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Math

The Math of Social Distancing Is a Lesson in Geometry (quantamagazine.org) 87

Posted by msmash from the closer-look dept.
Sphere packing might seem like a topic only a mathematician could love. Who else could get excited about finding the most efficient way to arrange circles in the plane, or spheres in space? But right now, millions of people all over the world are thinking about this very problem. From a report: Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in geometry: If each person must keep six feet away from everyone else, then figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles into floor plans. Of course there's a lot more to confronting COVID than just this geometry problem. But circle and sphere packing plays a part, just as it does in modeling crystal structures in chemistry and abstract message spaces in information theory.

It's a simple-sounding problem that's occupied some of history's greatest mathematicians, and exciting research is still happening today, particularly in higher dimensions. For example, mathematicians recently proved the best way to pack spheres into 8- and 24-dimensional space -- a technique essential for optimizing the error-correcting codes used in cell phones or for communication with space probes. So let's take a look at some of the surprising complications that arise when we try to pack space with our simplest shape. If your job involves packing oranges in a box or safely seating students under social distancing, the size and shape of your container is a crucial component of the problem. But for most mathematicians, the theory of sphere packing is about filling all of space. In two dimensions, this means covering the plane with same-size circles that don't overlap.
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The Math of Social Distancing Is a Lesson in Geometry

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  • WHO says that social distancing is 3ft or 1m .. When do you get 6? https://www.who.int/emergencie... [who.int]

    • Re: (Score:1, Informative)

      by 110010001000 ( 697113 )

      Because you need to be EXACTLY 6 feet apart. No more. No less. Otherwise you will get the virus. It is kind of like when you go a restaurant you need to wear a mask when you walk in. Once you sit down at a table the virus can't get you so you can take it off. And if you don't do it all, you must be a Trump voter.

      • Re: (Score:1, Troll)

        by spun ( 1352 )

        Nah, all sorts of idiots refuse to wear masks, not just Trump voters.

        You do realize, the mask is to protect others, right? You wear the mask in case you are asymptomatic. You wash your hands to protect yourself. Go ahead and argue the cold hard facts staring us in the face, then insult the "other side" for being sensible, then whine about persecution, then make it political, then whine about it being political.

        The pandemic is not political. Only one side is trying to make it political, because your cult lea

        • Re:6 feet? (Score:4, Insightful)

          by SuperKendall ( 25149 ) on Monday July 13, 2020 @04:07PM (#60294736)

          Nah, all sorts of idiots refuse to wear masks, not just Trump voters.

          Many Trump voters also wear masks [amazon.com]. But hey, thanks for the casual bigotry!

          You do realize, the mask is to protect others, right?

          You do realize they ALSO help you [mayoclinic.org], right? But then ignorance is to be expected from bigots.

          Beyond just whatever filtration and droplet blocking they offer, they also offer the benefit of preventing people from touching their own mouths with hands that may have touched a virus-laden surface, giving you more time between hand washing.

          The pandemic is not political

          The reaction however, has been nothing but. I find it hilarious your own post opens with a purely political statement and you claim this.

          Only one side is trying to make it political,

          Sorry but I don't buy you are stupid enough to believe what you just wrote here, not even a bigot such as yourself is that stupid or blind. Then again, bigotry is a powerful force for willful ignorance...

          The really funny thing is, because your own post is heavily political, if you truly believe only one "side" is making this political - it must be your own side, by your own actions!!!! BWA HAHAHAH HAHAAHAHAHAH.

          Enjoy your "sides", I'll just be here in the middle eyeing both sides with equal contempt.

          • Re:6 feet? (Score:5, Insightful)

            by JoshuaZ ( 1134087 ) on Monday July 13, 2020 @05:05PM (#60294976) Homepage

            While there is a certain unfortunate aspect to the poster you are trying to make it more partisan than it needs to be, the data does strongly show that mask wearing is higher in general the more left-wards someone's politics are. See https://www.nytimes.com/2020/06/02/health/coronavirus-face-masks-surveys.html [nytimes.com], https://thehill.com/homenews/news/504688-nearly-90-percent-of-americans-say-they-are-wearing-masks-in-public-as [thehill.com], and https://www.ipsos.com/en-us/news-polls/abc-coronavirus-poll-wave-14 [ipsos.com]. There are some complicating factors here; people who live in more urban environments and women are both more likely to report frequently wearing masks, and both of those are groups which lean more left, but even given that, this still looks like a strong correlation. It certainly isn't perfectly partisan; the majority of Americans regardless of political affiliation wear masks now at least sometimes.

            But there's a definite tendency of people who self-identify on the right or as Republicans to be less likely to wear masks. And deliberate mask non-compliance is a thing among a substantial minority of prominent Republican politicians (e.g. Jim Jordan https://home.sparklight.com/player/category/news/article/geobeats-watch_refusing_to_wear_mask_gop_rep_jim_jordan_cou-velephant [sparklight.com]). There's no similar level of mask refusal among Democratic leaders. The overarching picture should be clear: There's a broad consensus behind mask wearing even as there's a substantial fraction of Americans who aren't complying, and that fraction is disproportionately on the political right.

            • Wow, a well thought-out, apolitical, insightful reply--with citations. You must be on the wrong site...

            • Re:6 feet? (Score:5, Interesting)

              by fatwilbur ( 1098563 ) on Monday July 13, 2020 @08:41PM (#60295522)
              I'm usually loathe to call out generalities between the two political sides, but in this case I agree. The problem is actually each side's perspectives of the other's motives. The left assume those on the right are stupid or think this whole thing is a hoax, and the right assumes those on the left are gullible and just falling in line with their conformist, authoritarian ways.

              There's some truth to each and people like that in each camp, but I think the majority on each side actually has these as motives:
              Right: Our individual rights and freedoms are to be valued above all else, and this simply doesn't reach the enormous threshold of severity needed (if it even exists) to erode those rights. We've sent more people into wars to die in the past for the same rights.
              Left: If we all chip in just some small amount by wearing masks, distancing, etc., we can truly do some good for the greater society and save people's lives.
              Basically, I believe most people have good intentions. The general shit-behaviours and their consistency across the political spectrum is again the bigger problem, which is of course to be expected, since they are very intermixed populations of the same human beings. Regardless of what you think, people actually have very closely aligned moral rules, eg. violence is a bad thing and most of us would do what we could to save a life. It's only in the interpretations, outcomes, and approaches where there is stark disagreement. See the endless branches of Catholicism, or even the Maxism/Leninism/Stalinism/etcism of Communism; everyone shares the same ultimate values, but strong disagreement arises in the details.

              Given that, I definitely fall on the "right" side of the spectrum here. I realize how this can be difficult to understand and may seem ridiculous from someone's perspectives, but in most cases I do think our rights are so important that they deserve risking death. Now, this isn't about stupid risks.. I can clearly gauge the risk to my health from COVID-19 is extremely low.

              I also have read quite a bit on virology in the past, and do have vast experience in mathematics, computer science, and data analysis. There are some things we do not yet know 100% for COVID-19, but just simple statistical analysis and extending logic of how other viruses work, I am comfortable saying these things are overwhelmingly likely to be true as part of gauging risk: - The risk of death or severe disability from the acute sickness are extremely low for those under 50. - Latent viral infections are very rare, and not worth considering as a possibility in terms of current actions. - Airborne transmission of viruses is incredibly rare, and in most cases pure science fiction. Droplets do contain viruses, and thus coughing/sneezing does contain some risk of transmission. Transmission is so difficult in the first place (with any virus), chances are you need to be in the direct path of that cough/sneeze to even have a tiny measurable risk. Thus if you are in a hospital (or around anyone who's a very high acute risk) it makes sense to wear a mask, otherwise, wearing a mask is more for psychological purposes than any sound scientific reason of avoiding virus transmission. Perhaps the key fact here is just how hard it is for the luck of virus transmission to occur - it needs a very specific long-distance (in scale) vector and a lot of luck (over the course of billions of dice rolls). Maybe an illustrative example is with something like HIV, which has only a 0.67% chance of infection [wikipedia.org] risk when sharing needles with an infected person. From the same table you can see, although most people's perception is highly different, you have less than a 1/3,300 chance of contracting it from having bare sex with and infected woman. Most people would think that was a sure thing or much higher chance.

              The big point there is that primary transmission vector for corona, like most viruses, is surfa

              • Re:6 feet? (Score:4, Interesting)

                by enigma32 ( 128601 ) on Monday July 13, 2020 @09:07PM (#60295602)

                I agree with most of what you've said here, re: rights and risks.
                However, don't you think that anecdotal data points to some benefit from wearing masks? Furthermore, given the relatively small inconvenience, is it such a horrible thing to have to do on the off-chance that it might help someone else? We do give up some freedom in order to live in a cohesive society.

                You stated that contact transfer is the most common transfer mechanism for this virus. The CDC originally made similar claims, but has revised its stance to say that the virus is transferred mostly via respiratory droplets ( https://www.cdc.gov/coronaviru... [cdc.gov] ). This view closely aligns with guidance from the WHO ( https://www.who.int/news-room/... [who.int] ). (I personally take information from the WHO with a grain of salt-- but in this case, the CDC and the WHO concur.) How do you rectify this with your view that "any risk to [your] personal health from not wearing a mask is negligible"?

                I think you'd agree that society in general says it's not okay to knowingly infect someone with HIV. How do you draw the line between that and the high likelihood that you could infect others with SARS-CoV-2 without knowing it (see Florida right now), considering that the resulting disease is known to be fatal in some cases?

              • Right: Our individual rights and freedoms are to be valued above all else, and this simply doesn't reach the enormous threshold of severity needed (if it even exists) to erode those rights. We've sent more people into wars to die in the past for the same rights.

                Could you please cite where we endured 130,000 casualties in a war fought to ensure we aren't forced to wear an article of safety gear? Has anyone even asserted the right not to wear PPE prior to this year?

                Currently most states enforce seat belt laws. Police can stop and cite you for not wearing a seat belt - even in Texas. How is this not a violation of the same right? Masks aren't special - any article of safety gear could become a political symbol, and thus wearing or not wearing it could be considered p

                • Well, your science says it is effective and safe. Others say different. Why should we be forced to endanger ourselves because you say we must. Kids have dies in the masks. The scientific tests show the virus gets though. If you want to wear it go ahead, but forcing me to is the line.

                  Why would forcing people to get vaccines be different? Or forcing sterilization on the ones we don't think or good for society? Or forcing people to have no way to work and make a living. I remember this being done to the Jewish

                  • Speaking as someone living in one of those "hard hit democratic" areas, the issue is mostly with people either (1) working in service industries that aren't shut down, or (2) not wearing masks.

                    The general approach would work fine if people would actually follow it, as it has worked fine in other countries.

                    Well, your science says it is effective and safe. Others say different.

                    I haven't seen any groups of respected virologists claiming "different", and there is no such thing as "your science" and "my science"-- only science that hasn't reached a consensus yet (and also bad scien

                    • I haven't seen any groups of respected virologists claiming "different", and there is no such thing as "your science" and "my science"-- only science that hasn't reached a consensus yet (and also bad science). In this case, there are no respected scientists saying people shouldn't wear masks.

                      So because you can't read about what scientists around the world are finding about this virus and how it works, you think it does not exist. If you only read the sensational media making everything seem scary, then you will be scared. That is your fault, not mine!

                      Kids have dies in the masks.

                      Is this claim your only argument against wearing masks? There is a reason that you're not supposed to put masks on infants, but outside of that I'm not aware of any real risk posed by wearing them.

                      Again, you don't know about, so it does not exist. They were 17 year old teens in China. Two of them who died. Plus someone else, older gentleman, who had a lung collapse due to the mask wearing. And that ignores the effect it has on your immune sy

              • Fomite transmission from surfaces is, in all likelihood, extremely low. It was overestimated what impact it would have in the beginning. Intuitively, we can see this in practice: when people get things delivered to their homes or pick things up at the store, we aren't seeing massive infection numbers. We are, however, seeing infections in crowded places where people talk. Almost all transmission is indoors, through aerosols.

                https://www.thelancet.com/pdfs... [thelancet.com] (opinion piece)
                https://www.who.int/news-room/... [who.int]
                ht [globalnews.ca]

                • Re: (Score:2)

                  by fintux ( 798480 )

                  Exactly! Aerosol spread is they key. Asian countries know this already from the SARS epidemics. Western countries are still failing to account for this. The distance of 3-6 ft comes from 1930's, and it was when the aerosols couldn't be observed like with today's instruments. Masks are the key. Air purifiers, venting air etc. helps. Recirculating AC or fans are the worst thing one can have.

