Six Degrees of Separation is a popular conjecture which states that any two people in the world are connected with one another through a series of at most six friends. Let's test it out for the geocaching network. Here we'll define friendship between two cachers to mean that one has found a cache owned by the other.
To accomplish this cache, you'll need to do the following:
- Step 1: Random selection of target. Identify an arbitrary cacher using the following procedure: Consider the first letter in your geocaching name (See exceptions in the FAQ below.). Determine a distant country beginning with that same letter. Pick out a cache in that country at random. The owner of that cache will be your distant target, i.e. the one you want to connect with through a series of friends.
- Do not go on to Step 2 until you have independently completed Step 1.
- Step 2: Make the connection. Somehow, using any means at your disposal, get a series of friends that connects you to your target: Express your series in a form such as:
- cache0 finder0 owner0 date1
- cache1 finder1 owner1 date1
- cache2 finder2 owner2 date2
- ....
- cache6 finder6 owner6 date6
in which you are either finder1 or owner1, each successive pair has a cacher in common, your target is either the last owner or finder, and the last cache is in your target country. You need to have either found or placed cache0 but not necessarily any of the others.
- Step 3: Logging. Find and log the cache at the posted coordinates.
FAQ:
- What kinds of caches count? Physical caches, that is traditional, multi-caches, puzzles, letterboxes.
- What if my name doesn't begin with a letter? Then spell it out.
- There are no counties beginning with X. What should I do? Spell it out as 'Ex', so use an 'E'
- How about W? There are no caches in either country beginning with W. Use a 'D' as in 'Double-u'.
- Is Canada a distant country? Yes, if you're from Sri Lanka.
- Do the caches need to be unique? No. In fact if you're linking to someone through a commonly found cache, you'll need to list that cache and owner twice, once for each of you. Note this counts as two steps, not one.
- I just visited a qualifying country and found a cache there. Can I use it? Not unless there were no other caches in the country as that would appear to be too reasonable and logical to be arbitrary. However, you can use it to reach the country and go after the arbitrary cache from there.
- Can I simply track someone, such as a pilot, who visited my qualifying country and just use a cache he/she found as my target? No, that's backwards and not in the spirit of the problem. You have to pick the target first, then you can use any technique, such as the one you suggest, to reach it.
- Someone else has already found links to a cache in my country. Can I just use that? You can use part of it. You would need to reach a different cache in your country as well as start from a cache that you own or have found, and stay under seven steps.
- How should my claim be stated? To be sure the steps were done in the correct order, please log your claim clearly as Name: Target Country: Target Cache and Owner: Path: Thank you
- Is the idea to reach a country starting with my letter in the fewest steps? No. The objective is to verify the Six Degrees of Separation conjecture. If you can do it in fewer than six steps, that's okay.
- What if I can't do it? That would be very interesting. Let us all know about it.
More than you need to know: (added 7/8/11) Why the insistence on picking the target first? The Six Degrees of Separation Conjecture is that any two people are separated by at most six steps. We wish to demonstrate that for a particular pair, you and someone else. Since you have already been picked, the other cacher has to be picked at random, otherwise our test would be biased. Now to really prove the conjecture to be true we would need to demonstrate it for all (5,000,000)^2 pairs of cachers. To prove it false, we would need to demonstrate just one pair which couldn't be joined in at most six steps. But how to show that? Just our failure to find a short enough path between them doesn't mean one doesn't exist. We would need to somehow exhaust the possibilities. The geocaching network is dynamic. At times there are such pairs. Suppose a new cacher has joined but has never found or placed a cache. He's isolated. No path exists to anyone else. To eliminate that case, we'd need to re-define our network to include only cachers who have found a cache or have placed one that has been found. Is that network connected? Maybe, but somewhere in the geocaching world there could be two cachers, one placer and one finder, who have not done anything else. So we should just consider the largest connected set of cachers, which is probably almost all cachers. Suppose for that set there is a pair who cannot be joined in six or fewer steps disproving the conjecture. Then all we would need to do is use some weasel words such as "on average" or "generally" to make it true. In fact this is what has been done in some other areas of application.