7 ms·

What's the smallest country that can fit everyone standing six feet apart?

45 points by milkbikis 6y ago

sigmaprimus 6y ago
Things are pretty tight in Singapore, I wonder if you take into account places not safe to stand like roads and places occupied by walls, trees, bank vaults etc., if it would be impossible. Almost 6 million people in 7.8 billion square feet if it was just flat land = approx 1300 square feet per person if my math is right.
- eesmith 6y ago
  The density needs to exceed 223,563/sq. mile (says the essay). Singapore's density at 20,445/sq. mile is less than 1/2 that of Monaco, says its reference 5, which is https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_population_density https://en.wikipedia.org/wiki/List_of_countries_and_dependen... . Thus, only 10% of the land is needed, giving plenty of space for roads, etc. Of course, if you include walls then you can place people on either side of the wall without an infection problem, so that changes the calculation considerably. FWIW, I wondered if Vatican City could reach the limit during a papal audience. It looks like perhaps 15,000 people could be there for one? That alone gives a density of 88K/sq. mile (bearing in mind that Vatican City has nearly 6 popes per square mile - or nearly 12 if we include Popes Emeritus.) Then there's the staff, and the people visiting the museum, and others beyond the estimated population of 1,000. Even with those, it doesn't seem like it comes close to 223,563/sq. mile.
  - sigmaprimus 6y ago
    I stand corrected, also the model does not take into account the Z axis, magnitudes of area added by highrises.
    - robertlagrant 6y ago
      Yes - it really should be spheres, but ones that cannot use other spheres for support :-)
      - eesmith 6y ago
        I think "should be" pushes things beyond the limited humor there was. The 6 feet suggestion is based on the travel distance of possible virus-carrying particles, given people on a flat surface. Since gravity pulls particles downward, I suspect that being 5 feet above someone sick is better than being 6 feet below. Possibly even better than being 6 feet to the side.
meigwilym 6y ago
I may have missed something but shouldn't the radius be 3 feet? With a 6 foot radius, wouldn't everyone be 12 feet apart? The maths is new to me (I was OK up to πr2!) so this might be my mistake.
- kjaftaedi 6y ago
  The subject would be in the center of the circle.
  - meigwilym 6y ago
    Indeed, they would, with 6 feet to the edge of their circle, and another 6 feet from that edge to the next person.
    - radmarshallb 6y ago
      You are correct. The diameter should be 6 feet and the radius 3 feet.
      - marzell 6y ago
        That means people would only be at least 3 feet away, not 6 feet. The original assumption was right.. need a 6 foot radius, 12 foot diameter to meet social distancing guidelines
        kd5bjo 6y ago
        It’s a circle-packing model, which means there’s no overlap between the exclusion zones. A radius of 3 feet means you’re at least 3 feet away from the edge of anyone else’s circle. They are at the center of their circle, which is an additional 3 feet away, for a total of 6 feet.
        concerned_user 6y ago
        You are not accounting for the fact that next person is not at your circle edge but is inside his own circle, and it is his circle touching yours, not the center of his circle, so 2 persons inside 3 feet radius circles have 6 feet of distance in between. Your assumption is correct if you overlap circles in a way that everyone is on edge of someone else's circle.
grabball 6y ago
I find impossible to read those kind of things when you use the United States customary units
- dkersten 6y ago
  At least they’re not using “football fields” as a measurement unit...
  - glandium 6y ago
    Around here, it's in "Tokyo Dome"s. Just as useless.
- choeger 6y ago
  I don't know it is easy to translate feet from US to German. I just need to know which city the unit refers to: https://en.m.wikipedia.org/wiki/Obsolete_German_units_of_measurement https://en.m.wikipedia.org/wiki/Obsolete_German_units_of_mea... /S (honestly, once the US empire is gone for good, historians will have a good laugh about their stubborn refusal to adopt the metric system. Must be the worst case of NIH in history)
  - scraft 6y ago
    To be fair, over here in the UK, we have MPH for roads, stones and pounds for peoples weight (kilograms are becoming more popular, in particular for the under 25s), feet and inches for peoples height (meters becoming more popular for under 25s). So we have a bit of a hybrid really, I am 36 so get a bit of both, but my parents need everything converted to "old money" as they call it, they can't imagine what 25cm length is, they would need it in feet and inches. It is less stubborn for them, more, "why bother"? They can get by as is and have other things to occupy their time than trying to work out what familiar distances and weights are using a different scaler. Given that roads are still imperial as are lots of other things (mattress sizes, timber sizes, etc) it isn't like if they switched to metric it would even fix anything useful.
