The Lemon Fool

I was reading a guide to the new rules on this that suggested in order to maintain 2 metres social distancing for six people one needed an area the size of one quarter of a tennis court. This seems wrong to me.

A quarter of a tennis court is about 66sq mts. Surely even the simplest arrangement of six people in two lines of three at 2 metre distancing would only require an area of just over 2 metres by just over 4 metres = <10 metres at most.

Am I wrong?


John

redsturgeon wrote:I was reading a guide to the new rules on this that suggested in order to maintain 2 metres social distancing for six people one needed an area the size of one quarter of a tennis court. This seems wrong to me.

A quarter of a tennis court is about 66sq mts. Surely even the simplest arrangement of six people in two lines of three at 2 metre distancing would only require an area of just over 2 metres by just over 4 metres = <10 metres at most.

Am I wrong?


John

No.

There may be context in this. People are not points on a grid. If you're talking leisure, a person might adopt a posture covering quite a lot of ground, and be moving about.

"Two metres" makes provision for some of that, but who knows the extent?

ISTR in my first job after graduating, being told the law required office space to be 40 sq ft or 4 sq m per person. Though I'd hate to be, say, one of six in 24 sq m when another occupant had a cold!

For an accurate area, we need to know the shapes and sizes of the areas taken up by each person. Are they standing or lying down? Are they fat or skinny? Also, there is an exclusion area around the group (but exclusion areas from different groups can overlap). I suggest that each group needs a legal means of escape. If the 2m distance applies equally to everyone (and everyone is the same diameter), the most efficient packing would be for each person to stand on an intersection of an isometric grid and keep their arms in. Only people on the periphery of the cluster of groups would be able to leave, however.

I suggest that a hexagonal grid would be more practical. It would be more sociable for each group and it would leave holes to allow movement to allow people in and out (especially as not all groups will have six members).

A further complication is that the 2m restriction does not apply to members of the same household.


Julian F. G. W.

redsturgeon wrote:I was reading a guide to the new rules on this that suggested in order to maintain 2 metres social distancing for six people one needed an area the size of one quarter of a tennis court. This seems wrong to me.

A quarter of a tennis court is about 66sq mts. Surely even the simplest arrangement of six people in two lines of three at 2 metre distancing would only require an area of just over 2 metres by just over 4 metres = <10 metres at most.

Am I wrong?


John

I think you are. Wrong that is.

Each person needs a 2m exclusion zone around them to properly comply IMHO. although two people's exclusion zones can overlap, they still need it on all sides so your notional 2m x 4m grid also needs a 2m wide border all around it, to prevent a 7th person coming along and standing right next to any one of them. So that makes a 6m x 8m rectangle, which could easily be 1/4 of a tennis court.

And this still assumes each person occupies only a point in space.

(Multiple edits to get my arithmetic and punctuation right!)

redsturgeon wrote:I was reading a guide to the new rules on this that suggested in order to maintain 2 metres social distancing for six people one needed an area the size of one quarter of a tennis court. This seems wrong to me.

A quarter of a tennis court is about 66sq mts. Surely even the simplest arrangement of six people in two lines of three at 2 metre distancing would only require an area of just over 2 metres by just over 4 metres = <10 metres at most.

Am I wrong?

Possibly. The space they actually need to reserve for themselves extends, in the worst case, to 2 metres all round the edge of your rectangle, since nobody else can make use of it.

So just over 6 metres by just over 8 metres, so 50+ sq metres.

Like I said that's worst case, if there are lots of these grids adjacent to each other they only need to be 2 metres apart.

EDIT: snap, I think.

Scott.

The best way is probably to define the areas physically taken up by each household and extend this area by 1m outwards in all directions. As long as these extended areas do not overlap, a 2m distance is maintained.

Julian F. G. W.

One for the kids. Can you help the family in red, top right, leave by the exit without violating any social distancing rules? (My image.)


Julian F. G. W.

jfgw wrote:One for the kids. Can you help the family in red, top right, leave by the exit without violating any social distancing rules? (My image.)
Julian F. G. W.

If all the other b****** stand still, you know they're dead already.

jfgw is correct about hexagonal tiling - for six people (has Mr Cummings been doing his home-work...). With a bit of scaffolding one could extend this to three dimensions and really pack them in. Or with a bit of imagination extend to 24 dimensions in a Leech lattice if one has 196,560 friends.

I regret to say after seeing the crowds yesterday on beaches, in parks and even in newly & prematurely opened shops, I can see a definite second wave rising in 2 - 3 weeks time. There were crowds all over the place and little social distancing being practiced!

richfool wrote:I regret to say after seeing the crowds yesterday on beaches, in parks and even in newly & prematurely opened shops, I can see a definite second wave rising in 2 - 3 weeks time. There were crowds all over the place and little social distancing being practiced!

Yes, lots of people seem think this CV19 thing is all but done.

