https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&feed=atom&action=history2649: Physics Cost-Saving Tips - Revision history2024-03-28T15:05:25ZRevision history for this page on the wikiMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=316942&oldid=prev172.71.178.136: /* Explanation */ Correcting a new wikilink. Wikilinkifying an old direct wikimedia link, while I'm here.2023-07-04T18:04:20Z<p><span dir="auto"><span class="autocomment">Explanation: </span> Correcting a new wikilink. Wikilinkifying an old direct wikimedia link, while I'm here.</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 18:04, 4 July 2023</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>The smallest nuclear bomb, the {{w|W54}}, had a yield of between 10 and 1,000 tons of TNT. The largest conventional bomb, the {{w|GBU-43/B MOAB}}, has a yield of roughly 11 tons. The {{w|2020 Beirut explosion}} was roughly equivalent to 500 tons. So, while the helium-2 balloon bomb would be larger than all conventional bombs, it would still be smaller than most nukes. Handing out what are effectively small atomic bombs at a county fair would not go down well with any surviving local authorities, so merely being banned is a very mild punishment. Criminal charges such as mass murder and terrorism would be more likely if it weren't for the absurd impossibility of the scenario.</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 smallest nuclear bomb, the {{w|W54}}, had a yield of between 10 and 1,000 tons of TNT. The largest conventional bomb, the {{w|GBU-43/B MOAB}}, has a yield of roughly 11 tons. The {{w|2020 Beirut explosion}} was roughly equivalent to 500 tons. So, while the helium-2 balloon bomb would be larger than all conventional bombs, it would still be smaller than most nukes. Handing out what are effectively small atomic bombs at a county fair would not go down well with any surviving local authorities, so merely being banned is a very mild punishment. Criminal charges such as mass murder and terrorism would be more likely if it weren't for the absurd impossibility of the scenario.</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>The title text is likely also a pun, as the word "{{w|<del class="diffchange diffchange-inline">https://en.wikipedia.org/wiki/Local_ordinance</del>|ordinance}}" means a local law, and the very similar sounding word "[https://www.merriam-webster.com/dictionary/ordnance ordnance]" means artillery and other explosive weapons, which the baloon would qualify as.</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>The title text is likely also a pun, as the word "{{w|<ins class="diffchange diffchange-inline">Local ordinance</ins>|ordinance}}" means a local law, and the very similar sounding word "[https://www.merriam-webster.com/dictionary/ordnance ordnance]" means artillery and other explosive weapons, which the baloon would qualify as.</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>===Table of tips===</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>===Table of tips===</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>|-</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>|-</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} is equal to the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand (<del class="diffchange diffchange-inline">[https://en.wikipedia.org/wiki/Crypto_Wars#/media/</del>File:Munitions_T-shirt_(front).jpg most of the time<del class="diffchange diffchange-inline">]</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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} is equal to the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand (<ins class="diffchange diffchange-inline">{{w|</ins>File:Munitions_T-shirt_(front).jpg<ins class="diffchange diffchange-inline">|</ins>most of the time<ins class="diffchange diffchange-inline">}}</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;"><div>|-</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>|-</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</div></td></tr>
</table>172.71.178.136https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=316934&oldid=prevSqueakSquawk4: Ordanance pun2023-07-04T14:49:55Z<p>Ordanance pun</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 14:49, 4 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17" >Line 17:</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>{{cob}}</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>{{cob}}</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 smallest nuclear bomb, the {{w|W54}}, had a yield of between 10 and 1,000 tons of TNT. The largest conventional bomb, the {{w|GBU-43/B MOAB}}, has a yield of roughly 11 tons. The {{w|2020 Beirut explosion}} was roughly equivalent to 500 tons. So, while the helium-2 balloon bomb would be larger than all conventional bombs, it would still be smaller than most nukes. Handing out what are effectively small atomic bombs at a county fair would not go down well with any surviving local authorities, so merely being banned is a very mild punishment. Criminal charges such as mass murder and terrorism would be more likely if it weren't for the absurd impossibility of the scenario.</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 smallest nuclear bomb, the {{w|W54}}, had a yield of between 10 and 1,000 tons of TNT. The largest conventional bomb, the {{w|GBU-43/B MOAB}}, has a yield of roughly 11 tons. The {{w|2020 Beirut explosion}} was roughly equivalent to 500 tons. So, while the helium-2 balloon bomb would be larger than all conventional bombs, it would still be smaller than most nukes. Handing out what are effectively small atomic bombs at a county fair would not go down well with any surviving local authorities, so merely being banned is a very mild punishment. Criminal charges such as mass murder and terrorism would be more likely if it weren't for the absurd impossibility of the scenario.</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 title text is likely also a pun, as the word "{{w|https://en.wikipedia.org/wiki/Local_ordinance|ordinance}}" means a local law, and the very similar sounding word "[https://www.merriam-webster.com/dictionary/ordnance ordnance]" means artillery and other explosive weapons, which the baloon would qualify as.</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>===Table of tips===</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>===Table of tips===</div></td></tr>