                  There have been horrifying studies about even asymptomatic people having organ damage. For symptomatic people, for 1/3,

        • Re: (Score:2)

          by ddtmm ( 549094 )
          You rock!

    • Re:6 feet? (Score:4, Informative)

      by BeerFartMoron ( 624900 ) on Monday July 13, 2020 @03:40PM (#60294602)
      CDC Guidelines [cdc.gov]

    • 6 vs 3 ft (Score:5, Interesting)

      by spineboy ( 22918 ) on Monday July 13, 2020 @03:43PM (#60294616) Journal

      You are correct. The 6 ft distance came from initial droplet studies, which have been further tested. Bother are effective, however since the US is the Corona Capital right now, an increased distance will be safer, as the increased distance almost acts like "herd immunity" The CDC recs are likely for the rest of the world, where the percentage of SARS2-CoViD 19 pts is much lower than the US. THerefore, the chance of catching the disease is less, and distance can be decreased to reflect the lower odds.

      WHO recommends 3 ft

      CDC recommends 6 ft

      https://www.cdc.gov/coronaviru... [cdc.gov]

      I would suggest 6 ft for us Americans as we have all sorts of idiots who refuse to wear masks, insist on wearing it below their nose,insist that doctors (like me) are making it up to make the president look bad, hoax, etc

      • The 6 ft distance came from initial droplet studies, which have been further tested.

        Does it not seem odd to anyone else that we are all doing 6-ft distancing AND masks?

        I mean yes, it's defense in depth to do both... but even just a reduction to 3ft would mean a lot less pain in the ass space-wise for the whole world - as long as everyone was also wearing masks.

        It's all kind of funny that so many other variables like duration are left out of the picture.... I'd rather be standing next to someone touching th

        • generally 'touching people' for a min while standing next to them is not advisable, corona or not...

        • It's all about the percentages, like everything in medicine.

          You need exposure to roughly 1,000 viral particles to induce an infection. Humans shed roughly 40 viral particles a minute - so 25 minutes for enough exposure if you happen to catch them all.

          3ft vs 6 feet - loosely can use the R^2 law. Mask wearing significantly cuts down on the # of particles produced.

          So yeah 6ft and masks are a good thing in America

      • Correlation says that the higher the social distance recommendation, the higher the cases? 6ft in US, which has the higher cases, vs, much of the rest of the world, that has a lower social distance recommendation? I don't get it?

        • Re: (Score:2)

          by spineboy ( 22918 )

          it's all about percentages and chance of transmission. The chance of transmitting an airborne infection depends on the distance and the frequency of exposure to infected people. The higher a chance that the person is infected will increase the exposure risk. Increasing distance will decrease that risk - the R^2 law loosely applies here. So to mitigate the exposure risk , it's a balance between the percent of infected people and the distance.

      • Re: (Score:2)

        by rtb61 ( 674572 )

        The problem with the delusion of distancing, it has virtually zero impact on particulate matter spread. Skin particles that flake off the infected person, coated with the virus and you lose tens of thousands of skin particles all of the time https://www.reference.com/scie... [reference.com] a million a day and viruses are way smaller than a skin cell. Mask only protects you from inhaling the particles, it provides a good measure of protection because just one of the chunks of skins cells is a veritable survival raft for vi

        • Re: (Score:2)

          by spineboy ( 22918 )

          Ever hear of the R^2 law? - it's loosely applicable to shed particles as well. SKin flakes are generally not coated with live viral particles, at least with SARS2 - CoViD19. We avoid shaking hands, etc because people touch their faces all the time. This virus is mainly located in the respiratory epithelium.

