https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&feed=atom&action=historyTalk:2048: Curve-Fitting - Revision history2024-03-28T19:39:07ZRevision history for this page on the wikiMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=309672&oldid=prev162.158.154.150 at 19:56, 3 April 20232023-04-03T19:56:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="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;"><div>Personally, I think the exponential fit seems like the most reasonable interpretation of the data.</div></td><td class='diff-marker'> </td><td style="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;"><div>Personally, I think the exponential fit seems like the most reasonable interpretation of the data.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">'''Is the bottom right one considered as part of the Runge Phenomenon?"</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">As learnt in college, where trying to build an overlapping polynomial equation to a graph would create a working model until you move to the side and see the equation that worked until now going way off base 19:56, 3 April 2023 (UTC)D</ins></div></td></tr>
</table>162.158.154.150https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=178891&oldid=prev172.69.62.172 at 18:28, 2 September 20192019-09-02T18:28:21Z<p></p>
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<tr><td class='diff-marker'> </td><td style="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;"><div>The explanation for logistic curve currently says it is used for binary values. It's actually a lot more useful than that. For example, population growth is often described as a logistic curve. It appears to be climbing exponentially initially, but then tapers off as resources can no longer support the population. [[Special:Contributions/108.162.246.191|108.162.246.191]] 15:31, 8 November 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>The explanation for logistic curve currently says it is used for binary values. It's actually a lot more useful than that. For example, population growth is often described as a logistic curve. It appears to be climbing exponentially initially, but then tapers off as resources can no longer support the population. [[Special:Contributions/108.162.246.191|108.162.246.191]] 15:31, 8 November 2018 (UTC)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>:The explanation mentions the {{w|logistic regression}} ranging between "0" and "1". It uses the more general {{w|logistic function}} you probably refer to. The ''logistic regression'' uses in its basic form a ''logistic function'' to model a ''binary'' dependent variable. Both Wikipedia links explain the difference. Honestly, I'm not an expert on that matter but that binary interpretation wouldn't allow values above "1" or below "0" as shown in the picture. Maybe worth to be mentioned. Nonetheless all other fittings are also similar nonsense. Maybe we could mention the more general {{w|Sigmoid function}} but this only barely fits to the title "Logistic Curve". --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 23:09, 8 November 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>:The explanation mentions the {{w|logistic regression}} ranging between "0" and "1". It uses the more general {{w|logistic function}} you probably refer to. The ''logistic regression'' uses in its basic form a ''logistic function'' to model a ''binary'' dependent variable. Both Wikipedia links explain the difference. Honestly, I'm not an expert on that matter but that binary interpretation wouldn't allow values above "1" or below "0" as shown in the picture. Maybe worth to be mentioned. Nonetheless all other fittings are also similar nonsense. Maybe we could mention the more general {{w|Sigmoid function}} but this only barely fits to the title "Logistic Curve". --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 23:09, 8 November 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">Personally, I think the exponential fit seems like the most reasonable interpretation of the data.</ins></div></td></tr>
</table>172.69.62.172https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=165704&oldid=prevDgbrt at 23:09, 8 November 20182018-11-08T23:09:09Z<p></p>
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<tr><td class='diff-marker'> </td><td style="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;"><div>The explanation for logistic curve currently says it is used for binary values. It's actually a lot more useful than that. For example, population growth is often described as a logistic curve. It appears to be climbing exponentially initially, but then tapers off as resources can no longer support the population. [[Special:Contributions/108.162.246.191|108.162.246.191]] 15:31, 8 November 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>The explanation for logistic curve currently says it is used for binary values. It's actually a lot more useful than that. For example, population growth is often described as a logistic curve. It appears to be climbing exponentially initially, but then tapers off as resources can no longer