation of this comic, or whether there even is one, remains an open question.</div></td></tr>
</table>162.158.74.42//www.explainxkcd.com/wiki/index.php?title=1337:_Hack&diff=125833&oldid=1242321337: Hack2016-08-27T10:18:54Z<p><span dir="auto"><span class="autocomment">Background for ISEE-3/ICE: </span> Space between quantity and unit - " " is a non-breaking space (see e.g. <http://english.stackexchange.com/questions/15953>).</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>It was reported that the hardware to communicate with ISEE-3/ICE had been decommissioned. The Madrid DSS complex still has the special filter required to communicate with the ICE satellite, but because of frequency conflicts S-band uplink is not supported.[http://deepspace.jpl.nasa.gov/dsndocs/810-005/101/101E.pdf]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>It was reported that the hardware to communicate with ISEE-3/ICE had been decommissioned. The Madrid DSS complex still has the special filter required to communicate with the ICE satellite, but because of frequency conflicts S-band uplink is not supported.[http://deepspace.jpl.nasa.gov/dsndocs/810-005/101/101E.pdf]</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>On March 1 and 2, 2014 radio amateurs were able to detect the beacon signal from the retired NASA deep space probe ICE (International Cometary Explorer) using the <del class="diffchange diffchange-inline">20m </del>radio telescope at the Bochum Observatory (Germany).[http://amsat-uk.org/2014/03/09/radio-amateurs-receive-nasa-isee-3ice-spacecraft/]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>On March 1 and 2, 2014 radio amateurs were able to detect the beacon signal from the retired NASA deep space probe ICE (International Cometary Explorer) using the <ins class="diffchange diffchange-inline">20&nbsp;m </ins>radio telescope at the Bochum Observatory (Germany).[http://amsat-uk.org/2014/03/09/radio-amateurs-receive-nasa-isee-3ice-spacecraft/]</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Updates for ISEE-3/ICE===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Updates for ISEE-3/ICE===</div></td></tr>
</table>PeterMortensen//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125829&oldid=1258141724: Proofs2016-08-27T07:18:59Z<p>removing "standard" </p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The way that Ms Lenhart's proof refers to the act of doing math itself, is characteristic of metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While <del class="diffchange diffchange-inline">standard </del>mathematical theorems and their proofs deal with <del class="diffchange diffchange-inline">standard </del>mathematical objects<del class="diffchange diffchange-inline">, like </del>numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The way that Ms Lenhart's proof refers to the act of doing math itself, is characteristic of metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While <ins class="diffchange diffchange-inline">typical </ins>mathematical theorems and their proofs deal with <ins class="diffchange diffchange-inline">such </ins>mathematical objects <ins class="diffchange diffchange-inline">as </ins>numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td></tr>
</table>162.158.85.249//www.explainxkcd.com/wiki/index.php?title=821:_Five-Minute_Comics:_Part_3&diff=125827&oldid=124885821: Five-Minute Comics: Part 32016-08-27T04:00:43Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*"Fastest gun in the West" is a boast commonly made in Western movies, where it is used to mean that a person is the fastest at drawing his gun in a duel (or, alternatively, can fire his gun the fastest). It doesn't actually describe the gun itself, and certainly doesn't describe how fast the gun can gallop across the land.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*"Fastest gun in the West" is a boast commonly made in Western movies, where it is used to mean that a person is the fastest at drawing his gun in a duel (or, alternatively, can fire his gun the fastest). It doesn't actually describe the gun itself, and certainly doesn't describe how fast the gun can gallop across the land.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>*"It's what separates the ''men'' from the ''boys''" is a phrase used to describe "macho" activities that, apparently, only "real men" will participate/do well in; all the other men haven't grown up yet, and are thus "boys." {{w|Centrifuge}}s are used to rapidly separate a material from the liquid it's suspended in, <del class="diffchange diffchange-inline">so apparently they can also be used </del>to <del class="diffchange diffchange-inline">separate men from boys</del>.<del class="diffchange diffchange-inline">{{Citation needed}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*"It's what separates the ''men'' from the ''boys''" is a phrase used to describe "macho" activities that, apparently, only "real men" will participate/do well in; all the other men haven't grown up yet, and are thus "boys." {{w|Centrifuge}}s are used to rapidly separate a material from the liquid it's suspended in<ins class="diffchange diffchange-inline">; this is either a pun on the word "separate"</ins>, <ins class="diffchange diffchange-inline">or an attempt by Randall </ins>to <ins class="diffchange diffchange-inline">make the occupation of lab technician seem macho</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**In the film {{W|Moonraker_(film)|Moonraker}} {{W|James Bond}} was almost killed in a centrifuge used as a g-force training vehicle for pilots/astronauts - but he survived - and he for sure is a real man... See also [[123: Centrifugal Force]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**In the film {{W|Moonraker_(film)|Moonraker}} {{W|James Bond}} was almost killed in a centrifuge used as a g-force training vehicle for pilots/astronauts - but he survived - and he for sure is a real man... See also [[123: Centrifugal Force]].</div></td></tr>
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</table>162.158.255.127//www.explainxkcd.com/wiki/index.php?title=820:_Five-Minute_Comics:_Part_2&diff=125826&oldid=124883820: Five-Minute Comics: Part 22016-08-27T03:49:54Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*{{w|Black light}}s are a kind of lamp that filters out sub-purple light. This means that the only light it gives off is a small amount of purple light, plus plenty of ultraviolet light. Ultraviolet light is invisible to humans, but it is noticeable in a few ways; it hurts the eyes, which is why it's hard to focus on things under a black light; it causes sunburns, although the amount given off by a black light is far too insignificant to do this in a realistic time; and it causes a fluorescence reaction in semen, some food stains, and dust making them appear to glow, which is why the robes look dirty. As such, a "{{w|Lightsaber|blacklightsaber}}" would, indeed, be a bad idea.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*{{w|Black light}}s are a kind of lamp that filters out sub-purple light. This means that the only light it gives off is a small amount of purple light, plus plenty of ultraviolet light. Ultraviolet light is invisible to humans, but it is noticeable in a few ways; it hurts the eyes, which is why it's hard to focus on things under a black light; it causes sunburns, although the amount given off by a black light is far too insignificant to do this in a realistic time; and it causes a fluorescence reaction in semen, some food stains, and dust making them appear to glow, which is why the robes look dirty. As such, a "{{w|Lightsaber|blacklightsaber}}" would, indeed, be a bad idea.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>**It also causes a fluorescent reaction in several types of cloth - which is why it has been used in discothèques, because of the way people in white T-shirts will light up.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>**It also causes a fluorescent reaction in several types of cloth - <ins class="diffchange diffchange-inline">most notably white cotton, </ins>which is why it has been used in discothèques, because of the way people in white T-shirts will light up.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Interestingly, there is a "Black Lightsaber" in Star Wars canon; a unique, one-of-a-kind weapon known as the [http://starwars.wikia.com/wiki/Darksaber_(lightsaber) Darksaber].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Interestingly, there is a "Black Lightsaber" in Star Wars canon; a unique, one-of-a-kind weapon known as the [http://starwars.wikia.com/wiki/Darksaber_(lightsaber) Darksaber].</div></td></tr>
