NavList:

Thank you, Frank, for "finding" a little" navigational" value in my original query!

As I noted, the "riddle" was from Wittenstein "for the purpose of throwing some light on the nature of philosophy [I'm a philosophy major]. ... The actual distance would be nearly six inches. Wittgenstein declared that this is the kind of mistake that occurs in philosophy. It consists in being misled my a picture. In the riddle the length of the additional piece with the length of the whole cord. The picture itself is correct enough; for a piece of one yard long would be an insignificant fraction of the length of the whole cord. But we are misled by it to draw a wrong conclusion. A similar thing happens in philosoply: we are constantly by mental pictures which are in themselves correct. Another striking illustration of a misleading picture that Wittgenstein gave, was a drawing of the earth as a ball with the people at the antipode upside down and ourselves rightside up. The drawing, he said, does not mispresent; yet it tempts us to think that the inhabitants of the antipodes are beneath us, and that they really hang head downwards. (This illustration is discussed in the Investigations, 351.)" (Ludwig Wittengenstein: A Memoir, Normal Malcolm, 1958).

The riddle is a two-dimensional problem (I think). (It needs some simplying assumptions: radius of the perfectly spherical Earth, e.g.; 25,000 in circumference.)

I'm still trying to "verify" in my own (limited mind) the two solutions that I agree with. (And I have to give your wonderful verbose response a little more effort to fully understand...but I thank you profusely!!)

Thank you...and all those who "rose" to the challenge!!

Dr. Dale