support the population. [[Special:Contributions/108.162.246.191|108.162.246.191]] 15:31, 8 November 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:The explanation mentions the {{w|logistic regression}} ranging between "0" and "1". It uses the more general {{w|logistic function}} you probably refer to. The ''logistic regression'' uses in its basic form a ''logistic function'' to model a ''binary'' dependent variable. Both Wikipedia links explain the difference. Honestly, I'm not an expert on that matter but that binary interpretation wouldn't allow values above "1" or below "0" as shown in the picture. Maybe worth to be mentioned. Nonetheless all other fittings are also similar nonsense. Maybe we could mention the more general {{w|Sigmoid function}} but this only barely fits to the title "Logistic Curve". --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 23:09, 8 November 2018 (UTC)</ins></div></td></tr>
</table>Dgbrthttps://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=165693&oldid=prev108.162.246.191: Logistic curve2018-11-08T15:31:06Z<p>Logistic curve</p>
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<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>In both the '''logarithmic''' and '''exponential''' functions, I have deleted the term "+ ''c''" that was present in both. Simply put, these functions do not include an additive constant. To include the constant removes a basic property of e.g. exponential functions, which is that the function should grow by the same factor for equal increases in the value of ''x''. (In other words, if the functions doubles when ''x'' changes from 1 to 2, then it should double again when ''x'' changes from 2 to 3, or from 3 to 4, etc.) If this does not happen, the function is not exponential. [[User:Redbelly98|Redbelly98]] ([[User talk:Redbelly98|talk]]) 19:52, 13 October 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>In both the '''logarithmic''' and '''exponential''' functions, I have deleted the term "+ ''c''" that was present in both. Simply put, these functions do not include an additive constant. To include the constant removes a basic property of e.g. exponential functions, which is that the function should grow by the same factor for equal increases in the value of ''x''. (In other words, if the functions doubles when ''x'' changes from 1 to 2, then it should double again when ''x'' changes from 2 to 3, or from 3 to 4, etc.) If this does not happen, the function is not exponential. [[User:Redbelly98|Redbelly98]] ([[User talk:Redbelly98|talk]]) 19:52, 13 October 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">'''Logistic Curve'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">The explanation for logistic curve currently says it is used for binary values. It's actually a lot more useful than that. For example, population growth is often described as a logistic curve. It appears to be climbing exponentially initially, but then tapers off as resources can no longer support the population. [[Special:Contributions/108.162.246.191|108.162.246.191]] 15:31, 8 November 2018 (UTC)</ins></div></td></tr>
</table>108.162.246.191https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=164175&oldid=prevRedbelly98: Why I deleted the "+ c" term in the logarithmic and exponential functions.2018-10-13T19:52:16Z<p>Why I deleted the "+ c" term in the logarithmic and exponential functions.</p>
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<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>Excel's "smooth lines" are actually splines ([https://blog.splitwise.com/2012/01/31/mystery-solved-the-secret-of-excel-curved-line-interpolation/ third-order Bezier splines, apparently]) so they're not completely without mathematical merit.  Still wildly unsuited for extrapolation, but often very well suited to interpolation. [[User:JohnWhoIsNotABot|JohnWhoIsNotABot]] ([[User talk:JohnWhoIsNotABot|talk]]) 21:44, 24 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>Excel's "smooth lines" are actually splines ([https://blog.splitwise.com/2012/01/31/mystery-solved-the-secret-of-excel-curved-line-interpolation/ third-order Bezier splines, apparently]) so they're not completely without mathematical merit.  Still wildly unsuited for extrapolation, but often very well suited to interpolation. [[User:JohnWhoIsNotABot|JohnWhoIsNotABot]] ([[User talk:JohnWhoIsNotABot|talk]]) 21:44, 24 September 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">'''Specific functions'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">In both the '''logarithmic''' and '''exponential''' functions, I have deleted the term "+ ''c''" that was present in both. Simply put, these functions do not include an additive constant. To include the constant removes a basic property of e.g. exponential functions, which is that the function should grow by the same factor for equal increases in the value of ''x''. (In other words, if the functions doubles when ''x'' changes from 1 to 2, then it should double again when ''x'' changes from 2 to 3, or from 3 to 4, etc.) If this does not happen, the function is not exponential. [[User:Redbelly98|Redbelly98]] ([[User talk:Redbelly98|talk]]) 19:52, 13 October 2018 (UTC)</ins></div></td></tr>