          As far as this being some sort of hoax? I can say that with 25 years of practicing medicine, I've never seen morgue trucks parked outside multiple hospitals, yet here they are.

          The science that sugge

    • Re: (Score:2)

      by DogDude ( 805747 )
      WHO has said the more the better, but they make their recommendations for the whole world, and much of the world's population lives in China and India, where 2 m is difficult to maintain, so they set their target at 1 m. I don't remember where I read that, but it was a WHO document on their web site, for sure. I know that the US, at least is recommending 6 feet.

      • Re: (Score:2)

        by fintux ( 798480 )
        I live in Finland. We even hug from 3 feet apart. If 3 feet was enough to stop the spread, we would never have had an epidemic to begin with. The distancing is good especially outdoors, but indoors it is not enough. Indoors it all boils down to ventilation, mask wearing and having not too many people in a single room.

    • Re:6 feet? (Score:4, Informative)

      by RockyMountain ( 12635 ) on Monday July 13, 2020 @05:11PM (#60295000) Homepage

      True, WHO guidelines are based on 1m, while CDC guidelines are based on 6ft (close to 2m), and many governments have issued widely varying guidelines of 1m, 1.5m, 6ft, or 2m. I don't think that means that one is "right" and all the others are "wrong".

      These are different points along a risk-tradeoff continuum. Even 2m is not 100% safe of course, but I'd personally rather be 1m upwind of an infected individual than 3m downwind of one! "Acceptable" distance is a function of risk tolerance (both personal and societal), as well as both aggravating and mitigating factors, exposure time, ventilation, indoor vs outdoor, etc.

      When viewed societally rather than individually, "acceptable" risk is also a function of the local infection rates and available medical care capacity at the place and time -- keeping the society as a whole below the R=1 threshold is critical -- or aiming to get it there is R is still >1.

      When viewed individually, risk tolerance may be higher or lower. My wife has cancer. If I get infected, she probably will too. Obviously, my personal "acceptable" risk is lower than society's as a while. Luckily I can work remotely, but I feel for those with similar high-risk loved ones who must physically enter a workspace where distance is based on someone else's arbitrary measure of risk tolerance.

      All other factors being equal, the reduction in risk with distance is super-linear (exponential, I think?), so a little extra distance beyond the bare minimum goes a long way, and the WHO guidelines very clearly state that 1m is a minimum, not a recommended distance.

      Getting back to the WHO guidelines the parent post mentioned: Direct linear distance between individuals is not the only guideline WHO gives. They also recommend an overall density limitation of one individual per 10 square meters (see https://www.who.int/publicatio... [who.int]). Seen in that context, average distance between individuals would be well over 2m, even while certain individuals are 1m apart. Given that, the WHO and CDC guidelines really aren't that different.

      So, while 1m vs 2m is an interesting question too, don't get hung up on it to the point of distraction from the subject matter of the original post. Whatever "acceptable" distance is deemed appropriate for a PARTICLAR SITUATION, sphere-packing problems emerge.

      Here's a pretty good article explaining the relative risks at various distances, as well as mentioning some national differences in government guidelines or rules. https://www.bbc.com/news/scien... [bbc.com]. One interesting quote from it: "Scientists advising the UK government say spending six seconds at a distance of 1m from someone is the same as spending one minute at a distance of 2m. Being exposed to someone coughing is riskier. Being 2m away from a cough carries the same risk as someone talking to you for 30 minutes at the same distance."

    • Re: (Score:2)

      by MobyDisk ( 75490 )

      The CDC says 6 feet. [cdc.gov] OSHA's recommendation to avoid the flu [archive.org] also says 6 feet. This is the first I've heard of 3 feet.

  • that's computer science, not mathematics (Score:3)

    by swan5566 ( 1771176 ) on Monday July 13, 2020 @03:35PM (#60294590)
    ...though I'm sure many mathematicians dabble in complexity theory.