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</table>162.158.255.127//www.explainxkcd.com/wiki/index.php?title=1017:_Backward_in_Time&diff=125822&oldid=1227121017: Backward in Time2016-08-27T00:13:45Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[940|(Also, the workout website, Fitocracy has been mentioned previously in xkcd.)]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[940|(Also, the workout website, Fitocracy has been mentioned previously in xkcd.)]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Note that as of the time that this page was last cached, the comic was uploaded at {{#expr:100*sqrt((ln(({{#time:U}}-1329195600)/31536000+e^3)-3)/20.3444)}}% progress.</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>LegionMammal978//www.explainxkcd.com/wiki/index.php?title=475:_Further_Boomerang_Difficulties&diff=125819&oldid=123958475: Further Boomerang Difficulties2016-08-26T21:06:28Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The first strip shows [[Cueball]] throwing a boomerang, which doesn't come back. In [[939: Arrow]], a boomerang returns to Cueball, which can either be the same Cueball from this comic or another person.  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The first strip shows [[Cueball]] throwing a boomerang, which doesn't come back. In [[939: Arrow]], a boomerang returns to Cueball, which can either be the same Cueball from this comic or another person.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In the second strip he throws another boomerang, which somehow manage to hurt the {{w|ozone layer}} (as indicated by an off-screen voice). This is of course not possible with a boomerang, as it is a layer of ozone molecules very high up in the atmosphere.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In the second strip he throws another boomerang, which somehow manage to hurt the {{w|ozone layer}} (as indicated by an off-screen voice). This is of course not possible with a boomerang,<ins class="diffchange diffchange-inline">{{Citation needed}} </ins>as it is a layer of ozone molecules very high up in the atmosphere.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The third strip shows Cueball throwing something that ''appears'' to be a boomerang, but then [[Megan]] enters and reveals that it was their last banana - which she probably had expected to eat since she calls him an asshole.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The third strip shows Cueball throwing something that ''appears'' to be a boomerang, but then [[Megan]] enters and reveals that it was their last banana - which she probably had expected to eat since she calls him an asshole.</div></td></tr>
</table>108.162.218.107//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125814&oldid=1257971724: Proofs2016-08-26T19:44:08Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular <del class="diffchange diffchange-inline">theorem </del>is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²''. Therefore ''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular <ins class="diffchange diffchange-inline">condition </ins>is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²''. Therefore ''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td></tr>
</table>108.162.219.68//www.explainxkcd.com/wiki/index.php?title=1556:_The_Sky&diff=125812&oldid=1244931556: The Sky2016-08-26T18:17:05Z<p>Added more details about the "one of the favorite halves"</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In this comic [[Cueball]] and [[Megan]] admire a majestic sky on a beautiful day. This is one of the few comics where the scenery is drawn entirely in color, adding to the feeling of awe and natural wonder. The lighting on the clouds and the night sky in the upper corner suggest that this is either at sunset or sunrise and the picture is drawn to show the ever changing beauty of the many different stages of the sky. When the sun falls below the horizon the light produces many different colors which can often be breathtaking to witness. Similar things happen at sunrise.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In this comic [[Cueball]] and [[Megan]] admire a majestic sky on a beautiful day. This is one of the few comics where the scenery is drawn entirely in color, adding to the feeling of awe and natural wonder. The lighting on the clouds and the night sky in the upper corner suggest that this is either at sunset or sunrise and the picture is drawn to show the ever changing beauty of the many different stages of the sky. When the sun falls below the horizon the light produces many different colors which can often be breathtaking to witness. Similar things happen at sunrise.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Megan says that the sky is one of her favorite halves, an odd <del class="diffchange diffchange-inline">way to refer </del>to the <del class="diffchange diffchange-inline">sky and without the title text its difficult to figure out what </del>she <del class="diffchange diffchange-inline">means</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Megan says that the sky is one of her favorite halves, <ins class="diffchange diffchange-inline">which is </ins>an odd <ins class="diffchange diffchange-inline">thing </ins>to <ins class="diffchange diffchange-inline">say. There are exactly two halves, so being "one of" her favorite in a set of two items is at best a meaningless statement. The implication is that she quite enjoys this half, but may find </ins>the <ins class="diffchange diffchange-inline">other half equally or more enjoyable; in other words, </ins>she <ins class="diffchange diffchange-inline">likes it all</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The title text <del class="diffchange diffchange-inline">suggests she </del>is <del class="diffchange diffchange-inline">referring to </del>the <del class="diffchange diffchange-inline">earth </del>and the <del class="diffchange diffchange-inline">sky</del>. Both can be beautiful in their own right and, as the title text points out, <del class="diffchange diffchange-inline">beyond </del>the <del class="diffchange diffchange-inline">earth underfoot there is </del>more sky.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The title text <ins class="diffchange diffchange-inline">demonstrates that the other half which </ins>is <ins class="diffchange diffchange-inline">not </ins>the <ins class="diffchange diffchange-inline">sky is the ground, water, </ins>and <ins class="diffchange diffchange-inline">various other things on </ins>the <ins class="diffchange diffchange-inline">Earth</ins>. Both <ins class="diffchange diffchange-inline">of these halves </ins>can be beautiful in their own right<ins class="diffchange diffchange-inline">, </ins>and, as the title text points out, <ins class="diffchange diffchange-inline">if </ins>the <ins class="diffchange diffchange-inline">Earth were to be moved then underneath it would be </ins>more sky.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>108.162.216.87//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125797&oldid=1257811724: Proofs2016-08-26T13:52:20Z<p><span dir="auto"><span class="autocomment">Explanation: </span> rm "the"</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²''<del class="diffchange diffchange-inline">, therefor </del>''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²''<ins class="diffchange diffchange-inline">. Therefore </ins>''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The way<del class="diffchange diffchange-inline">, </del>Ms Lenhart's proof refers to the act of doing math itself, is characteristic <del class="diffchange diffchange-inline">to </del>metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in <del class="diffchange diffchange-inline">the </del>{{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The way <ins class="diffchange diffchange-inline">that </ins>Ms Lenhart's proof refers to the act of doing math itself, is characteristic <ins class="diffchange diffchange-inline">of </ins>metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to <del class="diffchange diffchange-inline">the </del>{{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The axiom of choice itself states that for every collection of nonempty sets, you can have a function that draws one element from each set of the collection. This axiom, once considered controversial, was added relatively late to the axiomatic set theory, and even contemporary mathematicians still study which theorems really require its inclusion. In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. {{w|Determinacy}} of infinite games is used as a tool in the set theory, however the deterministic process is rather a term of the {{w|stochastic process|stochastic processes theory}}, and the {{w|dynamical systems theory}}, branches of mathematics far from the abstract set theory, which makes the proof even more exotic. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The axiom of choice itself states that for every collection of nonempty sets, you can have a function that draws one element from each set of the collection. This axiom, once considered controversial, was added relatively late to the axiomatic set theory, and even contemporary mathematicians still study which theorems really require its inclusion. In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. {{w|Determinacy}} of infinite games is used as a tool in the set theory, however the deterministic process is rather a term of the {{w|stochastic process|stochastic processes theory}}, and the {{w|dynamical systems theory}}, branches of mathematics far from the abstract set theory, which makes the proof even more exotic. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