</table>Redbelly98https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163240&oldid=prevJohnWhoIsNotABot at 21:44, 24 September 20182018-09-24T21:44:04Z<p></p>
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<tr><td class='diff-marker'> </td><td style="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;"><div>Just want to note that the Piecewise models is actually a type of modelling often used in housing economics. It has been used to check if different types of housing are priced according to different rules. [[Special:Contributions/172.68.34.34|172.68.34.34]] 22:05, 21 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>Just want to note that the Piecewise models is actually a type of modelling often used in housing economics. It has been used to check if different types of housing are priced according to different rules. [[Special:Contributions/172.68.34.34|172.68.34.34]] 22:05, 21 September 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">Excel's "smooth lines" are actually splines ([https://blog.splitwise.com/2012/01/31/mystery-solved-the-secret-of-excel-curved-line-interpolation/ third-order Bezier splines, apparently]) so they're not completely without mathematical merit.  Still wildly unsuited for extrapolation, but often very well suited to interpolation. [[User:JohnWhoIsNotABot|JohnWhoIsNotABot]] ([[User talk:JohnWhoIsNotABot|talk]]) 21:44, 24 September 2018 (UTC)</ins></div></td></tr>
</table>JohnWhoIsNotABothttps://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163082&oldid=prev172.68.34.34: Added information about Piecewise model2018-09-21T22:05:28Z<p>Added information about Piecewise model</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 22:05, 21 September 2018</td>
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<tr><td class='diff-marker'> </td><td style="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;"><div>Anyways, what is the actual regression of the plot? {{unsigned ip|162.158.154.241}}</div></td><td class='diff-marker'> </td><td style="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;"><div>Anyways, what is the actual regression of the plot? {{unsigned ip|162.158.154.241}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>:This also must be better explained: We don't know what the points represent. The fraction of apples vs. bananas harvested by time, the position of stars in the sky, on a logarithmic scale, linear, or maybe the height of mountains in New Jersey... There are just some dots on paper with no further meaning. Thus everything Randall presents is valid by some means but an actual regression does not exist. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:32, 21 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>:This also must be better explained: We don't know what the points represent. The fraction of apples vs. bananas harvested by time, the position of stars in the sky, on a logarithmic scale, linear, or maybe the height of mountains in New Jersey... There are just some dots on paper with no further meaning. Thus everything Randall presents is valid by some means but an actual regression does not exist. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:32, 21 September 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">Just want to note that the Piecewise models is actually a type of modelling often used in housing economics. It has been used to check if different types of housing are priced according to different rules. [[Special:Contributions/172.68.34.34|172.68.34.34]] 22:05, 21 September 2018 (UTC)</ins></div></td></tr>
</table>172.68.34.34https://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163071&oldid=prevDgbrt at 20:32, 21 September 20182018-09-21T20:32:28Z<p></p>
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42" >Line 42:</td>
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<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>I hate to be negative here, as obviously some users have put a lot of effort into explaining the details behind each of the curve-fitting methods, but there's absolutely no explanation for Randall's comments on each method.  While someone might learn something about the various methods by reading the explanation, they would not gain any insight on what Randall is saying about each method.  In addition, the Connecting Lines explanation totally missed the fact that this isn't really even a curve-fitting method - it's just a feature of graphing software (in this case, Excel) where a smooth line is drawn through each data point from left to right rather than an example of overfitting to the data set. I think we could do better. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 02:53, 21 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>I hate to be negative here, as obviously some users have put a lot of effort into explaining the details behind each of the curve-fitting methods, but there's absolutely no explanation for Randall's comments on each method.  