Maximum caching saturation - a mathematician's perspective

[+CheekyBrit]

How many geocaches can fit on earth? I figured some of you might have this thought experiment running through your mind too.
Math tells us hexagonal packing of circles is how to cram the most in. Massive oversimplification but in a 1 mile square area 115 geocaches can fit inside (the overlap from this square to others and underlap from other squares to this cancel out evenly thankfully so this will tessellate nicely. This has each waypoint 528' (1/10th mile or 161 meters) from each of 6 other waypoints. There will be some irregularities at the non rectangular edges like wonky coastlines but this works for a good average. Also, existing geocaches are not packed anywhere near as tightly as we would need for maximum packing around them, but say we shifted all existing geocaches for this daft thought experiment.

The city I live in, Pocatello, is 32.38 Miles² and could fit 3723 caches.
The county I live in, Bannock county, is 1147 Miles² and could fit 131,905 caches
The State I live in, Idaho, is 83,642 Miles² and could fit 9,618,830 caches

The USA is 3,797,000 Miles²  and could fit 436,655,000 caches

The land area of Earth is 196,900,000 Miles² and could fit 22,643,500,000 caches. THAT is max geocache saturation (not counting events, virtuals, webcams, and earth caches - that has no upper bound)

Bonus question
So how many can a person find? Could someone find all of them in a lifetime?
Nearly endless events could be crammed into that same space, requiring that they are separated by 2 hours or 20 miles. Then geocaches can be archived after 90 days (to avoid them being considered 'temporary' and against the rules). I somewhat doubt anyone is going to be able to find 22.6 billion caches within 90 days so not enough geocaches really isn't a limiting factor. For fun, let's even ignore travel limitations.
Take the most geocaches found in a day - 8694 by Lærry. That is about 6 geocaches a minute!?!?! Possible with pre-signed challenges, but hardly sustainable lifelong. There's also little time for bathing, sleeping, eating, or any other necessities there. But humor me.

The longest human lifespan in recent recorded history is Jeanne Calment at a whopping 122 years, 164 days. That's a whopping 44724 days including the 30 leap years from 1875-1997. Assume you were born fully able to geocache and ran non stop your whole 122 odd years, you'd need to do 506,294 caches a day, or about 6 a second to get every geocache on the planet at max saturation. At the best rate we've seen, the Lærry rate of 8694 a day, you could do 388,830,456 geocaches.
But wait, there was that chap in the bible, Methuselah, the crowning prince of age outliers at 969 years old. He lived for about 353927 days. Live a life full to the brim of geocaching as long as Methuselah at the non stop pace of Lærry and you could do 3,077,041,338. Wimpy attempt, that's only 13.6% of planetary cache saturation. To date mondou2 has found 236,921 geocaches, which is absolutely astounding, but only 0.007% of the Lærry Methuselah potential.

This may sound completely daft, and you'd be right in thinking that. But with that in mind, I met an 8 year old geocacher who has found a geocache every day of their entire life since birth thanks to the help of their eager parents. We have a contender!

[+lee737]

How many could a person find? The other week at a mega, we found 180-odd in a day. Mostly pre-solved Wherigos, so basically a D1.5 T1.5 trad trail. I was pooped by the end of that day. So I don't stand a chance of finding them all!

 

[+baer2006]

Nice writeup ! The style reminded me a bit of xkcd's "What If?" . And BTW, Lærry's record rate is simply the result of account splitting and then re-logging the vast majority of finds on a single day.

 

Anyway, the solution to "Find all caches in a lifetime" (or at least almost all) is much simpler. Super-high (pseudo-)finds-per-day numbers are usually achieved by "divide and conquer" tactics: A group of cachers splits up, everyone finds separate caches but signs with the "team name of the day", and in the end every member of the group logs all the finds of the day. There is no limit to the size of the group, so you only have to do this:

• Organize a world-wide "log them all" day (or week/month - no need to rush)
• Announce that every geocacher is part of "Team World"
• Cachers everywhere go out, and log every possible cache as "Team World" in the logbook. Coordinating visits to more remote caches can be organized by local communities.
• The most difficult part is collecting the list of caches, which have actually been found and signed. But I'm sure that the combination of a pre-agreed standard log text (e.g. "Found by Team World") and clever scripting can do the trick.

Afterwards, every member of "Team World", i.e. every geocacher, can log all the finds as their own.

 

I leave the actual implementation of this plan as an exercise to the reader

[+niraD]

7 hours ago, CheekyBrit said:

This may sound completely daft, and you'd be right in thinking that.

 

 

Your subject line reminded me of an old joke...

 

A certain hotel was hosting three conventions: a convention of physicists, a convention of engineers, and a convention of mathematicians. The first night, a fire happened to break out in the room of one of the physicists. The physicist quickly calculated the size of the fire, its thermal mass, the size of the ice bucket, the flow rate of the faucet in the bathroom, etc., and then extinguished the fire according to his calculations. With the last drop of water, the last ember of the fire was extinguished. The physicist went back to bed.

 

The next night, a fire happened to break out in the room of one of the engineers. The engineer quickly calculated the size of the fire, its thermal mass, the size of the ice bucket, the flow rate of the faucet in the bathroom, etc., the same as the physicist. Then he multiplied everything by three and extinguished the fire according to his calculations. When he finished, the fire was out, but everything in the room was drenched. The engineer went back to bed with soggy sheets.

 

The next night, a fire happened to break out in the room of one of the mathematicians. The mathematician quickly observed the fire, the ice bucket, and the faucet. He determined that a solution did exist, and went back to bed with warm, dry sheets.

[+kroger23]

Hmm... Do the rules say geocaches can only be hidden on land?

No need to limit ourselves...

[Darwin473]

16 hours ago, kroger23 said:

Hmm... Do the rules say geocaches can only be hidden on land?

 

Well there was this one cache that I remember reading about, down in the depths... 

 

Can't find it now though. Anybody know the one I'm talking about?

[+lee737]

This one?

https://www.geocaching.com/geocache/GCG822_rainbow-hydrothermal-vents

 

[+Vicious Cycle]

12 minutes ago, lee737 said:

This one?

https://www.geocaching.com/geocache/GCG822_rainbow-hydrothermal-vents

 

What country icon would you get if you found that one?

[+niraD]

1 hour ago, Vicious Cycle said:

1 hour ago, lee737 said:

https://www.geocaching.com/geocache/GCG822_rainbow-hydrothermal-vents

What country icon would you get if you found that one?

The page says, "In Arquipélago dos Açores, Portugal" so I would assume Portugal.

[+lee737]

I've often thought about this one since my son showed me it years ago.... if you tried to have a challenge published that literally only a (theoretical) handful of people worldwide had any chance of finding, it would be knocked back.... yet you can place a trad on the deep sea floor....

[Darwin473]

23 hours ago, lee737 said:

This one?

https://www.geocaching.com/geocache/GCG822_rainbow-hydrothermal-vents

 

 

Surprisingly, no. Either there is more than one, or more likely my terrible memory is giving me false information! The one I recall had a photo of the "cache", which was a metal plate on the sea floor inscribed with the cache number and something else. The reason I remember it, was I had "planned" (ie never-gonna-happen fantasy) to get a magnetic TB to stick to it, but then thinking the plate probably wouldn't be steel so a magnet wouldn't stick.

 

Even if I had the spare money to go a few miles down, I doubt my wife would let me!