</table>SqueakSquawk4https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=298696&oldid=prevFephisto: The abstract point still stands, also the munitions T-shirt is a reference and joke to a previous xkcd.2022-11-14T16:20:47Z<p>The abstract point still stands, also the munitions T-shirt is a reference and joke to a previous xkcd.</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>|-</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>|-</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} is equal to the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand, <del class="diffchange diffchange-inline">their value is similarly limited.</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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} is equal to the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand <ins class="diffchange diffchange-inline">([https://en.wikipedia.org/wiki/Crypto_Wars#/media/File:Munitions_T-shirt_(front).jpg most of the time])</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;"><div>|-</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>|-</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</div></td></tr>
</table>Fephistohttps://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=297936&oldid=prev172.70.219.36: /* Explanation */2022-11-01T16:55:04Z<p><span dir="auto"><span class="autocomment">Explanation</span></span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 16:55, 1 November 2022</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>==Explanation==</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>==Explanation==</div></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;">{{incomplete|Created by a FAUX VECTOR - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</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;"><div>This is another one of [[Randall|Randall's]] [[:Category:Tips|Tips]], this time with a series of Physics Cost-Saving Tips. It also continues the previous [[2648: Chemicals]] comic's jocular theme of tricks to supposedly save money based on misinterpretations of science.  </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 is another one of [[Randall|Randall's]] [[:Category:Tips|Tips]], this time with a series of Physics Cost-Saving Tips. It also continues the previous [[2648: Chemicals]] comic's jocular theme of tricks to supposedly save money based on misinterpretations of science.  </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>
</table>172.70.219.36https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=297815&oldid=prev172.70.214.253: /* Table of tips */ tighten2022-10-31T00:34:04Z<p><span dir="auto"><span class="autocomment">Table of tips: </span> tighten</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 00:34, 31 October 2022</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s<del class="diffchange diffchange-inline">. Regular Euclidean vectors </del>have a magnitude and direction (velocity, for example). Pseudovectors are usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s<ins class="diffchange diffchange-inline">, which </ins>have a magnitude and direction (velocity, for example). Pseudovectors are usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>|-</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>|-</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></td></tr>
</table>172.70.214.253https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=297813&oldid=prev172.70.214.253: Clarify2022-10-31T00:33:13Z<p>Clarify</p>
<table class="diff diff-contentalign-left" data-mw="interface">
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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 00:33, 31 October 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28" >Line 28:</td>
<td colspan="2" class="diff-lineno">Line 28:</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s. <del class="diffchange diffchange-inline"> '''Quick Explanation:''' </del>Regular vectors have a magnitude and direction (velocity, for example). <del class="diffchange diffchange-inline"> The actual, physical magnitude and direction don't depend on the coordinate system.  </del>Pseudovectors <del class="diffchange diffchange-inline">also have magnitude and direction, but the direction can flip if you use a different coordinate system.  '''More Detailed Explanation:''' pseudovectors </del>are usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s. Regular <ins class="diffchange diffchange-inline">Euclidean </ins>vectors have a magnitude and direction (velocity, for example). Pseudovectors are usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>|-</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>|-</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></td></tr>
</table>172.70.214.253https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=296450&oldid=prev172.70.135.118: /* Table of tips */2022-10-11T17:52:43Z<p><span dir="auto"><span class="autocomment">Table of tips</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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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 17:52, 11 October 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28" >Line 28:</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" Euclidean vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a Euclidean vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s, the <del class="diffchange diffchange-inline">former </del>usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s<ins class="diffchange diffchange-inline">.  '''Quick Explanation:''' Regular vectors have a magnitude and direction (velocity</ins>, <ins class="diffchange diffchange-inline">for example).  The actual, physical magnitude and direction don't depend on the coordinate system.  