While someone might learn something about the various methods by reading the explanation, they would not gain any insight on what Randall is saying about each method.  In addition, the Connecting Lines explanation totally missed the fact that this isn't really even a curve-fitting method - it's just a feature of graphing software (in this case, Excel) where a smooth line is drawn through each data point from left to right rather than an example of overfitting to the data set. I think we could do better. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 02:53, 21 September 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:You're not negative, Randall's comments are missing which I've just added into the incomplete reason. And sure other explanations still need a review. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:32, 21 September 2018 (UTC)</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>Everyone is missing the deeper trolling here of the fisheries community at large, which shall become blindingly clear here. First, this is cartoon number 2048 (2^11), a highly interesting number. Notably, this is the year all fisheries were projected to be collapsed by Worm et al. (2006) Science 314:787-790, a prediction which gained huge attention in the media and took on a life of its own. The prediction was based on fitting a power curve to some data on collapses in catch trends. Numerous rebuttals followed, one of which pointed out that a linear fit to the data is a better fit, and predicts all fisheries collapsed in 2114 (Jaenike et al. 2007, Science 316:1285a). A list of rebuttals is found here: https://sites.google.com/a/uw.edu/most-cited-fisheries/controversies/2048-projection. Later work by the same author and critics found a different prediction and showed rebuilding of fisheries is likely (Worm et al. 2009 Science 325:578-585). Second, lest you think this is a conspiracy theory, I note that in xkcd cartoon 887, Munroe specifically notes this prediction "The future according to google search results... 2048: "Salt-water fish extinct from overfishing" https://xkcd.com/887/. Third, this kind of model-fitting exercise has long plagued fisheries researchers attempting to predict recruitment from spawning biomass. {{unsigned ip|108.162.246.11}}</div></td><td class='diff-marker'> </td><td style="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;"><div>Everyone is missing the deeper trolling here of the fisheries community at large, which shall become blindingly clear here. First, this is cartoon number 2048 (2^11), a highly interesting number. Notably, this is the year all fisheries were projected to be collapsed by Worm et al. (2006) Science 314:787-790, a prediction which gained huge attention in the media and took on a life of its own. The prediction was based on fitting a power curve to some data on collapses in catch trends. Numerous rebuttals followed, one of which pointed out that a linear fit to the data is a better fit, and predicts all fisheries collapsed in 2114 (Jaenike et al. 2007, Science 316:1285a). A list of rebuttals is found here: https://sites.google.com/a/uw.edu/most-cited-fisheries/controversies/2048-projection. Later work by the same author and critics found a different prediction and showed rebuilding of fisheries is likely (Worm et al. 2009 Science 325:578-585). Second, lest you think this is a conspiracy theory, I note that in xkcd cartoon 887, Munroe specifically notes this prediction "The future according to google search results... 2048: "Salt-water fish extinct from overfishing" https://xkcd.com/887/. Third, this kind of model-fitting exercise has long plagued fisheries researchers attempting to predict recruitment from spawning biomass. {{unsigned ip|108.162.246.11}}</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="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;"><div>Anyways, what is the actual regression of the plot? {{unsigned ip|162.158.154.241}}</div></td><td class='diff-marker'> </td><td style="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;"><div>Anyways, what is the actual regression of the plot? {{unsigned ip|162.158.154.241}}</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:This also must be better explained: We don't know what the points represent. The fraction of apples vs. bananas harvested by time, the position of stars in the sky, on a logarithmic scale, linear, or maybe the height of mountains in New Jersey... There are just some dots on paper with no further meaning. Thus everything Randall presents is valid by some means but an actual regression does not exist. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:32, 21 September 2018 (UTC)</ins></div></td></tr>
</table>Dgbrthttps://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163069&oldid=prevDgbrt: Please sign your comments and enter new comments at the bottom.2018-09-21T20:14:01Z<p>Please sign your comments and enter new comments at the bottom.</p>