</table>Slashme//www.explainxkcd.com/wiki/index.php?title=925:_Cell_Phones&diff=125791&oldid=125768925: Cell Phones2016-08-26T13:25:19Z<p><span dir="auto"><span class="autocomment">Explanation: </span> I don't know how that lasted that long</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>After hearing about the "Cell Phones Don't Cause Cancer" study, which refutes a claim made by the ''{{w|World Health Organization}}'' (just Google the debate, the comic doesn't focus much on it), [[Black Hat]] plots "Total Cancer Incidence" per 100,000 and "Cell Phone Users" per 100 on the same graph. The graph in frame 3 shows an exponential rise in cancer followed by an exponential rise in cell phone usage, which makes Black Hat comically come to the conclusion that cancer causes cell phones.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>After hearing about the "Cell Phones Don't Cause Cancer" study, which refutes a claim made by the ''{{w|World Health Organization}}'' (just Google the debate, the comic doesn't focus much on it), [[Black Hat]] plots "Total Cancer Incidence" per 100,000 and "Cell Phone Users" per 100 on the same graph. The graph in frame 3 shows an exponential rise in cancer followed by an exponential rise in cell phone usage, which makes Black Hat comically come to the conclusion that cancer causes cell phones.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The comic highlights a well-known fallacy known as ''{{w|post hoc ergo propter hoc}}'', often shortened to simply ''post hoc.'' The Latin translates to "after this, therefore because of this," referring to the common mistake that because two events happen in chronological order, the former event must have caused the latter event. The fallacy is often the root cause of many superstitions (e.g., a person noticing he/she wore a special bracelet before getting a good test score thinks the bracelet was the source of his/her good fortune <del class="diffchange diffchange-inline">when it was more likely to be her socks.</del>), but it often crosses into more serious areas of thinking. In this case, the scientific research community, which often prides itself on its intellectual aptitude, is gently mocked for being nonetheless prone to such poor reasoning all too often. The different possibilities are generally known as causation, when one thing is proven to cause another, or correlation, when changes in one thing are aligned with changes in another, but there is no proof that they are actually related.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The comic highlights a well-known fallacy known as ''{{w|post hoc ergo propter hoc}}'', often shortened to simply ''post hoc.'' The Latin translates to "after this, therefore because of this," referring to the common mistake that because two events happen in chronological order, the former event must have caused the latter event. The fallacy is often the root cause of many superstitions (e.g., a person noticing he/she wore a special bracelet before getting a good test score thinks the bracelet was the source of his/her good fortune), but it often crosses into more serious areas of thinking. In this case, the scientific research community, which often prides itself on its intellectual aptitude, is gently mocked for being nonetheless prone to such poor reasoning all too often. The different possibilities are generally known as causation, when one thing is proven to cause another, or correlation, when changes in one thing are aligned with changes in another, but there is no proof that they are actually related.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The title text refers to the way Black Hat holds the laptop in panel 2. Being that Cueball (and Randall, for that matter) are quite into computers, the potential damage to a laptop screen either from the weight of its lower body or the pressure of the user's fingers on the LCD screen is enough to make him squirm in discomfort.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The title text refers to the way Black Hat holds the laptop in panel 2. Being that Cueball (and Randall, for that matter) are quite into computers, the potential damage to a laptop screen either from the weight of its lower body or the pressure of the user's fingers on the LCD screen is enough to make him squirm in discomfort.</div></td></tr>
</table>Lackadaisical//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125781&oldid=1257761724: Proofs2016-08-26T12:27:36Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. <del class="diffchange diffchange-inline">The axiom </del>of <del class="diffchange diffchange-inline">choice itself </del>is a <del class="diffchange diffchange-inline">non-constructive axiom </del>in <del class="diffchange diffchange-inline">mathematics</del>, <del class="diffchange diffchange-inline">it asserts </del>the <del class="diffchange diffchange-inline">existence </del>of <del class="diffchange diffchange-inline">objects</del>, <del class="diffchange diffchange-inline">without providing a method </del>of <del class="diffchange diffchange-inline">constructing them</del>, <del class="diffchange diffchange-inline">in particular there is no deterministic process by </del>which <del class="diffchange diffchange-inline">we can define objects whose existence can only be proved using </del>the <del class="diffchange diffchange-inline">axiom of choice</del>. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to the {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">The axiom of choice itself states that for every collection of nonempty sets, you can have a function that draws one element from each set of the collection. This axiom, once considered controversial, was added relatively late to the axiomatic set theory, and even contemporary mathematicians still study which theorems really require its inclusion. </ins>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. <ins class="diffchange diffchange-inline">{{w|Determinacy}} </ins>of <ins class="diffchange diffchange-inline">infinite games </ins>is <ins class="diffchange diffchange-inline">used as </ins>a <ins class="diffchange diffchange-inline">tool </ins>in <ins class="diffchange diffchange-inline">the set theory</ins>, <ins class="diffchange diffchange-inline">however </ins>the <ins class="diffchange diffchange-inline">deterministic process is rather a term </ins>of <ins class="diffchange diffchange-inline">the {{w|stochastic process|stochastic processes theory}}</ins>, <ins class="diffchange diffchange-inline">and the {{w|dynamical systems theory}}, branches </ins>of <ins class="diffchange diffchange-inline">mathematics far from the abstract set theory</ins>, which <ins class="diffchange diffchange-inline">makes </ins>the <ins class="diffchange diffchange-inline">proof even more exotic</ins>. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class.</div></td></tr>
</table>162.158.133.138//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125776&oldid=1257741724: Proofs2016-08-26T08:33:35Z<p>The explanation for the hover text was completely off. It has nothing to do with Determinacy.</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. <del class="diffchange diffchange-inline">It may be an allusion to the proposed {{w|</del>axiom of <del class="diffchange diffchange-inline">determinacy}} of the set theory. It </del>is, <del class="diffchange diffchange-inline">however, {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with </del>the <del class="diffchange diffchange-inline">axiom </del>of <del class="diffchange diffchange-inline">choice</del>, <del class="diffchange diffchange-inline">which builds another layer </del>of the <del class="diffchange diffchange-inline">joke</del>. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. <ins class="diffchange diffchange-inline">The </ins>axiom of <ins class="diffchange diffchange-inline">choice itself </ins>is <ins class="diffchange diffchange-inline">a non-constructive axiom in mathematics</ins>, <ins class="diffchange diffchange-inline">it asserts </ins>the <ins class="diffchange diffchange-inline">existence </ins>of <ins class="diffchange diffchange-inline">objects</ins>, <ins class="diffchange diffchange-inline">without providing a method </ins>of <ins class="diffchange diffchange-inline">constructing them, in particular there is no deterministic process by which we can define objects whose existence can only be proved using </ins>the <ins class="diffchange diffchange-inline">axiom of choice</ins>. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class.</div></td></tr>