Pseudovectors also have magnitude and direction, but </ins>the <ins class="diffchange diffchange-inline">direction can flip if you use a different coordinate system.  '''More Detailed Explanation:''' pseudovectors are </ins>usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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>|-</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>|-</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} <del class="diffchange diffchange-inline">can thereby be represented as </del>the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand, their value is similarly limited.</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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} <ins class="diffchange diffchange-inline">is equal to </ins>the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects are exempt from the laws of supply and demand, their value is similarly limited.</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>|-</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>|-</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</div></td></tr>
</table>172.70.135.118https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=296096&oldid=prev172.69.33.235: filled in missing word2022-10-05T17:13:40Z<p>filled in missing word</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 17:13, 5 October 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31" >Line 31:</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>|A square wave can be broken down into an infinite supply of valuable sine waves</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>|A square wave can be broken down into an infinite supply of valuable sine waves</div></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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} can thereby be represented as the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects exempt from the laws of supply and demand, their value is similarly limited.</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>|{{w|Fourier analysis}} can decompose any periodic function into a series of {{w|sine wave}}s. A {{w|square wave}} can thereby be represented as the sum of an infinite series of sine waves. However, the sine waves are not removed or separated individually, so such a {{w|Fourier transform}} does not produce a "supply" of sine waves for practical use in any tasks other than analysis, and as abstract mathematical objects <ins class="diffchange diffchange-inline">are </ins>exempt from the laws of supply and demand, their value is similarly limited.</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>|-</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>|-</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</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>|Cut waste by buying lighter isotopes that don't have any dead-weight neutrons</div></td></tr>
</table>172.69.33.235https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=296062&oldid=prev172.70.131.44: /* Table of tips */2022-10-04T15:42:17Z<p><span dir="auto"><span class="autocomment">Table of tips</span></span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 15:42, 4 October 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26" >Line 26:</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>|-</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>|-</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>|Try replacing regular vectors with pseudovectors whenever possible</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>|Try replacing regular vectors with pseudovectors whenever possible</div></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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" <del class="diffchange diffchange-inline">Euclidian </del>vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a <del class="diffchange diffchange-inline">Euclidian </del>vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>|[[File:Torque animation.gif|frame|right|Relationship of pseudovectors {{w|torque}} ('''τ''') and {{w|angular momentum}} ('''L''') to "regular" <ins class="diffchange diffchange-inline">Euclidean </ins>vectors {{w|Position (vector)|position}} ('''r'''), {{w|force}} ('''F'''), and linear {{w|momentum}} ('''p''') in an oscillatory rotating system. Not shown is the {{w|centripetal force}} of the spoke's {{w|Tension (physics)|tension}}, a <ins class="diffchange diffchange-inline">Euclidean </ins>vector towards the axle proportional to linear momentum, converting it to angular momentum.]]</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>The prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s, the former usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</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 prefix "pseudo-" refers to an inauthentic variation of something. Fakes are usually cheaper than their original brand-name product, while often working just as well, so the comic implies a {{w|pseudovector}} could be a less expensive substitute for a regular vector. On the contrary, pseudovectors, or axial vectors, are distinct from regular {{w|Euclidean vector}}s, the former usually being involved with rotation or physical effects that share properties with rotation, similar to the relationship between angles and lengths. Pseudovectors are formed from the {{w|cross product}}s of Euclidean vectors, in three dimensions, and while similar to Euclidean vectors, there is no physical meaning to their specific direction, only their magnitude and portions of their position. For example, {{w|angular momentum}} is described by a pseudovector, labeled '''L''' in the comic, {{w|Normal (geometry)|normal}} to the {{w|plane of rotation}}, originating from the center of rotation, with magnitude equal to the angular velocity of rotation '''ω''' multiplied by the {{w|moment of inertia}} '''I'''. (The comic's diagram is drawn according to very uncommon {{w|Right-hand rule#Coordinates|left-handed coordinates}} instead of the standard {{w|right-hand rule}}. Randall is right-handed.[https://www.youtube.com/watch?v=j1tcyEo2tQk&t=28s])</div></td></tr>