    - 6y ago
andrewaylett 6y ago
If we're packing circles, don't we need to take into account that the 6ft distance is to the next person -- that is the centre of the next circle, rather than the boundary of it? That means circles of radius 3ft, for a total of 8,693 square miles.
cromulent 6y ago
You can fit all the humans on earth into a 1km cube. Average volume of a human is 66l [1]. Make it 130l to allow some unused space due to imperfect packing. 7.6 billion * 130l = 988 000 000 000 liters. 1 cubic kilometer = 1 000 000 000 000 liters. [1] https://www.wolframalpha.com/input/?i=average%20volume%20of%20human%20body https://www.wolframalpha.com/input/?i=average%20volume%20of%...
- Simon_says 6y ago
  You wouldn't enjoy it.
- garmaine 6y ago
  A better reference: https://what-if.xkcd.com/4/ https://what-if.xkcd.com/4/ "What would happen if you were to gather a mole (unit of measurement) of moles (the small furry critter) in one place?"
harry8 6y ago
"Stand on Zanzibar" Memories of enjoying it with that one.
metaphor 6y ago
As a more practical usecase, how many other EEs have leveraged circles-in-a-circle packing tables such as [1] to approximate cable diameter and/or size conduit? Would be interesting to learn how other disciplines have applied such a tool to solve real-world problems. [1] http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html
swarnie_ 6y ago
1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1 cm = 10 mm Its not that hard America.
deleted 6y ago
[deleted]
tenant 6y ago
So, my country which feels big to me couldn't do it. This reinforces my belief that there are way too many of our species on this planet. Given that 2.1 or so is the replacement rate, a "hard" limit of two child per woman would be decent compromise as this would equate to somewhere around 1.7 taking into account women who don't want to /can't have children. In one generation, if there were no unintended consequences this would drop the population by 15%. Sometime in the 2100s it would be half what it is today and my country could easily fit everyone!
- colechristensen 6y ago
  Most of the most-developed countries in the world are reproducing below the replacement rate already, populations only growing because of immigration. https://en.wikipedia.org/wiki/List_of_sovereign_states_and_dependencies_by_total_fertility_rate https://en.wikipedia.org/wiki/List_of_sovereign_states_and_d...
  - tenant 6y ago
    I was thinking globally since the discussion was about the global population.
    - colechristensen 6y ago
      There seems to be a generational lag between infant mortality (or mortality before reproduction) and fertility rate. Many places still have very high mortality-before-reproduction rates and correspondingly high birthrates, or at least generational recent ones. It seems, simply, that overpopulation is a problem which solves itself. High standard of living seems to come with high costs and emphasis on investing in children far more combined with delaying children until proper resources can be had. The result? Fewer children. The doom and gloom about overpopulation was overblown and doesn't look to be a problem. We have enough food production capability (especially with new lands to open up with global warming), hunger comes from dysfunctional economies, not lack of food. It doesn't make much sense to think about global population as a whole when there is such variability. You can't compare Manhattan to sub-Saharan Africa at all, they are totally different worlds (or perhaps a hundred or two years apart developmentally).
iamthepieman 6y ago
This only works if the target country is a circle itself. The packing method becomes much more difficult when you have to deal with arbitrarily complex shapes. We run into this type of problem in windfarm planning. You have a ridge with discontinuous bands of acceptably sloped terrain, usually highly irregular shapes and you have to fit wind turbines along it, taking into account the minimum clearance between turbines and pack as many as possible within. This type of problem is NP-Hard and almost always ends up being done manually due to additional constraints. These include, access road placement, viewsheds, and turbulence modelling.
m11a 6y ago
This seems to be a dramatic simplification, to the point where the results aren't helpful at all, unless I'm missing something. A lot of this is private property. Offices, people's houses, a farmer's farmland. We can't go inside, or trample on the crops of farmers. Then you need to subtract roads - because you can't walk on a road and definitely not a motorway. So really, shouldn't the land area used be the publicly accessible pedestrian area? And I dunno about others, but my footpaths are less than a metre long in width in my residential area. In the commercial areas, they tend to be less than 6 metres.

