Outer Reaches of the Palindrome Page: 33
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through the levels of some hierarchical system, we unexpectedly find ourselves right back where
we started.32 Bach's "Endlessly Rising Canon" is an example of Hofstadter's Strange Loops; it is
a canon that morphs from key to key until it achieves a sense of resolution in the same key that it
started from. Another example comes from the painting of Dutch artist, M. C. Escher. According
to Hofstadter:
To my mind, the most beautiful and powerful visual realizations of this notion of Strange
Loops exist in the work of the Dutch graphic artist M. C. Escher, who lived from 1902 to
1972. Escher was the creator of some of the most intellectually stimulating drawings of
all time. Many of them have their origin in paradox, illusion, or double-meaning.
Mathematicians were among the first admirers of Escher's drawings, and this is
understandable because they often are based on mathematical principles of symmetry or
pattern ... but there is much more to a typical Escher drawing than just symmetry or
pattern; there is often an underlying idea, realized in artistic form. And in particular, the
strange loop is one of the most recurrent themes in Escher's work.33
A third example of the recursive Strange Loop is the Epimenides paradox; Epimenides, who was
a Cretan, coined the famous loop, "All Cretans are liars." This statement is perhaps the most
simple example of a self-reflexive loop: if all Cretans are liars, and Epimenides is a Cretan, then
he's lying about the fact that he's an inherent liar, and so on.34 And, of course, a final example of
a strange loop is an actual palindrome, where, though the literal, contextual meaning rarely
evokes copies of itself (except in rare, powerful palindromes, like, "Did I poop? I did!"), the
letter-by-letter journey will always end in the manner that it began- on the letter that it started
with.33
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McConnell, Michael Constantine. Outer Reaches of the Palindrome, thesis, December 2003; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc4407/m1/36/: accessed May 22, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .