https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&user=162.158.103.163&feedformat=atomexplain xkcd - User contributions [en]2024-03-29T07:59:00ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2286:_6-Foot_Zone&diff=1894072286: 6-Foot Zone2020-03-28T22:36:09Z<p>162.158.103.163: /* Explanation */ Two takes on density</p>
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<div>{{comic<br />
| number = 2286<br />
| date = March 27, 2020<br />
| title = 6-Foot Zone<br />
| image = 6_foot_zone.png<br />
| titletext = Technically now it's a 34-foot zone.<br />
}}<br />
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==Explanation==<br />
{{incomplete|Created by 8 HORSES. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic is the 11th comic in a row in a [[:Category:COVID-19|series of comics]] related to the {{w|2019–20 coronavirus pandemic|2020 pandemic}} of the {{w|coronavirus}} - {{w|SARS-CoV-2}}.<br />
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This comic is about {{w|social distancing}}, a common practice to prevent the spread of the COVID-19 disease. It has been suggested to maintain 6&nbsp;feet (i.e. 1.83&nbsp;m - in e.g. France and Britain the suggested distance is 2&nbsp;m) of distance between yourself and other people, to prevent the transmission of respiratory droplets from you to others (or vice versa).<br />
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[[Randall]] takes this 6 feet of distance, and does calculations of the "area" of distancing, "border", population density, and "real estate value". He finally culminates in determining the number of horses that could also fit in the space.<br />
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Randall's border length and approximate area calculations are based on a zone with an outside radius of approximately 6.8 feet or 82 inches (2.07 m), meaning that the person has a radius of approximately 0.8 feet or 10 inches (0.24 m). That is, 2π(6.8ft) = 42.7 ft and π<sup>-1</sup>(6.8ft)<sup>-2</sup> = 145 ft<sup>2</sup>.<br />
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Note that the way population density should be calculated is not obvious. One way to think about it is to divide the number of people in the zone by the surface area of the zone. This describes the properties of exclusion zone itself. Randall used that approach in the comic, resulring in π<sup>-1</sup>(6.8ft)<sup>-2</sup> = 190,000 mi<sup>-2</sup>. A different way to look at it is to consider the crowd in which everyone obeys the distancing rules. That would result in 0.9069(π<sup>-1</sup>)(3.8ft)<sup>-2</sup> = 560,000 mi<sup>-2</sup> population density. When people stand 6ft apart from each other, their exclusion zones are overlapping; instead we can use smaller circles with 3.8 ft radius that are not overlapping. 0.9069 is the packing density of circles in the plane.<br />
For comparison, the density in Monaco (the most densely-populated country in the world) is 48,000 people/square mile.<br />
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The title text is a pun using the alternate definition of foot, noting that a human has two feet and a horse has four, so 8 × 4 + 2 = 34 feet.<br />
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==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:Guide to the 6 foot Social Distancing Zone<br />
:Profile image of person with 6 foot distance measurements on both sides<br />
:Overhead image of person within a roughly circular shape extending 6 feet in all directions from the person. The dimensions of the person account for the non-circular shape.<br />
:Approximate area: 145 square feet<br />
:Border length: 43 feet<br />
:Population density: 190,000 people/square mile<br />
:Value at NYC real estate price per square foot: $195,000<br />
:Maximum number of horses that could fit inside it with you, estimated using the dimensions in the US Forest Service Equestrian Design Handbook: 8<br />
{{comic discussion}}<br />
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[[Category:COVID-19]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Animals]]</div>162.158.103.163https://www.explainxkcd.com/wiki/index.php?title=Talk:2286:_6-Foot_Zone&diff=189406Talk:2286: 6-Foot Zone2020-03-28T22:29:54Z<p>162.158.103.163: Comment</p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