</table>172.70.131.44https://www.explainxkcd.com/wiki/index.php?title=2649:_Physics_Cost-Saving_Tips&diff=292963&oldid=prev172.70.91.78: Undo revision 292938 by Liv2splain (talk) I'm reverting because I think it's not just the one edit, but also careless ones (capital on *one* instance of "helium", for no good reason), etc.2022-08-16T19:44:07Z<p>Undo revision 292938 by <a href="/wiki/index.php/Special:Contributions/Liv2splain" title="Special:Contributions/Liv2splain">Liv2splain</a> (<a href="/wiki/index.php/User_talk:Liv2splain" title="User talk:Liv2splain">talk</a>) I'm reverting because I think it's not just the one edit, but also careless ones (capital on *one* instance of "helium", for no good reason), etc.</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 19:44, 16 August 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13" >Line 13:</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>It suggests four ways to reduce costs or provide something for free for physicists to save money on their research. For instance getting free electrons from a conductor or replacing regular {{w|helium}} with {{w|Isotopes_of_helium#Helium-2_(diproton)|helium 2}}. None of these would provide any real advantages even when possible to implement, and could even be very dangerous, see below in the [[#Table of tips|table]]. Obtaining money from physics experiments was also described in [[2007: Brookhaven RHIC]].</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>It suggests four ways to reduce costs or provide something for free for physicists to save money on their research. For instance getting free electrons from a conductor or replacing regular {{w|helium}} with {{w|Isotopes_of_helium#Helium-2_(diproton)|helium 2}}. None of these would provide any real advantages even when possible to implement, and could even be very dangerous, see below in the [[#Table of tips|table]]. Obtaining money from physics experiments was also described in [[2007: Brookhaven RHIC]].</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>In the title text, Randall claims to have been banned from the county fair for handing out helium-2 balloons because of the instant massive explosions caused by its radioactive decay (that helium-2 decays fast is mentioned in the comic, with a joke suggestion to use it quickly). He jokes that the balloons violated a local ordinance. {{w|Gas balloon|Helium balloons}} are often given out at county fairs and similar events, but they are filled with {{w|helium-4}} and therefore inert (a very small part will be {{w|<del class="diffchange diffchange-inline">Helium</del>-3}}, 2 ppm). A balloon filled with helium-2 is a practical impossibility because of its nanosecond half-life. Assuming a 12-inch diameter balloon at 1 atmosphere of pressure, the balloon-bomb would have a yield of roughly 17 {{w|TNT equivalent|tons of TNT equivalent}}.</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>In the title text, Randall claims to have been banned from the county fair for handing out helium-2 balloons because of the instant massive explosions caused by its radioactive decay (that helium-2 decays fast is mentioned in the comic, with a joke suggestion to use it quickly). He jokes that the balloons violated a local ordinance. {{w|Gas balloon|Helium balloons}} are often given out at county fairs and similar events, but they are filled with {{w|helium-4}} and therefore inert (a very small part will be {{w|<ins class="diffchange diffchange-inline">helium</ins>-3}}, 2 ppm). A balloon filled with helium-2 is a practical impossibility because of its nanosecond half-life. Assuming a 12-inch diameter balloon at 1 atmosphere of pressure, the balloon-bomb would have a yield of roughly 17 {{w|TNT equivalent|tons of TNT equivalent}}.</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>{{cot|[[User:SqueakSquawk4|Calculations]]}}</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>{{cot|[[User:SqueakSquawk4|Calculations]]}}</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>{{User:SqueakSquawk4}} <!-- SqueakSquawk4 prefers this not be subst:ed --></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>{{User:SqueakSquawk4}} <!-- SqueakSquawk4 prefers this not be subst:ed --></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>|Conductors are a great source of free electrons (may carry charges)</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>|Conductors are a great source of free electrons (may carry charges)</div></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>|{{w|Charge carrier|Free}} {{w|electron}}s are electrons that are not tightly bound to specific atoms so they can move freely, such as in {{w|conduction band}}s of the {{w|metallic bond}}s throughout the iron ingot depicted in the comic. Randall interprets "free" in a different sense, meaning no cost. The charges free electrons carry are electric, not monetary as implied by the pun.</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>|{{w|Charge carrier|Free}} {{w|electron}}s are electrons that are not tightly bound to specific atoms so <ins class="diffchange diffchange-inline">[https://www.youtube.com/watch?v=TGUteH93xNo </ins>they can move freely,<ins class="diffchange diffchange-inline">] </ins>such as in {{w|conduction band}}s of the {{w|metallic bond}}s throughout the iron ingot depicted in the comic. Randall interprets "free" in a different sense, meaning no cost. The charges free electrons carry are electric, not monetary as implied by the pun<ins class="diffchange diffchange-inline">. Ordinary matter usually contains electrons, but although the {{w|dielectric}} layer of a {{w|capacitor}} can collect electrons, it is not easy to store pure electrons, as they repel each other. When a {{w|Solution (chemistry)|solution}} has free electrons, it becomes {{w|alkaline}} ({{w|Base (chemistry)|basic}}) and corrosive. Randall has [https://what-if.xkcd.com/140/ explained the problems] with collecting a large number of electrons before</ins>.</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;"></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>
</table>172.70.91.78