In a village in which no man shaves himself, who shaves the barber? http://en.wikipedia.org/wiki/Barber_paradox Perhaps I should ask Wolfram Alpha? Alpha Answer: "Wolfram|Alpha doesn't understand your query" At 08:16 AM 3/2/2013, Fred lunnon wrote:
I conjecture that the fixed point is independent of the input, and constitutes the Question of Life, the Universe and Everything.
[The answer was earlier conjectured by Adams to be 42, until I pointed out in a post prompted by Conway that it is actually 24.] WFL
On 3/2/13, Henry Baker <hbaker1@pipeline.com> wrote:
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.