</table>162.158.86.173//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125774&oldid=1257721724: Proofs2016-08-26T02:30:26Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²'', therefor ''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' which in turn rearranges to 2''b²''=''a²'', therefor ''a²'' is even (as any integer multiplied by 2 is even), which means that ''a'' is an even number, as an even number squared is always even and an odd number squared is always odd. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', meaning ''b²''=2''k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Alternatively, instead of a proof by contradiction the setup could be for a one way function. For example, it is relatively easy to test that a solution to a differential equation is valid but choosing the correct solution to test can seem like black magic to students.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of reasoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
</table>173.245.52.76//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125772&oldid=1257701724: Proofs2016-08-25T22:57:47Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'', which means that ''a'' is an even number. This means, that ''a=2k'' and ''2b²=(2k)²=4k²'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a {{w|rational number}} means that, for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}. Yet, multiplying this equation by itself, we get 2=''a²/b²'' <ins class="diffchange diffchange-inline">which in turn rearranges to 2''b²''=''a²'', therefor ''a²'' is even (as any integer multiplied by 2 is even)</ins>, which means that ''a'' is an even number<ins class="diffchange diffchange-inline">, as an even number squared is always even and an odd number squared is always odd</ins>. This means, that ''a=2k'' and ''2b²=(2k)²=4k²<ins class="diffchange diffchange-inline">'', meaning ''b²''=2''k²</ins>'', so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of <del class="diffchange diffchange-inline">resoning</del>" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The way, Ms Lenhart's proof refers to the act of doing math itself, is characteristic to metamathematical proofs, for example {{w|Gödel's incompleteness theorems}}, which, at first sight, may indeed look like black magic, even if in the end they must be a "perfectly sensible chain of <ins class="diffchange diffchange-inline">reasoning</ins>" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 {{w|Kurt Gödel}} was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. It may be an allusion to the proposed {{w|axiom of determinacy}} of the set theory. It is, however, {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the axiom of choice, which builds another layer of the joke. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. It may be an allusion to the proposed {{w|axiom of determinacy}} of the set theory. It is, however, {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the axiom of choice, which builds another layer of the joke. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
</table>Hppavilion1//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125770&oldid=1257671724: Proofs2016-08-25T22:09:10Z<p><span dir="auto"><span class="autocomment">Explanation: </span> removed 'undergraduate,' no indication this is a graduate class</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. It may be an allusion to the proposed {{w|axiom of determinacy}} of the set theory. It is, however, {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the axiom of choice, which builds another layer of the joke. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. It may be an allusion to the proposed {{w|axiom of determinacy}} of the set theory. It is, however, {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the axiom of choice, which builds another layer of the joke. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in <del class="diffchange diffchange-inline">the </del>her <del class="diffchange diffchange-inline">undergraduate </del>class.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her <ins class="diffchange diffchange-inline">prior </ins>class.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>Miamiclay//www.explainxkcd.com/wiki/index.php?title=397:_Unscientific&diff=125769&oldid=124835397: Unscientific2016-08-25T17:45:49Z<p>Expounded jab at String Theorists</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the first and second frames, [[Megan]] can be seen accusing {{w|MythBusters}} of not actually "doing science" because of its lack of {{w|Rigour|rigor}} - a debate beyond the scope of this Wiki. The {{w|zombie}} of deceased physicist, {{w|Richard Feynman}}, comes to explain to [[Megan]] that she has failed to recognize the purpose of MythBusters. He explains that MythBusters' value is getting people to accept and understand the importance of experimentation in the scientific method, and that more complex lessons (such as on rigor) would be wasted on people who don't understand those basics.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the first and second frames, [[Megan]] can be seen accusing {{w|MythBusters}} of not actually "doing science" because of its lack of {{w|Rigour|rigor}} - a debate beyond the scope of this Wiki. The {{w|zombie}} of deceased physicist, {{w|Richard Feynman}}, comes to explain to [[Megan]] that she has failed to recognize the purpose of MythBusters. He explains that MythBusters' value is getting people to accept and understand the importance of experimentation in the scientific method, and that more complex lessons (such as on rigor) would be wasted on people who don't understand those basics.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In the last frame, [[Cueball]] attempts to save himself and [[Megan]] from zombie Feynman by implying that physicists, being extremely intelligent, would have more desirable brains. Also, being a lab, the number of brains available would be higher than just two. Feynman's closing remark implies that {{w|String theory|string theorists}} are less intelligent than <del class="diffchange diffchange-inline">other types of physicists</del>. This notion fits appropriately with Feynman's description of the core of science. Moreover, Feynman's own career involved applying physics to real world applications (such as for the Manhattan Project), whereas the work of string theorists is theoretical and untested.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In the last frame, [[Cueball]] attempts to save himself and [[Megan]] from zombie Feynman by implying that physicists, being extremely intelligent, would have more desirable brains. Also, being a lab, the number of brains available would be higher than just two. Feynman's closing remark implies that {{w|String theory|string theorists}} <ins class="diffchange diffchange-inline">have no brains; the joke being that string theorists </ins>are <ins class="diffchange diffchange-inline">presumably </ins>less intelligent than <ins class="diffchange diffchange-inline">Cueball and Megan, who were merely watching television prior to being attacked</ins>. This notion fits appropriately with Feynman's description of the core of science. Moreover, Feynman's own career involved applying physics to real world applications (such as for the Manhattan Project), whereas the work of string theorists is theoretical and untested.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The title text starts by rebounding against the complaint of validity as science by purportedly tackling a ''really'' big scientific inquiry. Then veers away into two far more esoteric proposed fields of study, of which at least one is not even determinable by the scientific method{{Citation needed}}.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The title text starts by rebounding against the complaint of validity as science by purportedly tackling a ''really'' big scientific inquiry. Then veers away into two far more esoteric proposed fields of study, of which at least one is not even determinable by the scientific method{{Citation needed}}.</div></td></tr>
