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		<id>https://www.explainxkcd.com/wiki/index.php?action=history&amp;feed=atom&amp;title=Talk%3A410%3A_Math_Paper</id>
		<title>Talk:410: Math Paper - Revision history</title>
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		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;action=history"/>
		<updated>2026-04-13T17:38:04Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=327804&amp;oldid=prev</id>
		<title>Firestar233: comment</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=327804&amp;oldid=prev"/>
				<updated>2023-11-02T23:21:36Z</updated>
		
		<summary type="html">&lt;p&gt;comment&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 23:21, 2 November 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot; &gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I do not agree. Here is how it should work. You should define that a divides b if and only if there is a natural number n such that an = b. This way, natural numbers don't get new divisors when you move to the Gaussian plane. Consequently the extended sigma function gives the same value as the classical one when applied to a natural number. So, natural numbers will be friends according to the new definition if and only if they are friends according to the old definition and we are indeed allowed to say that the new definition extends the old one (Burghard von Karger). {{unsigned ip|162.158.93.28}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I do not agree. Here is how it should work. You should define that a divides b if and only if there is a natural number n such that an = b. This way, natural numbers don't get new divisors when you move to the Gaussian plane. Consequently the extended sigma function gives the same value as the classical one when applied to a natural number. So, natural numbers will be friends according to the new definition if and only if they are friends according to the old definition and we are indeed allowed to say that the new definition extends the old one (Burghard von Karger). {{unsigned ip|162.158.93.28}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:So you're saying that the only friends imaginary friends have are imaginary? [[User:Firestar233|guess who]] ([[User talk:Firestar233|if you want to]] | [[Special:Contributions/Firestar233|what i have done]]) 23:21, 2 November 2023 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Firestar233</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=129607&amp;oldid=prev</id>
		<title>Gmcgath: Poetic license</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=129607&amp;oldid=prev"/>
				<updated>2016-10-30T22:08:30Z</updated>
		
		<summary type="html">&lt;p&gt;Poetic license&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 22:08, 30 October 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l11&quot; &gt;Line 11:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 11:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::I thought it was pretty plainly evident that Cueball is the presenter - going along with the XKCD theme of banning/revoking Cueball's privilege due to &amp;quot;inappropriately&amp;quot; wasting people's time at an ostensibly serious event. Also, in relative agreement with 108.162.216.76, I think that Panel 3 is his feeble attempt to continue to look serious (or straight/deadpan) while thinking of a way to respond, followed in Panel 4 with a slightly defeated shoulder/head slump (giving up with trying to perpetuate his premise). Panel 5 could be viewed as a plain admission, but I prefer to see it as a final, hail-Mary attempt to maintain the graces of the audience without ''actually lying'' to them. -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 16:09, 5 March 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::I thought it was pretty plainly evident that Cueball is the presenter - going along with the XKCD theme of banning/revoking Cueball's privilege due to &amp;quot;inappropriately&amp;quot; wasting people's time at an ostensibly serious event. Also, in relative agreement with 108.162.216.76, I think that Panel 3 is his feeble attempt to continue to look serious (or straight/deadpan) while thinking of a way to respond, followed in Panel 4 with a slightly defeated shoulder/head slump (giving up with trying to perpetuate his premise). Panel 5 could be viewed as a plain admission, but I prefer to see it as a final, hail-Mary attempt to maintain the graces of the audience without ''actually lying'' to them. -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 16:09, 5 March 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:::They are probably beat panels more than anything else. -Pennpenn [[Special:Contributions/108.162.250.155|108.162.250.155]] 00:13, 27 March 2015 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:::They are probably beat panels more than anything else. -Pennpenn [[Special:Contributions/108.162.250.155|108.162.250.155]] 00:13, 27 March 2015 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There's a joke among amateur songwriters that a forced rhyme or other dubious technique might lead to revoking the writer's &amp;quot;poetic license.&amp;quot; [[User:Gmcgath|Gmcgath]] ([[User talk:Gmcgath|talk]]) 22:08, 30 October 2016 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Gmcgath</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=100558&amp;oldid=prev</id>
		<title>Davidy22 at 04:50, 29 August 2015</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=100558&amp;oldid=prev"/>
				<updated>2015-08-29T04:50:23Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 04:50, 29 August 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot; &gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I do not agree. Here is how it should work. You should define that a divides b if and only if there is a natural number n such that an = b. This way, natural numbers don't get new divisors when you move to the Gaussian plane. Consequently the extended sigma function gives the same value as the classical one when applied to a natural number. So, natural numbers will be friends according to the new definition if and only if they are friends according to the old definition and we are indeed allowed to say that the new definition extends the old one (Burghard von Karger).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I do not agree. Here is how it should work. You should define that a divides b if and only if there is a natural number n such that an = b. This way, natural numbers don't get new divisors when you move to the Gaussian plane. Consequently the extended sigma function gives the same value as the classical one when applied to a natural number. So, natural numbers will be friends according to the new definition if and only if they are friends according to the old definition and we are indeed allowed to say that the new definition extends the old one (Burghard von Karger). &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;{{unsigned ip|162.158.93.28}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Davidy22</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=100530&amp;oldid=prev</id>
		<title>162.158.93.28: Better definition</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=100530&amp;oldid=prev"/>
				<updated>2015-08-28T14:55:40Z</updated>
		