  • The wrong problem (Score:3)

    by burtosis ( 1124179 ) on Monday July 13, 2020 @03:40PM (#60294604)
    Instead of trying to pack as many sardines in as possible, perhaps it’s better to take a more nuanced approach by attempting to remove the existing vectors. Require things such as better air filters in hvac systems, better air exchange or ventilation, mask use, remove things you need to touch like door handles (by sensor or if you are on a budget a foot stop), etc. Putting a plan together that outlines when these make sense and how to roll them out universally (at least country wide) is going to make a bigger impact on transmission rate than packing 42 people in a room instead of 39.

    • Require things such as better air filters in hvac systems, better air exchange or ventilation,

      I think AC systems and filtration have been improving naturally for some time (are not most filters these days HEPA filters?). Also extremely expensive for most places to implement upgrades in these areas, beyond better filters if they are not using them already...

      remove things you need to touch like door handles (by sensor or if you are on a budget a foot stop)

      That to me seems like the hugest area for improvement

      • Re: (Score:3)

        by jbengt ( 874751 )

        (are not most filters these days HEPA filters?)

        No, they are not. You would be lucky to get MERV 8 filters in most run-of-the-mill new HVAC systems.
        And upgrading filters in most systems would result in increased pressure drops requiring increases in fan speed and motor HP. So not easy or cheap.

        • You can compensate for a filter with a greater pressure drop for a given flow rate in some systems by allowing for a filter that is simply deeper (thicker), thereby increasing the surface area. Some systems this may not be feasible to retrofit, some it may be a very simple modification, others may not need modification. Some HVAC systems service only a few people’s needs, some get tens of thousands or more on a daily basis and thus there is a different level of concern. This is why you have a pla

    • Require things such as better air filters in hvac systems, better air exchange or ventilation, ...

      Changes like these are being implemented, but take time to implement, until they can be social distancing will have to do. Better filters cause a higher pressure drop, requiring bigger fans or resulting in lower air flow rates. There are industry guidelines recommending changes in air systems, but in some areas they may be restricted by energy conservation regulations (hopefully waived for the pandemic) or may be complicated to actually implement in an effective way.

  • Sphere packing might seem like a topic only a mathematician could love.

    My thesis was on a similar (but more complicated) topic. And, yes.

    ...figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles.... ...mathematicians recently proved the best way to pack spheres into 8- and 24-dimensional space...

    What the heck kind of restaurant are you expecting to go to? Have I completely missed some astounding breakthroughs in the combined fields of physics and restaurant design?

    • Have I completely missed some astounding breakthroughs in the combined fields of physics and restaurant design?

      I believe bistromathematics have remain unchanged since five-part thesis by Douglas Adams

  • except that math is racist now.

  • Not a packing problem ... (Score:3)

    by dogsbreath ( 730413 ) on Monday July 13, 2020 @03:56PM (#60294690)

    People are not ping pong balls packed in a box: they are not static.

    People move and interact so any efficiency algorithm has to account for access to a space, safe interaction when required, and egress. Not so simple.

    Also the moving about while others are doing the same. For example: grocery shopping has become much like a game of Pacman.

  • The theory is all fine, but what is the formula to get people to actually respect social distancing? So far I've only come up with the death stare.

    • either with impatient people who are crowding you in a checkout line, with people in the supermarket wearing a mask with their nose exposed, or with the intellectually impaired who think that those construction-dust masks with the valve on the front are medically effective in preventing others from breathing in their virus effusions.

  • It misses the shape of the room (Score:4, Insightful)

    by jonbryce ( 703250 ) on Monday July 13, 2020 @04:11PM (#60294766) Homepage

    It says you should pack people in hexagons. Which is fine if it is an open space. However, while you reduce the space between people, you increase the space around the walls. Whether or not that makes things more efficient overall depends on the size of the room.

    Lets say you have a room that is 4 metres by 3 metres, and you want to keep everyone 1 metre apart.

    If you pack them in as rectangles, you get 12 people in the room.

    If you pack them in as hexagons, you get only 11 people in the room. You will have about 27cm of free space along the long edge of the room, and in the middle row you will have 50cm of free space on either side of the line of people.

    The other problem is, what if someone who isn't next to the door wants to get out?