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<tr><td class='diff-marker'>−</td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;">Anyways, what is the actual regression of the plot?</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>House of Cards: Not a real method, but a common consequence of mis-application of statistical methods: a curve can be generated that fits the data extremely well, but immediately becomes absurd as soon as one glances outside the training data sample range, and your analysis comes crashing down "like a house of cards". This is a type of _overfitting_</div></td><td class='diff-marker'> </td><td style="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;"><div>House of Cards: Not a real method, but a common consequence of mis-application of statistical methods: a curve can be generated that fits the data extremely well, but immediately becomes absurd as soon as one glances outside the training data sample range, and your analysis comes crashing down "like a house of cards". This is a type of _overfitting_</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="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;"><div>I hate to be negative here, as obviously some users have put a lot of effort into explaining the details behind each of the curve-fitting methods, but there's absolutely no explanation for Randall's comments on each method.  While someone might learn something about the various methods by reading the explanation, they would not gain any insight on what Randall is saying about each method.  In addition, the Connecting Lines explanation totally missed the fact that this isn't really even a curve-fitting method - it's just a feature of graphing software (in this case, Excel) where a smooth line is drawn through each data point from left to right rather than an example of overfitting to the data set. I think we could do better. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 02:53, 21 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>I hate to be negative here, as obviously some users have put a lot of effort into explaining the details behind each of the curve-fitting methods, but there's absolutely no explanation for Randall's comments on each method.  While someone might learn something about the various methods by reading the explanation, they would not gain any insight on what Randall is saying about each method.  In addition, the Connecting Lines explanation totally missed the fact that this isn't really even a curve-fitting method - it's just a feature of graphing software (in this case, Excel) where a smooth line is drawn through each data point from left to right rather than an example of overfitting to the data set. I think we could do better. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 02:53, 21 September 2018 (UTC)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="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;"><div>Everyone is missing the deeper trolling here of the fisheries community at large, which shall become blindingly clear here. First, this is cartoon number 2048 (2^11), a highly interesting number. Notably, this is the year all fisheries were projected to be collapsed by Worm et al. (2006) Science 314:787-790, a prediction which gained huge attention in the media and took on a life of its own. The prediction was based on fitting a power curve to some data on collapses in catch trends. Numerous rebuttals followed, one of which pointed out that a linear fit to the data is a better fit, and predicts all fisheries collapsed in 2114 (Jaenike et al. 2007, Science 316:1285a). A list of rebuttals is found here: https://sites.google.com/a/uw.edu/most-cited-fisheries/controversies/2048-projection. Later work by the same author and critics found a different prediction and showed rebuilding of fisheries is likely (Worm et al. 2009 Science 325:578-585). Second, lest you think this is a conspiracy theory, I note that in xkcd cartoon 887, Munroe specifically notes this prediction "The future according to google search results... 2048: "Salt-water fish extinct from overfishing" https://xkcd.com/887/. Third, this kind of model-fitting exercise has long plagued fisheries researchers attempting to predict recruitment from spawning biomass.</div></td><td class='diff-marker'>+</td><td style="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;"><div>Everyone is missing the deeper trolling here of the fisheries community at large, which shall become blindingly clear here. First, this is cartoon number 2048 (2^11), a highly interesting number. Notably, this is the year all fisheries were projected to be collapsed by Worm et al. (2006) Science 314:787-790, a prediction which gained huge attention in the media and took on a life of its own. The prediction was based on fitting a power curve to some data on collapses in catch trends. Numerous rebuttals followed, one of which pointed out that a linear fit to the data is a better fit, and predicts all fisheries collapsed in 2114 (Jaenike et al. 2007, Science 316:1285a). A list of rebuttals is found here: https://sites.google.com/a/uw.edu/most-cited-fisheries/controversies/2048-projection. Later work by the same author and critics found a different prediction and showed rebuilding of fisheries is likely (Worm et al. 2009 Science 325:578-585). Second, lest you think this is a conspiracy theory, I note that in xkcd cartoon 887, Munroe specifically notes this prediction "The future according to google search results... 