How does a lapsed mathematician describe crowds on a beach?  I shall come to the pseudo-mathematical observation in due course, but first a little recollection and rant.

I’ve just been visiting my dad.  He’s in Brighton (or Hove, if you’re local enough to the area to have heard of it).  That’s the south coast of England, directly south from London.  Though he’s several blocks back from the sea front, it’s an easy walk to the beach.

Like the rest of Blighty, it was hot, dry and sunny.  It has been like that almost uninterrupted since about early May, which makes this an exceptional summer (our weather -in all seasons – is normally much more mixed).  I took advantage of that to go down to the beach for a swim every day: Brighton and Hove have a huge amount of public beach, endowed by nature with benign conditions, meaning no natural hazards unless you count the power of the waves breaking in rough weather.

I tend to prefer it a little cloudier, cooler, wetter, as that’ll leave the beach a little less busy.  But this time I was pleasantly surprised: only on the Sunday was it truly ghastly.  I guess there’s been so much high-summer weather the novelty’s worn off.  So all in all, the most pleasurable week of beach I’ve had in a long time.  But I was struck by two rather gratuitously restrictive (and widely ignored) notices on the wide paved promenade:

• No cycling
• Keep dogs on leads

Now I was there with neither bike nor dog, so have no axe to grind.  Nevertheless I find those notices stupid and mildly annoying in such a huge wide open space.  So I took it upon myself to make a mental note of such real nuisances as I encountered to blight my time there.  Let’s see where bikes and dogs figure in such a list.  In order of nuisance (with the first two overwhelmingly the Big Ones):

1. Barbecues
   Far and away the biggest nuisance was the barbecues.  The pervasive miasma of thick, greasy smoke blights a huge area: not just the beach but also the promenade, and including the main road where it competes with the fumes of heavy traffic.  There are “no barbecues” notices on some sections of beach, but that’s about as effective as 1980s trains that had “no smoking” in half a carriage while the other half was full of smokers.
2. Ghetto-blasters
   The other nuisance to blight an area well beyond the perpetrator, though far less than a barbecue.  Come to think of it, the worst instance was a car radio.  It was parked with the occupants inside, with a thumping bass audible from a lot further away than the car could be seen.  But that was a one-off.
3. Smokers
   There were relatively few smokers, and subjectively seemed to be divided 50/50 between the twin nasties of tobacco and pot.  This was, however, a very minor nuisance: only on the last day was the weather such as to allow the stench to blight a slightly wider area, so that I’d be suffering it for more than a couple of seconds.
4. Tripwires
   Not dogs – on or off the lead.  Nor humans.  But dog leads are a bit of a hazard.  And on the last day there were some characters out there with the more insidious hazard: the stealth tripwire – aka fishing line.
5. Beach Patrol
   Two guys on annoying “quad bikes”, trailing noise, fumes, and ugly tracks on the beach.  Surely if there’s a beach patrol and it needs more mobility than a pair of legs, they should have honest bikes.  With MTB wheels for the beach.
6. Ad-hoc
   Not much litter: there seem to be folks cleaning the beach.  But still annoying when something like a crisp packet did appear.  Ditto some other things like the smell of suncream on some people.
   As you can tell, we’re running into the realms of the utterly non-serious here, so let’s have a final entry that could easily have appeared higher up:
7. Transport and Toys
   There were lots of cyclists, and lots of boats.  That is, inoffensive boats like rowing boats, canoes, and various boards.  Over eight days, the total annoyance amounted to no more than two cyclists (one looking at his phone not where he was going, the other just inconsiderate) and one boat I had to evade.  In other words, a huge majority were entirely considerate and well-behaved.

So it seems those prohibited things really don’t make it onto the scale of nuisance at all.  How depressing that someone’s priorities are so desperately warped.

OK, enough rant.  I’m supposed to have an insightful observation, right.  OK, here goes.

A bathing beach is saturated if the crowd is such that both
(a) Open-ish spaces are sufficiently limited that you actively look for the best available.
and
(b) As you approach your best-available space, someone else gets there first, having had the same idea ahead of you.
The measure of saturation is how many times you repeat step (b).

Happy to say it was surprisingly non-saturated over this past week.