Ok... 34 feet, in total, but how many hands? (All of which you should wash!) [[Special:Contributions/162.158.34.210|162.158.34.210]] 23:34, 27 March 2020 (UTC)<br />
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: Love it. Given the extra 1.7 feet for the person, a radius of 20.53 hands. If it were just 6 feet, 18 hands -- brad --[[Special:Contributions/108.162.216.122|108.162.216.122]] 00:55, 28 March 2020 (UTC)<br />
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So Randall is figuring about 1.7 feet diameter for the person. --[[Special:Contributions/172.68.174.70|172.68.174.70]] 00:40, 28 March 2020 (UTC)<br />
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The 190,000 people / mile^2 assumes (I'm guessing) flat ground. Skyscrapers make a difference [citation needed] -- brad --[[Special:Contributions/108.162.216.122|108.162.216.122]] 00:55, 28 March 2020 (UTC)<br />
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Interesting that the population density he gives ignores circle packing. Population should be 174,000. -- coyne -- [[Special:Contributions/162.158.122.156|162.158.122.156]] 04:06, 28 March 2020 (UTC)<br />
: Circle packing is unimportant since he's just giving the population of this one circle. He's taking a radius of 6 foot ''around'' that person without specifying what he considers to be the radius of the person, but it can be inferred from the numbers: <br>from area: <math>\sqrt{145/\pi} \approx 6.8</math>, <br>from circumference: <math>43/(2\pi) \approx 6.8</math>, <br>from population density: <math>\sqrt{1/190000/\pi} \cdot 5280 \approx 6.8</math>,<br>so apparently he considers a person to have a radius of 0.8 ft, or about 0.5 m diameter, which seems reasonable. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 05:11, 28 March 2020 (UTC)<br />
: Note that even if you want to know the population of optimally packed people, your number is still wrong since the circles overlap: your circle is supposed to exclude other people, it doesn't exclude other people's circles. Optimally you'd have a triangular lattice of people with a lattice distance of 7.6 ft (assuming we want 6 ft between people and we consider people to be circles of radius 0.8 ft). This yields a population density of 1 person per <math>\tfrac{1}{4}\sqrt{3} \cdot 7.6^2 \text{ ft}^2</math>, which is about 1.1 million people per square mile. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 05:24, 28 March 2020 (UTC)<br />
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Much as I love thinking about circle packing density in the plane, I think the above explanation is slightly overthinking the issue. The population density figure appears to be using the idea that one person's zone contains one person; 1 person / (145 ft^2) does indeed equal 192,000 people/square mile. So, he's not saying that 'given these constraints, we can pack people at this maximum density'. He's saying 'given this area, and counting it as a tiny sovereignty, we can calculate its population density to be this'. For this reason, I don't think you should say that the 'population density' figure has an error, only that it is calculated in a different sense than you were thinking about. [[User:Dextrous Fred|Dextrous Fred]] ([[User talk:Dextrous Fred|talk]]) 18:58, 28 March 2020 (UTC)<br />
:I agree. My first instinct on what the population density figure means was the same as one used in the comic. [[Special:Contributions/162.158.103.163|162.158.103.163]] 22:29, 28 March 2020 (UTC)<br />
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Possibly a play on the fact that horses are measured in hands? --orbitalbuzzsaw--<br />
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Page 207 of [https://www.fs.fed.us/t-d/pubs/pdfpubs/pdf07232816/pdf07232816dpi72pt10.pdf US Forest Service Equestrian Design Guidebook for Trails, Trailheads, and Campgrounds] says minimum corral size is 12x12 feet. I didn't find a more likely sounding Forest Service publication. So I assume the ''handbook'' in the comic is a fictional publication. [[User:Hamjudo|Hamjudo]] ([[User talk:Hamjudo|talk]]) 13:15, 28 March 2020 (UTC)<br />
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Always knew cities were bad for humanity. As are airplanes. Need them both to create a pandemic. [[User:Seebert|Seebert]] ([[User talk:Seebert|talk]]) 18:32, 28 March 2020 (UTC)</div>162.158.103.163