</table>162.158.74.78//www.explainxkcd.com/wiki/index.php?title=925:_Cell_Phones&diff=125768&oldid=112833925: Cell Phones2016-08-25T16:44:45Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This comic is a good explanation of the correlation/causation fallacy, where one party states two unrelated events and posits that they must have influenced each other.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This comic is a good explanation of the correlation/causation fallacy, where one party states two unrelated events and posits that they must have influenced each other.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>After hearing about the "Cell Phones Don't Cause Cancer" study, which refutes a claim made by the World Health Organization (just Google the debate, the comic doesn't focus much on it), [[Black Hat]] plots "Total Cancer Incidence" per 100,000 and "Cell Phone Users" per 100 on the same graph. The graph in frame 3 shows an exponential rise in cancer followed by an exponential rise in cell phone usage, which makes Black Hat comically come to the conclusion that cancer causes cell phones.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>After hearing about the "Cell Phones Don't Cause Cancer" study, which refutes a claim made by the <ins class="diffchange diffchange-inline">''{{w|</ins>World Health Organization<ins class="diffchange diffchange-inline">}}'' </ins>(just Google the debate, the comic doesn't focus much on it), [[Black Hat]] plots "Total Cancer Incidence" per 100,000 and "Cell Phone Users" per 100 on the same graph. The graph in frame 3 shows an exponential rise in cancer followed by an exponential rise in cell phone usage, which makes Black Hat comically come to the conclusion that cancer causes cell phones.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The comic highlights a well-known fallacy known as ''{{w|post hoc ergo propter hoc}}'', often shortened to simply ''post hoc.'' The Latin translates to "after this, therefore because of this," referring to the common mistake that because two events happen in chronological order, the former event must have caused the latter event. The fallacy is often the root cause of many superstitions (e.g., a person noticing he/she wore a special bracelet before getting a good test score thinks the bracelet was the source of his/her good fortune when it was more likely to be her socks.), but it often crosses into more serious areas of thinking. In this case, the scientific research community, which often prides itself on its intellectual aptitude, is gently mocked for being nonetheless prone to such poor reasoning all too often. The different possibilities are generally known as causation, when one thing is proven to cause another, or correlation, when changes in one thing are aligned with changes in another, but there is no proof that they are actually related.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The comic highlights a well-known fallacy known as ''{{w|post hoc ergo propter hoc}}'', often shortened to simply ''post hoc.'' The Latin translates to "after this, therefore because of this," referring to the common mistake that because two events happen in chronological order, the former event must have caused the latter event. The fallacy is often the root cause of many superstitions (e.g., a person noticing he/she wore a special bracelet before getting a good test score thinks the bracelet was the source of his/her good fortune when it was more likely to be her socks.), but it often crosses into more serious areas of thinking. In this case, the scientific research community, which often prides itself on its intellectual aptitude, is gently mocked for being nonetheless prone to such poor reasoning all too often. The different possibilities are generally known as causation, when one thing is proven to cause another, or correlation, when changes in one thing are aligned with changes in another, but there is no proof that they are actually related.</div></td></tr>
</table>162.158.85.123//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125767&oldid=1257531724: Proofs2016-08-25T15:29:28Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">{{incomplete|More on the match, especially the title text.}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those <ins class="diffchange diffchange-inline">dark-magic </ins>(<ins class="diffchange diffchange-inline">unclear, incomprehensible</ins>) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those <del class="diffchange diffchange-inline">{{w|Magic_</del>(<del class="diffchange diffchange-inline">programming</del>)<del class="diffchange diffchange-inline">#Variants|Dark Magic}} </del>proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">If this actually refers to the </del>proof <del class="diffchange diffchange-inline">being magical</del>, <del class="diffchange diffchange-inline">or just </del>to the <del class="diffchange diffchange-inline">fact </del>that <del class="diffchange diffchange-inline">many students often feel like the resulting proof just appeared without any reason</del>, <del class="diffchange diffchange-inline">i.e</del>. <del class="diffchange diffchange-inline">either the teacher did not do it clearly</del>, <del class="diffchange diffchange-inline">or the student </del>is <del class="diffchange diffchange-inline">not up to the task of understanding proofs of </del>that <del class="diffchange diffchange-inline">complexity</del>, is <del class="diffchange diffchange-inline">not clear</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">The </ins>proof <ins class="diffchange diffchange-inline">she starts setting up resembles a {{w|proof by contradiction}}. This kind of proof assumes that a particular theorem is true</ins>, <ins class="diffchange diffchange-inline">and shows that this assumption leads </ins>to <ins class="diffchange diffchange-inline">a contradiction, which disproves </ins>the <ins class="diffchange diffchange-inline">initial assumption. For example assumption that √2 is a {{w|rational number}} means </ins>that, <ins class="diffchange diffchange-inline">for some natural ''a'' and ''b'', √2=''a/b'', where ''a/b'' is an {{w|irreducible fraction}}</ins>. <ins class="diffchange diffchange-inline">Yet</ins>, <ins class="diffchange diffchange-inline">multiplying this equation by itself, we get 2=''a²/b²'', which means that ''a'' </ins>is <ins class="diffchange diffchange-inline">an even number. This means, </ins>that <ins class="diffchange diffchange-inline">''a=2k'' and ''2b²=(2k)²=4k²''</ins>, <ins class="diffchange diffchange-inline">so ''b'' must be even too. But if both ''a'' and ''b'' are even, ''a/b'' cannot be irreducible. Contradiction means that the initial assumption </ins>is <ins class="diffchange diffchange-inline">false, and √2 cannot be a rational number</ins>.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof <del class="diffchange diffchange-inline">she starts setting up resembles a </del>{{w|<del class="diffchange diffchange-inline">proof by contradiction</del>}}<del class="diffchange diffchange-inline">. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics</del>, <del class="diffchange diffchange-inline">much </del>like <del class="diffchange diffchange-inline">summoning of demons is associated with </del>black magic<del class="diffchange diffchange-inline">. This is usually done by relying on knowledge </del>of the <del class="diffchange diffchange-inline">constraints </del>of <del class="diffchange diffchange-inline">the form (for example</del>, <del class="diffchange diffchange-inline">having </del>the <del class="diffchange diffchange-inline">square root </del>of <del class="diffchange diffchange-inline">2 be ''a/b'' where ''a'' </del>and <del class="diffchange diffchange-inline">''b'' are both integers and have no common factors when </del>proving <del class="diffchange diffchange-inline">that the square root of 2 is irrational)</del>. <del class="diffchange diffchange-inline">This common usage is then shown to be not the case </del>in <del class="diffchange diffchange-inline">the comic as the proof then goes </del>to <del class="diffchange diffchange-inline">claim </del>that <del class="diffchange diffchange-inline">the answer will be written in a specific place </del>(<del class="diffchange diffchange-inline">though this could be taken as indicating </del>that <del class="diffchange diffchange-inline">the result </del>is <del class="diffchange diffchange-inline">finite or </del>has <del class="diffchange diffchange-inline">a simple algorithm for continuing it). This may also be a reference to proof by induction</del>, <del class="diffchange diffchange-inline">which </del>can be <del class="diffchange diffchange-inline">thought </del>of as a <del class="diffchange diffchange-inline">proof </del>of the <del class="diffchange diffchange-inline">existence of an infinite number of more specific proofs</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The <ins class="diffchange diffchange-inline">way, Ms Lenhart's </ins>proof <ins class="diffchange diffchange-inline">refers to the act of doing math itself, is characteristic to metamathematical proofs, for example </ins>{{w|<ins class="diffchange diffchange-inline">Gödel's incompleteness theorems</ins>}}, <ins class="diffchange diffchange-inline">which, at first sight, may indeed look </ins>like black magic<ins class="diffchange diffchange-inline">, even if in the end they must be a "perfectly sensible chain </ins>of <ins class="diffchange diffchange-inline">resoning" like </ins>the <ins class="diffchange diffchange-inline">rest </ins>of <ins class="diffchange diffchange-inline">good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions, points