		<summary type="html">&lt;p&gt;Better definition&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:55, 28 August 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot; &gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:I do not agree. Here is how it should work. You should define that a divides b if and only if there is a natural number n such that an = b. This way, natural numbers don't get new divisors when you move to the Gaussian plane. Consequently the extended sigma function gives the same value as the classical one when applied to a natural number. So, natural numbers will be friends according to the new definition if and only if they are friends according to the old definition and we are indeed allowed to say that the new definition extends the old one (Burghard von Karger).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>162.158.93.28</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=87127&amp;oldid=prev</id>
		<title>108.162.250.155 at 00:13, 27 March 2015</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=87127&amp;oldid=prev"/>
				<updated>2015-03-27T00:13:03Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 00:13, 27 March 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot; &gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I don't know. In panel three DOES look straight at the commenter in the audience in a deadpan way, like he'd been caught unawares by the person's observation, but in panel four seems to look down, head tilted towards the floor as if wondering &amp;quot;aww shit, now what do I do?&amp;quot; Or like he felt slightly ashamed of being caught. [[Special:Contributions/108.162.216.76|108.162.216.76]] 22:56, 27 February 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I don't know. In panel three DOES look straight at the commenter in the audience in a deadpan way, like he'd been caught unawares by the person's observation, but in panel four seems to look down, head tilted towards the floor as if wondering &amp;quot;aww shit, now what do I do?&amp;quot; Or like he felt slightly ashamed of being caught. [[Special:Contributions/108.162.216.76|108.162.216.76]] 22:56, 27 February 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::I thought it was pretty plainly evident that Cueball is the presenter - going along with the XKCD theme of banning/revoking Cueball's privilege due to &amp;quot;inappropriately&amp;quot; wasting people's time at an ostensibly serious event. Also, in relative agreement with 108.162.216.76, I think that Panel 3 is his feeble attempt to continue to look serious (or straight/deadpan) while thinking of a way to respond, followed in Panel 4 with a slightly defeated shoulder/head slump (giving up with trying to perpetuate his premise). Panel 5 could be viewed as a plain admission, but I prefer to see it as a final, hail-Mary attempt to maintain the graces of the audience without ''actually lying'' to them. -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 16:09, 5 March 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::I thought it was pretty plainly evident that Cueball is the presenter - going along with the XKCD theme of banning/revoking Cueball's privilege due to &amp;quot;inappropriately&amp;quot; wasting people's time at an ostensibly serious event. Also, in relative agreement with 108.162.216.76, I think that Panel 3 is his feeble attempt to continue to look serious (or straight/deadpan) while thinking of a way to respond, followed in Panel 4 with a slightly defeated shoulder/head slump (giving up with trying to perpetuate his premise). Panel 5 could be viewed as a plain admission, but I prefer to see it as a final, hail-Mary attempt to maintain the graces of the audience without ''actually lying'' to them. -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 16:09, 5 March 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:::They are probably beat panels more than anything else. -Pennpenn [[Special:Contributions/108.162.250.155|108.162.250.155]] 00:13, 27 March 2015 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>108.162.250.155</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=61859&amp;oldid=prev</id>
		<title>Brettpeirce at 16:09, 5 March 2014</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=61859&amp;oldid=prev"/>
				<updated>2014-03-05T16:09:34Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 16:09, 5 March 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot; &gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I don't know. In panel three DOES look straight at the commenter in the audience in a deadpan way, like he'd been caught unawares by the person's observation, but in panel four seems to look down, head tilted towards the floor as if wondering &amp;quot;aww shit, now what do I do?&amp;quot; Or like he felt slightly ashamed of being caught. [[Special:Contributions/108.162.216.76|108.162.216.76]] 22:56, 27 February 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:I don't know. In panel three DOES look straight at the commenter in the audience in a deadpan way, like he'd been caught unawares by the person's observation, but in panel four seems to look down, head tilted towards the floor as if wondering &amp;quot;aww shit, now what do I do?&amp;quot; Or like he felt slightly ashamed of being caught. [[Special:Contributions/108.162.216.76|108.162.216.76]] 22:56, 27 February 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;::I thought it was pretty plainly evident that Cueball is the presenter - going along with the XKCD theme of banning/revoking Cueball's privilege due to &amp;quot;inappropriately&amp;quot; wasting people's time at an ostensibly serious event. Also, in relative agreement with 108.162.216.76, I think that Panel 3 is his feeble attempt to continue to look serious (or straight/deadpan) while thinking of a way to respond, followed in Panel 4 with a slightly defeated shoulder/head slump (giving up with trying to perpetuate his premise). Panel 5 could be viewed as a plain admission, but I prefer to see it as a final, hail-Mary attempt to maintain the graces of the audience without ''actually lying'' to them. -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 16:09, 5 March 2014 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Brettpeirce</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=61339&amp;oldid=prev</id>
		<title>108.162.216.76 at 22:56, 27 February 2014</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=61339&amp;oldid=prev"/>
				<updated>2014-02-27T22:56:23Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 22:56, 27 February 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot; &gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;I think no one's noticed the &amp;quot;Straight man's deadpan stare&amp;quot; in panels 3 and 4. After being rudely interrupted in panel two, the lecturer stares silently at the person who stopped him in panel 3. Note the shape of the lecturer's head: his forehead and chin are facing towards the right as revealed by the angled features at the top and bottom of his head. In panel 4 the lecturer turns and stares at the reader and stands silent. Note the completely round shape of the head. This is the classic deadpan stare.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;I think no one's noticed the &amp;quot;Straight man's deadpan stare&amp;quot; in panels 3 and 4. After being rudely interrupted in panel two, the lecturer stares silently at the person who stopped him in panel 3. Note the shape of the lecturer's head: his forehead and chin are facing towards the right as revealed by the angled features at the top and bottom of his head. In panel 4 the lecturer turns and stares at the reader and stands silent. Note the completely round shape of the head. This is the classic deadpan stare.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:I don't know. In panel three DOES look straight at the commenter in the audience in a deadpan way, like he'd been caught unawares by the person's observation, but in panel four seems to look down, head tilted towards the floor as if wondering &amp;quot;aww shit, now what do I do?&amp;quot; Or like he felt slightly ashamed of being caught. [[Special:Contributions/108.162.216.76|108.162.216.76]] 22:56, 27 February 2014 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>108.162.216.76</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=58301&amp;oldid=prev</id>
		<title>ExternalMonolog: Edited my own edit</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=58301&amp;oldid=prev"/>
				<updated>2014-01-21T20:24:22Z</updated>
		