2048: "Salt-water fish extinct from overfishing" https://xkcd.com/887/. Third, this kind of model-fitting exercise has long plagued fisheries researchers attempting to predict recruitment from spawning biomass. <ins class="diffchange diffchange-inline">{{unsigned ip|108.162.246.11}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins class="diffchange diffchange-inline">"Ad hoc filter: Drawing a bunch of different lines by hand, keeping in only the data points perceived as "good". Also not useful. " – I guess it rather refers to data filtering, where for each point you take several points around and try to calculate some kind of mean, e.g. by rejecting most extreme points, or calculating median (see https://en.wikipedia.org/wiki/Median_filter). So it is an algorithm, not actually drawing lines by hand. Still it is tricky to draw conclusions and you can easily fool yourself with this method. {{unsigned ip|162.158.93.21}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="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;"><div><del class="diffchange diffchange-inline">"Ad hoc filter: Drawing a bunch of different lines by hand</del>, <del class="diffchange diffchange-inline">keeping in only </del>the <del class="diffchange diffchange-inline">data points perceived as "good". Also not useful. " – I guess it rather refers to data filtering, where for each point you take several points around and try to calculate some kind </del>of <del class="diffchange diffchange-inline">mean, e</del>.<del class="diffchange diffchange-inline">g</del>. <del class="diffchange diffchange-inline">by rejecting most extreme points, or calculating median (see https://en.wikipedia.org/wiki/Median_filter). So it is an algorithm, not actually drawing lines by hand. Still it is tricky to draw conclusions and you can easily fool yourself with this method</del>.</div></td><td class='diff-marker'>+</td><td style="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;"><div><ins class="diffchange diffchange-inline">Anyways</ins>, <ins class="diffchange diffchange-inline">what is </ins>the <ins class="diffchange diffchange-inline">actual regression </ins>of <ins class="diffchange diffchange-inline">the plot? {{unsigned ip|162</ins>.<ins class="diffchange diffchange-inline">158</ins>.<ins class="diffchange diffchange-inline">154</ins>.<ins class="diffchange diffchange-inline">241}}</ins></div></td></tr>
</table>Dgbrthttps://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163016&oldid=prevCRGreathouse: WAIT NO, NO, DON'T EXTEND IT!2018-09-21T14:20:23Z<p>WAIT NO, NO, DON'T EXTEND IT!</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 14:20, 21 September 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >Line 7:</td>
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<tr><td class='diff-marker'> </td><td style="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;"><div>I'm pretty sure it refers to the TV show house of cards, the dots representing the quality of the series increasing until Netflix renewed it a bit too much {{unsigned ip|172.68.26.65}}</div></td><td class='diff-marker'> </td><td style="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;"><div>I'm pretty sure it refers to the TV show house of cards, the dots representing the quality of the series increasing until Netflix renewed it a bit too much {{unsigned ip|172.68.26.65}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>:This was my initial interpretation as well, since you can hypothetically extend a literal house of cards indefinitely.[[Special:Contributions/172.68.58.83|172.68.58.83]] 14:23, 20 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>:This was my initial interpretation as well, since you can hypothetically extend a literal house of cards indefinitely.[[Special:Contributions/172.68.58.83|172.68.58.83]] 14:23, 20 September 2018 (UTC)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">Could someone familiar with the show expand on this? ''Also a potential reference to the TV show, House of Cards ("WAIT NO, NO, DON'T EXTEND IT!").'' Some context on what that line meant in House of Cards would be helpful. - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 14:20, 21 September 2018 (UTC)</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"></td><td class='diff-marker'> </td><td style="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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="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;"><div>I'm a little mystified by the alt-text. Cauchy and Lorentz both seem like mathematically capable people. What am I missing? [[Special:Contributions/172.69.62.226|172.69.62.226]] 17:46, 19 September 2018 (UTC)</div></td><td class='diff-marker'> </td><td style="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;"><div>I'm a little mystified by the alt-text. Cauchy and Lorentz both seem like mathematically capable people. What am I missing? [[Special:Contributions/172.69.62.226|172.69.62.226]] 17:46, 19 September 2018 (UTC)</div></td></tr>
</table>CRGreathouse