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What's the smallest country that can fit everyone standing six feet apart? (banga.github.io)
45 points by milkbikis 11 months ago | hide | past | favorite | 59 comments



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.


The subject would be in the center of the circle.


Indeed, they would, with 6 feet to the edge of their circle, and another 6 feet from that edge to the next person.


You are correct. The diameter should be 6 feet and the radius 3 feet.


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


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.


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.


Ah you're right, thanks! I didn't notice the comments here before, will fix.


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.


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.


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%...


You wouldn't enjoy it.


A better reference: 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?"


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


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.


"Stand on Zanzibar"

Memories of enjoying it with that one.


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.


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_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.


I stand corrected, also the model does not take into account the Z axis, magnitudes of area added by highrises.


Yes - it really should be spheres, but ones that cannot use other spheres for support :-)


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.


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


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_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)


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.


I think the important distinction here is that the UK is definately on the path to transitioning away sensibly in that imperial units haven't been taught at any school at any level for many years. All product units (litres, kgs etc) in shops are given in both metric and imperial, with the metric part required by law and the imperial part there for old people's convenience.


In an odd way, the US is fully metricized: they’re one of the original signatories of the Treaty of the Metre, and redefined all of their legacy units in terms of SI ones [1]. SI units are used directly in the sciences and most products have the SI equivalent listed alongside the traditional measure. I understand that industries with international supply chains, like the auto industry, are also mostly metric these days.

There just hasn’t been much of a reason for the purely-domestic parts of the market to switch: house builders are looking for 2x4 lumber, and won’t buy from a lumberyard that calls it 50x100mm. Knowing that, the sawmills continue producing the 1.5x3.5 inch profile that’s called “2x4” and anything else is a specialty item. Who has an incentive to push through the change?

[1] https://en.m.wikipedia.org/wiki/Mendenhall_Order


> and the imperial part there for old people's convenience.

And also because that's what was used to actually design the container. Milk bottles in 1 / 2 / 4 / 6 pints (imperial pints, not US pints), 454 g jam jars.


More U.K. “fun” examples:

• Beer served in pints by on-licenses, millilitres by off-licences

• Even though distances are all in miles, and petrol/diesel sold in litres, fuel efficiency is in either g/km or miles-per-gallon


>• Beer served in pints by on-licenses, millilitres by off-licences

Sure but a pint is defined as 568ml. The only one that really is quirky is how people haven't yet grasped kilometers yet they're the easiest to grok, it's just 1.6 * miles.


Sure but a pint is defined as 568ml.

. . . which I have previously determined to be within 0.5ml of the traditional volume.


The metric fuel efficiency measure is litres per 100km.

This way round makes more sense -- "how much will it cost to travel X km" is a more common question than "how far can I travel with Y litres or £Z".


_Personally_ the only time I care about mpg is when looking at how far I can travel on a tank of fuel. Or, when the fuel warning light comes on (you have 5L of fuel left, how far is that going to get you).

In essence I'd argue that most of the use of the any fuel efficiency metric is to simply rank cars, rather than to ever back out a genuinely useful cost/distance number. At which point furlongs per quart would be as effective as anything else...


Huh, I’ve never seen that used. Yes it is better.


I think it's almost always in the small print, such as on page 15 (or 27 if you look at the document's numbers) of this Ford brochure.

MPG (l/100km) Combined: 52.3 (5.4)

https://indd.adobe.com/view/5e31eb47-fa8c-4be9-b739-b19d58c8...


Canada has gone mostly metric, now, but growing up on a farm a few decades ago, I definitely got a hybrid. People's heights and weights were imperial, other things were mostly metric. Gravel roads were miles, highways kilometres. Oven temperatures were Fahrenheit, human temperatures Celsius. The really perverse one is that when referring to gallons, we had to specify US or imperial.


Heh, it’s funny you use the past tense when listing those.

- People’s heights are, I guess, officially metric. My drivers’s license lists me as 173cm. But at the exit from most convenience stores, there’s a measuring stick on the wall (for the security cameras to have a height reference), and they’re exclusively in feet-inches.

