A offline comment by Bill G. prompted me to think about the following problem: Let gt(x) be "Google translate" of some corpus x from some language D into some language R. Let gt^-1(y) be the "Google translate" of y in the language R back to the language D. Let rt(x) by the "round trip" translate of x in D to R and back to D. What are the fixed points of rt(x) ? They obviously imply fixed points of gt(rt(x)). It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n. What types of phrases might cause rt^n(x) to "explode" without bound? Are there any "implosions", where rt^n(x) becomes empty? Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ? For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.