    • Re:It misses the shape of the room (Score:4, Informative)

      by Joe2020 ( 6760092 ) on Monday July 13, 2020 @04:30PM (#60294862)

      Not sure how much walls "reflect" the virus, but I'm sure it's not like it would bounce right off as light beams off a mirror. Nor will anyone sit directly at the wall, but want to have a little bit of distance so not to touch it. Walls then cannot be infected nor do these spread the virus unless people touch them. So you should be able to clip the "bubble" of those who sit at the walls. Even more so by those who sit in the corners.

      Hexagons will only provide an advantage in cases where you can have every odd row pack one extra person when compared to rectangles. Other than this do I believe you're right.

      • Fine, I make the room 3 metres x 2 metres, put people along the edge and corners. Everything else stays the same, including the result.

    • Is this an Ur-geek thing to optimize the number of people you can cram into a room maintaining the 6-foot social distance when the 6-foot number is a rough approximation to prevent too many people from being crammed into a room?

      Is this an Ur-lawyer thing to parse whether the 6-foot "rule" applies to hexagons or only to squares?

      The 6-foot number is an approximation so people aren't packed too closely, and people here are treating it as a math puzzle as to how many people you can stuff into a room before

  • This was hard enough to achieve already, now they're expecting us to float in mid air.

  • Or maybe... (Score:3)

    by sunking2 ( 521698 ) on Monday July 13, 2020 @04:50PM (#60294922)

    You could just say 25% or 50% capacity depending on the venue, which is what is actually happening. You aren't going to calculate this on a per building or venue basis. You're going to choose a number that likely meets or exceeds in most cases and is easy to apply across the board. The worlds super computers are not working this problem.

    Social distancing is way more about peoples behavior than the numbers behind it. Come up with all the math solutions you want. You really think complex math goes into Costco deciding across the board that they will limit to 600/hour access to their store?

  • Are there any enforceable standards that are required for masks that are worn in public and measurable distances?

  • 6 foot rule taken way too far (Score:3)

    by Moof123 ( 1292134 ) on Monday July 13, 2020 @05:39PM (#60295090)

    2 feet in passing by someone going the opposite direction outside unmasked is low risk.
    6 feet apart masked waiting in a line, even indoors, for 10 minutes is low risk.
    6 feet indoors 8 hours a day talking all day in a call center unmasked is probably high risk .

    Fresh air, distance, lack of talking, masks, hand washing, etc all help. The 6 foot rule is a very blunt tool resulting from the need to dumb things down enough for people to actually be able to follow. Even at that we fail to get folks to wear masks and stay 6' apart indoors.

  • Someone mentioned a trick from centuries ago where children wore hats with 3 foot brims. 2 kids with these would naturally stand 6 feet apart to avoid knocking hats. This was to avoid some disease of the time. I think bringing this back wouldn't be the worst idea.

  • I hate this. This is the very definition of garbage-in, garbage-everywhere.

    Staying six-feet away from each-other misses the point. Obviously, the point is to not spread bio-fluids. And obviously a six-foot-tall person's bio-fluids aren't likely to reach another six-foot-tall person standing six-feet away. And we care less about a droplet landing on their food than we do about it hitting them in the eye.

    So six-feet is reasonable. Seven feet is better. Five feet ain't as good. Two feet is useless.

    But,

  • As a geometry exercise, the problem is interesting enough. But as a public health issue, circle or sphere packing as discussed in the original source is just half of the equation. The missing point of the discussion is density.

    A poster above gave an example "Lets say you have a room that is 4 metres by 3 metres, and you want to keep everyone 1 metre apart. If you pack them in as rectangles, you get 12 people in the room. If you pack them in as hexagons, you get only 11 people in the room."
    Actually, you w

  • I can't believe there's maths in terms of social distancing.....nevertheless this was quite interesting. Won't be surprised if a social distancing maths question would appear in a maths test hahaha.

  • There is no hard and fast rule that 6 feet is somehow the magical distance where a virus transmission force-field exists. It is simply a guideline.

    Elsewhere in the world, the guideline is commonly referred to as "two meters" - guess what, two meters is not the same as six feet, it is significantly further.

    I am not saying that 6 feet is "not enough" - I am saying rather that I really wish regulators would look at this through a more complex risk-based lense than turning a guideline into a hard-and-fast rule.

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