		<summary type="html">&lt;p&gt;Edited my own edit&lt;/p&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:24, 21 January 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot; &gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;I think no one's noticed the &amp;quot;Straight man's deadpan stare&amp;quot; in panels 3 and 4. After being rudely interrupted in panel two, the lecturer stares silently at the person who stopped him in panel 3. Note the shape of the lecturer's head: his chin &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;is &lt;/del&gt;facing towards the right. In panel 4 the lecturer &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;faces &lt;/del&gt;the reader and stands silent. Note the completely round shape of the head. This is the classic deadpan stare.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;I think no one's noticed the &amp;quot;Straight man's deadpan stare&amp;quot; in panels 3 and 4. After being rudely interrupted in panel two, the lecturer stares silently at the person who stopped him in panel 3. Note the shape of the lecturer's head: his &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;forehead and &lt;/ins&gt;chin &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;are &lt;/ins&gt;facing towards the right &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;as revealed by the angled features at the top and bottom of his head&lt;/ins&gt;. In panel 4 the lecturer &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;turns and stares at &lt;/ins&gt;the reader and stands silent. Note the completely round shape of the head. This is the classic deadpan stare.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>ExternalMonolog</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=58300&amp;oldid=prev</id>
		<title>ExternalMonolog: Comment on explanation: reference to physical humor and reference to participants identity</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=58300&amp;oldid=prev"/>
				<updated>2014-01-21T20:14:51Z</updated>
		
		<summary type="html">&lt;p&gt;Comment on explanation: reference to physical humor and reference to participants identity&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:14, 21 January 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l4&quot; &gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I think no one's noticed the &amp;quot;Straight man's deadpan stare&amp;quot; in panels 3 and 4. After being rudely interrupted in panel two, the lecturer stares silently at the person who stopped him in panel 3. Note the shape of the lecturer's head: his chin is facing towards the right. In panel 4 the lecturer faces the reader and stands silent. Note the completely round shape of the head. This is the classic deadpan stare.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Also, am I the only one who assumed that Cueball himself is the lecturer and the person interrupting him is likely the proffessor of the class?[[User:ExternalMonolog|ExternalMonolog]] ([[User talk:ExternalMonolog|talk]]) 20:14, 21 January 2014 (UTC)ExternalMonolog&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>ExternalMonolog</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=56680&amp;oldid=prev</id>
		<title>173.245.53.186 at 15:04, 5 January 2014</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:410:_Math_Paper&amp;diff=56680&amp;oldid=prev"/>
				<updated>2014-01-05T15:04:33Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 15:04, 5 January 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot; &gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Despite what this comic implies, the divisor function is defined over the Gaussian integers. There still is a problem, though. If a divides b, then so does -a, along with ai and -ai. The divisors will inevitably sum to zero. You could get around this by ignoring all the numbers that aren't in a given quadrant. I personally like the idea of using ones where the real part is greater than the imaginary part (although that still does become a problem with multiples of 1+i). This way, a friend of a natural number will also be a natural number (though it's only the same as what you'd get normally if all the factors are three mod four). {{unsigned ip|199.27.128.167}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Does someone care to hazard a guess about the alt text? Are there any possible papers that could have been written about those three fields? [[Special:Contributions/173.245.53.186|173.245.53.186]] 15:04, 5 January 2014 (UTC)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>173.245.53.186</name></author>	</entry>

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