45 points by milkbikis 6y ago

Things are pretty tight in Singapore, I wonder if you take into account places not safe to stand like roads and places occupied by walls, trees, bank vaults etc., if it would be impossible. Almost 6 million people in 7.8 billion square feet if it was just flat land = approx 1300 square feet per person if my math is right.

eesmith 6y ago
The density needs to exceed 223,563/sq. mile (says the essay). Singapore's density at 20,445/sq. mile is less than 1/2 that of Monaco, says its reference 5, which is https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_population_density https://en.wikipedia.org/wiki/List_of_countries_and_dependen... . Thus, only 10% of the land is needed, giving plenty of space for roads, etc. Of course, if you include walls then you can place people on either side of the wall without an infection problem, so that changes the calculation considerably. FWIW, I wondered if Vatican City could reach the limit during a papal audience. It looks like perhaps 15,000 people could be there for one? That alone gives a density of 88K/sq. mile (bearing in mind that Vatican City has nearly 6 popes per square mile - or nearly 12 if we include Popes Emeritus.) Then there's the staff, and the people visiting the museum, and others beyond the estimated population of 1,000. Even with those, it doesn't seem like it comes close to 223,563/sq. mile.
- sigmaprimus 6y ago
  I stand corrected, also the model does not take into account the Z axis, magnitudes of area added by highrises.
  - robertlagrant 6y ago
    Yes - it really should be spheres, but ones that cannot use other spheres for support :-)
    - eesmith 6y ago
      I think "should be" pushes things beyond the limited humor there was. The 6 feet suggestion is based on the travel distance of possible virus-carrying particles, given people on a flat surface. Since gravity pulls particles downward, I suspect that being 5 feet above someone sick is better than being 6 feet below. Possibly even better than being 6 feet to the side.

meigwilym 6y ago

I may have missed something but shouldn't the radius be 3 feet? With a 6 foot radius, wouldn't everyone be 12 feet apart? The maths is new to me (I was OK up to πr2!) so this might be my mistake.

kjaftaedi 6y ago
The subject would be in the center of the circle.
- meigwilym 6y ago
  Indeed, they would, with 6 feet to the edge of their circle, and another 6 feet from that edge to the next person.
  - radmarshallb 6y ago
    You are correct. The diameter should be 6 feet and the radius 3 feet.
    - marzell 6y ago
      That means people would only be at least 3 feet away, not 6 feet. The original assumption was right.. need a 6 foot radius, 12 foot diameter to meet social distancing guidelines
      - kd5bjo 6y ago
        It’s a circle-packing model, which means there’s no overlap between the exclusion zones. A radius of 3 feet means you’re at least 3 feet away from the edge of anyone else’s circle. They are at the center of their circle, which is an additional 3 feet away, for a total of 6 feet.
      - concerned_user 6y ago
        You are not accounting for the fact that next person is not at your circle edge but is inside his own circle, and it is his circle touching yours, not the center of his circle, so 2 persons inside 3 feet radius circles have 6 feet of distance in between. Your assumption is correct if you overlap circles in a way that everyone is on edge of someone else's circle.

grabball 6y ago

I find impossible to read those kind of things when you use the United States customary units

dkersten 6y ago
At least they’re not using “football fields” as a measurement unit...
- glandium 6y ago
  Around here, it's in "Tokyo Dome"s. Just as useless.
choeger 6y ago
I don't know it is easy to translate feet from US to German. I just need to know which city the unit refers to: https://en.m.wikipedia.org/wiki/Obsolete_German_units_of_measurement https://en.m.wikipedia.org/wiki/Obsolete_German_units_of_mea... /S (honestly, once the US empire is gone for good, historians will have a good laugh about their stubborn refusal to adopt the metric system. Must be the worst case of NIH in history)
- scraft 6y ago
  To be fair, over here in the UK, we have MPH for roads, stones and pounds for peoples weight (kilograms are becoming more popular, in particular for the under 25s), feet and inches for peoples height (meters becoming more popular for under 25s). So we have a bit of a hybrid really, I am 36 so get a bit of both, but my parents need everything converted to "old money" as they call it, they can't imagine what 25cm length is, they would need it in feet and inches. It is less stubborn for them, more, "why bother"? They can get by as is and have other things to occupy their time than trying to work out what familiar distances and weights are using a different scaler. Given that roads are still imperial as are lots of other things (mattress sizes, timber sizes, etc) it isn't like if they switched to metric it would even fix anything useful.
  - 6y ago

andrewaylett 6y ago

If we're packing circles, don't we need to take into account that the 6ft distance is to the next person -- that is the centre of the next circle, rather than the boundary of it? That means circles of radius 3ft, for a total of 8,693 square miles.

