Quarter of the Way There Multi-Cache
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Difficulty:
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Terrain:
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Size: 
(small)
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First four stages are 'micro' in size with the final stage in a plastic Lock & Lock container suitable for small trade items. This should qualify me for the first ever Philosocache!
This is a five-stage multi that lends a nod to one of those old paradoxes that philosophers/mathematicians came up with long before I was born (that I never really quite understood). Much of the text explaining this paradox comes from the December 19, 2005 posting on Philosophy, et cetera: Traversing the Infinite (www.philosophyetc.net/2005/12/traversing-infinite.html). If you want to get a good laugh (or get light-headed), you should read some of the responses to that post...and they wonder why they have a tough time picking up women in bars! Zeno's paradox said that to go a certain distance, you must first traverse an infinite number of fractional distances (first half the distance, then half the remainder, then half of the new remainder, ad infinitum [that's to infinity for us lay people]). Infinity is NEVER ENDING--there's always more, so adding up all those pieces should produce an infinite distance that could never be crossed. That whole 'crossing an infinite distance' applies not only to large universe-type scales, but to also moving across the room to turn on a light switch or your finger pushing the 'off' button on your remote control. How can you possibly move an infinite distance? The paradox is we shouldn't be able to move at all, yet we do! Luckily for us, the time it takes to traverse each interval is also accelerating with each interval traversed in half the time of the previous one (or so they say--I'm not entirely convinced). Hey! I see some eyes glazing over out there. Remember, this will be on your midterm! OK, where was I, Oh yes... If we're traveling at a constant speed, and cross half the distance in one minute, then we will reach our destination after two minutes. The time it takes to traverse each of the intervals follows the pattern: {1, 1/2, 1/4, ... 1/(2^n) ...} which sums to 2. The paradox only gets off the ground if we make the false assumption that an infinite series cannot yield a finite sum. Contrary to Zeno (who never moved again after coming up with this paradox), movement is possible after all. What a relief! So what does that have to do with this cache? Well, this multi operates on the same principal, except with each stage, you are traveling one quarter of the distance of the previous stage. The total distance should be under 25 miles, so bring good walking shoes (or be sure to have enough gas in your tank to drive the first few stages). Going from the first to the second stage will be exactly 16 miles. Make sure you have all the distances figured out ahead of time--don't worry, they laid out Nebraska in preparation for just this kind of cache. So how do I use my GPS on this cache? Use your GPS to find the first stage using the posted coordinates and on all later stages to keep track of how far (and what direction) you have gone. GPS use on the final stage is critical, since you will need to accurately gauge the final distance to put you at the correct spot! What direction do I go at each stage? Find George at the closest convenient stopping point, and he will tell you which way to go, just like on a map. He never lies! Please do not mess with George as he is a VERY cranky senior citizen, and if he gets turned around, he may send you in the wrong direction. Please use common sense when picking a spot to park--plenty of room on the shoulder! This cache should be available during winter. The first four stages are about eye level, but the final cache stage may be hidden under snow after a significant snow storm.
Additional Hints
(Decrypt)
Trbetr unf n abfr sbe qverpgvba (ur jnf n fheirlbe). Qb lbh? Pnpur jvyy or sbhaq ng gur onfr bs gur arnerfg ovttrfg fgvpx. Gur fhz bs nyy qvtvgf va gur pbbeqvangrf vf 45.
Treasures
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