or lines</ins>, the <ins class="diffchange diffchange-inline">metamathematical theorems treat other theorems as objects </ins>of <ins class="diffchange diffchange-inline">interest. In this way you can propose </ins>and <ins class="diffchange diffchange-inline">prove theorems about possibility of </ins>proving <ins class="diffchange diffchange-inline">other theorems</ins>. <ins class="diffchange diffchange-inline">For example, </ins>in <ins class="diffchange diffchange-inline">1931 {{w|Kurt Gödel}} was able </ins>to <ins class="diffchange diffchange-inline">prove </ins>that <ins class="diffchange diffchange-inline">any mathematical system based on arithmetics </ins>(that is <ins class="diffchange diffchange-inline">using numbers) </ins>has <ins class="diffchange diffchange-inline">statements that are true</ins>, <ins class="diffchange diffchange-inline">but </ins>can be <ins class="diffchange diffchange-inline">neither proved nor disproved. This kind </ins>of <ins class="diffchange diffchange-inline">metamathematical reasoning is especially useful in the {{w|set theory}}, where many statements become impossible to prove and disprove if the {{w|axiom of choice}} is not taken </ins>as a <ins class="diffchange diffchange-inline">part </ins>of the <ins class="diffchange diffchange-inline">axiomatic system</ins>.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the <del class="diffchange diffchange-inline">{{w|</del>axiom of choice<del class="diffchange diffchange-inline">}} </del>is made by a deterministic process. <del class="diffchange diffchange-inline">The </del>{{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the <del class="diffchange diffchange-inline">{{w|</del>axiom of choice<del class="diffchange diffchange-inline">}}</del>, which <del class="diffchange diffchange-inline">is the continuation </del>of the joke <del class="diffchange diffchange-inline">of these dark magic proofs</del>. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the axiom of choice is made by a deterministic process<ins class="diffchange diffchange-inline">, that is a process which future states can be developed with no randomness involved</ins>. <ins class="diffchange diffchange-inline">It may be an allusion to the proposed </ins>{{w|axiom of determinacy}} <ins class="diffchange diffchange-inline">of the set theory. It </ins>is<ins class="diffchange diffchange-inline">, however, </ins>{{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the axiom of choice, which <ins class="diffchange diffchange-inline">builds another layer </ins>of the joke. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in the her undergraduate class.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in the her undergraduate class.</div></td></tr>
</table>162.158.133.138//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125753&oldid=1257471724: Proofs2016-08-25T11:29:31Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in the her undergraduate class<del class="diffchange diffchange-inline">..</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in the her undergraduate class.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>RChandra//www.explainxkcd.com/wiki/index.php?title=804:_Pumpkin_Carving&diff=125749&oldid=116870804: Pumpkin Carving2016-08-25T06:36:39Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the 4th frame, [[Cueball]] is referencing the {{w|Banach-Tarski paradox}}, a theorem which states that it is possible to carve a three-dimensional ball, in this case a pumpkin, into a finite number of "pieces," and then reassemble the "pieces" into two different balls identical to the original. This paradox has been proven for just about anything theoretically, but requires infinitely complicated pieces, which are impossible for anything made of physical {{w|atomic theory|atoms}} rather than mathematical {{w|point (geometry)|points}}. The person off-screen in that frame references the {{w|Axiom of Choice}}, which says that given a set of buckets or bins, each containing one or more objects, it is possible to select exactly one object from each bucket. The Banach-Tarski rests on several axioms which are fairly well respected, but also requires the Axiom of Choice to work correctly. So a person who does not believe in the Axiom of Choice would not have been able to do what [[Cueball]] managed to do.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the 4th frame, [[Cueball]] is referencing the {{w|Banach-Tarski paradox}}, a theorem which states that it is possible to carve a three-dimensional ball, in this case a pumpkin, into a finite number of "pieces," and then reassemble the "pieces" into two different balls identical to the original. This paradox has been proven for just about anything theoretically, but requires infinitely complicated pieces, which are impossible for anything made of physical {{w|atomic theory|atoms}} rather than mathematical {{w|point (geometry)|points}}. The person off-screen in that frame references the {{w|Axiom of Choice}}, which says that given a set of buckets or bins, each containing one or more objects, it is possible to select exactly one object from each bucket. The Banach-Tarski rests on several axioms which are fairly well respected, but also requires the Axiom of Choice to work correctly. So a person who does not believe in the Axiom of Choice would not have been able to do what [[Cueball]] managed to do.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The title text says that {{w|Solomon|King Solomon}} developed the Banach-Tarski theorem first. This is a reference to the story of two women being brought before him. Both were arguing that a particular child was their own. Solomon said that the solution was to cut the baby in half and give each woman one of the halves. One of the two women said that the other should have the baby whole. Solomon then knew she was the true mother, and gave her the child. The joke is that Solomon may <del class="diffchange diffchange-inline">not </del>have intended to <del class="diffchange diffchange-inline">kill </del>the child, but, believing that two whole children could be made from the one, intended give a baby to each woman, and the Banach-Tarski paradox states that, were the baby infinitely divisible, it should <del class="diffchange diffchange-inline">be </del>possible.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The title text says that {{w|Solomon|King Solomon}} developed the Banach-Tarski theorem first. This is a reference to the story of two women being brought before him. Both were arguing that a particular child was their own. Solomon said that the solution was to cut the baby in half and give each woman one of the halves. One of the two women said that the other should have the baby whole. Solomon then knew she was the true mother, and gave her the child. The joke is that Solomon may have <ins class="diffchange diffchange-inline">actually </ins>intended to <ins class="diffchange diffchange-inline">cut </ins>the child, but, believing that two whole children could be made from the one, intended <ins class="diffchange diffchange-inline">to </ins>give a baby to each woman, and the Banach-Tarski paradox states that, were the baby infinitely divisible, it should <ins class="diffchange diffchange-inline">have been </ins>possible.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>162.158.202.150//www.explainxkcd.com/wiki/index.php?title=1720:_Horses&diff=125748&oldid=1254751720: Horses2016-08-25T04:56:08Z<p>added a comma</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This segues into a scene with [[White Hat]], bragging to Cueball and Megan about the features of a car (either to sell the car or simply boast; it's unclear whether White Hat is acting as a salesman) by comparing the features to those of horses. Car engines are traditionally measured in {{w|horsepower}}, which (roughly) compares the power output of the engine to that of a horse. White Hat goes a step further, claiming he can measure the car's onboard computer's driving abilities in the equivalent number of "horses", comparing the car's ability to mitigate for a drunk driver and/or avoid obstacles to that of a horse. (White Hat has been [http://www.explainxkcd.com/wiki/images/9/9f/lorenz_-_sale_2.png depicted as a salesman] before in [[1350: Lorenz]] and similarly earlier in [[260: The Glass Necklace]]).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This segues into a scene with [[White Hat]], bragging to Cueball and Megan about the features of a car (either to sell the car or simply boast; it's unclear whether White Hat is acting as a salesman) by comparing the features to those of horses. Car engines are traditionally measured in {{w|horsepower}}, which (roughly) compares the power output of the engine to that of a horse. White Hat goes a step further, claiming he can measure the car's onboard computer's driving abilities in the equivalent number of "horses", comparing the car's ability to mitigate for a drunk driver and/or avoid obstacles to that of a horse. (White Hat has been [http://www.explainxkcd.com/wiki/images/9/9f/lorenz_-_sale_2.png depicted as a salesman] before in [[1350: Lorenz]] and similarly earlier in [[260: The Glass Necklace]]).