An Eternal Golden Braid Mystery Cache
Hidden : 2/21/2012
Difficulty:
5 out of 5
Terrain:
2.5 out of 5

Size: Size: small (small)

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Geocache Description:


Douglas Hofstadter
(1945-)

This cache can only be found upon completion of the following caches:

   GC3CB66 - Gödel
   GC3CB67 - Escher
   GC3CB68 - Bach

Located in each are a set of numbers which are to be used to complete the coordinates for this bonus cache. It will be up to you to figure out the proper order. The order is not necessarily the same for both the North and West coordinates. The only guidance in determining this order is that it is not random. But then again, the worst-case scenario is that you have to check a total of 36 different locations...

This will be a challenge to most as the prerequisite caches are not necessarily simple. But after finding those, this cache should be no problem at all! But if you do get stuck, just read on about our friends The Tortoise and Achilles as they may unstick the gears in your head...


Tortoise's Problem

(Achilles is out enjoying a nice stroll in the forest and happens upon The Tortoise.)

Achilles: Good day, Mr. T!

Tortoise: Oh hello, Achilles! I did not see you approach.

Achilles: Didn’t you? I have been walking straight towards you on the very same path. You only had to look right in front of you.

Tortoise: Even though you may have been in front of me, my mind was elsewhere. I was meditating on a certain problem.

Achilles: Let me hear about this problem, dear Mr. T...

Tortoise: Earlier today, just as I started upon my walk, I got to thinking about some of the greatest minds that this world has ever known.

Achilles: Stephen Hawking? Albert Einstein? Isaac Newton?

Tortoise: Certainly they are great minds, but no. In particular, I was musing upon the three artists: Kurt Gödel, M.C. Escher, and Johann Sebastian Bach.

Achilles: How is Gödel an artist? Was he not a mathematician?

Tortoise: Ehhh... not quite. He was a logician, to be precise.

Achilles: Really? I didn’t know there is a difference, Mr. T.

Tortoise: But there is, my old friend. However, that does not matter in the terms of this puzzle.

Achilles: Alright. Please continue, good sir.

Tortoise: Coming up this very path on which you are now coming up and I going down, I realized that these three great minds had something magical in common.

Achilles: Humor me by stating what this magical link is?

Tortoise: Egad! I should gladly tell you if you would not continue to interrupt my narrative!

Achilles: Then I shall interrupt no more. My sincere apologies to you...

Tortoise: Even as you say this, I feel as though I shall still be interrupted yet again. Right?

Achilles: Right.

Tortoise: Now the magical chain that binds these great artists (and yes, they are artists) is this fantastic concept known as a strange loop.

Achilles: A strange loop? Pray tell me, what is this fantastic concept known as a strange loop?

Tortoise: Let’s see... Perhaps you are familiar with Gödel’s Incompleteness Theorem? Or Drawing Hands by Escher? Or Canon 5 from Bach’s Musical Offering?

Achilles: Good friend, I am not familiar with a single one of those items which you mentioned.

Tortoise: Oh. In layman’s terms, I would say that they all involve self-reference.

Achilles: Like how?

Tortoise: Dear Achilles, Gödel’s Incompleteness Theorem states that it is impossible to create a complete set of axioms that can be consistently applied to all natural numbers. Through self-reference and metamathematics, it shows that there are true statements that cannot be proven.

Achilles: Egad! Can you say that again in layman’s terms?

Tortoise: No. To continue, Escher was a master of self-reference in his art. Stairways that climb in circles, a never-ending stream of water, and in the former example a pair of hands drawing each other are all signs of strange loops. And finally -

Achilles: Bach?

Tortoise: Right. Canon 5 from his musical offering is a most peculiar example in which to the ear, the music continues to ascend yet never really ascends. That is why this work is sometimes called “the endlessly rising canon.”

Achilles: Ahh... so what exactly is the problem you need help with?

Tortoise: I cannot remember where I put my car keys.

Achilles: Dear Mr. T! As I recall, you don’t even have a car!

(The Tortoise thoroughly thanked Achilles and wished him well on his walk before hurriedly heading home.)

Congratulations to MamaMarmot and UrbanMarmot on FTF! And a special thanks to mmammel, who helped to inspire and test these caches! If you ever are in Maryland, you now have some practice towards solving this fine puzzle cache!

Additional Hints ()

Byq ryz, nyqre, ovepu: na rgreany jbbqra tynqr?

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

Attributes

No attributes available

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