I was chatting by text with someone the other day and she said (something along the lines of) "I'm so happy lockdown is being lifted, I can't wait to see the back of this virus. Just a few weeks now and we'll be back to normal in time for summer."

Shock horror. I suspect this expectation is widespread amongst those who don't pay much attention to the technical stuff of pandemics.

stewamax wrote:Or with a bit of imagination extend to 24 dimensions in a Leech lattice if one has 196,560 friends.

Damn! I'm 196,559 short

Julian F. G. W.

jfgw wrote:

stewamax wrote:Or with a bit of imagination extend to 24 dimensions in a Leech lattice if one has 196,560 friends.

Damn! I'm 196,559 short

Julian F. G. W.

Just as well if they're leeches.

Mike4 wrote:I was chatting by text with someone the other day and she said (something along the lines of) "I'm so happy lockdown is being lifted, I can't wait to see the back of this virus. Just a few weeks now and we'll be back to normal in time for summer."

Well it's hard to get the full detail of what is being said via "text talk", but I don't have an issue with what is being communicated there from one interpretation of those words. Hard to say if that is the correct interpretation though.

UncleEbenezer wrote:

jfgw wrote:

stewamax wrote:Or with a bit of imagination extend to 24 dimensions in a Leech lattice if one has 196,560 friends.

Damn! I'm 196,559 short Julian F. G. W.

Just as well if they're leeches.

These Leeches are intimately related to John Conway's Monster (see the thread about him above).

stewamax wrote:These Leeches are intimately related to John Conway's Monster (see the thread about him above).

On a point of order, that description "John Conway's Monster" is rather misleading, as he neither conjectured that it exists (that was done by Bernd Fischer and Robert Griess) nor constructed it and thereby proved that it exists (that was done by Robert Griess some years later). He did do quite a bit of important work on it, including discovering some smaller (but still big!) related groups and finding a simplified construction, but "Robert Griess's Monster" would be a better attribution. More details in https://en.wikipedia.org/wiki/Monster_group.

And anyone who wants to know more about the Leech lattice can find a lot of details in https://en.wikipedia.org/wiki/Leech_lattice. But if you don't understand those details, don't ask me to explain them - it would be pretty close to a case of the blind leading the blind!

Gengulphus

richfool wrote:I regret to say after seeing the crowds yesterday on beaches, in parks and even in newly & prematurely opened shops, I can see a definite second wave rising in 2 - 3 weeks time. There were crowds all over the place and little social distancing being practiced!

Many of those will believe that it doesn't exist, was made in a lab and is being spread by 5G.

The shapes of the graphs (sub-exponential even before the lockdown), evidence of prior T-cell immunity, and T-cell immunity in those who have been mildly infected without producing antibodies suggest to me that we are much closer to herd immunity than one might otherwise suggest. (That is no excuse to take chances, though.)

We need some puzzles in this thread to bring it back on topic.

Let's assume that the virus diminishes exponentially with distance (say, to 10% in one meter so it will be down to 1% in two meters, 0.1% in three meters, etc.) If 2m social distancing is required for the closest possible 2-dimensional packing (isometric grid), what distance is required to provide the same level of protection in three dimensions? Assume that people are dimensionless and that the virus is spread from each infected person isotropically.

How about a Leech lattice?


Julian F. G. W.

Mike4 wrote:

richfool wrote:I regret to say after seeing the crowds yesterday on beaches, in parks and even in newly & prematurely opened shops, I can see a definite second wave rising in 2 - 3 weeks time. There were crowds all over the place and little social distancing being practiced!

Yes, lots of people seem think this CV19 thing is all but done.

I was chatting by text with someone the other day and she said (something along the lines of) "I'm so happy lockdown is being lifted, I can't wait to see the back of this virus. Just a few weeks now and we'll be back to normal in time for summer."

Shock horror. I suspect this expectation is widespread amongst those who don't pay much attention to the technical stuff of pandemics.

It feels weird that today we can arrange to meet in groups of six legally. Then one sees crowds of rather more than six mingling on beaches, or thinking "hang on!" we've been meeting every thursday for the clap. Yes, I and more than four neighbours were talking last thursday in the street, so what is supposed to start today is old news.

As regards the beaches, I suspect the rush will die down soon and good sense will prevail. It's like when one releases cattle on to fresh pasture in Spring - then go gambling around for a while then calm down.


Arb.

Gengulphus wrote:... the description "John Conway's Monster" is rather misleading, as he neither conjectured that it exists (that was done by Bernd Fischer and Robert Griess) nor constructed it and thereby proved that it exists (that was done by Robert Griess some years later). He did do quite a bit of important work on it, including discovering some smaller (but still big!) related groups and finding a simplified construction, but "Robert Griess's Monster" would be a better attribution. More details in https://en.wikipedia.org/wiki/Monster_group.

Agreed. I think though it was Conway (with the late Simon Norton) who coined the name Monstrous Moonshine