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The title text features more comparisons of the car to horses. Apparently the car has 240% of a horse's decision-making ability while producing only 30% as much poop. So even with 3.5 horse-intelligence it may only have 2.4 times the decision-making ability (assuming it's the same car). A cars "poop" would be its exhaust, which is usually not found on the road in the form of solid waste but could still nonetheless be measured, as it contains mass.  While no source is stated for the 30% ratio, the point that cars are less polluting than horses is surprisingly valid when regarding waste left in the street. Before the invention of the automobile, city streets were commonly filled with horse manure. Of course the amount of pollution created by the cars of the world makes them much more toxic both for humans breathing the exhaust fumes and on the larger scale with the climate. (Then again, if there where a horse for each horsepower in all the cars, then that would also be a problem with the release of methane gas etc.)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The title text features more comparisons of the car to horses. Apparently the car has 240% of a horse's decision-making ability while producing only 30% as much poop. So even with 3.5 horse-intelligence it may only have 2.4 times the decision-making ability (assuming it's the same car). A cars "poop" would be its exhaust, which is usually not found on the road in the form of solid waste but could still nonetheless be measured, as it contains mass.  While no source is stated for the 30% ratio, the point that cars are less polluting than horses is surprisingly valid when regarding waste left in the street. Before the invention of the automobile, city streets were commonly filled with horse manure. Of course the amount of pollution created by the cars of the world makes them much more toxic both for humans breathing the exhaust fumes and on the larger scale with the climate. (Then again, if there where a horse for each horsepower in all the cars, then that would also be a problem with the release of methane gas<ins class="diffchange diffchange-inline">, </ins>etc.)</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that riding a horse while drunk is in fact still dangerous and illegal in many places (for example, {{w|Licensing Act 1872|the UK and Ireland}}). A badly-driven horse can throw off its owner, trample passersby, fall on bad surfaces, and destroy any wagon or carriage it's pulling. A self-driving car should be able to understand road rules, which a horse will not - which is presumably why the cars in the comic and the title text are both specified as being more intelligent than a horse.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that riding a horse while drunk is in fact still dangerous and illegal in many places (for example, {{w|Licensing Act 1872|the UK and Ireland}}). A badly-driven horse can throw off its owner, trample passersby, fall on bad surfaces, and destroy any wagon or carriage it's pulling. A self-driving car should be able to understand road rules, which a horse will not - which is presumably why the cars in the comic and the title text are both specified as being more intelligent than a horse.</div></td></tr>
</table>108.162.215.214//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125747&oldid=1257461724: Proofs2016-08-25T03:07:42Z<p>Comment about proof by induction.</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics, much like summoning of demons is associated with black magic. This is usually done by relying on knowledge of the constraints of the form (for example, having the square root of 2 be ''a/b'' where ''a'' and ''b'' are both integers and have no common factors when proving that the square root of 2 is irrational). This common usage is then shown to be not the case in the comic as the proof then goes to claim that the answer will be written in a specific place (though this could be taken as indicating that the result is finite or has a simple algorithm for continuing it).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics, much like summoning of demons is associated with black magic. This is usually done by relying on knowledge of the constraints of the form (for example, having the square root of 2 be ''a/b'' where ''a'' and ''b'' are both integers and have no common factors when proving that the square root of 2 is irrational). This common usage is then shown to be not the case in the comic as the proof then goes to claim that the answer will be written in a specific place (though this could be taken as indicating that the result is finite or has a simple algorithm for continuing it)<ins class="diffchange diffchange-inline">. This may also be a reference to proof by induction, which can be thought of as a proof of the existence of an infinite number of more specific proofs</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
</table>108.162.245.109//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125746&oldid=1257281724: Proofs2016-08-25T00:42:53Z<p>italics</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics, much like summoning of demons is associated with black magic. This is usually done by relying on knowledge of the constraints of the form (for example, having the square root of 2 be a/b where a and b are both integers and have no common factors when proving that the square root of 2 is irrational). This common usage is then shown to be not the case in the comic as the proof then goes to claim that the answer will be written in a specific place (though this could be taken as indicating that the result is finite or has a simple algorithm for continuing it).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The proof she starts setting up resembles a {{w|proof by contradiction}}. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics, much like summoning of demons is associated with black magic. This is usually done by relying on knowledge of the constraints of the form (for example, having the square root of 2 be <ins class="diffchange diffchange-inline">''</ins>a/b<ins class="diffchange diffchange-inline">'' </ins>where <ins class="diffchange diffchange-inline">''</ins>a<ins class="diffchange diffchange-inline">'' </ins>and <ins class="diffchange diffchange-inline">''</ins>b<ins class="diffchange diffchange-inline">'' </ins>are both integers and have no common factors when proving that the square root of 2 is irrational). This common usage is then shown to be not the case in the comic as the proof then goes to claim that the answer will be written in a specific place (though this could be taken as indicating that the result is finite or has a simple algorithm for continuing it).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In the title text the decision of whether to take the {{w|axiom of choice}} is made by a deterministic process. The {{w|axiom of determinacy}} is {{w|Axiom_of_determinacy#Incompatibility_of_the_axiom_of_determinacy_with_the_axiom_of_choice|incompatible}} with the {{w|axiom of choice}}, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is standing facing left in front of a whiteboard writing on it. Eleven left aligned lines of writing is shown as unreadable scribbles. A voice interrupts her from off-panel right.]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is standing facing left in front of a whiteboard writing on it. Eleven left aligned lines of writing is shown as unreadable scribbles. A voice interrupts her from off-panel right.]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:Miss Lenhart: ... Let's assume there exists some function ''F''(a,b,c...) which produces the correct answer-</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:Miss Lenhart: ... Let's assume there exists some function ''F''(<ins class="diffchange diffchange-inline">''</ins>a,b,c<ins class="diffchange diffchange-inline">''</ins>...) which produces the correct answer-</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): Hang on.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): Hang on.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the coordinates (x, y). If <del class="diffchange diffchange-inline">we-</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the coordinates (<ins class="diffchange diffchange-inline">''</ins>x, y<ins class="diffchange diffchange-inline">''</ins>). If <ins class="diffchange diffchange-inline">we—</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): I ''knew'' it!</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): I ''knew'' it!