- Peoples’ weights on home scales are still pretty much exclusively in pounds. Doctors may have switched to kilograms, but I’m pretty sure asking someone how much they weigh in kg would result in a blank stare while they try dividing by 2.2 in their head.

- The entire official highway system has moved to kilometres, and you’ll pretty much never see a sign in miles. But... the grid system for gravel roads (from the Dominion Land Survey) is in miles and obviously we can’t go around changing everyone’s property boundaries, so they’ll stay in miles forever. Most rural folks know the 1 mile x 2 mile grid, and directions from one farm to another will almost always be (2 miles east, 3 miles south)

- I think oven temperatures remain in Fahrenheit because of our collective shared culture with the US. Most recipes you’re going to find have cooking temperatures in F. More things have shifted towards C though; growing up I recall house temperatures to generally being in F, and now they’re frequently in C.

- Fuck gallons.

(Source: Saskatchewan resident)


Well, I've found most people younger than me do seem to know their height/weight in metric whereas I don't have a clue even though I use metric for just about everything else. There may still be a bit of an urban/rural divide to it as well as age and perhaps, province or region.


If I'm not mistaken TV's are measured in inches the world over.


Complaints about systems of measurement is the topic every Internet forum should prohibit in their rules, but none does. It's strange. Politics is tame in comparison!

A foot is the distance light in a vacuum travels in 1.01 nanoseconds. A meter is the distance light travels in 3.33 nanoseconds. It is not really a big deal what you name that, they are both totally arbitrary. They have no relationship to any core feature of the Universe except by some reverse-engineered arbitrary constant. (You start by defining that there are 9192631770 transitions between the two hyperfine ground states of caesium-133 atoms in a second. You then build the meter by saying that light in a vacuum travels 299792458 meters in 1 second. There is no special meaning to 9192631770 or 299792458; they are totally made-up bullshit constants that mean nothing. Kilograms are even worse; before 2019 it was just a big arbitrary ball of metal in a museum. I won't even mention how the base unit has the prefix "kilo". How crazy someone is for not using the elegant kilogram/meter/second unit system. It's just so pure and natural!)

It seems pointless to me to argue over (or worse, get high-and-mighty over) what these constants are called. SI has a bunch of bullshit constants. The imperial system has a bunch of bullshit constants. It's bullshit all the way down, my friend. As long as you know what constants to use, which is why we name units, then it doesn't really matter which you use. None is better than the other.

Arguments about units usually devolve into how crazy it is that people use fractions with imperial units. But nobody using the units for real things uses fractions; for low precision applications, sure, people will say "a half inch", but when precision matters, it's "500 thou". And people use fractions with meters/kilograms/seconds, they say "half a second" when they really mean "500ms" or "500.000000000ms" or whatever. (This is all weird to me because fractions exist in real life -- you can fold a sheet of paper into thirds. But there is no way to express it in a decimal dimension. You can make three sections that are 33mm, 33mm, and 34mm, but that's not quite right. So I guess you make them 33.33333333333mm, 33.33333333333mm, and 33.33333333334mm?)

It gets weirder when you start using the SI prefixes. There are names for every power of ten, but people only use certain prefixes with certain base units. Nobody ever talks about centiamps, but they'll happily use centimeters. Nobody ever uses deci-anythings, but there it is on the trivia test for SI prefixes. And of course, computer people thought that prefixes would be pretty useful, but we make bytes from 8 bits and not 10, so a kilobyte is 1024 bytes... for some reason. (It's 8192 bits, of course!) Decades later someone decided this was stupid and invented new words for every SI prefix just for computer people. The best case is that you sneak in an extra letter for every quantity ("1KiB") and people will think you made a typo and interpret it as 1024 bytes... exactly as they would if you wrote "1KB". If you want to refer to 1000 bytes you ... just say 1000 bytes because there is no byte prefix that means 1000 unambiguously. (The only people smart enough to benefit from this were marketers. They could write 1K and say "well we thought you were using SI prefixes" and convince customers that they were getting 1KiB of storage for the price of 1000 bytes. If it sounds too good to be true it probably is.)