cromulent 6y ago

You can fit all the humans on earth into a 1km cube. Average volume of a human is 66l [1]. Make it 130l to allow some unused space due to imperfect packing. 7.6 billion * 130l = 988 000 000 000 liters. 1 cubic kilometer = 1 000 000 000 000 liters. [1] https://www.wolframalpha.com/input/?i=average%20volume%20of%20human%20body https://www.wolframalpha.com/input/?i=average%20volume%20of%...

Simon_says 6y ago
You wouldn't enjoy it.
garmaine 6y ago
A better reference: https://what-if.xkcd.com/4/ https://what-if.xkcd.com/4/ "What would happen if you were to gather a mole (unit of measurement) of moles (the small furry critter) in one place?"

harry8 6y ago

"Stand on Zanzibar" Memories of enjoying it with that one.

metaphor 6y ago

As a more practical usecase, how many other EEs have leveraged circles-in-a-circle packing tables such as [1] to approximate cable diameter and/or size conduit? Would be interesting to learn how other disciplines have applied such a tool to solve real-world problems. [1] http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html

swarnie_ 6y ago

1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1 cm = 10 mm Its not that hard America.

deleted 6y ago

[deleted]

tenant 6y ago

So, my country which feels big to me couldn't do it. This reinforces my belief that there are way too many of our species on this planet. Given that 2.1 or so is the replacement rate, a "hard" limit of two child per woman would be decent compromise as this would equate to somewhere around 1.7 taking into account women who don't want to /can't have children. In one generation, if there were no unintended consequences this would drop the population by 15%. Sometime in the 2100s it would be half what it is today and my country could easily fit everyone!

colechristensen 6y ago
Most of the most-developed countries in the world are reproducing below the replacement rate already, populations only growing because of immigration. https://en.wikipedia.org/wiki/List_of_sovereign_states_and_dependencies_by_total_fertility_rate https://en.wikipedia.org/wiki/List_of_sovereign_states_and_d...
- tenant 6y ago
  I was thinking globally since the discussion was about the global population.
  - colechristensen 6y ago
    There seems to be a generational lag between infant mortality (or mortality before reproduction) and fertility rate. Many places still have very high mortality-before-reproduction rates and correspondingly high birthrates, or at least generational recent ones. It seems, simply, that overpopulation is a problem which solves itself. High standard of living seems to come with high costs and emphasis on investing in children far more combined with delaying children until proper resources can be had. The result? Fewer children. The doom and gloom about overpopulation was overblown and doesn't look to be a problem. We have enough food production capability (especially with new lands to open up with global warming), hunger comes from dysfunctional economies, not lack of food. It doesn't make much sense to think about global population as a whole when there is such variability. You can't compare Manhattan to sub-Saharan Africa at all, they are totally different worlds (or perhaps a hundred or two years apart developmentally).

iamthepieman 6y ago

This only works if the target country is a circle itself. The packing method becomes much more difficult when you have to deal with arbitrarily complex shapes. We run into this type of problem in windfarm planning. You have a ridge with discontinuous bands of acceptably sloped terrain, usually highly irregular shapes and you have to fit wind turbines along it, taking into account the minimum clearance between turbines and pack as many as possible within. This type of problem is NP-Hard and almost always ends up being done manually due to additional constraints. These include, access road placement, viewsheds, and turbulence modelling.

m11a 6y ago

This seems to be a dramatic simplification, to the point where the results aren't helpful at all, unless I'm missing something. A lot of this is private property. Offices, people's houses, a farmer's farmland. We can't go inside, or trample on the crops of farmers. Then you need to subtract roads - because you can't walk on a road and definitely not a motorway. So really, shouldn't the land area used be the publicly accessible pedestrian area? And I dunno about others, but my footpaths are less than a metre long in width in my residential area. In the commercial areas, they tend to be less than 6 metres.