</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>Wwoods//www.explainxkcd.com/wiki/index.php?title=590:_Papyrus&diff=125744&oldid=122371590: Papyrus2016-08-24T21:21:31Z<p><span dir="auto"><span class="autocomment">Explanation: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">(</del><span style="font-family:papyrus"> One of the comics in the "[[:Category:My Hobby|My Hobby]]" series, this one touches on the fact that {{w|Papyrus (typeface)|Papyrus}} ([http://www.explainxkcd.com/wiki/index.php?title=590:_Papyrus&oldid=92915 the font]) is considered to be overused by many typography geeks, including the font's own creator. Pretending that he doesn't know that, [[Cueball]] gives [[Ponytail]] a heartfelt card written in that font just to see her twitch. </span><del class="diffchange diffchange-inline">)</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><span style="font-family:papyrus"> One of the comics in the "[[:Category:My Hobby|My Hobby]]" series, this one touches on the fact that {{w|Papyrus (typeface)|Papyrus}} ([http://www.explainxkcd.com/wiki/index.php?title=590:_Papyrus&oldid=92915 the font]) is considered to be overused by many typography geeks, including the font's own creator. Pretending that he doesn't know that, [[Cueball]] gives [[Ponytail]] a heartfelt card written in that font just to see her twitch. </span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">(</del><span style="font-family:papyrus"> The title text says that [[Randall]] actually ''likes'' Papyrus, even if it ''is'' overused, and refers to the fact that he will soon be receiving hate-mails from people who dislike Papyrus.  Those e-mails will be written in {{w|Helvetica}}, another commonly-used sans-serif font that is highly esteemed by typography geeks, designers, and often hipsters. Those would call that font for '' beautifully-{{w|Kerning|kerned}}''. See also [[1015: Kerning]]. </span><del class="diffchange diffchange-inline">)</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><span style="font-family:papyrus"> The title text says that [[Randall]] actually ''likes'' Papyrus, even if it ''is'' overused, and refers to the fact that he will soon be receiving hate-mails from people who dislike Papyrus.  Those e-mails will be written in {{w|Helvetica}}, another commonly-used sans-serif font that is highly esteemed by typography geeks, designers, and often hipsters. Those would call that font for '' beautifully-{{w|Kerning|kerned}}''. See also [[1015: Kerning]]. </span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Transcript==</div></td></tr>
</table>108.162.237.216//www.explainxkcd.com/wiki/index.php?title=1608:_Hoverboard&diff=125735&oldid=1252891608: Hoverboard2016-08-24T17:38:56Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*To experience the interactivity of this game, visit the {{xkcd|1608|original comic}}.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*To experience the interactivity of this game, visit the {{xkcd|1608|original comic}}.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del class="diffchange diffchange-inline">incomplete</del>|There is now a [[#List of details and references|table below]] where explanation of individual scenes can be listed. Many of the scenes are not yet explained. These are clearly marked with red text. Please help filling out the detail if you can. More details about the coins (why 169?) and the dimensions (what are the actual size in km, and how fast does the hoverboard then move).}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{{<ins class="diffchange diffchange-inline">w</ins>|There is now a [[#List of details and references|table below]] where explanation of individual scenes can be listed. Many of the scenes are not yet explained. These are clearly marked with red text. Please help filling out the detail if you can. More details about the coins (why 169?) and the dimensions (what are the actual size in km, and how fast does the hoverboard then move).}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The "comic" is actually a {{w|browser game}} made to celebrate the release of [[Randall|Randall's]] new book, ''[[Thing Explainer]]'', which was released on the same day as this comic: ''Tuesday'' November 24, 2015.  The comic thus appeared on a Tuesday, replacing that week's normal Wednesday release to coincide with the release day.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The "comic" is actually a {{w|browser game}} made to celebrate the release of [[Randall|Randall's]] new book, ''[[Thing Explainer]]'', which was released on the same day as this comic: ''Tuesday'' November 24, 2015.  The comic thus appeared on a Tuesday, replacing that week's normal Wednesday release to coincide with the release day.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>173.245.48.99//www.explainxkcd.com/wiki/index.php?title=708:_Sex_Dice&diff=125734&oldid=120577708: Sex Dice2016-08-24T17:33:24Z<p>This is not legitimate trivia, as it concerns a fan work.</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Guy lying: I... ''fondle'' the castle guard? That doesn't seem right.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Guy lying: I... ''fondle'' the castle guard? That doesn't seem right.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Hairbun: It did 6 damage, though.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Hairbun: It did 6 damage, though.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Trivia==</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">*Someone took this comic and made it [http://xkcdsw.com/2527 slightly worse]... </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">**In this version the regular dice comes up with 4, so four breast. </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">**Hence they ended up having a threesome to accommodate this dice roll...</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{comic discussion}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{comic discussion}}</div></td></tr>
</table>108.162.216.62//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125728&oldid=1257271724: Proofs2016-08-24T16:16:55Z<p><span dir="auto"><span class="autocomment">Explanation: </span> rewording</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Explanation==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{incomplete|More on the match, especially the title text.}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{incomplete|More on the match, especially the title text.}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those {{w|Magic_(programming)#Variants|Dark Magic}} proofs. She <del class="diffchange diffchange-inline">denies that </del>but it soon turns out that it <del class="diffchange diffchange-inline">will be, and </del>Cueball exclaims that he just knew it would be <del class="diffchange diffchange-inline">one of those</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those {{w|Magic_(programming)#Variants|Dark Magic}} proofs. She <ins class="diffchange diffchange-inline">says no, </ins>but it soon turns out that it <ins class="diffchange diffchange-inline">is; </ins>Cueball exclaims that he just knew it would be.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td></tr>
</table>Garik//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125727&oldid=1257221724: Proofs2016-08-24T15:59:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{incomplete|More on the match, especially the title text.}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{incomplete|More on the match, especially the title text.}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those {{w|Dark Magic}} proofs. She denies that but it soon turns out that it will be, and Cueball exclaims that he just knew it would be one of those.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Miss Lenhart]] is back teaching a math class. She begins a proof when one of her students ([[Cueball]]) interrupts her asking if this is one of those {{w<ins class="diffchange diffchange-inline">|Magic_(programming)#Variants</ins>|Dark Magic}} proofs. She denies that but it soon turns out that it will be, and Cueball exclaims that he just knew it would be one of those.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.</div></td></tr>
</table>Zorlax the Mighty//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=125722&oldid=1257211724: Proofs2016-08-24T15:03:03Z<p><span dir="auto"><span class="autocomment">Transcript: </span> </span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:[Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the <del class="diffchange diffchange-inline">coordinants </del>(x, y). If we-</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the <ins class="diffchange diffchange-inline">coordinates </ins>(x, y). If we-</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): I ''knew'' it!</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:Cueball (off-panel): I ''knew'' it!</div></td></tr>
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</table>N0lqu