So this all continues to be arbitrary. What about fastener sizes? The metric system gave us the intuitive ISO metric screw thread. How big is an M4 screw? The minor diameter is 3.242mm, which is obvious from the name. An M4 socket head cap screw accepts a 3mm wrench. An M10 screw accepts an... 9... erm... 8mm wrench. (The SAE/UTS system makes even less sense, if that's possible. It's wire gauges and threads per inch, I think.)

Anyway, my point is that it's all super arbitrary and to do anything you need a lookup table. You can go look at a cesium atom and you'll have no idea how that defines the meter, kilogram, second, or inch without a lookup table. You'll never be able to make a screw with just one number ("M4"). So it's not really worth making snide comments about.

To answer your actual question, why does the US use the metric system? Because we started doing science and engineering before the metric system was invented. There was no reason to switch because there are no benefits in switching. It's all arbitrary.


> my point is that it's all super arbitrary

Granted. Yet it is wrong of you to imply that makes all measurement systems equally bad.

> There was no reason to switch because there are no benefits in switching.

SI has two advantages designed into it, namely easy conversion between unit orders of magnitude (e.g. 1 ℓ = 10 dℓ = 100 cℓ = 1000 mℓ), and easy conversion between units (e.g. 1 t water = 1 ㎥ water, 1 ℓ water = 1 ㍹ water).


At least they’re not using “football fields” as a measurement unit...


Around here, it's in "Tokyo Dome"s. Just as useless.


Indeed, it seems odd in a "maths" context with nice formatted formulas. Do US kids in science class use the metric system?


> Do US kids in science class use the metric system?

In general, yes. Though like everything else in the US education system, it’s really up to the local school boards. When I went through a couple of decades ago, we did almost everything in SI units with the occasional oddball problem in traditional units to make sure we knew how to do the conversions.


Your neighbours to the north do it the same way. In school (elementary, high school), all of the science classes are going to be in SI units, minus maybe a lesson or two in unit conversion. It wasn’t really until engineering school where they started really forcing us to be comfortable with problems that had a bunch of unit conversions; the engineers were really happy to give us problems with grams, pounds, miles, and litres, and expect us to get the right answers.


That sounds about right. I (vaguely) remember having to do some thermodynamics problems in BTUs and Rankine temperatures without converting to SI, but that was certainly the exception.

Once I got into the engineering curriculum, we were also expected to be able to do simple torque and force problems in pounds (force or mass, depending on context), feet (distance), foot-pounds (energy), and pound-feet (torque). Mostly it was to show that all the concepts work in both systems, I think. In case you found yourself working in an industry that hadn’t switched to metric.


Author here. I also prefer metric in general, but the "6 feet" guideline has been so recognizable that I decided to convert to imperial to preserve it. It also helps compare with San Francisco where I live, which is famously 7x7 miles.


I'm surprised an Indian person has used US units

How long does it take immigrants in the US to "go native"?


India is a Commonwealth country, and I wouldn't be surprised if a lot of people still think in imperial (not US customary) units.

Also, here in the UK, for the purposes of identifying COVID-19 symptoms, a fever is being defined as 38.6 °C = 100.0 °F, so US recommendations are clearly having an influence in other countries.


The US doesn't recognize 100.0 °F as a fever. That's within normal range.


There are different definitions of "fever" in medical websites. Some say anything above a person's normal average temperature is a fever, with it being considered a serious fever if the temperature is above 100.4°F.


100 F is 37.8 (more precisely 37.77777...) C.


Indeed. It's the Celsius figure that I misquoted.

https://www.gov.uk/government/publications/coronavirus-covid...


A decade is not enough in my experience. I think the answer is never.


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!


Investing in education, and women's education in particular, is one of the most effective ways of bringing down birth rates over time. It obviously has all sorts of other advantages too, which I don't need to go into here.

You just need to glance at China's current demographics to see that hard limits on number of children is not a good idea, both societally (in terms of treatment of women and prospects, for want of a better word, for large numbers of single men) and economically (such as the burden of numbers of children and pensioners per working age adult).

The Economist did a brief piece on Africa's demographics recently. It's an interesting read.

https://www.economist.com/special-report/2020/03/26/africas-...


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_d...


I was thinking globally since the discussion was about the global population.


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).




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